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DISTANCE USER'S GUIDE

1. SAS SPLUS GOF SAS NCLASS nclass SPLUS GOF SAS SPLUS Description This command has two purposes The first purpose is to specify the distance intervals for plotting a scaled version of the histogram of distances against the function g x and f x and for the chi square goodness of fit test pg 76 77 The second purpose is to specify that the PLOT file should be created for SAS GRAPH or SPLUS See Program Files for a complete description of this file It isan ASCII file and can be modified with a text editor If the data are entered and analyzed ungrouped EXACT the first 2 forms can be used to define the intervals which are used for plotting the data and for the chi square goodness of fit test The first form specifies the intervals exactly and the second form provides a shortcut approach of specifying nclass equal intervals Note the syntax from previous versions of GOF lt will also work You can enter up to 3 of these commands to specify different sets of intervals If you do not specify this command and the data are analyzed as ungrouped 3 sets of intervals are constructed with equally spaced cutpoints and the number of intervals being the n and 2 3 n and 3 2 n You can optionally specify SAS or SPLUS after the intervals to create a PLOT file If you want to use the default intervals and create the PLOT file use the second form of the command If the data are entered groupe
2. Description Prints either the option values or the data values to the OUTPUT file but not to the screen STORE Syntax LOG APPEND STORE OUTPUT filename RECORD REPLACE Description The STORE command copies the contents of a program file into a named DOS file If the file specified by the filename already exists an error is issued Use APPEND to append to an existing file Use REPLACE toreplace an existing file If you specify a file which is currently being used by the program an error will be issued The following example creates an error because ASSIGN opens TEST OUT and then STORE attempts to write to TEST OUT which is already open ASSIGN OUTPUT TEST OUT STORE LOG TEST OUT Examples Store LOG into the file TEST LOG and append to the current contents of the file STORE LOG TEST LOG APPEND Store OUTPUT into the file TEST OUT and replace its contents if it already exists STORE OUTPUT TEST OUT REPLACE 21 OPTIONS gt Various options can be set to control program operation Once an option value has been set it retains its value until you change it or exit the program The data options define the characteristics of the data collected and how they are to be entered The model fitting options define values to be used in fitting a probability density function to the distance data some of which can be overridden in the estimation procedure Print options control the amount and forma
3. 1 W Adjustments Function Cosines Term selection mode Sequential Term selection criterion Likelihood ratio test Estimator 2 Key Uniform k y 1 W Adjustments Function Simple polynomials Term selection mode Sequential Term selection criterion Likelihood ratio test Estimator 3 Key Half normal k y Exp y 2 2 A 1 2 Adjustments Function Hermite poynomials Term selection mode Sequential Term selection criterion Likelihood ratio test Estimator 4 Key Hazard Rate k y 1 Exp y A 1 A 2 Adjustments Function Cosines Term selection mode Sequential Term selection criterion Likelihood ratio test Estimator selection None display all estimates Estimation functions constrained to be nearly monotone non increasing Variances Variance of n Empirical estimate from sample Variance of f 0 MLE estimate Goodness Based on Glossary ems number of observed objects single or clusters of animals total length of transect line s number of samples point transect effort typically K k length of time searched in cue counting encounter rate n L or n K or n T width of line transect or radius of point transect distance to i th observation cluster size of i th observation probability for regression test probability for chi square goodness of fit test Parameters or functions of parameters m number of parameters in the model ACI i th parameter in the estimated probabilit
4. CLUSTER WIDTH value TEST 0 MEAN X BIAS XLOG io GXLOG Description The CLUSTER command like the DISTANCE command is used to modify the way the duster sizes are used in the estimate of density By default the WIDTH is chosen to match the truncation value set by the DISTANCE command and DISTANCE computes a size bias regression estimate BIAS GXLOG by regressing the log s natural logarithm specified as log in the output against Q x where x is the distance at which the cluster was observed The WIDTH switch specifies that only cluster sizes for observations within a distance less than WIDTH are used in the calculation of the expected cluster size This treatment of the data can only be accomplished if the distances and cluster sizes are both entered as ungrouped The MEAN switch specifies that the expected cluster size is to be estimated as the average mean cluster size Likewise the BIAS switch specifies that expected cluster size is to be estimated by a size bias regression defined by the value of the switch Value Meaning x Regress cluster size against distance x XLOG Regress log s against distance x GX Regress cluster size s against G x GXLOG Regress log s against x The TEST switch specifies the value of the significance level to test whether the regression was significant If it is non significant the average cluster size is used in the estimate of density The de
5. valuel SE value2 Description For cue counting pg 8 9 270 275 valuel is the average rate at which animals issue visual or auditory detection cues The rate should be given in the same units of time as the values given for sampling effort in the data For example if effort is measured in hours then the cue rate should be number of cues per hour The cue rate must be a positive number gt 0 Optionally a standard error for the cue rate can be given with value2 This standard error is accounted for in the estimated standard error of the density and abundance estimates This option is only used if TYPE CUE is specified Default CUERATE 1 SE 0 Example An estimate of the cue rate is 12 per hour with a standard error of 2 per hour The sample effort for this cue counting example be specified in hours sampled CUERATE 12 SE 2 DEFAULT Syntax DEFAULT Description This command resets all of the options to their default values Remember that an option remains in effect until it is changed or DISTANCE is terminated The default values for each of the options are PVALUE 0 15 PRINT SELECT TYPE LINE SELECT SEQUENTIAL SQUEEZE OFF OBJECT SINGLE MAXTERMS 5 BOOTSTRAPS 1000 DISTANCE PERP EXACT UNITS METERS ITERATIONS 100 SEED 0 LENGTH UNITS KILOMETERS LOOKAHEAD 1 SF 1 AREA UNITS HECTARES EPSILON 1 0E 7 CUERATE 1 SE 0 24 DISTANCE Syntax WIDTH width NCLASS nclass PERP DISTANCE CONVERT value UNITS
6. 3 goodness of fit plots and tests are to use 5 equal MATOR KEY HN ADJ HERMITE TIMATOR KEY UNIF ADI POLY intervals AN aera The second analysis is nearly identical except that TANCEASS 9 JWIDTHE 20205 distances are grouped into 5 equal intervals A EE between 0 20m for the analysis The same T WIDTH 20 0 intervals are used for the plot and goodness of fit ad test The third analysis computes a bootstrap variance and confidence interval for density using a half normal Hermite detection model Figure 16 Abbreviated listing of input for example 2 EXAMPLE2 INP 74 Output As inthe first example each of the 4 models is fitted using the SELECTION SEQUENTIAL term selection mode The final model for each estimator is shown in Figure 17 DISTANCE chooses the half normal key function with no adjustments as the best model because it has the smallest AIC value The AIC values from Figure 17 match the values in Table 5 1 of Buckland et al 1993 and the half normal Hermite is shown to be the smallest For the half normal model a parameter estimate table is given followed by plots of the estimated detection function g r and the estimated probability density function f r for the radial distances Figure 18 The density estimate is 70 822 animals ha and the 95 confidence interval is 52 140 96 199 Figure 19 The estimated encounter rate n K is 4 3667 3 5585 5 3583 animals per point transect The data
7. VARF BOOTSTRAP and 4 how much output should be generated PRINT Density and abundance estimates are comprised of the following components 1 detection probability 2 encounter rate and 3 expected cluster size if the detected objects are clusters It is possible to restrict estimation to one or more of these components without estimating density however all components must be estimated to obtain an estimate of density You will use the commands DENSITY DETECTION ENCOUNTER and SIZE to define which components will be estimated If you do not use any of these commands each component and density is estimated by default Likewise if you use the DENSITY command density and all of its components are estimated If you use any or all of the DETECTION ENCOUNTER and SIZE commands and not the DENSITY command only the specified components are estimated For example ESTIMATE ENCOUNTER ALL END will only estimate encounter rate 43 ESTIMATE gt Estimates of density and its components can be made at different levels of the sampling hierarchy Sample lt Stratum lt All The DENSITY DETECTION ENCOUNTER and SIZE commands are used to specify the level at which each quantity is estimated Different levels can be used for the various quantities although some combinations are incompatible An error message is given if the levels are incompatible The lowest level of resolution specified for DENSITY is the default level for eac
8. the data but it will not let the curve dip down at the origin In some instances this will allow the estimator to achieve a better fit at the origin which is the point of interest Setting MONTONE NONE will allow the curve to take any possible form except that it must remain non negative Monotonicity is achieved by constraining the function at a fixed set of points In some circumstances it is possible that the curve can be non monotone between the fixed points Typically this results from trying to over fit the data with too many adjustments with a long tailed distribution Truncate the data rather than attempting to over fit Default MONOTONE STRICT 57 ESTIMATE gt PICK Syntax NONE PICK Es AIC Description If more than one ESTIMATOR command is given a choice must be made as to which model will be used for the final estimate pg 50 51 73 76 The command PICK AIC instructs the program to choose the model that minimizes Akaike s Information Criterion The command PICK NONE instructs the program not to choose a model and to present the results of each If no command is given PICK AIC is assumed Note prior to Version 1 20 this command was not available and the results of all estimators were displayed i e PICK NONE assumed If the BOOTSTRAP command is given and PICK NONE is specified a bootstrap procedure is performed for each estimator Whereas if PICK AIC the bootstrap is performed and the estimato
9. 30 0000 00000 00000 0114 37948 4293 10253 1 4046 0221 1 0000 0000 00000 00000 0222 130 11 0000 00000 00000 0223 74194 0000 00000 00000 0224 48112 1137 38332 60388 0225 51962 1137 41399 65219 0226 2 0785 1137 1 6560 2 6088 0241 1 8610 4441 48243 7 1791 nan Oe oa SS NOA 0 0 0 0 0 0 0 0 0 0 Figure 4 Example STATS file for first estimate prcoedure of input file given in Figure 1 In addition Figure 5 gives the resulting STATS file for the second estimate procedure in Figure 1 modified to show the results for each estimator PICK NONE Records for the detection probability and density modules are output in the STATS file for each estimator The BOOTSTRAP file contains a set of STAT records for each bootstrap By default a new BOOTSTRAP file BOOT OUT is created for each bootstrap analysis If you want to append to the results of other bootstrap results from the same analysis ASSIGN the file with the APPEND switch When the results of the bootstrap are summarized all of the bootstrap estimates are included This enables you to run a large bootstrap analysis in batches eg 5 batches of 200 to get 1000 bootstraps If the bootstraps are appended make sure you use the default SEED 0 which assigns a random seed from the computer clock or change the SEED between batches otherwise the same set of estimates will be repeated in each batch The format of the records are as described under STATS with the ex
10. BOOTSTRAP command If you choose a bootstrap variance estimate you can use a default value of O for the SEED which starts the random number generation with a random seed from the computer clock or you can specify a SEED in the OPTIONS section so that the same set of random numbers is generated in different runs NOTE This command is of limited use and is only included for compatibility to previous versions The BOOTSTRAP command should be used to get bootstrap variances and confidence intervals Default VARF MLE VARN Syntax POISSON VARN b EMPIRICAL Description This command specifies the type of variance estimation technique for encounter rate The value POISSON specifies that the distribution of n number of observations is Poisson pg 50 88 109 110 EMPIRICAL specifies that the variance should be calculated empirically from the replicate SAMPLEs pg 90 92 If only one SAMPLE is defined in the data the POISSON assumption is used unless a value bis specified If a value b is specified it is used as a multiplier such that var n bn pg 186 198 The Poisson assumption is equivalent to specifying b 1 The default for VARN is EMPIRICAL unless there is only one SAMPLE in which case the default is POISSON Default VARN EMPIRICAL 60 EXAMPLES For each example the DISTANCE input is contained in a file which is placed into YourD7 rectory during installation The output for an example can be generated by
11. CD YourD7 rectory prior to issuing the DIST command Either of the above commands runs DISTANCE interactively DISTANCE displays a title screen and the DISTANCE gt prompt on the screen DISTANCE is ready for you to enter commands and data from the keyboard Alternatively DISTANCE can read commands and data entered into text files with an editor eg EDIT or saved from within DISTANCE see the ASSIGN and STORE commands described later Thelatter approach which eliminates redundant entry of commands and data is described under Batch Operation and the ASSIGN command Until you become familiar with DISTANCE we recommend entering commands and data interactively A Simple Example DISTANCE needs three types of information to perform an analysis 1 OPTIONS defines the type of sampling and data measurement units and various other settings which affect data entry and analysis 2 DATA defines the sampling structure strata amp samples sampling effort eg line length and appropriate observation data i e distance and cluster size and 3 ESTIMATE defines the parameters to be estimated how the data are to be treated in the analysis which estimators are to be used and how variances are to be estimated This information is entered via commands that define option values structure data input and initiate and control estimation Reasonable default values have been chosen for many of the options Figure 1 on the next page give
12. The encounter rate for the i sample is computed as the number of observations n detected divided by the sample effort eg length of a line transect The number of observations n is determined after left or right truncation of the data note the notation for number of observations per sample is the same as that used for frequency of observations in a distance interval but they represent 40 different values Sample effort was chosen as a generic term to represent very different measures of sampling intensity which determine the amount of area searched for the various types of distance sampling For point transects the basic unit of sample effort is 1 for each time a complete point or web is sampled If some constant fraction c of the complete circle is searched for all of the points it is easiest to set effort 1 and use the command SF at the OPTION gt prompt where c is the proportion of the drcle searched However if only some of the point transects are searched partially set the effort for those samples to the fraction of the circle searched Do not set both the effort to c and SF c As an example if for 1 point transect only 1 2 the circle was searched once and the remaining points were completely searched once let SF remain at its default value of 1 and enter the effort for each sample as follows DATA SAMPLE EFFORT 0 5 SAMPLE EFFORT 1 SAMPLE EFFORT 1 fetc If a series of point transects are surveyed along
13. as point transects Default TYPE LINE 34 DATA gt Distance data are entered at the DATA gt prompt There are two ways of entering data 1 from the INPUT file either the keyboard or an ASSIGN INPUT file or 2 from a separate file specified with the INFILE command Data are structured and entered in a hierarchical manner The levels of the hierarchy can be viewed as follows STRATUM SAMPLE 1 SAMPLE k o roa i OBSERVATIONS FOR OBSERVATIONS FOR SAMPLE 1 SAMPLE k The structure is specified by the order in which the commands and data are entered A STRATUM command is entered to begin a stratum and a SAMPLE command is entered to define and begin a sample All observation data e g distances cluster sizes for a sample i e line or point follow the SAMPLE command For example if the data are from two strata each with two samples conceptually the data are entered as follows STRATUM 1 SAMPLE 1 OBSERVATIONS FOR SAMPLE 1 SAMPLE 2 OBSERVATIONS FOR SAMPLE 2 STRATUM 2 SAMPLE 3 OBSERVATIONS FOR SAMPLE 3 SAMPLE 4 OBSERVATIONS FOR SAMPLE 4 It is not necessary to stratify the data An equally valid layout for the above example would be SAMPLE 1 OBSERVATIONS FOR SAMPLE 1 SAMPLE 2 OBSERVATIONS FOR SAMPLE 2 SAMPLE 3 OBSERVATIONS FOR SAMPLE 3 SAMPLE 4 OBSERVATIONS FOR SAMPLE 4 Incomplete assignment of the data to strata is not allowed The following example would not be a 35 valid layout
14. be used when running program DISTANCE interactively Example To obtain a description of the SELECTION command at the OPTIONS gt prompt enter HELP SELECTION To obtain a description of the INFILE command at the DATA gt prompt enter HELP INFILE 19 LIST Syntax LOG LIST OUTPUT RECORD DATA OPTIONS Description LISTallows you to browse the contents of the LOG OUTPUT or RECORD files It will also display the current data LIST DATA or the current values of the program options LIST OPTIONS The command LIST is not intended for use in batch files LIST sends output to the screen with Browse and it will wait until an ESC key is pressed before continuing If you want to output data and options to the output file use PRINT DATA or PRINT OPTIONS at the DISTANCE gt prompt Example LIST LOG LIST OPTIONS OPTIONS Syntax OPTIONS Description OPTIONS initiates a separate command processor for setting various options which affect program operation and output The prompt will change to OPTIONS gt after typing this command Further information on setting options is given in the OPTIONS gt prompt section PAUSE Syntax PAUSE Description Pauses program in between commands until the Enter key is pressed It can be useful when running program DISTANCE in batch mode eg for demonstration purposes 20 DISTANCE gt PRINT Syntax OPTIONS PRINT A DATA
15. commands are Estimator Key Hazard not retained i e each ESTIMATOR command was repeated in Estimator Key Hnormal the second analysis Estimator Key Uni form End a List Output Not all input to DISTANCE will look exactly like Figure Estimate 1 However it does illustrate the basic structure of input to oe ee DISTANCE and the interactive nature of the analysis Not all Estimator Key Uni form of the possible options need to be specified if the default values Distance Width 3 are acceptable For example the command TYPE LINE could End be deleted for this example because it is the default value The format for data entry will vary depending on the type of sampling and data defined by the options In this example the Distance command within Options defines grouped interval distance data pg 14 will be entered i e the number of observations within each distance interval is entered rather than the distance for each observation We have created numerous template files like Figure 1 that are installed into YourDi rectory The template files which are described in the EXAMPLES section provide generic sets of commands and illustrate the data format for various sampling situations They can be modified with any text editor to include your data and other commands or options for your specific analysis Figure 1 Example input file Entering Commands The three primary commands issued at the DISTANCE gt prompt are 1 OP
16. data pg 62 65 Model selection pg 73 77 includes 1 selecting how many and which adjustment terms are induded in the model term selection and 2 selecting a best model estimator from the specified set of competing models The default method of selecting terms term selection mode is defined by the SELECTION command under OPTIONS gt Its value can be overridden with the SELECT switch of the ESTIMATOR command Related options indude LOOKAHEAD and MAXTERMS There are 4 types of term selection modes described below 1 SEQUENTIAL 2 FORWARD 3 ALL and 4 SPECIFY Themaximum number of adjustment terms that can be included in the model is limited by the value of MAXTERMS number of parameters in the key function and less frequently by either the number of observations 44 ESTIMATE gt for ungrouped data or the number of distance intervals for grouped distance data DISTANCE will i ssuea warning message if the number of parameters is being limited by the amount of data Term selection mode SPECIFY implies the user will specify which adjustment terms are included in the model Typically this is used to specify that a key function without adjustment terms is to be fitted to the data as in the following example ESTIMATE ESTIMATOR KEY HNOR NAP 0 SELECT SPECIFY END It is not necessary to include the SELECT switch but it will prevent DISTANCE from issuing a warning message that you are specifying the model It is also possi
17. data from example 1 The first model is the key function with no adjustments Each succeeding model adds another adjustment term and compares the test criterion to the previous model The order of the cosine term refers to the valuei in 17x cos Ww For polynomial adjustment functions order represents the exponent of the polynomial Estimated models 1 3 for the uniform cosine in this example are 65 Effort samp Width obse Model Uni Model Uni Cos Likelihood ratio test between models Model Model Uni Cos Likelihood ratio test between models Model Figure 8 Model selection fitting output from uniform cosine model 1 f x Ww 1 x LG 1 0 665098 cos W w 0 1 0 637621 cos TX Wy w Qc ood todo AAA AAA Probability Function Estimation id Model Selection Fitting AAA A A A AA A AA AAA AA AA AAA AA AA A 48 00000 12 19 00000 99 les rvations 1 Form key ky 1 w Results Convergence was achieved with Final Ln likelihood value Akaike information criterion Final parameter values 1 function evaluations 291 49946 582 99890 2 Form key kCy 1 w ine adjustments of order s Results Convergence was achieved with Final Ln likelihood value Akaike information criterion Final parameter values 665098 7 function evaluations 280 48949 562 97890 land 2 Likelihood ratio test value 22 0199 Probability of a grea
18. entering DIST I examplefilename O outputfi lename and replacing examp left Tename and outputf7 Tename with appropriate filenames The general structure of the output and a detailed description of model selection output is given with Example 1 Less detailed description is given with Example 2 Example 1 Description This example of line transect sampling is described in Chapter 4 of Buckland et al 1993 Twelve lines samples covering 48 km were sampled and n 105 objects were observed from a half normal detection curve True density is 79 788 groups km and 239 4 animals km Cluster size for each observation was generated from a Poisson distribution with E s 3 The analysis of cluster density is described in Sections 4 3 4 7 of Buckland et al 1993 and the estimation of expected cluster size in Section 4 8 1 We have further structured this example by arbitrarily splitting the 12 samples into 2 strata to illustrate a stratified analysis Input The input file is named EXAMPLE1 INP An abbreviated listing excluding most of the data is given in Figure 6 The input file contains commands to 1 assign filenames for the output and log 2 specify options 3 structure and input the data and 4 perform 3 analyses The options specify that perpendicular distance is measured in metres length is measured in kilometres and area is specified to be km for density estimates Also each observation is defined to be a cluster and an appr
19. exceed more than one line but cannot exceed 255 characters Commands can only be split across lines between switches and between list elements Blank space is allowed within commands except embedded spaces are not allowed within command and switch names and list values All characters beyond the semi colon are ignored and can be used as comments The following are some examples which demonstrate valid and invalid ways of entering commands OVERVIEW Valid command syntax Invalid command syntax ASSIGN INPUT FILE TST NOECHO ASSIGN I NPUT FILE TST NOECHO or or ASSIGN INPUT FILE TST ASSIGN INPUT NOECHO FILE TST When commands are entered interactively and the Enter key is pressed before completing the command DISTANCE will respond with waiting for input This mode continues until you exceed 255 characters or a semi colon is entered to complete the command Commands can be entered in any combination of upper and lower case letters because all characters are changed to upper case For Titles and Labels put characters within single quotes to maintain lower case or to use special characters eg or For example Ti tle Analysis of survey 1 14 will be a valid command which will set thetitleto Analysis of survey 1 14 with the upper and lower case maintained in the output If you wish to include a single quote in the label or title use two contiguous single quotes to specify a single quote in the label For examp
20. function These are less important warnings but may suggest that you are overfitting the function adding too many adjustment terms and need to truncate the data However in some situations the constraints are reasonable given the shape of the data Taco todo AAA ADA Probability Function Estimation de Parameter Estimates ARA A A A RA A AA A AA AA AA AAA AA AA A eee Effort 48 00000 samples 12 Width 19 00000 observations 9 Model Uniform key k y 1 w Cosine adjustments of order s 1 Point Standard Percent Coef 95 Percent Parameter Estimate Error of Variation Confidence Interval 6651 87637E 01 63049E 02 75999E 01 10106 Figure 9 Estimates of model coefficients and f 0 for uniform cosine model of example 1 Following model selection and fitting a table of parameter estimates Figure 9 is given which indudes 1 estimated coefficients parameters for the key and adjustment functions 2 either f 0 for line transects or A 0 for point transects and 3 sampling correlation of the estimated coefficients if m gt 1 The next 2 pages of the output display the shape of the detection function and how well the chosen model fits the data The plot of the detection probability function Figure 10 displays a histogram of the distance data and the function values fff The y axis is the probability of detecting an object cluster or single at a given distance from the line or point given it
21. is at that distance For this example Figure 10 at 19m it is estimated that only 20 of the clusters are detected A histogram is another way of representing the distribution of the data and gross deviations between the 2 shapes may indicate the model poorly fits the data or numerical problems were encountered in fitting the model A chi square test of the model fit is given following the plot Figure 11 For this example P 0 85272 which suggests the fit is adequate If P is much less than 0 05 a closer look should be given to deviations between the histogram and estimated function Although test rejection does not preclude using the model it does suggest 67 AI Probability Function Estimation Detection Probability Plot E OEI do do doo do do o fttttt pfff ffr fff E ff f ff ff fo 3 D e E e c E i o n q pff f f ff poor ff ff f ff ff fft fff E fff OO REE ALSO t4 11 400 15 200 Perpendicular distance in metres Figure 10 Detection probability plot for uniform cosine model of example 1 ADA AD ADA todo toot ok tok tok Probability Function Estimation Chi Square Goodness of Fit Test ee ee ee ee AA A AA AA AA AAA AA ee ee ee eee Cut Observed Expected Chi square Points Values Values Values 7864 Degrees of Freedom Probability of a greater chi square value 852
22. is either R or P for radial or perpendicular distance The fourth character is U or G for ungrouped exact or grouped interval distances And the fifth character is either U or C for unclustered or clustered The files are LTPUU TPL line transect perpendicular distances Ungrouped Unclustered LTRUU TPL linetransect radial distances angles Ungrouped Unclustered LTPUC TPL linetransect perpendicular distances Ungrouped Clustered LTRUC TPL line transect radial distances angles Ungrouped Clustered LTPGU TPL linetransect perpendicular distances Grouped Unclustered LTPGC TPL linetransect perpendicular distances Grouped Clustered PTRUU TPL point transect radial distance Ungrouped Unclustered PTRUC TPL point transect radial distance Ungrouped Clustered PTRGU TPL point transect radial distance Grouped Unclustered PTRGC TPL point transect radial distance Grouped Cluster There is a corresponding input file for each template file which contains some dummy data entered as an illustration Do not consider these input files as representative of the quantity or quality of the data for real situations The template file only illustrate a subset of the possible commands and values for switches If you use the templates make sure to change the measurement units title etc for your specific situation 82
23. memory should be sufficient on a machine with at least 640K of memory unless numerous TSR Terminate Stay Resident programs or large device drivers eg network drivers are used A problem exists if either of the following error messages is given upon running DISTANCE Not enough memory or Heap space limit exceeded Check the amount of free available memory for your computer with either of the DOS commands CHKDSK or MEM Several solutions are given below for insufficient memory 1 Load device drivers or TSR s into high memory if you have DOS 5 0 or higher 2 Use the alternate executable file described below which requires less memory but runs slower 3 Reduce the memory setting for the overlay area described below or 4 Do not load optional TSR s or device drivers while running DISTANCE It is possible to change the memory requirements within certain limits If you increase the memory the speed may increase and vice versa The program memory is changed by setting the environment variable BLINKER with the set command before running DISTANCE The format of this command is SET BLINKER 00xx where OO represents Overlay Opsize and xx is the amount of memory in kilobytes KB The default value is 40 and it can be set to as low as 28 and as high as 128 If you increase the memory requirements beyond the amount of free conventional memory a fatal error will be given when you attempt to run the program An example setting is SET BL
24. prompt file manipulation commands can be issued to assign clear list print and store files DOS commands from within DISTANCE can be issued from this prompt The following are valid commands at the DISTANCE gt prompt Procedure Initiation DATA enter distance sampling data ESTIMATE estimation of density OPTIONS sets various program options File Manipulation ASSIGN assign filenames CLEAR Clear file contents LIST list file contents to screen PRINT print options data STORE store file contents Miscellaneous DOS execute a DOS command EXIT exit program HELP display help files PAUSE pause execution The commands are described below in alphabetical order 16 ASSIGN Syntax LOG l APPEND ASSIGN PLOT filename l RECORD l REPLACE BOOTSTRAP STATS l APPEND ECHO ASSIGN OUTPUT filename l REPLACE NOECHO ASSIGN filename NOECHO ASSIGN filename Description Assigns filenames tothe INPUT LOG RECORD OUTPUT PLOT BOOTSTRAP STATS and HELP files The filename must be a valid DOS filename or one of the following special names LOG can be SCRATCH or SCREEN OUTPUT can be SCREEN RECORD can be SCRATCH and STATS can be set to NULL to terminate output of statistics If you use SCRATCH the file is maintained and can be LISTedand CLEARed but is deleted upon exiting DISTANCE unless it is explicitly stored with a STORE command Assig
25. the number of times a sample is searched and eis the effort for a single visit eg e is the length of the line or is 1 for a point transect if c 1 For example if a point transect is observed twice in a short time period the sample is specified as SAMPLE EFFORT 2 All of the observations from both visits to the point would follow the SAMPLE command Re sampling the same line or point for immobile objects is inappropriate for obvious reasons The LABEL can be used to give a label for the sample which is used to label the output if the density is estimated for each sample The quote marks are only necessary to maintain lowercase letters and to include the special characters and Only the first 50 characters of the label are used Note An early test version of DISTANCE used the syntax SAMPLE effort That form is still accepted but the current syntax is preferred Examples SAMPLE EFFORT 1 LABEL SAMPLE A SAMPLE EFFORT 14 2 STRATUM Syntax STRATUM LABEL label name AREA asize Description The STRATUM command starts entry of the data associated with a stratum The LABEL switch can be used to give a label that identifies the stratum in the output if density is estimated separately for each stratum The quote marks are only necessary to maintain lowercase letters Only the first 50 characters of the label are used The AREA switch specifies gives the size of the stratum if appropriate The area size must be i
26. variance of density is partitioned into its components to illustrate the relative importance of each component of density For example the percentage of var D attributable to f 0 in this example is computed as CV f 0 CVD 100 2 100 COD 18 7 0 1664 Encounter rate variance is typically the largest contributor to variance of density These percent variance quantities can help guide future sampling design efforts Summary tables of encounter rate detection probability expected cluster size and density estimates comprise the final section of the output Figure 12 is an example of the summary tables for detection probability The summary tables give estimates by level stratum sample and by detection model if results for each model are requested Summary tables are always created even if PRINT SUMMARY or PRINT NO ALL is specified The analysis and output for the second estimate procedure of this example is similar to the first analysis However analysis is limited to estimating detection probability and expected cluster size for all of the data with a half normal Hermite detection model Restricting analysis to detection probability is useful for fitting an initial model to determine a truncation point w such that g w t Werecommend t 0 15 for line transects and t 0 10 for point transects The third estimate procedure illustrates a stratified analysis in which density is estimated for each stratum bu
27. were generated with an expected encounter rate of 5 An estimate of abundance N is not given because an area size was not specified on a STRATUM command The estimate of average detection probability P is 0 491 Qed dod dod AAA AAA Probability Function Estimation bs Model Selection Fitting i ee A A AA A AA A AA AA AA A AA AA ee ee ee eee Effort 30 00000 samples 30 Width 20 00000 observations 131 Half normal key k y Exp y 2 2 A 1 2 Results Convergence was achieved with Final Ln likelihood value Akaike information criterion parameter values key k y 1 W 12 function evaluations 381 15551 764 31100 11 027619 imple polynomial adjustments of order s 2 Results Convergence was achieved with Final Ln likelihood value Akaike information criterion parameter values key kCy 1 9 ine adjustments of order s Results Convergence was achieved with Final Ln likelihood value Akaike information criterion parameter values 14 function evaluations 381 23905 764 47810 856296 8 function evaluations 381 75331 765 50670 Hazard Rate key k y 1 Exp Cy A 1 A 2 Results Convergence was achieved with Final Ln likelihood value Akaike information criterion 10 function evaluations 381 60819 767 21640 parameter values 11 803076 2 357346 Minimum AIC 764 3110 Estimator chosen based on minimum AIC Mode1 Half norm
28. will provide a non parametric bootstrap of f 0 or h 0 and if the population is clustered E s However the variances and confidence intervals are conditional on the sample size and do not include the variance of the encounter rate The OBS switch has been included for completeness but its routine use is not recommended Reasonable confidence intervals for density could only be obtained by adding a variance component for the encounter rate It is also possible to include the OBS switch with SAMPLES however this is not recommended unless the number of observations per sample is reasonable gt 15 By default issuing the BOOTSTRAP command without switches is equivalent to BOOTSTRAP SAMPLES INSTRATUM Werecommend the default or dropping the INSTRATUM if sampling across strata is appropriate The use of STRATUM is only appropriate if the strata represent an additional level of sampling eg independent observers stratum traversing an independent set of line transects sample The bootstrap summary is given at the end of the output Two sets of confidence intervals are given 1 log based confidence intervals based on a bootstrap standard error estimate and 2 2 5 and 97 5 quantiles of the bootstrap estimates i e percentile confidence intervals See Program Files for a complete description of the BOOTSTRAP file Example Resample strata and samples within each stratum BOOTSTRAP STRATUM SAMPLES 47 CLUSTER Syntax
29. within ESTIMATE gt Output The type of output will vary depending on the analysis and the restrictions placed on the type of output however the general structure is as follows Estimation Options Listing A short semi narrative description of the estimation options and detection models and a glossary of terms Figure 7 Il Probability Function Estimation Estimation of average detection probability p equivalent to P or P in Buckland et al 1993 and related quantities f 0 effective strip width ESW or h 0 and effective detection radius EDR It is organized in the following manner a Model Fitting and Selection b Parameter Estimation Table c Detection Probability Plot s d Chi square goodness of fit test If DISTANCE chooses the best model default of P7 ck AIQ section a is repeated for each detection model and b d is only given for the best model If several detection models are considered and Pick None is specified sections a d are repeated for each model 111 Expected Cluster Size Estimation this section is generated if Object Cluster in OPTIONS gt If a size bias regression estimator is used a plot of the data and regression equation are also given This section is repeated for size bias regression if several detection models are considered and the best model is not chosen by DISTANCE IV Density Estimation Results a summary table of estimation results including density and abundance if
30. 0454E 02 12908E 01 49065 59385E 01 38737 62147 14 009 84780 12 444 15 772 4 3667 43808 k 3 5585 5 3583 11 134 96 199 Density Numbers hectares EDR meters Component Percentages of Var D Detection probability Encounter rate 3 40 7 Figure 19 Density estimation results for ungrouped analysis with the half normal Hermite model of example 2 The second analysis which groups the distances into intervals prior to analysis produces very similar results Figure 20 The half normal Hermite model is also chosen and no Hermite adjustment terms are included The model selection results from the output can be compared to Table 5 1 of Buckland et al 1993 The estimate of density is slightly less at 69 059 animals ha and the precision is comparable In this case grouping has no advantage and was only done as a demonstration However in many real situations distances are either recorded in intervals or may be heaped to convenient numbers and should often be analyzed as grouped data The third analysis restricts estimation to a half normal Hermite detection model and computes a bootstrap variance and confidence interval with 400 bootstrap samples Figure 21 The default bootstrap re samples with replacement from the samples points in this example In each bootstrap sample the number of detections n and set of distances depends on the random selection of point transects The analysis of each bootstrap sample includes s
31. 5 0 e Bo 0 0 59 ia Bie Re Soe os 32 SEE a o is DA ti Sta 08 Sie OS 33 O OL asesan Sie 20 bor 2a 5 Satay Star 2s bles 08a Bian oe ae a tana Siena a 8a 8G 33 Title AA oa see A A ee ads 33 LDL st AAA AAA 34 DATA gt End II ADA AAA 39 EOS HA A A A da 39 TA A Ada 39 BISU nd taa 40 A A A E ORE OT A 40 A A A A A O NO 42 ESTIMATE gt B OtSrAP Sa IATA 47 Cluster sarao rasa ricerca 48 DeCMSUY sais BAS bata 49 DIETER Sosa E EA AREA 50 EMSTAVICE a aaa 51 FRCOUNICK dns anat 53 EG A E EN O EV RO ES NO NAO O 53 ESTIOTALO asa AAA at 54 CO Aaa ae 55 CUE darian 56 HO A a 57 MAA a e es 57 DICK astas 58 PANG A A A as 58 A A E eee eae E RRE RR RR RNA 59 V E a ao 60 Examples Example 1 Description iia iaa 61 PUE lt a a dai NE 61 OUEPUE ea hw a bi oe oa aa ae ae a a an a 63 Example 2 DescHPUON garoa Bate awl ly aaa ae aa aa ee 74 UW AAA AAA 74 CUUDUN Serra AAA te ee a ee a ee ee 75 Further Example Input Files iis insiecs ina ela tea aera aaa 79 Template Files 35 40 odedid bd 4b ddr ES 82 INTRODUCTION INTRODUCTION DISTANCE provides an analysis of distance sampling data to estimate density and abundance of a population We assume the reader is familiar with the concepts of distance sampling For details about data collection and analysis methods refer tothe following book Buckland S T Anderson D R Burnham K P and Laake J L 1993 Distance sampling estimating abundance of biological populations Chapman
32. 6 48 02 37 18 1 32 08 80 sample effort 4 label Line 8 36 14 24 56 26 1 32 1 42 9 26 sample effort 4 label Line 9 4 86 74 14 36 03 sample effort 4 label Line 10 38 48 1 36 end est est key unif dist int 0 4 8 1 2 1 6 2 density by stratum end A cue counting example in which distances were recorded in intervals options type cue cuerate 34 98 se 4 74 selection specify dist radial int 0 0 0 2 0 3 0 4 0 6 0 8 1 0 1 5 2 0 3 0 units nautical miles area units naut miles sq end Notice that the last two samples have no observations because they only contain a semi colon on a separate line data sample effort 114 4 4 8 29 42 72 132 111 172 sample effort 50 sample effort 24 end only the hazard key is fit with no adjustment terms estimate 80 est key haz nap 0 end Linetransect sampling in which the data are entered ungrouped but then grouped in the analysis This is often useful to overcome heaping In different estimate procedures different intervals are used to determine its effect If the data had been entered grouped this different grouping could only have been accomplished by re entering the data There are 10 different lines so the variance of n will be computed empirically by default options dist measure inches units meters width 2 length measure feet units meters area units square meters title ITlustrative examples from Wildlife Monograph 72 e
33. 72 The program has limited capability for pooling The user should judge the necessity for pooling and if necessary do pooling by hand Figure 11 Chi square goodness of fit test for uniform cosine model of example 1 68 further models should be examined or that problems in data collection may exist such as heaping The intervals used for constructing the histogram and chi square test are determined by the GOF command which for this example was set with 5 equal intervals If the data are ungrouped exact and a GOF command is not given 3 default sets of intervals are used with a plot and chi square test for each If the distance data are grouped intervals the intervals used for analysis are used for the plot and test For the first ESTIMATE procedure of this example estimation output is generated for each of the four detection models specified If PICK NONE was not specified the model selection fitting Figure 8 would be repeated for each estimation followed by a description of the choice of the best model which minimized the AIC Figures 9 11 would be given for the best model only If more than one detection model is specified and a best model is not chosen the estimation results for each are given in a summary table Figure 12 The AIC values in Figure 12 correspond to the ungrouped truncated w 19m results in Table 4 1 of Buckland et al 1993 The half normal Hermite model has the smallest AIC value although the value
34. 80 30 190 20 180 67 130 17 400 71 200 23 70 37 167 0 400 90 180 77 250 7 80 26 150 35 260 7 200 90 300 65 150 10 100 50 120 20 400 30 150 35 120 0 100 70 200 16 120 5 200 25 120 0 300 15 130 0 150 40 370 0 100 40 200 70 250 0 250 40 250 37 75 58 200 75 150 45 150 50 250 35 200 40 300 55 360 20 360 20 200 50 250 35 100 20 150 40 300 60 100 5 end estimate est key unif dist width 400 0 end In the following example Burnham et al 1980 Wildl Monogr 72 the data have been divided 79 in half for two strata and the density is obtained by stratum These data were obtained from a simulated sampling plane on a 4x8 sheet of plywood so we have changed the units for area and specified the area size for each strata which is 16 sq feet options dist measure inches width 24 length measure feet area units square feet title Illustrative examples from Wildlife Monograph end data stratum label Circle Survey D area 1 area 16 sample effort 4 label Line 1 59 04 57 84 1 48 1 48 sample effort 4 label Line 2 92 15 98 34 26 58 1 16 1 10 1 12 sample effort 4 label Line 3 54 94 1 00 56 26 24 48 1 64 76 54 1 41 sample effort 4 label Line 4 48 81 14 30 22 1 74 1 34 1 10 stratum label Circle Survey D area 2 area 16 sample effort 4 label Line 5 34 4 86 44 06 1 56 3 46 96 1 26 01 42 1 42 sample effort 4 label Line 6 64 76 42 2 78 1 46 1 10 sample effort 4 label Line 7 0
35. ARPLOT FXFIT FXIT SUMMARY N N N N N N N N RESULTS Y Y Y Y Y Y N N SELECT Y Y Y Y Y Y Y N ALL Y Y Y Y Y Y Y Y By default YES EXPLAIN is set to provide a printed explanation of the estimation options and models chosen Note in Versions prior to 1 20 the default was NO and it was set to YES with the more limited PRINT OPTIONS command SIZE Syntax SAMPLE SIZE by STRATUM ALL Description This command explicitly specifies that expected cluster size should be estimated and the resolution at which the estimate s should be made by SAMPLE by STRATUM or ALL data This command is only necessary if density is not being estimated or to specify a level of resolution different from density The level of resolution for estimating cluster size must be less than or equal to the level for estimating detection probability if a size bias regression estimate is computed Example A user wishes to examine detection probability and expected cluster size but not density at this point ESTIMATE ESTIMATOR KEY UNIF DETECTION ALL SIZE ALL END 59 Syntax BOOTSTRAP Description This command specifies the type of variance estimation technique for f 0 MLE specifies that the theoretical variance estimate should be used BOOTSTRAP specifies that a parametric bootstrap should be performed This is a bootstrap variance estimate of f 0 or A O and not of density so it should not be confused with the
36. DISTANCE USER S GUIDE Version 2 2 J effrey L Laake National Marine Mammal Laboratory Alaska Fisheries Science Center NMFS 7600 Sand Point Way NE Seattle Washington 98115 Stephen T Buckland School of Mathematical and Computational Sciences University of St Andrews North Haugh St Andrews Fife KY 16 9SS Scotland David R Anderson Colorado Cooperative Fish and Wildlife Research Unit National Biological Survey Fort Collins Colorado 80523 Kenneth P Burnham Colorado Cooperative Fish and Wildlife Research Unit National Biological Survey Fort Collins Colorado 80523 1996 Use Agreement As a user of this software you are entitled to copy this documentation and the program for your own or your local institution s use e g university laboratory department research center You are not allowed to distribute this software under the name DISTANCE or any other name singly or as part of a package from which you derive any reimbursement DISTANCE contains routines from the Numerical Algorithms Group Ltd library of mathematical and statistical routines These routines are proprietary software of NAG Ltd and have been included with their permission NAG retains copyright for those portions of the software NAG should not be held responsible for the contents or use of this program nor should they be contacted with regards to any problems with its use We and our respective agencies make no warranties expressed or implied with r
37. E END A user wishes to explore the variability in encounter rate by listing the encounter rate for each stratum The variance of the encounter rate for each stratum is computed empirically for each stratum with more than one sample otherwise it is assumed to be Poisson ESTIMATE ENCOUNTER by STRATUM END A user wishes to only see the average encounter rate and an estimate of its variance The variance of the encounter rate is computed empirically if there is more than one sample otherwise it is assumed to be Poisson ESTIMATE ENCOUNTER ALL END END Syntax Description END Finishes definition of the estimation procedure and initiates estimation After the analysis is completed the D7 stance gt prompt reappears 53 ESTIMATE gt ESTIMA TOR Syntax UNIFORM HNORMAL COSINE ESTIMATOR KEY NEXPON ADJUST POLY HAZARD HERMITE SPECIFY SELECT SEQUENTIAL ORDER 0 1 0 2 O nap FORWARD ALL NAP nap START aC1 a 2 a nkp nap AIC CRITERION ILR Description The ESTIMATOR command specifies the type of model for detection probability g x pg 46 49 to estimate f 0 or h 0 The KEY switch specifies the key function to be used and the ADJUST switch specifies the type of adjustment function The SELECT switch specifies the type of adjustment term selection which overrides the default value specified by the SELECTION command in the OPTIONS
38. Hall London which replaces the older monograph Burnham K P Anderson D R and Laake J L 1980 Estimation of density from line transect sampling of biological populations Wildlife Monograph No 72 Throughout this Guide the notation pg xxx xxx refers to relevant page numbers in Buckland et al 1993 which contain details on the notation concepts and analysis methods DISTANCE evolved from program TRANSECT Burnham al 1980 However DISTANCE is quite different from its predecessor as a result of changes in analysis methods and expanded capabilities The name DISTANCE was chosen because it can analyze several forms of distance sampling data pg 4 7 line transect point transect variable circular plot and cue count By contrast TRANSECT was designed only for line transect data In addition the following features have been added 1 A wider choice of estimation models developed around a key adjustment function pg 46 48 approach is included Monotonicity constraints can be imposed on the models pg 73 The best model is selected from the chosen set of models pg 73 77 2 Several methods of adjustment term selection pg 112 399 400 are available including sequential forward selection and fitting all possible combinations In addition specific adjustment terms can be selected 3 Clustered populations i e animals observed in groups pg 12 13 are fully supported with size bias analysis pg 79 80 of expect
39. INKER 0028 which will decrease the memory requirements by 12K Two executable files are included to provide some flexibility in memory speed and limits on the amount of data that can be analyzed The requirements and limits of each are as follows DIST EXE requires approximately 480K of conventional memory and has the following limits 1000 observations 700 samples 100 strata DISTL EXE requires approximately 470K of conventional memory and has the following limits 5000 observations 2000 samples 400 strata DISTL requires less memory and has larger limits only because the program is heavily overlaid and as a result will run more slowly Hopefully the limits of DIST EXE will be sufficient for most applications If so you can save disk space by deleting DISTL EXE after it is installed If you choose to use DISTL EXE do either of the following 1 usethe command DISTL in place of DIST to execute the program or 2 rename DIST EXE to another filename and rename DISTL EXE to DIST EXE 3 OVERVIEW How to Start DISTANCE If you want to start DISTANCE from any disk drive and directory place YourD7 rectory in the computer s PATH statement eg SET PATH CA CA DOS C YourDi rectory Then simply enter DIST to start the program If YourD rectory is not included in your PATH start DISTANCE by entering YourDi rectory DIST where YourDirectory is the directory in which you installed DIST EXE or change to YourDi rectory
40. ORD record of all keyboard entry PLOT SAS or S command data file for plots BOOTSTRAP output of estimates from bootstrap runs STATS estimation statistics file All output files can be ASSIGNed and CLEARed The first 3 can be LISTed and STOREd with the appropriate commands see DISTANCE gt section LOG is used to record all errors and warning messages Initially LOG is the screen If INPUT and DATA are assigned to files it is important to assign LOG to a permanent file so that error messages are not missed amidst the stream of output List this file to make sure that all commands and data were entered properly Error messages sent to the assigned log file are no longer sent to the screen If INPUT and DATA are assigned to files their contents are echoed to the log file so an error message is associated with the incorrect entry Set NOECHO on the INPUT and DATA file assignment and the entries will not be echoed to the LOG file The NOECHO is most useful for lengthy DATA files after all errors have been eliminated OVERVIEW RECORD is a complete recording of all keyboard entry RECORD is initially a SCRATCH file which is temporary and it is deleted upon exiting from DISTANCE The RECORD file can be STOREd or ASSIGNed to save its contents to repeat an analysis at a later time Saving the RECORD is a useful way to learn how to set up data files by entering commands and data interactively and having the results stored in RECORD All lines ent
41. ORWARD see SELECTION value specifies the number of adjustment terms which should be added to improve the fit before the added terms are considered to be non significant pg 399 400 For example if LOOKAHEAD 2 and a model with 2 adjustment terms does not significantly improve the fit over a mode with 1 term a model with 3 adjustment terms is fitted If the 3 term model is an improvement over a 1 term model the algorithm will continue with the 3 term model as the new base model If it is not an improvement the 1 term model would be chosen If LOOKAHEAD 1 the default in the above example the 3 term model would not have been examined because upon finding the 2 term model was not an improvement the 1 term model would have been used Default LOOKAHEAD 1 MAXTERMS Syntax MAXTERMS value Description Value is the maximum number of model parameters pg 62 68 The maximum number of adjustment terms defined as m pg 65 that may be added is MAXTERMS minus the number of parameters in the chosen key function defined as k pg 65 MAXTERMS must be less than or equal to5 This option is only useful to limit the number of model combinations with the term selection mode that considers also possible combinations of adjustment terms SELECTION ALL Usethe NAP switch on the Estimator command to specify an exact number of adjustment terms to be used The maximum number of adjustment terms is also limited by the number of observations for
42. T INP has as its first 2 lines ASSIGN OUTPUT DIST OUT REPLACE ASSIGN LOG DIST LOG REPLACE is the same as entering DIST I DIST INP O DIST OUT REPLACE L DIST LOG REPLACE However if the input file contains ASSIGN commands the O and L assignments will not override those values If you wish explore running the program in batch mode by using one of the example input files which have been included on the installation disk The example files are installed into YourD7 rectory during the installation process see Installation nstructions These files have been constructed from the examples in Burnham et al 1980 and Buckland et al 1993 All of the example input files have a 7np file extension Some of the example filenames are Pgxx 7np where xx refers to the page number in Burnham et al 1980 Other filenames are EXn 7np where n refers to one of the numbers of the Illustrative Examples in Burnham et al 1980 or CHxxx Tnp which refers to the chapter and example number in Buckland et al 1993 15 DISTANCE gt DISTANCE gt DISTANCE gt stheinitial command prompt When the commands DATA ESTIMATE and OPTIONS are issued at the DISTANCE gt prompt the prompt is changed to DATA gt ESTIMATE gt and OPTIONS gt respectively The valid commands for each of the prompts are defined in individual sections of this Guide Each section is identified by the outlined title on the top of the page Also at the DISTANCE gt
43. T can be assigned to a file DIST INP with the ASSIGN command ASSIGN INPUT DIST INP which instructs DISTANCE to take all further commands and data from the file DIST INP until it encounters 1 an EXIT 2 the end of the file 3 a new ASSIGN command or 4 an INFILE command The DATA file contains the data to be entered at the DATA gt prompt By default DATA is taken from the INPUT file Thus ifthe INPUT file is assigned to a disk file the DATA file is also assigned to this same file by default The DATA file can be assigned to its own separate file by using the INFILE command described under DATA gt section This can be done independently of assigning the INPUT file Figure 2 gives an example to illustrate this relationship OVERVIEW INPUT file assigned to DIST INP INPUT file assigned to DIST INP DATA assigned to DIST DAT Enter Enter ASSIGN INPUT DIST INP ASSIGN INPUT DIST INP File DIST INP File DIST INP OPT DIST INT 0 1 2 3 OPT END DIST INT 0 1 2 3 DATA END SAMPLE EFFORT 12 5 DATA 10 8 6 INFILE DIST DAT END END ESTIMATE ESTIMATE ESTIMATE KEY UNIF ESTIMATE KEY UNIF END END File DIST DAT SAMPLE EFFORT 12 5 10 8 6 Figure 2 Example of INPUT and DATA file contents The ASSIGN statement is entered interactively to DISTANCE or the file is used as a batch input file Z DIST INP Output The output files are OUTPUT analysis output LOG error file REC
44. TE gt The INTERVALS command is used to specify u distance intervals for analyzing data in a grouped manner when the data were entered ungrouped The value c is the left most value and so it can be used for left truncation If there is no left truncation specify c 0 The values c C gt Cu are the right end points for the u intervals The value c is the right most point and is used as the WIDTH which defines the right truncation point If all of the distances are less than or equal toc DISTANCE will not truncate data on the right unless RTRUNCATE is set Perpendicular distance intervals can also be created for analysis with the NCLASS and WIDTH commands NCLASS intervals of equal length are created between Left and Width if both NCLASS and WIDTH are given The SMEAR switch is used only if TYPE LINE and radial distance angle measurements were entered DISTANCE RADIAL Angle defines the angle sector around the angle measurement and Pdist defines the proportional sector of distance to use as the basis for the smearing pg 319 322 If an observation is measured at angle a and radial distance r it is smeared uniformly in the sector defined by the angle range a angle atangle and distance range r 1 pdist r 1 pdist The NCLASS and WIDTH switches must also be given to define a set of equal perpendicular distance intervals The proportion of the sector contained in each perpendicular distance interval is summed as an observation
45. TIONS 2 DATA and 3 ESTIMATE These commands initiate a procedure to begin entering a section of input and change the prompt to OPTIONS gt DATA gt and ESTIMATE gt respectively A section of input is completed by entering the command END After completing the OPTIONS gt and DATA gt input sections the DISTANCE gt prompt will reappear However after completing the ESTIMATE gt section the analysis is performed before the DISTANCE gt prompt reappears You can issue the OPTIONS DATA and ESTIMATE commands repeatedly and in any order however the order is important in most circumstances For example data must be entered before estimation is initiated and options which define the type of data must be entered before entering the data unless the default values are acceptable However after entering data or performing an analysis options which do not change the basic data format can be changed If you change options 5 OVERVIEW it is only necessary to set those options you want to change All unchanged values remain as they were last set Unlike OPTIONS gt if you re enter DATA gt previously entered data are cleared from memory The ESTIMATE gt procedure can be re entered any number of times without regard to previous analyses Be aware of the command prompt because different commands are accepted at each prompt Some commands have the same name but perform different functions at different prompts For example the DISTANCE co
46. a line and the distance between the points is small relative to the size of the area it is more reasonable to consider the line of points as a replicate rather than the point In this case each line would be represented as a sample and the effort would be the number of point transects along the line if c 1 for each point or the sum of the fraction of the circle observed at each point if c lt 1 for one or more points For line transect sampling effort is the length of a line l for each time it is sampled As with point transects if only 1 side of the line transect is searched sampling effort can be adjusted for a few lines by halving the line length or it can be adjusted for all lines by setting the value of SF 0 5 at the OPTIONS gt prompt to adjust all of the lines A partial example is illustrated below with the first 3 lines each sampled a single time and the lengths are 10 5 12 1 and 1 5 miles respectively OPTIONS LENGTH UNITS MTles END DATA SAMPLE EFFORT 10 5 SAMPLE EFFORT 12 1 SAMPLE EFFORT 1 5 fetc For cue counting the sampling effort is the time spent searching The discussion above also applies to cue counting 41 In some studies to increase the number of observations of animals lines or points are sampled more than once in a short period of time pg 91 These should not be treated as independent spatial replicates Instead define a SAMPLE for each point or line but set effort to be te where t is
47. acking down errors in the data because errors are printed in the LOG directly after the incorrect data line If the data are not ECHOed it may be 39 difficult to determine which line of data contains the error Once you are certain that the data are free of errors using NOECHO will reduce the amount of output to the LOG file The INFILE contents must contain the SAMPLE command and the corresponding data associated with the SAMPLE The file may also contain STRATUM commands However the file cannot contain the data without the SAMPLE commands The following is an invalid use of the INFILE command because the observation data for the first sample are either missing or they are included in TEST DAT which is not valid DATA SAMPLE EFFORT 1 INFILE TEST DAT However if FILE1 DAT and FILE2 DAT contain SAMPLE commands and data the following is valid DATA STRATUM LABEL STRATUM 1 INFILE FILE1 DAT STRATUM LABEL STRATUM 2 INFILE FILE2 DAT DATA INFILE FILE1 DAT INFILE FILE2 DAT NOECHO END LIST Syntax LIST Description Lists values of the entered data SAMPLE Syntax SAMPLE EFFORT value LABEL label name Description The SAMPLE command defines the sample effort and initiates entry of the observation data for a sample The sample observation pairing is necessary for empirical and bootstrap variance estimation pg 90 91 94 96 of the encounter rate numbers observed per unit effort pg 186 198
48. al fitting SELECTION SEQUENTIAL with LOOKAHEAD 1 and the criterion is a likelihood ratio test CRITERION LR with a default significance level of 0 15 PVALUE 4 results for each detection model are given because DISTANCE has been instructed not to pick the best model PICK NONE and 5 the goodness of fit test and plot use 5 equal intervals over the range 0 19 The second ESTIMATE procedure illustrates how to restrict estimation to certain parameters of interest In this example only expected cluster size STze AIT and detection probability f 0 Detection All are estimated for all of the data combined Density is not estimated because a Dens ty command is not included See ESTIMATE gt for an explanation of these commands A stratified analysis is illustrated in the third ESTIMATE procedure Density is estimated for each stratum Density by Stratum but a common f 0 is estimated across strata Detection all An overall pooled density estimate is computed as an area weighted average of the stratum estimates The half normal H ermite is the only detection model considered Expected duster size is estimated by the mean cluster size Output is limited to an explanation of estimation options and summary tables by the command Print No all Yes explain The switch No all eliminates all output other than summary tables and the switch Yes explaTn reinstates the explanation of the estimation options see PRINT command
49. al key k y Exp y 2 2 A 1 2 Figure 17 Excerpts from output of example 2 showing model selection for the first ESTIMATE procedure 75 AIR IGG IOI aCe I Rae iea ar ae aera Probability Function Estimation Detection Probability Plot t E k AE AE AE EE E AE AE AE EEE E AE AE AE AE EE AE E AE AE AEE AEEA urbano ff pe A p x ff p if p ff ff p x f p A p p oe I p A p off p f a ff p ff p ff p p ff e fff p ff p nr fps p fff p f Hy p i p E p E p e Hy 12 000 16 000 20 000 Radial distance in meters HARI Probability Function Estimation Probability Density Plot a AAA IOC ICI OIE Ise ar ae sear SEO Iara teak FFFFFFFFF fff IEEE apponi ff ff ta ff tos toos f a aaa paraa E OE ff af aras qua a ta af ff f A Hy A Al i sii E ETETE TEELT fi Spn l El Hy 12 000 16 000 20 000 Radial distance in meters Figure 18 Plots of Q r and f r and matching histograms for the half normal Hermite model of example 2 76 Qa dod dod AAA AAA y Density Estimation i Results AAA A A A A AA AA AA AAA AAA AAA AAA AAA Effort 30 00000 samples 30 Width 20 00000 observations 131 Model Half normal key k y Exp y 2 2 A 1 2 Point Standard Percent Coef 95 Percent Parameter Estimate Error of Variation Confidence Interval 10191E 01 12334E 02 8
50. ance amp angle DISTANCE RADTAL treated as an independent replicate for variance estimation pg 90 98 For each SAMPLE a measure of the and duster sizes sampling intensity or effort eg line length for line transects must be specified and optionally a label 4 Grouped perpendicular distances Db can be given Ungrouped cluster sizes 3 Ungrouped radial distances angles Perpendicular Distance DISTANCE PERP Observation data are the distances and cluster sizes for the set of detected objects The type of data and their format the way they Ungrouped perpendicular distances and duster sizes Legend l are entered Table 1 depend on the For i 1 n number of observations f the foll OPTIONS i radial distance measurement values O e TollowIng perpendicular distance measurement 1 TYPE 2 OBJECT and 3 i angle measurement in degrees DISTANCE TYPE defines the type of Se sampling and determines the For 1 u number of intervals appropriate distance measurement n number of observations in jY distance interval i e perpendicular distance x for Table 1 Data entry formats assuming objects are dusters _ ine transects and radial distance If objects are single animals cluster sizeis always Landis r for point transects or cue not entered counting pg 4 8 OBJECT specifies whether the population is clustered 36 or not pg 12 13 If the population is dustered the size s
51. area size is given This section is also repeated for each detection model if the best model is not chosen V Estimation Summary summary tables of Encounter Rate Detection Probability Expected Cluster Size and Density Abundance These tables summarize estimates of each quantity and related values at the chosen level Sample Stratum All of estimation Estimates are also summarized by detection model where appropriate VI Bootstrap Summary of Density Abundance if a bootstrap analysis for density is requested tables summarizing bootstrap coefficient of variation CV and confidence interval are given The amount of output can be restricted at a general level with the PRINT command within OPTIONS gt and in greater detail with the PRINT command within ESTIMATE gt Werecommend that you accept the default level of output until you become familiar with the analysis techniques 63 II E Estimation Options E A Listing hi OOOO Parameter Estimation Specification Encounter rate for all data combined Detection probability for all data combined Expected cluster size for all data combined Density for all data combined Distances Analysis based on exact distances Width specified as 19 00000 Clusters Analysis based on exact sizes Expected value of cluster size computed by regression of log s i on g x i unless regression is non significant with significance level 050 Estimators Estimator 1 Key Uniform k y
52. ation floppy disk is in drive A If either disk is designated by another letter use that letter wherever we use C or A Create a separate directory for the DISTANCE program and associated files by entering the following commands Es CDA MD YourDirectory and replace YourD7 rectory with the name you want to give the directory eg DISTANCE After creating a directory install DISTANCE by entering the following A INSTALL A YourDirectory For example A INSTALL A C DISTANCE will install the software from drive A into the directory DISTANCE on drive C Various files will be installed 1 DIST EXE the default executable file 2 DISTL EXE an alternate executable file 3 DIST HLP a text document containing help accessed by the program 4 BROWSE COM a file listing utility 5 README a text file containing any corrections or new material not in this Guide if needed and 6 numerous template and example input files described in the EXAMPLES section INTRODUCTION Program Requirements and Limitations DISTANCE will only run on an IBM PC or compatible microcomputer A numeric co processor is not required but will improve the speed substantially note a co processor is built into an 80486DX processor or above Approximately 1 MB of disk space plus additional space for input and output files is required Also your computer s configuration file CONFIG SYS should specify FILES 20 or greater Available conventional
53. ble to specify any combination of terms and give starting values for their coefficients DISTANCE does not select the terms to include in the model but does estimate the parameters to fit the model to the data For example ESTIMATE ESTIMATOR KEY UN1IFORM NAP 2 SELECT SPECIFY ORDER 1 3 END specifies the model as the following 2 term cosine series for which the parameters a and a are estimated 1 a cos a cos Ww Ww ALL as its name implies examines all possible combinations of a limited number of adjustment terms If zis the maximum number of parameters MAXTERMS z and k is the number of parameters in the key function then there are 2 combinations of the adjustment terms Each model is fitted to the data and the model with the smallest value of the Akaike s nformation Criterion AIC is selected f x Z SEQUENTIALand FORWARD both consider a subset of models with different combinations of adjustment terms For each of these term selection modes a sequence of models is considered An adjustment term is added at each step of the sequence The sequence of models can be represented as M key function with no adjustment terms M key function with 1 adjustment term M key function with 2 adjustment terms M key function with v 1 adjustment terms A stopping rule CRITERION is either based on a likelihood ratio test or minimizing AIC Model M is chosen if there is no model in the sequence M a My
54. can the help information Press the Esc key toleavehelp HELP should only be used interactively INFILE Syntax ECHO INFILE filename l NOECHO Description This command redirects data entry to the file given by filename if it is found After all data are entered from filename further input is obtained from the INPUT file either the keyboard or ASSIGNed INPUT file The only exception is if the specified data file contains another INFILE command It will then chain jump to the next file specified by the INFTLE command Upon completion of the second file assuming it does not have any INFILE statements DISTANCE will return tothe INPUT file and not the data file Thus the files cannot betruly nested because any data after the first INFTLE command will beignored Multiple INFTLE commands can be given throughout the INPUT file to enable several data files to be merged together F or this reason it is suggested that you do not indude the END statement in the file containing the data because it will halt data entry The ECHO and NOECHO switches control whether the data are ECHOed tothe LOG file By default if commands are being ECHOed to the LOG file the data will be ECHOed likewise if the commands are not echoed NOECHO the data will not be ECHOed by default see the ECHO switch on the ASSIGN command These default values can be changed by adding either the ECHO or NOECHO switch The ECHO is most useful in tr
55. ception that a title record is not included 12 OVERVIEW Example input in Figure 1 0 0111 51 000 0000 00000 0112 4 0000 0000 00000 0113 142 30 0000 00000 0114 35840 4028 10437 0121 2 0000 0000 00000 0122 108 33 0000 00000 0124 59869 6316 18694 0125 55677 6316 17385 0126 1 6703 6316 52156 0221 1 0000 0000 00000 0222 106 91 0000 00000 0223 45113 0000 00000 0224 50318 1354 38386 0225 66245 1354 50536 0226 1 9874 1354 1 5161 0321 1 0000 0000 00000 0322 106 69 0000 00000 0323 55245 0000 00000 0324 51245 1208 40241 0325 65047 1208 51079 0326 1 9514 1208 1 5324 0141 2 1871 1491 55459 0241 1 8382 4249 59323 0341 1 8721 4205 61075 O O0wOoOO rv Ur Un Un nanan LR BP fH BRQOoCoCoCSCSCCaSaCSaSCSCCeee 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 S Figure 5 Example STATS file for second estimate prcoedure of input file given in Figure 1 modified to output results from each estimator Startup File An ASCII file named STARTUP DST can be created which contains commands that are executed each time DISTANCE starts This is particularly useful to change default values for options As an example assume that all of your sampling is from point transects TYPE POINT and you want to squeeze all of the output SQUEEZE 0N by default Also you would like the default output file to be named DISTANCE LST and you want it replaced each time This is accomplished by creating a fi
56. ction f x H 1 tacos z tacos 23 Ww Ww Ww However with SEQUENTIAL selection the adjustment term cos 32x w could not be added without first adding the adjustment term cos 27x w The additional level to model fitting is to choose between the competing models ESTIMATORS This model selection step is determined by the PICK command It has 2 values NONE and AIC If you assign the value NONE DISTANCE will not choose between the different models and will report the estimates for each model However if you accept the default value AIC pg 75 76 DISTANCE will only compute estimates based on the model which has the smallest AIC value 46 ESTIMATE gt BOOTSTRAP Syntax STRATUM BOOTSTRAP SAMPLES OBS INSTRATUM Description The BOOTSTRAP command initiates a non parametric bootstrap pg 94 95 119 120 155 158 of the density estimation procedure The number of bootstraps performed is determined by the BOOTSTRAP command in OPTIONS The basic resampling unit of the bootstrap is a SAMPLE however if strata are replicates they can also be re sampled with the STRATUM switch If both are specified re sampling occurs at both levels see example below The switch INSTRATUM can be set to restrict the resampling of samples or observations within stratum It would be used if density is estimated by stratum or sampling was stratified apriori The switch OBS can be set to resample distances Using BOOTSTRAP OBS
57. d S T Anderson D R and Burnham K P 1996 DISTANCE User s Guide V2 2 Colorado Cooperative Fish amp Wildlife Research Unit Colorado State University Fort Collins CO 82pp TABLE OF CONTENTS INTRODUCTION Installation Instructions A A A Wee eS Program Requirements and Limitations ooooooooooooo OVERVIEW How to Start DISTANCE rta toutes ue deel ious deed AAA A Simple Example viii hoe baad oboe A eee Entetine Commands ibid Progtant Files suda MP aa ad CUIDUE lr AAA StartUp a a A A A A A A A Batch Operation a a REA EA AAA A AAA AAA AAA AAA al A A A beat Boe oe E 5 etl Bat Sacchi Sal Sn actus bla Soa a eta aN 2 Said tele eh eo hte Seca th oh late ea ed ae PAUSE eso rra bolle Bile bebe able ees OPTIONS gt TAC ts O OSEA IA A RT AAEE EEEE ANO BOOTA EE ARDE A ERRE RT ER A ARE E eden eto ER O DISTA AA AAA A tes nse a A saan ANS TOPS AVC Cy a re ie IT TE eas AAA a ene ene eae BS gee ERE AAA axe wey AAA ee Be ee eS Length is a A AE A te ew oa ASE EDDIE AAA AED A ten oe Si a 29 Lookahedd asmenini A A a Soe A bia oe Sone 29 Maxteris 2 ii oe bole Bio aie Be oe Nan oie bo We ble oie ble ake lg oie bie ake 30 OU CCE sesh E Me coh bale IA ae Mote d a Leh POG Me Se hee Me Mah 30 PNG toi Bion 9a 5p 0e Blan gp ap We hte hg len ake lg 6a Boar SMe 31 Pval es remire Sie ce 5G ale ity ta ii Siw se pale a Sie oe Sea 31 Seed aras bly oe bbe bie te Soe o Btw te Spake ier ate So ore 32 SOCIO ir Stone
58. d in rods and converted to feet with a user specified conversion factor because the program will not recognize the Rods unit 10 of the observations will be right truncated in the analysis DIST PERP MEASURE Rods UNITS Feet CONVERT 16 5 RTRUNCATE 0 10 END Syntax Description END completes entry of options and returns to the Di stance gt prompt EPSILON Syntax EPSILON value Description Value is a relative measure of closeness of parameter estimates obtained between iterations in assessing the maximum of the likelihood function pg 65 66 The default value is 1 0E 7 which means roughly 6 digits of accuracy is achieved EPSILON can be set to any value between 0 1 and 1 0E 8 Typically it is not necessary to change its value unless error messages are given indicating difficulty with fitting the model Default EPSILON 1 0E 7 HELP Syntax HELP HELP command_name Description If you type HELP several pages of introductory information will be displayed If you type HELP command_name a description of the specific command will be given Use PgUp and PgDn or the up and down arrow keys to scan the help information Press the Esc Escape key to leave help HELP should only be used interactively It will work in batch mode but it will interrupt processing until you press the Esc key ITERATIONS Syntax ITERATIONS value Description Value is the maximum number of iterations that the alg
59. d or entered ungrouped and analyzed as grouped DISTANCE INTERVALS used in ESTIMATE then only the third form can be used to specify that the PLOT file should be constructed It is not possible to specify goodness of fit intervals other than those used to analyze the data Examples Data are ungrouped and 2 different sets of intervals are specified GOF NCLASS 5 GOF 0 5 10 20 30 40 50 Data are grouped but the SAS plot file is desired GOF SAS 56 HELP Syntax HELP HELP command_name Description If you type HELP several pages of introductory information will be displayed If you type HELP command_name a description of the specific command will be given Use PgUp and PgDn or the up and down arrow keys to scan the help information Press the Esc key to leave help MONOTONE Syntax WEAK MONOTONE STRICT NONE Description The estimators are constrained by default to be strictly monotonically non increasing i e MONOTONE STRICT the detection curve is either flat or decreasing as distance increases from 0 to w pg 73 In some instances depending on the tail of the distribution this can cause a poor fit at the origin x 0 Two options exist 1 truncate the observations in the tail or 2 use the command MONOTONE WEAK or MONOTONE NONE MONTONE WEAK will only enforce a weak monotonicity constraint i e 0 gt f x for all distances x This will allow the curve to go up and down as it fits
60. e the orientation of the object relative to the observer Angle values can be limited to the half circle interval 0 180 or to the quadrant 0 90 by entering the acute angle formed by the line and the ray from the observer to the object At present the angle and radial distance measurements cannot be entered as interval grouped values However if the angle distance data are collected in intervals the analysis can be modified with the SMEAR switch of the DISTANCE command at the ESTIMATE gt prompt Frequencies n for the grouped distance data must be non negative They are typically integral values but are not restricted to integers For grouped distance data with a clustered population DISTANCE checks to make sure that the sum of the frequencies of the grouped distances matches the number of entered clustered sizes i e n Mm gt M n An error message is issued and the data are discarded if they do not match When the data are entered as frequencies it is not necessary to enter all of the frequencies in the tail if they are zero For example if there were 7 distance intervals the following could be entered 5 2 0 1 and the remaining 3 frequencies for intervals in the tail would be assumed to be zero The format for data entry depends on the data being entered Table 1 displays the possible formats assuming OBJECT CLUSTER f you enter the data from the keyboard DISTANCE will display the appropriate order and format The same forma
61. ed abundance estimate uses the area from the first stratum 1 DENSITY by STRATUM DESIGN REPLICATE 2 DENSITY by STRATUM DESIGN STRATA WEIGHT NONE In all other cases the area is totalled from all of the strata Default For DENSITY by SAMPLE DESIGN REPLICATE For DENSITY by STRATUM DESIGN STRATA WEIGHT AREA Examples An estimate is needed for each stratum and it will be weighted by stratum area DENSITY BY STRATUM An estimate is needed for each stratum and there are enough observations in each sample to get an estimate from each The strata represent different platforms surveying the same area so the strata are treated as replicates DENSITY BY SAMPLE DENSITY BY STRATUM DESIGN REPLICATE DETECTION Syntax SAMPLE DETECTION by STRATUM ALL Description This command explicitly specifies that detection probability and its functionals f 0 h 0 should be estimated and the resolution at which the estimate s should be made by SAMPLE by STRATUM or ALL data Example Density is estimated by stratum but the estimates are based on an estimate of f 0 for all the data 50 ESTIMATE gt DENSITY by STRATUM DETECTION ALL Estimate detection by stratum choosing between 2 models but do not estimate any other parameters Different models may be selected for each stratum ESTIMATE DETECTION BY STRATUM ESTIMATOR KEY HAZ ESTIMATOR KEY UNIF END DISTANCE Syntax DISTANCE WIDTH val
62. ed cluster size and estimation of cluster density and density abundance of animals 4 Stratified estimates of density and abundance can be constructed pg 99 102 5 Both left truncation pg 15 273 277 377 379 and right truncation pg 15 50 106 109 of the data are supported 6 Bootstrap resampling can be requested for robust estimates of variance pg 94 96 119 120 155 158 DISTANCE understands and interprets a relatively simple command language You tell DISTANCE what you want to do by entering commands and data The command approach was chosen over a menu or question answer interface because it easily allows the program to be used in either interactive or batch mode commands and data stored in files This Guide describes the commands and the way you will use them to analyze a set of data In addition we give several examples showing the commands and data used as input and an explanation of the output INTRODUCTION Installation Instructions A single floppy disk accompanies this manual It contains the following files that must be installed before use DIST ARC contains the executable program and help files README installation instructions and other notes as needed INSTALL BAT batch file for program installation EXAMPLES ARC _ contains example input files PKUNZIP EXE program to unpack the ARC files We assume that you will be installing the software onto your hard disk which is designated by C and the install
63. ed is the command name ESTIMATOR because all of the switches have default values Default Values KEY HNORMAL ADJUST COSINE SELECT SEQUENTIAL or value set in OPTIONS CRITERION LR except if SELECT ALL Examples Use the following to fit a model with a half normal key function by default and Hermite polynomials for adjustment functions DISTANCE fits all possible combinations of adjustment terms and uses AIC to choose the best set of adjustment terms ESTIMATOR ADJ HERM SEL ALL Use the following to fit a model that uses the uniform key function with simple polynomial adjustment functions ESTIMATOR KEY UNIFORM ADJ POLY Use the following to fit a model that uses the hazard key without adjustments ESTIMATOR KEY HAZARD SELECT SPECIFY NAP 0 Use the following to fit a 2 term cosine series with terms of order 1 and 3 and specify the parameter starting values note nkp 0 for a uniform key ESTIMATOR KEY UNIF SELECT SPECIFY NAP 2 ORDER 1 3 START 0 3 0 05 GO Syntax GO value SE value Description This command assigns a value to g 0 which is assumed to be 1 unless a value is assigned with this command The SE switch is used to specify a standard error for the estimate so that estimation uncertainty of g 0 can be incorporated into the analytical variance of density Default GO 1 0 SE 0 0 Example GO 0 85 SE 0 12 55 ESTIMATE gt GOF Syntax GOF INTERVALS c C5
64. electing and fitting the model In this case only the half normal Hermite detection model was considered but the number of Hermite adjustment terms was allowed to vary The bootstrap model choice is not limited to the model chosen in the original analysis If it were the bootstrap and analytical variances would be very similar However it is the uncertainty in model selection which we want to capture with the bootstrap analysis If several detection models were specified full model selection would be performed for each bootstrap sample The Bootstrap Summary Figure 21 includes 1 point estimate of density 2 bootstrap estimate of the coefficient of variation 17 05 which is SE D D CV 100 77 Qa dod dod AAA AAA y Density Estimation i Results AAA A A A A AA AA AA AAA AAA AAA AAA AAA Effort 30 00000 samples 30 Width 20 00000 observations 131 Model 1 Half normal key k y Exp y 2 2 A 1 2 Point Standard Percent Coef 95 Percent Parameter Estimate of Variation Confidence Interval 99369E 02 12351E 02 E 77958E 02 12666E 01 50317 62540E 01 39475 64137 14 187 88165 12 561 16 023 3 5585 5 3583 Density Numbers hectares EDR meters Component Percentages of Var D Detection probability Encounter rate 1 39 5 Figure 20 Density estimation results for grouped analysis with the half normal Hermite model of example 2 where SE 6 is the bootstrap estimate of standa
65. ered from the keyboard are sent to the RECORD including incorrect commands Edit the file to remove errors or unneeded commands before using as an ASSIGNed INPUT file RECORD can be LISTed to observe its contents and it can be CLEARed to purge its contents OUTPUT contains the results of the data analysis OUTPUT is sent to the screen and it is appended to the default file named DIST OUT Suppress the file copy of the OUTPUT and only get the screen copy by entering ASSIGN OUTPUT SCREEN Suppress the screen copy and keep the file copy with the name filename by entering ASSIGN OUTPUT F17 Tename NOECHO OUTPUT can also be STOREd after it has been displayed on the screen The STORE command copies the output from the default file DIST OUT to a file of your choice When you STORE the OUTPUT file the default file DIST OUT is CLEARed New output is appended to the previous contents of DIST OUT by default Use an ASSIGN CLEAR or STORE command to avoid appending to unwanted output Note Do not use the DOS commands in this program to rename or delete a file which is being used by DISTANCE If you want to overwrite the default output file each time you start DISTANCE put the command ASSIGN OUTPUT DIST OUT REPLACE intothe startup file which is described below PLOT is created if the SAS or SPLUS switch is used with the goodness of fit GOF command in the ESTIMATE gt procedure PLOT contains data and commands to create a high quality graphics
66. espect to this software and its fitness for any particular purpose In no event will we be liable for indirect or consequential damages including without limitation loss of income or use of information Acknowledgments Weare grateful for the support of our respective agencies and other sources of support for the production and distribution of this User s Guide In particular the Colorado Division of Wildlife provided funding to eff Laake during the development of most of version 1 of program DISTANCE Some programming on version 1 was completed while J eff Laake was employed by WEST Inc Version 2 of DISTANCE was initiated and completed since J eff became employed by the National Marine Fisheries Service Support for Steve Buckland s time has been from the Scottish Agricultural Statistics Service Both David Anderson and Ken Burnham extend their appreciation for support to their long time employer the U S Department of Interior We thank Gary White for comments on an earlier version of this User s Guide David Borchers for the suggestion to produce a quick reference card and Alejandro Anganuzzi for providing code for smearing analysis Support for some aspects of version 2 of DISTANCE the production of this User s Guide and for all the printing and some distribution costs of this Guide were funded by the National Marine Fisheries Service under contract PO 43ABNF 202826 we appreciate this support from NMFS Citation Laake J L Bucklan
67. fault value for the significance level is set by PVALUE in OPTIONS If the TEST switch is not specified the size bias regression estimate will be used regardless of the test value Examples Estimate the expected cluster size from the log s vs 9 x regression but use the average cluster size if the correlation is non significant as determined by the level set with PVALUE default 0 15 CLUSTER BIAS GXLOG TEST 48 DENSITY Syntax NONE DENSITY by SAMPLE DESIGN REPLICATE NONE DENSITY by STRATUM DESIGN STRATA REPLICATE EFFORT WEIGHT AREA DENSITY by ALL Description These commands define the levels at which density estimates are made and how these estimates are weighted If the DENSITY by ALL command is used or if none of the commands DENSITY ENCOUNTER DETECTION SIZE are given all of the data are used to make one overall estimate of density If the DENSITY BY SAMPLE command is given density is estimated for each sample The DESIGN value defines how the estimates should be treated to create a pooled estimate If DESIGN REPLICATE default each sample is treated as an independent replicate from the stratum or the entire area In this case the estimates are weighted by effort e g line length to get a stratum density estimate if DENSITY by STRATUM is also specified or a pooled overall density estimate see eqns 3 11 3 14 in Buckland et al 1993 If DESTGN NONE
68. for the data because it is incompletely stratified SAMPLE 1 OBSERVATIONS FOR SAMPLE 1 STRATUM 1 SAMPLE 2 OBSERVATIONS FOR SAMPLE 2 At the very minimum one SAMPLE and its observation data must be defined Observation data must always be preceded by a SAMPLE command and are entered in a variety of formats described below The STRATUM command which begins a stratum also may specify a label and an area size The most obvious use for a stratum is to represent different areas which were sampled or the same area at different times Estimates of density can be obtained separately by stratum and then combined over strata Use the DENSITY command at the ESTIMATE gt prompt to define how stratum estimates are combined Another use for strata is to represent a second level of replicate sampling within the same area For example several observers or several different platforms of observation Or strata can be used to stratify the data based on some characteristic of the population e g sex or cluster size pg 77 78 Point transects or cue counts 7 YPE POINT or CUE 1 Grouped radial distances ni The SAMPLE command Ungrouped cluster sizes Six S A defines the basic sampling unit It T represents a line for line transects Ungrouped radial distances and Sista Sa a point for point transects a web for cluster sizes 3 gt trapping webs and a search period Line Transects TYPE LINE for cue counting Each SAMPLE is Radial dist
69. frequency and these non integer frequencies grouped data are analyzed to estimate detection probability Note Distances specified by WIDTH LEFT and INTERVALS should be in the same units used for the entered data even if the distance units are converted in the analysis Examples Truncate the distances at 100 feet hence only use those less than or equal to 100 feet in the analysis This value would be used even if the distances were converted to meters for analysis The conversion is applied to the input width of 100 feet DIST WIDTH 100 The distance data were entered ungrouped but they were actually collected in these intervals alternatively to mediate the effects of heaping these intervals were chosen to analyze the data DIST INT 0 10 20 30 40 50 60 70 80 90 100 The above example could also be entered as DIST NCLASS 10 WIDTH 100 52 ENCOUNTER Syntax SAMPLE ENCOUNTER by STRATUM ALL Description This command explicitly specifies that encounter rate should be estimated and the resolution at which the estimate s should be made by SAMPLE by STRATUM or ALL data This command is only necessary if density is not being estimated Examples A user wishes to explore the variability in encounter rate by listing the encounter rate for each sample The variance of the encounter rate for each sample is assumed to be Poisson because the sample is a single entity ESTIMATE ENCOUNTER by SAMPL
70. h of its components if they are unspecified For example ESTIMATE ESTIMATOR KEY UNI FORM DENSITY BY STRATUM END will estimate density and each of its components for each stratum defined in the data The lowest level for density must coincide with a level assigned to encounter rate The level of any component cannot be lower then the lowest level specified for density For example the following is not valid ESTIMATE ESTIMATOR KEY UNI FORM DENSITY BY STRATUM DETECTION BY SAMPLE END If a size bias regression estimate of expected cluster size is computed the level for SIZE must be no greater than the level for DETECTION This feature is most useful for estimating density by stratum when too few observations exist in each stratum to estimate f 0 or h 0 A solution is to assume 0 is the same for all strata which is illustrated in the following example ESTIMATE ESTIMATOR KEY UNI FORM DENSITY BY STRATUM DETECTION ALL END All of the observations are pooled to estimate a common value for f 0 which is used in each stratum density estimate Possibly the most confusing aspect of estimation with DISTANCE will be the specification of models for detection probability and model selection A model is specified with the ESTIMATOR command which defines a type of key function and adjustment function The adjustment function is actually a series of terms which are added to the key function to adjust the fitted function to the
71. his example using a likelihood ratio test Model 2 is judged significantly better than Model 1 P 0 000003 but Model 3 is not significantly better than Model 2 P 0 545446 Thus a 1 term cosine model is chosen as the best fit for a uniform cosine detection model Model 2 would also be chosen if AIC was the criterion because the AIC increased from 562 9789 for Model 2 to 564 6135 for Model 3 If the significance level for the likelihood ratio test is 0 15 the likelihood ratio and AIC criterion will almost always choose the same model for sequential model fitting The other adjustment term selection modes SELECTION FORWARD and ALL produce similar output but consider a larger 66 set of models rather than just adding terms sequentially however only rarely does the chosen model disagree with the model chosen by sequential fitting Model fitting and selection output is not generated if either PRINT RESULTS is set in OPTIONS gt or FXFIT is included in the NO list of the PRINT command within ESTIMATE gt If you are unfamiliar with the analysis techniques do not restrict the output because it includes messages about any problems encountered fitting a particular model In particular a message that parameters are reaching an upper or lower bound suggests that you have requested an unreasonable fit and may need to truncate the data Also messages are given if parameters are being constrained for monotonicity or to maintain a non negative
72. ht most distance for grouped data Typically c 0 and c w Intervals can also be specified by using the NCLASS and WIDTH and optionally the LEFT switch These switches will create nclass equal width distance intervals between the values of left and width i e each interval is of length width left nclass For ungrouped data it is also possible to specify left and right truncation with the LEFT and WIDTH switches pg 15 Any values outside of these bounds are excluded from the analysis Right truncation as a percentage of the observations can also be specified for both grouped and ungrouped data with RTRUNCATE switch The value of t must be between 0 and 1 In the analysis no more than t 100 of the data is truncated from the right For ungrouped data the width is set at the distance which represents the 1 t 100 quantile For grouped data intervals are truncated from the right as long as no more than t 100 of the data is truncated If t 0 and the data are ungrouped data the width is set to the largest distance measurement and if the data are grouped the width is set to the endpoint for the right most interval 25 with a non zero frequency For ungrouped data if both the WIDTH and RTRUNCATE switch are specified the RTRUNCATE value specifies the value of width The DISTANCE command is also used to define the measurement unit for distances MEASURE label a label for the units in which distance was measured Single quote
73. ifications are optional because each has a default value If left unspecified the output will be appended to DIST OUT the log output will come to the screen and the startfile is assumed to be named STARTUP DST We strongly recommend specifying a log file and examining its contents to make sure all commands and data were entered correctly All of the switches for the ASSIGN command can be used with the file specifications except with S For example DIST I DIST INP O DUCKS OUT REPLACE NOECHO will use DIST INP as the input file and DUCKS OUT as the output file It will replace any file currently named DUCKS OUT Ifthe REPLACE switch is not used and the specified file already exists DISTANCE displays an error message and appends the output to the default file DIST OUT By default output is also displayed on the screen as the data are read and analyzed Using NOECHO after the output file suppresses the screen output Spaces are not allowed anywhere within a file specification nor between it and its associated switches however there should be one or more spaces between the file specifications The following would be an invalid way to run the program in batch mode because the space indicated by the will create an error DIST I DIST INP O DIST OUT NOECHO A A One way to reduce typing is to specify the ASSIGN statements for the OUTPUT and LOG file in the INPUT file For example entering 14 OVERVIEW DIST 1 D1ST INP where DIS
74. label RADIAL MEASURE label RTRUNCATE t LEFT 1eft INTERVALS C C EXACT Synonyms RIGHT WIDTH Description This command describes numerous features about the distance data and defines the default values for estimation The format of the data entry within DATA gt is determined by the values set with this command Whereas the DISTANCE command at the ESTIMATE gt prompt only determines how the distance data are analyzed In the EXAMPLES section the difference and use of the 2 commands are illustrated For line transect data TYPE LINE this command defines whether the data will be entered as either perpendicular distances or as radial distance and angle measurements pg 4 6 PERP perpendicular distance was measured for a line transect RADIAL radial distance and angle were measured in line transects For TYPE POINT which includes trapping webs or CUE pg 6 8 DISTANCE RADIAL is assumed and only radial distances are expected Distances can be entered as ungrouped or grouped pg 13 14 Ungrouped implies an exact distance is entered for each observation in the data Grouped means a set of distance intervals is given and the frequency of observations in each interval is entered Ungrouped distances are indicated by the switch EXACT and grouped data is indicated by the INTERVALS switch which also specifies the distance intervals C C G G G G The value q specifies the left most distance and c the rig
75. label is recognized by its first 3 characters which allows variations in spelling For example if you enter METRES it will use METRES as the label and will recognize it based on MET Values are given in uppercase but can be entered in upper or lowercase If DISTANCE recognizes the UNITS and MEASURE labels and you specify the CONVERT switch it will display a warning message that you are overriding the conversion value Values for WIDTH LEFT and INTERVALS should be given in original measurement units and not in converted units Default DIST PERP UNITS Meters MEASURE Meters EXACT LEFT 0 RTRUNCATE 0 Examples Perpendicular distance measured in intervals of 2 feet to a distance of 10 feet and converted to metres meters for analysis The grouped data are entered as the frequency of observations in each of the 5 distance intervals see DATA gt Notice that WIDTH is specified in the original measurement units of feet and not in meters DIST PERP MEASURE Feet UNITS Metres WIDTH 10 NCLASS 5 26 Radial distance measured and analyzed in the specified intervals of feet The label will be displayed in uppercase because it is not in quotes If this is line transect data the program will generate an error because grouped data entry is not allowed for distance angle data see SMEAR as an option for the DISTANCE command in the ESTIMATE procedure DIST RADIAL MEASURE Feet INTERVALS 0 2 5 8 12 25 Perpendicular distance measure
76. le LABEL Fred s sample will become Fred s sample in the output Command switch and value names can be abbreviated to the fewest number of characters that avoids ambiguity eg entering D when DISTANCE and DENSITY are potential commands would be ambiguous but DI or DE would not be ambiguous If the value is ambiguous or unrecognized an error is issued which lists the potential values However if you enter extraneous characters that do not match a name the name will not be recognized For example DIX will not be interpreted as DISTANCE and will generate an error The best strategy is to use as few characters as needed to make the command simple to type but readable Descriptions of the commands are given below The commands are organized alphabetically within input prompt DISTANCE gt OPTION gt DATA gt and ESTIMATE gt For each command the format and description of the command are given Examples are often given to illustrate the command and where appropriate synonyms for command and switch names are listed Similar command descriptions can be obtained interactively within DISTANCE via the HELP command Obtain help with a particular command by entering at the appropriate command prompt HELP command_name For example at the DISTANCE gt prompt entering HELP ASSIGN will display information about the ASSIGN command One or more screens of information will be displayed which are similar to the format of the command descriptions gi
77. le named STARTUP DST with the following contents ASSIGN OUTPUT DISTANCE LST REPLACE OPTIONS TYPE POINT SQUEEZE 0N END 13 OVERVIEW Any valid command can be used in this file DISTANCE will look for STARTUP DST in the current directory and in the directory which contains DIST EXE After processing any commands in STARTUP DISTANCE prompts for more commands if in interactive mode or reads commands from the INPUT file if in batch mode The name of the STARTUP file can be changed when starting DISTANCE from the DOS prompt by including an optional argument DIST S startfi le The optional argument will work when running the program interactively or in batch mode as described below DISTANCE will look for the file named startf7 Te in the current directory If the file is not found DISTANCE will look for STARTUP DST Batch Operation Batch operation mode is simply an efficient method of running numerous analyses by reducing the amount of typing All command and data entry is identical in batch and interactive mode Batch mode is equivalent to running the program interactively and using ASSIGN statements to specify the input output and log files except that DISTANCE is terminated upon completion of processing the input file DISTANCE is run in batch mode by specifying filenames when DISTANCE is initiated The full specification is DIST I infile O outfile L logfile S startfile The outfile logfile and startfile spec
78. luster sizes pg 79 80 Default PVALUE 0 15 31 SEED Syntax SEED value Description SEED specifies the random number seed for generating a sequence of random numbers for bootstrap samples pg 155 158 Value should be a large odd number preferably greater than 2 000 000 If you use the same seed the same sequence of random numbers will be generated You can use SEE D the default which will use a value from the computer s clock to generate a seed Default SEED 0 SELECTION Syntax SEQUENTIAL SELECTION FORWARD ALL SPECIFY Description This command specifies the default mode for adjustment term selection in the ESTIMATE procedure for fitting the detection function The SELECT switch of the ESTIMATOR command overrides the default value Seethe ESTIMATE gt section for a description of adjustment term and model selection SEQUENTIAL add adjustments sequentially e g for simple polynomial in increasing order of the exponent FORWARD equivalent to forward selection in regression select the adjustment term which produces the largest increase in the maximum of the likelihood function ALL fit all combinations of adjustment terms with the key function and use the model with smallest Akaike Information Criterion AIC value SPECIFY user specified number of adjustment terms and possibly order of the adjustments Default SELECTION SEQUENTIAL 32 SF Syntax Descri
79. mal Hermite m AIC Chi p f 0 p ESWw Stratum Stratum 1 Average cluster size ECS Stratum Stratum 2 Average cluster size ECS Stratum Stratum 1 Half normal Hermite DS D N Stratum Stratum 2 Half normal Hermite DS D N Pooled Estimates Figure 15 Summary tables generated from the third estimation E E E Te Tee a eee ea ae ae eee ae aa Estimation Summary x Encounter rates AI 95 Confidence Interval II Estimation Summary x Detection probability x AI Estimate 95 Confidence Interval 562 60 93093 85632E 01 8 88 98 71837E 01 10208 61462 8 88 98 51561 73265 11 678 8 88 98 9 79 AI Estimation Summary x Expected cluster size x AI 65 13 920 95 Confidence Interval E E E TC Tee eee aa ae ee ee eae x Estimation Summary E x Density Abundance x JE E E SE E E E E SE SE SE E E SE SE SE E E SE EEEE EEEE EE 95 ITT Tee eee aa a ee ee ae aa Estimation Summary E E Density Abundance Eo JE E E E 3E E E E SE SE SE E E SE E SE E E E EEEE EEEE E 95 procedure of example 1 73 Confidence Interval Confidence Interval 124 40 363 99 Example 2 Description This example of point transect sampling is described in chapter 5 of Buckland et al 1993 Thirty points k 30 were sampled from an area with true density of 79 6 animals per hectare Observations were of single animals and 144 animals were detected Only 131 of the animals were de
80. mmand at the OPTIONS gt prompt defines how the distance data will be input but at the ESTIMATE gt prompt the DISTANCE command defines how distances will be analyzed The header at the top of each page in this Guide identifies the appropriate prompt for the command Except for the distance or frequencies and cluster size measurements all information is entered via commands The format for entering data varies depending on the type of data and is described in detail in the DATA gt section The information contained in each command varies but the general syntax for a command is the same for all commands The general command syntax is command_base switch1 switch2 switchn The command_base can be one of the following forms command_name or command_name 11st where 77st is one or more elements separated by commas A switch can also be one of the following forms switch_name or switch_name list where 77st is one or more elements separated by commas Use commas to separate list elements not spaces If the elements are separated by spaces unpredictable results will occur The switches are not required but the base portion of the command is required The base portion is either just the command name or a command name followed by and a list of one or more elements F or example for the ASSIGN OUTPUT command ASSIGN OUTPUT FILENAME is the base portion of the command Each command must end with a semi colon A command can
81. n the units specified by AREA UNITS For example if AREA UNITS Sq Kilometers is given in OPTIONS gt STRATUM AREA 1500 specifies an area of 1500 square kilometers Examples STRATUM LABEL STRATUM A STRATUM STRATUM AREA 1500 LABEL Plains area 42 ESTIMATE gt ESTIMATE gt The following are valid commands at the ESTIMATE gt prompt BOOTSTRAP bootstrap variance confidence intervals CLUSTER estimation of expected cluster size DENSITY resolution of density estimation DETECTION resolution of detection probability estimation DISTANCE analysis treatment of distances ENCOUNTER resolution of encounter rate estimation END initiates estimation ESTIMATOR model for g x GO estimate of g 0 and its standard error GOF intervals for goodness of fit test display HELP help information MONOTONE monotonicity constraints on g x PICK method of model choice PRINT detailed control of output SIZE resolution of expected cluster size estimation VARF variance estimation of f 0 VARN variance estimation of n The commands are described below in alphabetical order You will use these commands to define 1 which quantities you want to estimate and at what level of resolution DENSITY DETECTION ENCOUNTER SIZE 2 how distance and cluster size are treated in the analysis and which models are used for estimation DISTANCE CLUSTERS ESTIMATOR MONOTONE PICK GOF GO 3 how variances are estimated VARN
82. nd data sample effort 4 label Line 1 59 04 57 84 1 48 1 48 samp le effort 4 label Line 2 92 15 98 34 26 58 1 16 1 10 1 12 sample effort 4 label Line 3 54 94 1 00 56 26 24 48 1 64 76 54 1 41 sample effort 4 label Line 4 48 81 14 30 22 1 74 1 34 1 10 samp le effort 4 label Line 5 34 4 86 44 06 1 56 3 46 96 1 26 01 42 1 42 samp le effort 4 label Line 6 64 76 42 2 78 1 46 1 10 samp le effort 4 label Line 7 06 48 02 37 18 1 32 08 80 sample effort 4 label Line 8 36 14 24 56 26 1 32 1 42 9 26 sample effort 4 label Line 9 4 86 74 14 36 03 samp le effort 4 label Line 10 38 48 1 36 end estimate est key unif dist int 0 4 8 1 2 1 6 2 end estimate est key unif dist int 0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 end 81 Template Files Template files with the extension TPL and examples of the template files with the extension INP are put into YourD7 rectory during installation The template files contain the shell for a command and data entry input file that you can modify with an editor and then use as an input file They illustrate the commands and data formats for line or point transects perpendicular or radial grouped or ungrouped and clustered or unclustered data The filenames have been constructed to represent the type of analysis The first 2 characters are either LT or PT for line or point transect Thethird character
83. ning HELP is only necessary if you change the name of the HELP file or store it in a directory other than the one containing DIST EXE The default values for each file are LOG SCREEN STATS NULL PLOT SAS PLT OUTPUT DIST OUT RECORD SCRATCH INPUT KEYBOARD BOOTSTRAP BOOT OUT HELP DIST HLP For output files if you ASSIGN a file that already exists and do not specify either APPEND or REPLACE an error is issued and output is sent to the default file For INPUT filenames if the file does not exist an error message is issued By default the contents of INPUT files are echoed in the LOG Use the NOECHO switch to override this default If you use ECHO the default for the ASSIGN OUTPUT command output is sent to the SCREEN as well as the file If you use NOECHO SCREEN output is suppressed If sufficient memory is available assigning the STATS or BOOTSTRAP file toa RAMDRIVE can reduce execution time Examples ASSIGN INPUT TEST INP ASSIGN OUTPUT TEST OUT REPLACE ASSIGN PLOT SPLUS OUT APPEND 17 CLEAR Syntax LOG CLEAR OUTPUT RECORD Description CLEARempties the contents of the LOG OUTPUT or RECORD files It has no effect on the LOG file if the LOG file is the SCREEN Example CLEAR OUTPUT DATA Syntax DATA Description DATA initiates a separate command processor for entering distance data The prompt will change to DATA gt See the section on the DATA gt prompt for furthe
84. nvert the estimated density to new units for area It is needed for atypical units If DISTANCE recognizes the measurement unit for DISTANCE and LENGTH for line transects and if it recognizes the Area UNITS label it will calculate the appropriate conversion factor However if one or more of the UNITS is not recognized you will need to specify the conversion value with the CONVERT switch The Area units recognized by the program are those listed under the DISTANCE command and HECTARES HEC and ACRES ACR For example the unit can be entered as Squared Meters or Metres Squared because DISTANCE recognizes the unit based on the character string MET Seethe DISTANCE command below for a definition of recognized units Default AREA UNITS HECTARES Examples Distances are measured in feet but analyzed in meters length is measured in miles and density is estimated as numbers per square kilometer DISTANCE will do necessary unit conversions because all unit labels are recognized DISTANCE MEASURE FEET UNITS Meters LENGTH UNITS MiTles AREA UNITS Sq kilometers BOOTSTRAPS Syntax BOOTSTRAPS value Description Value is the number of bootstrap samples pg 94 96 119 120 155 158 which should be generated For a reasonable variance estimate this number should be at least 100 We recommend setting BOOTSTRAPS 1000 to construct a bootstrap confidence interval Default BOOTSTRAPS 1000 23 CUERATE Syntax CUERATE
85. of each observed cluster must be entered DISTANCE defines whether the distance data are entered as grouped pg 14 15 or ungrouped pg 13 14 and whether distance for line transects is entered as perpendicular distance x or as a radial distance r and angle 9 measurement from which perpendicular distance is calculated i e x r sin 9 pg 4 6 For ungrouped distances a measurement e g x is entered for each observed object i For grouped distances the frequency of observations n n n n in each of u intervals are entered pg 14 15 The corresponding intervals of distance are defined by the set of cutpoints c G G C specified by the INTERVALS switch of the DISTANCE command Very few restrictions are applied to the data values Distances x or r must be non negative 20 The distance units are defined by the DISTANCE command at the OPTIONS gt prompt Cluster sizes s must be positive and the units are assumed to be integral values of animals but the input value is not restricted to be an integer Angle 9 measurements pg 5 should be entered in degrees between 0 360 assuming the standard full circle representation This representation for the angle is provided as a convenience and it is not required The orientation of the object is not included in the analysis Angle measurements are used only to calculate the perpendicular distance At present angle measurements cannot be entered or used with point transects to indicat
86. on correlation r 3 p value for correlation significance r p 4 estimate of expected cluster size corrected for size bias 4 density abundance 1 density of clusters or animal density if non clustered 2 density of animals if clustered 3 number of animals if survey area specified implies a value for CV LCL UCL and DF are included otherwise they are set to zero Figure 3 Definitions of module and statistic codes in STATS file 11 OVERVIEW An example ofthe STATS fileis given in Figure 4 for the example input file given in Figure 1 The first 4 records are the statistic records for the encounter rate module the module field the fourth field from the left equals 1 For this module the estimator number is always 1 because these statistics are independent of the estimator The remaining records are all dependent on the estimator and the estimator field is always 2 because the half normal cosine estimator was chosen as the best estimator and it was listed second in the estimate procedure Figure 1 Six records are listed for each of the statistics in the detection probability module field 4 2 and 1 record for the density module field 4 4 Records for cluster size are not listed because the input was for unclustered data and the abundance statistic is not given because there was no area size specified Example input in Figure 1 0 0111 54 000 0000 00000 00000 0112 4 0000 0000 00000 00000 0113 142
87. opriate value for an output title is specified The sampled area is composed of two strata each representing an area of 50 km Six lines were sampled in each stratum The line lengths effort are 5 2 6 4 3 1 4 4 5 7 3 and 4 kms Perpendicular distance and cluster size measurements are entered as a list with each pair of measurements for an observation on a line For example the first observation from transect 1 was a single animal cluster size 1 at 7 8595 metres from the line Note the data are computer generated and the precision is exaggerated beyond what is needed Several measurements could be put on the same line up to 80 characters per line but the layout shown is more readable Observation data for this example are entered corresponding to format 5 Table 1 see DATA gt Option values are important to the structure and input of the data For example if OBJECT CLUSTER is removed from the option list cluster sizes are not expected If the cluster sizes are not removed from the data each cluster size would be read in as a perpendicular distance measurement and it would falsely appear that twice as many observations had been made 61 assign output examplel out replace assign log examplel log replace options dist units metres Jength units kilometres area units sq kilometres object cluster title Chapter 4 example 1 pgs 105 115 122 125 end data stratum Label Stratum 1 Area 50 sample effo
88. orithm will perform to determine the parameters that maximize the likelihood function pg 65 66 Default ITERATIONS 100 LENGTH Syntax LENGTH CONVERT value UNITS label MEASURE label Description This command sets the measurement unit for line length pg 4 6 and any desired conversion to different units for analysis It is not necessary to convert line length but may be desirable depending on the original units MEASURE label a label for the units in which line length was measured Single quotes are only required to retain lowercase Only the first 15 characters are used UNITS label a label for the units for length after conversion if any Single quotes are only required to retain lowercase Only the first 15 characters are used CONVERT value value specifies a conversion factor which is used as a multiplier to convert length measured in atypical units 28 See further explanation under DISTANCE for the MEASURE UNITS and CONVERT switches The LENGTH command is used for line transects only Default LENGTH UNITS KILOMETERS MEASURE KILOMETERS Example Length is entered in miles but converted to kilometers for display and analysis LENGTH UNITS Kilometers MEASURE Miles LIST Syntax LIST Description Lists current values of the program options and the program limits to the screen LOOKAHEAD Syntax LOOKAHEAD value Description For term selection modes SEQUENTIAL and F
89. ple 2 78 Further Example Input Files The following are a variety of example input files which illustrate various commands and data entry formats Line transect sampling with grouped perpendicular distances The distances were measured in meters and line length was 1 kilometer so the default units were accepted Density will bein units of hectares Note text to the right of a semi colon on a command line is treated as a comment options title Wildlife Monograph no 72 pg 74 dist int 0 1 2 3 4 5 7 9 11 15 20 end because there is only one sample varn poisson assumption data sample effort 1 label Stake data 8 6 4 13 7 8 7 6 5 4 end with the first estimator the program will choose no of terms with the second a 1 term cosine Fourier series will be fit estimate est key unif est key unif nap 1 select specify end The following is a line transect sampling example in which radial distance and angle were recorded instead of perpendicular distance options title Wildlife Monograph No 72 Example page 65 dist radial end It was not necessary to line up the data like it is below but it does make it easier to account for all of the data Each observation could have also been put on a separate line data samp le effort 60 0 label Hemmingway data 100 46 150 10 200 17 150 38 200 55 200 25 200 55 250 39 160 8 140 31 130 42 130 23 100 0 100 47 120 0 200 40 200 55 170 25 250 7 230 18 180 57 120 35 1
90. plot specifically with SAS GRAPH or SPLUS If you do not Assign a filename for PLOT the results are appended to the contents of the file SAS PLT PLOT can be used as input to other graphics packages as well if the SAS or S specific commands are removed The data format is X distance Histogram x g x or FOO Any graphics package which can produce 2 plots on the same graph can be used to plot the function fitted to the data g x or f x overlaying a histogram representation of the data by connecting a line to each point as a function of x The values of Histogram x will plot horizontal bars and the values ofthefunction will produce a smooth curve Note for point transects 2 figures are produced The first is the detection function g r and the second is the probability density function of observed radial distances f r STATS contains esti mates and other statistics which are used internally by the program for summarization and are not saved at program termination unless it is ASSIGNed to a disk file For each analysis ESTIMATE a set of records is output to STATS Thefirst record is the title of the analysis A blank record is output if you do not specify a title The remaining records all have the same format but some field meanings change depending on the record type which is determined by the value of Module and Statistic The record structure is as follows 10 OVERVIEW Stratum stratum number or O if the estimate is for a
91. procedure see the discussion on adjustment term selection above If SELECT SPECIFY is chosen you can specify the number of adjustment parameters the order of the adjustment term and starting values for the parameters The number of adjustment parameters is set with the NAP Number of Adjustment Parameters NAP must be less than or equal to MAXTERMS nkp number of key parameters The orders of the adjustment term s are specified with the ORDER switch Starting values START for the key and adjustment parameters can be given if the optimization algorithm suggests there are problems in finding the maximum of the likelihood function The first nkp starting values in the list should be the values for the key parameters and the remaining are for the nap adjustment parameters One reason for using the SELECT and NAP switches is to specify that only the key function should be fitted to the data An example is given below CRITERION specifies the manner in which the number of adjustment terms is chosen for SELECT FORWARD and SEQUENTIAL LR specifies that a likelihood ratio test pg 74 75 be performed using the PVALUE specified in OPTIONS AIC specifies using the Akaike s Information Criterion pg 75 76 for adjustment term selection Multiple ESTIMATORS can be specified within an ESTIMATE procedure and the best model is selected or estimates are given for each model see PICK 54 ESTIMATE gt The only portion of the command requir
92. ption SFdefines the value of the sampling fraction which is typically 1 pg 53 However if only one side of a transect line is observed c 0 5 or if some fraction of the circle surrounding a point transect is searched c is the fraction searched e g c 0 5 if a semi circle is observed For cue counting c is the proportion of a full circle that is covered by the observation sector For a sector of 90 45 either side of the line with cue counting c 0 25 Default SF 1 SQUEEZE Syntax JON SQUEEZE OFF Synonyms ON YES TRUE OFF NO FALSE Description If this option is set off a formfeed and title line is printed at the top of each page If it is set on a formfeed is not included which has the effect of squeezing the output Default SQUEEZE 0FF TITLE Syntax TITLE yourtitle Description This command sets a value for the title which is printed at the top of each page Yourtitle should contain no more than 50 characters Excess characters are not used There is only 1 title line Re specifying the title will replace the previous value 33 TYPE Syntax POINT TBE SSE ENE Is CUE Description This option defines the type of sampling pg 3 8 which determines what types of data can be entered and how data are analyzed POINT point transect data pg 6 7 LINE line transect data pg 4 6 CUE cue counting data pg 8 9 Trapping webs pg 7 8 should be treated
93. r is chosen for each analysis Thus even though a single estimator is chosen for the point estimate different estimators can be chosen for each bootstrap and the standard errors and interval estimates incorporate the uncertainty of the model selection process Default PICK AIC PRINT Syntax PRINT YES option list NO option list Description This command can further expand or limit the output from the estimate procedure beyond what is defined by the PRINT command in OPTIONS The PRINT command in OPTIONS allows hierarchical control of the output and defines the default values for this print command and thus retains its functionality However this command can be used to define whether each component is printed to the OUTPUT file by specifying it either in the YES or NO list The following are the values of the option list Option List All Used in place of listing all options Fxplot Function histogram plots Estimate Density estimate table Fxtest Chi square goodness of fit test Explain Explanation of estimation options Sbarest Estimates of E S F xest Function parameter estimates Sbarplot Size bias regression plot F xfit Function fitting model selection Fxiterations Iterations of MLE 58 ESTIMATE gt Below are listed the default values of the print options as defined by the value set by PRINT in OPTIONS Y Y es and N No OPTIONS PRINT command value ESTIMATE FXEST FXPLOT FXTEST SBAREST SB
94. r information DOS Syntax DOS command_name Description Executes the DOS command given by command_name and then returns back to the DISTANCE gt prompt This will work for DOS commands and small programs It is limited by the amount of free memory available on your computer If acommand_name is not given the DOS prompt will appear DISTANCE remains in the background and you can issue several DOS commands This is termed shelling out It is necessary to type EXIT at the DOS prompt to return to DISTANCE Do not issue the command to start DISTANCE again because this will run DISTANCE within itself Unexpected and possibly unpleasant results will occur Examples DOS EDIT filename DOS DIR C DISTANCE gt ESTIMATE Syntax ESTIMATE Description ESTIMATEinitiates a separate command processor for estimation of density The prompt will change to ESTIMATE gt Various commands that can be given to control estimation are described in the ESTIMATE gt prompt section EXIT Syntax EXIT Synonyms STOP QUIT END or BYE Description Stops DISTANCE and returns control to DOS HELP Syntax HELP HELP command_name Description If you type HELP several pages of introductory information are displayed If you type HELP command_name a description of the specific command is given Use PgUp and PgDn or the up and down arrow keys to scan the help information Press the Esc key to leave help HELP should only
95. r size If thereis nota significant size bias the average cluster size will be more precise Density estimation results are summarized in a table Figure 14 which provides estimates standard errors and confidence intervals for detection probability and related quantities f 0 P ESW for line transects or h 0 P EDR for point transects encounter rate n L for line transects n K for point transects or n T for cue counting expected cluster size ADA AAA DAA Density Estimation R s Results E AA AA A A A AA A AA A AA AA AA A AA AA AAA A ee eee Effort i 48 00000 samples 12 Width 19 00000 observations 99 Model 1 Uniform key k y 1 W Cosine adjustments of order s 1 Point Standard Percent Coef 95 Percent Parameter Estimate Error of Variation Confidence Interval 87637E 01 63049E 02 k 75999E 01 10106 60057 43207E 01 z 52081 69253 11 411 82093 9 8954 13 158 2 0625 29152 E 1 5134 2 8108 90 375 14 334 64 806 126 03 2 8586 14358 2 2 5877 3 1578 258 35 183 21 364 30 Density Numbers sq kilometres ESW metres Component Percentages of Var D Detection probability Encounter rate 2 72 2 Cluster size 9 1 Figure 14 Density estimation results for uniform cosine model with data from example 1 71 and density of clusters groups if Object CTuster density D and abundance N if area size is specified Measurement units for the estimated quantities are given In addition the
96. rd error 3 a 95 log normal confidence interval 50 822 98 692 which is constructed as defined in section 3 7 1 of Buckland et al 1993 with the bootstrap standard error estimate and 4 a 95 bootstrap percentile confidence interval 49 346 95 547 which is the lower and upper 2 5 percentiles of the distribution of the estimates Section 3 7 4 of Buckland et al 1993 The first interval makes a parametric assumption about the shape of the distribution but uses a bootstrap constructed variance A reasonable interval can be constructed with as few as 100 200 bootstrap samples The second interval makes no assumptions about the distribution but requires many more samples 1000 is recommended to obtain reliable estimates of the tail probabilities of the sampling distribution of 6 In this case the bootstrap intervals are only slightly different than the analytical interval 52 140 96 199 which is constructed using an empirical variance for encounter rate and an analytical variance of f 0 see Sections 3 7 1 3 7 2 of Buckland et al 1993 ADA DD ADA AAA Bootstrap Summary id dx Density Abundance ie ADA DAD ADA DADA Pooled Estimates 95 Confidence Interval Hal f normal Hermite D x 50 822 49 346 95 547 Note Confidence interval 1 uses bootstrap SE and log normal with z 1 96 Interval 2 is the 2 5 97 5 quantiles of the bootstrap estimates Figure 21 Bootstrap analysis for half normal H ermite model of exam
97. rt of samples and of observations are the quantities for the particular data subset being analyzed The number of observations depends on the right width and left truncation values The label for left truncation is only given if it is non zero The right truncation value for the expected cluster size estimation can differ from the value used throughout the remainder of the analysis with a resulting difference in the number of observations In Figure 8 the identifier text does not contain stratum sample labels because the analysis is for all of the data combined The total effort line length is 48 for the 12 samples lines combined The analysis width is set at 19m and the resulting number of observations is 99 6 distances are greater than 19m If the results are specific to a particular detection model e g detection probability size bias regression a mode label which identifies the key and adjustment functions follows the identifier block Figure 9 For some pages of output in particular plots the page is not labelled with an identifier block The identifier from previous pages should be considered to extend until a new identifier is given Analysis of detection probability is the most detailed aspect of the output and deserves an in depth description We will use the results from the uniform cosine model as an example Figure 8 displays the results of fitting a sequence of models with term selection mode SELECTION SEQUENTIAL to the
98. rt 5 label Line 1 95 SCPROARWUNNWHWNHER sample effort 2 label Line 2 9 1468 1 6 3828 2 21 2129 3 sample effort 4 label Line 12 0 9703 6 6183 12 4475 4 8554 15 4140 end estimate dist width 19 cluster test 0 05 est key unif adj cosine est key unif adj poly est key hn adj hermite est key hazard adj cosine gof nclass 5 pick none end estimate dist width 19 est key hn adj hermite size all detection all gof nclass 5 cluster test 0 05 end estimate dist width 19 est key hn adj hermite density by stratum gof nclass 5 cluster mean print no a11 yes explain detection all end Figure 6 Abbreviated input listing for example 1 EXAMPLE1 INP 62 Each of the three Estimate End command sets performs an analysis note indentation of the commands is for readability and is not required The first ESTIMATE procedure specifies 1 observations with a perpendicular distance exceeding 19m are excluded w 19 and the analysis is performed on ungrouped exact measurements 2 expected cluster size is to be analyzed by the default size bias regression but if the observed probability exceeds a significance level of 0 05 the average cluster size should be used instead 3 4 detection models should be examined uniform cosine uniform polynomial half normal Hermite and hazard cosine By default selection of adjustment terms is determined by sequenti
99. s an example of command and data input which are organized into sections procedures corresponding to the type of information For this example the Options section defines 1 line transect sampling was used 2 line length is measured in miles 3 density is to be expressed in numbers per hectare and 4 distance perpendicular is measured in intervals of 1 foot to a maximum distance width of 4 feet OVERVIEW The Data section defines 1 4 lines were sampled with lengths of 11 2 14 3 5 6 and Options 111 2 miles and Type Line 2 the number of animals sighted in each of the 4 1 foot Sei em i Area Units Hectares intervals for each line sample eg for line 2 4 were Distance Intervals 0 1 2 3 4 seen at distances between 0 and 1 foot 3 were seen Units Feet at distances greater than 1 foot but within 2 feet End likewise none were seen between 2 and 3 feet and pee Sample Effort 11 2 2 were seen between 3 and 4 feet 5 6 2 1 Two analyses are requested one for each Estimate procedure Sample Effort 14 3 In each analysis 3 estimators are defined from which o a DISTANCE chooses the best model pg 73 77 In the second 2 0 1 0 analysis the observations beyond 3 feet are truncated pg 15 Sample Effort 111 2 Between the first and second analysis the output is displayed E gee 6 7 0 List to the screen for review Notice that the options and data an are retained for the second analysis but esti mate
100. s are only required to retain lowercase Only the first 15 characters are used UNITS label a label for the units for distance after conversion if any Single quotes are only required to retain lowercase Only the first 15 characters are used CONVERT value value specifies a conversion factor which is used as a multiplier to convert the input distances for atypical units MEASURE and UNITS switches are used to convert from the unit in which the data are recorded and entered MEASURE to the unit for analysis UNITS It is not necessary to convert distances to different units for analysis as long as it is a unit that is recognized by DISTANCE see list below It is only provided as a convenience and it is probably easier to leave measurements in their original units If you do convert units take note that values such as f 0 h 0 effective strip width E SW pg 23 56 and effective detection radius EDR pg 154 175 are expressed in the converted units Thus the point estimate and standard errors will change by the conversion factor from the measured to analysis units If you are not converting distance units you can specify the units with either switch MEASURE or UNITS The most common measurement units are recognized by DISTANCE and there is no need to enter a conversion value CONVERT value The following are the recognized measurement unit labels CENTIMETERS METERS KILOMETERS MILES INCHES FEET YARDS NAUTICAL MILES Each
101. s for the first 3 models are all very dose Qe dod AAA E Estimation Summary E Detection probability pi AAA A A A AAA AA AA A A A AA AA AAA A Pooled Estimates Estimate 95 Confidence Interval Uniform Cosine m 562 98 Chi p 85272 f 0 87637E 01 3 75999E 01 p 60057 z 52081 ESW 1 411 9 8954 Uni form Pol ynomial m 0000 AIC 563 29 Chi p 83365 FCO 76560E 01 70108E 01 83607E 01 p 68745 62951 75072 ESW 3 062 r 11 961 14 264 Half normal Hermite m 0000 AIC 562 60 Chi p 93093 F 0 85632E 01 71837E 01 p 61462 51561 ESW 1 678 9 7965 Hazard Cosine m 2 0000 AIC 565 22 Chi p 60223 f 0 81677E 01 r 64724E 01 p 64438 k 51063 ESW 12 243 9 7019 Figure 12 Summary of estimation result for each model in example 1 69 AI Expected Cluster Size Estimation FIO IC TOR IC TO I Ce TO I Ce IO k 3E A dE ae ee a ae ede Effort 48 00000 samples 2 12 Width E 19 00000 observations 99 Model Uniform key k y 1 W Cosine adjustments of order s Expected cluster size estimated based on regression of log s i on g x i Regression Estimates 274238 Std error 451992E 01 Intercept 1 12179 Std error 266964E 01 Correlation 1299 Students t 1 28992 Df 97 Pr T lt t 100073 Expected cluster size 2 6882 Standard error 15345 Mean cluster size 2 8586 Standard error 14358 Test p value greater than specified significance level 050 Average cl
102. sample or all data Sample sample number or 0 if the estimate is for a stratum or all data Estimator number of the estimator in the order given in the Estimate procedure Module number of the parameter module Figure 3 Statistic number of the statistic within the parameter module Figure 3 Value estimate value Cv coefficient of variation of estimate or 0 0 Ld lower confidence limit or 0 0 Ud upper confidence limit or 0 0 Df degrees of freedom for interval or O The modules and statistics within each module are listed in Figure 3 in the order in which they are summarized in the output The FORTRAN format for each record is 2 1x i3 3 1x i1 1x g12 5 1x f7 4 1x 2 g12 4 1 i4 Each field is separated by a space so the records can be read into a spreadsheet or other program as space delimited or as fixed width format The record for a module statistic type is only output if it is relevant and it was computed in the analysis Module Statistic Parameter Estimate 1 encounter rate 1 number of observations n 2 number of samples k 3 effort L or K or T 4 encounter rate n L or n K or n T 2 detection probability 1 total number of parameters m 2 AIC value 3 chi square test probability chi p 4 f 0 or h 0 5 probability of detection P 6 effective strip width ESW or effective detection radius EDR 3 duster size 1 average cluster size 2 size bias regressi
103. t f 0 is estimated by pooling all of the data This is useful if f 0 cannot be estimated reliably for each stratum but estimates of density by stratum are needed The output is limited to the summary tables which are given in Figure 15 A summary table is given for each component encounter rate detection probability expected cluster size and density Estimates are given by stratum for each component except f 0 which was estimated by combining data from both strata The final summary table provides pooled estimates of density and abundance Note If you run Examplel inp which is described in Buckland et al 1993 you may notice minor differences in some of the estimates These differences result from a change in the way DISTANCE creates the constraints for monotonicity and positivity are created In prior versions the constraints were maintained at a grid of equally spaced points On some occasions this allowed monotonicity to be violated close to the origin This was changed to a grid which puts more points near the origin and fewer with increasing distance from the origin This both improves the monotonicity constraint and provides a better fit Notice that the likelihood is slightly larger with the current version than the output in the book The differences are primarily with the untruncated cases which havea long tail that create problems in fitting 72 Stratum Stratum 1 n k L n L Stratum Stratum 2 Pooled Estimates Half nor
104. t of program output and bootstrap options control the number of bootstrap samples and the random number seed used to generate a bootstrap sequence Below are the valid commands at the OPTIONS gt prompt by category Miscellaneous Output DEFAULT _ options reset to default PRINT controls amount of output END ends options command SQUEEZE controls output pagination HELP help with options TITLE value of output title LIST lists option values Data Options Model Fitting AREA set area quantities EPSILON tolerance for fitting CUERATE set cuerate ITERATIONS max of iterations DISTANCE set distance quantities LOOKAHEAD max for sequential fit LENGTH set length quantities MAXTERMS max no of adjustments OBJECT SINGLE or CLUSTER PVALUE significance level level SF sampling fraction SELECTION term selection mode TYPE POINT LINE or CUE Bootstrap BOOTSTRAPS no of bootstrap samples SEED random number seed Each option and its possible values are individually described below in alphabetical order 22 AREA Syntax AREA CONVERT value UNITS label Description This command defines the area unit for expressing density D pg 1 The switches are UNITS label a label for the unit of area of the density estimate The single quotes are only required to retain lowercase Only the first 15 characters are used CONVERT value value specifies a conversion factor which is used as a multiplier to co
105. t should be used for data stored in a file INFILE f thereis any confusion as to the appropriate format enter part or all of your data from the keyboard to see how they should be formatted Your keyboard entry can be stored in a file using STORE RECORD from which a more complete input file can be constructed with an editor Examples of each of the data entry formats are given in template files described in the EXAMPLES section It is important that the data match the OPTIONS used to define the data With very few restrictions placed on the input data it is possible to create situations in which data are input without error but the data are incorrectly interpreted Consider what would happen if the population is treated as unclustered OBJECT SINGLE but cluster sizes are entered with the distances format 2 or 5in Table 1 DISTANCE would incorrectly treat each of the cluster sizes as a distance and the result would be to double the sample size Depending on the distance measurement units a plausible but incorrect detection curve may result A similar situation could occur if distance for line transects was defined as perpendicular DISTANCE PERP but radial distances and angles were entered 37 In each of the data formats the data can be put on as many lines as needed but each line must not exceed 80 characters Values on a line must be separated with commas or one or more spaces Notice that a semi colon separates different types of input data
106. tected within the chosen truncation point of 20m Input The input file is named EXAMPLE2 INP An abbreviated listing is given in Figure 16 The input file contains commands to 1 assign filenames for the output and log 2 specify options 3 structure and input the data and 4 perform 3 analyses The options specify that point transect ASSIGN OUTPUT EXAMPLE2 OUT REPLACE sampling was used distance is measured in meters ASSIGN LOG EXAMPLE2 LOG REPLACE ASSIGN BOOT EX2BOOT DAT REPLACE and density is expressed in units of numbers per eee ature hectare Also the number of bootstrap samples is DIST RADIAL UNITS met Dr i i i i AREA UN Teethectares rae As 100 ang i opp SPSS mss aa BOOTSTRAPS 400 Ape Chapter 5 point transect example pgs 142 158 The DATA section of the input file has a cion SAMPLE for each of the 30 points The effort for Many ae each point is 1 The radial distance for each 13 79 20 96 observation is listed below the point from which it j was detected The data values are separated by EREE commas but could also be separated by one or more 13 31 10 05 10 55 0 61 14 40 4 89 5 58 1 65 Spaces 18 597 Three analyses are specified by the three T EY HN ZADI HERMITE ESTIMATE procedures The first analysis specifies T MATOR KEYSUNIE 1 four different detection models from which Ne DISTANCE will choose the best model O 2 distances are to be truncated at 20m and ATE
107. ter value 000003 2 selected over model 1 based on likelihood ratio test 3 form key kCy 1 w ine adjustments of order s Results Convergence was achieved with Final Ln likelihood value Akaike information criterion Final parameter values 637621 dyz 19 function evaluations 280 30672 564 61350 079247 2 and 3 Likelihood ratio test value 3655 Probability of a greater value 545446 2 selected over model 3 based on likelihood ratio test of example 1 27x Ww 0 079247 cos For each model the results include 1 number of iterations actually likelihood function evaluations needed to find the maximum of the likelihood function note each iteration can be printed 2 the final In likelihood value 3 value of Akaike s Information Criterion AIC 2 In likelihood 2m where m is the number of parameters includes key function parameters and 1 parameter for each adjustment term 4 final parameter values A i i 1 m with the first parameters being for the key function and the remainder for the adjustment terms in order 5 a likelihood ratio test between the current model and the base model and 6 a statement describing which model is best based on the chosen decision criterion The criterion for model choice is either minimizing AIC or a likelihood ratio test which compares the computed probability to the specified significance level PVALUE in OPTIONS gt In t
108. the sample estimates are not pooled If DENSITY BY STRATUM is specified an estimate is made for each stratum A stratum estimate is a pooled estimate of the sample estimates within the stratum if DENSITY by SAMPLE is specified or it is an estimate based on the data within the stratum An overall pooled estimate of density is made unless DESIGN NONE is specified If DESTGN REPLICATE the stratum estimates are treated as replicates to create a pooled estimate and variance weighted by effort eqns 3 11 3 14 in Buckland et al 1993 treating stratum as a sample If DESTGN STRATA the pooled estimate is a weighted sum of the estimates and the variance is a weighted sum of the stratum variances Section 3 8 1 in Buckland et al 1993 Weighting is defined by the WEIGHT switch If WEIGHT NONE the densities are summed which is only useful if the population is stratified as by sex or age If WEIGHT AREA the densities are weighted by area which is the same as adding abundance estimates and if WELTGHT EFFORT the densities are weighted by effort Prior to version 2 1 a combined estimate of abundance N was created by multiplying the 49 ESTIMATE gt combined density estimate by the sum of the areas specified on each of the STRATUM commands This produces obviously erroneous results when DENSITY by STRATUM DESIGN REPLICATE is used and the area size is repeated on each STRATUM To avoid this problem in the following two situations the combin
109. ue INTERVALS c C C3 C LEFT 1 RTRUNCATE t NCLASS nclass SMEAR angle pdist Description The DISTANCE command is used to specify the way the distances should be treated in the analysis It can be used to specify left and right truncation of the distance to group the distances into intervals prior to analysis and to smear radial distance angle measurements into perpendicular distance intervals Right truncation pg 15 50 106 109 is specified with either the WIDTH or RTRUNCATE switch If WIDTH w only distances less than or equal to w are used in the analysis If RTRUNCATE t the right truncation distance is set to use 1 t 100 of the data If the data are ungrouped the 1 t 100 percentile is used as the truncation distance If the distances are grouped or being analyzed as such the truncation distance is set to the u interval end point where u is the smallest value such that no more than t 100 of the distances are truncated The value of t 0 trims the intervals to the right most interval with a non zero frequency If both the WIDTH and RTRUNCATE are specified the value of RTRUNCATE defines the truncation unless the WIDTH is used with NCLASS see below Left truncation pg 15 273 277 is accomplished with the LEFT switch which works in an analogous fashion to WIDTH If LEFT T1 only distances greater than or equal to 7 are used in the analysis If LEFT is not specified it is assumed to be 0 51 ESTIMA
110. ungrouped data or number of distance intervals for grouped data Default MAXTERMS 5 OBJECT Syntax SINGLE OBJECT CLUSTER Description This option defines whether objects are detected individually SINGLE or as dusters CLUSTER pg 11 13 SINGLE Object always detected as a single animal or other entity eg duck nest CLUSTER Object detected as a cluster e g herd flock pod of whales Default OBJECT SINGLE 30 PRINT Syntax SELECTION PRINT RESULTS ALL SUMMARY Description This option sets the default level of printing in the output The various settings are hierarchical and more control over the amount of results can be obtained with the PRINT command in the ESTIMATE gt procedure ALL print fitting iterations model selection results and estimation results SELECTION print model selection results and estimation results RESULTS print estimation results only SUMMARY NONE only summary tables are printed Note if you choose RESULTS or SUMMARY warnings are not given about the algorithm having difficulties fitting a particular model or constraining the fit to achieve monotoni city Default PRINT SELECTION PVALUE Syntax PVALUE ca Description a is the significance level of likelihood ratio tests pg 74 75 to determine significance of adding adjustment terms and is the default value for the significance test for size bias regression of c
111. use cluster sizes which were observed within a pre specified distance or perform a size bias regression this can only be done if distances and cluster size measurements are entered in pairs Proper estimation with the true interval nature of the distance data is obtained by specifying INTERVALS with the DISTANCE command at the ESTIMATE prompt pg 110 111 149 150 This also allows one or more intervals to be combined into larger intervals in the analysis A simple example with unrealistically small numbers of observations and intervals is given below to show how interval distance data are entered as exact using the midpoint and then analyzed using the intervals in which they were collected OPTIONS DIST PERP lt exact Ts assumed OBJECT CLUSTER END DATA SAMPLE EFFORT 14 5 52 54 51 1 56 1 52 2 57 SAMPLE EFFORT 4 5 51 1 54 2 52 2 5 6 END ESTIMATE DIST INTERVALS 0 1 2 3 lt data originally collected in these Intervals ESTIMATE KEY HN ADJUST POLY END The commands which are valid at the DATA gt prompt are described below in alphabetical order 38 END Syntax Description Finishes data entry and returns to the Di stance gt prompt HELP Syntax HELP HELP command_name Description If you type HELP several pages of introductory information will be displayed If you type HELP command_name a description of the specific command will be given Use PgUp and PgDn or the up and down arrow keys to s
112. uster size will be used E E E A AE AE AE e I E E 3E 3E I ITC I Sk E E E AE E aa ae ee eee 7 Cluster Size Regression Plot E AE E E AE TO IGG TORIC TO IC TOR I Ck Jo aE AE fe aa tet EREE 4G oo o oo 00 o 000000 kokk ele e de kkk eee e dede dede eee Detection Probability g0 9 Figure 13 Expected cluster size estimation for example 1 with the uniform cosine model 70 The output for expected cluster size estimation depends on whether size bias is considered If the estimator is the mean cluster size the output consists of the mean and its standard error However if a size bias regression is performed regression summary statistics and an estimate of expected cluster size and its standard error are given and followed by a plot of the regression line and observed values If a significance test is performed the results of the test are explained For this example Figure 13 the slope is not significantly different from zero and the expected cluster size is estimated by the average cluster size A one sided t test is performed because size bias will typically increase the observed average cluster size at larger detection distances If the size bias regression uses distance as the independent variable the resulting slope will be positive and if G x is used a negative slope will result Typically if the test is non significant there is little difference between the average cluster size and size bias estimate of expected cluste
113. ven in this documentation Thelines around a list of items indicates that one item from the list should be chosen OVERVIEW Program Files DISTANCE reads commands and data from input files and creates several output files as illustrated below Input Files gt DISTANCE gt Qutput Files INPUT keyboard OUTPUT CSCREEN amp DIST OUT DATA keyboard RECORD SCRATCH LOG SCREEN PLOT SAS PLT BOOT BOOT OUT STATS SCRATCH The default names for the input and output files are given in parentheses Note SCRATCH is a temporary file which disappears at the end of the program unless saved Each file can be given a different name The contents of each file and the ways in which they can be manipulated are described below The file manipulation commands are described under DISTANCE gt If DISTANCE terminates abnormally scratch files e g beginning with XX or ZZ that are normally deleted may remain in your directory You can delete these files if they exist Input INPUT and DATA arethe 2 sources of input INPUT is the primary source of commands and data DATA can be assigned to a separate file with the INFTLE command By default command and data entry are interactive INPUT and DATA are assigned to the keyboard Enter commands and data interactively until you become familiar with DISTANCE However both input sources can be independently assigned to disk files which contain the commands and data For example INPU
114. when both grouped and ungrouped data formats are used for clustered populations and specifies the end of data input for the sample Unlike commands information entered beyond the semi colon will create an error The following example for format 1 would not be valid because distances are grouped and cluster sizes ungrouped N 07 N3 S1 S7 S3 0 Sp Instead the grouped data frequencies and ungrouped data cluster sizes must start on a separate line as shown in Table 1 If there are no observations for a SAMPLE data values are not given but the semicolons must still be entered to indicate a sample of size O For formats 1 and 4 two semicolons must be given on separate lines and for formats 2 3 and 5 only one semi colon is required If the observed objects are clusters we recommend that you do not use format 1 and 4 in Table 1 Instead we recommend that the measurements distance and cluster size be entered ungrouped EXACT formats 2 or 5 even if they were recorded in intervals grouped Use the interval midpoint as the distance measurement for each observation in an interval This enables a more detailed analysis because the distance and cluster size measurements are paired for each object For instance if a WIDTH is chosen which truncates some of the distance observations it is not possible to discard the appropriate cluster sizes unless the measurements are paired as they are in ungrouped data entry Likewise if you wish to
115. which provides a significantly better fit as determined by the specified CRITERION The LOOKAHEAD option determines the length I of the sequence of models that is examined before choosing model M SEQUENTIAL and FORWARD only 45 ESTIMATE gt differ in their choice of which adjustment term is included at each step in the sequence SEQUENTIAL term selection adds the terms sequentially based on the order of the term For polynomial adjustment functions the order of the adjustment term is the exponent of the polynomial Terms are added in the following sequence xt x For cosine adjustments cosine terms are added in the following sequence cos trx w cos t 1 7x w The beginning value t is determined by the shape of the key function FORWARD selection adds 1 term at a time but not necessarily in sequential order For each model in the sequence each term not already in the model is added and the adjustment term which increases the likelihood the most is chosen as the term to add For example to find model M z k models are fitted to the data each with a single adjustment term of a different order e g x xt or xX The term which maximizes the likelihood is selected for model M Model M would then consider adding another term not included in M With FORWARD selection it is possible to select models that cannot be selected with the SEQUENTIAL mode For example the following model might be chosen with FORWARD sele
116. y density function pdf f 1 u value of pdf at zero for line transects u Wtp ESW effective detection area for line transects HCO 2 PT v PI W W p is the effective detection area for point transects probability of observing an object in defined area for line transects effective strip width Wp for point transects effective detection radius W sqrt p estimate of density of clusters estimate of expected value of cluster size estimate of density of animals estimate of number of animals in specified area Figure 7 Options listing for first ESTIMATE procedure of example 1 64 Each of the above sections of output is labelled at the top with a sub title which is outlined with asterisks Most of the output is also labelled with a block of text below the sub title which identifies the data subset being analyzed Text in the identification block will vary depending on the level Stratum Sample All at which parameters are estimated and the analysis options Full identification text includes Stratum Stratum Label Number Sample Sample Label Effort Amount of effort samples Number of replicate lines points Width Right truncation value Left Left truncation value observations Number of observations If the analysis is pooled over all of the data neither the stratum nor sample labels are given If the analysis is by stratum the stratum label is given and if by sample both the stratum and sample labels are given The effo

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