Multi-Distribution Annually-Pulsed Size
Contents
1. Day relative to January 1 when series 1 was sampled 142. of frequency series 1 0 1315120E 01 Proportion age for age class 2 of frequency series 1 0 OR PORPRPRHRHEE Sometimes you will see one of the parameters has a negative value Don t worry the program has the correct value stored Introductory User Manual Once the program has run through the Simplex minimization it is a good idea to save your algorithm data Next try running the data through the Marquardt minimization using numerical derivatives Don t worry about the Bayesian Priors stuff We won t be using it in this example The Marquardt minimization window looks like the following E Marquardt minimization uses derivatives works best when model behaviour is close to linear progress is insensitive to step size x Interrupt Note 1 iterations and 114 function calls Current Min gt 67 78465 Last Min gt 69 40517 Abs TC gt 1 6205E 00 Current minimum found at these adjusted parameter values 01 02 03 04 10 11 13 14 18 19 1 1 9 3 2 1 8 2 1 5 1348940E 02 1190058E 01 2728325E 02 0556134E 02 1046172E 00 9466609E 01 3207282E 02 7314272E 07 9260512E 01 4368715E 01 Mean of L infinity von Bertalanffy 0 SD of L infinity von Bertalanffy 0 Mean of k von Bertalanffy 0 SD of k von Bertalanffy 0 Mean size for Gaussian selectivity 0 SD for Gaussian selectivity 0 von Bertalanffy s t0 the age in years at which size is zero 0 Value of W
3. wish you can be more specific with the final date and correct for the month in which the animal was caught This data is from Microsoft Excel and in its present form cannot be read by the analysis program Our next step now that we have taken an initial look at what data is required is to format the data so that it can be used by the program Introductory User Manual Formatting the data Size frequency data will need to be in the following form HEHE HHHH HHHH i e fixed width comma delimited text The first six characters are read as the midpoint of the size interval The next four are read as the frequency of animals in that interval At least one frequency set must be included but you can have up to eight sets To optimize model speed sort the records in order of size interval Growth increment data will need to be in the following form HHH FHA FT AHH HEHE i e fixed width comma delimited text Each set of six characters is read as follows set number initial size growth increment initial date final date You cannot include anything more than this To optimize model speed sort the increment records in order of initial size We recommend saving Excel xls data sets as Comma Delimited Text csv files This will automatically add in the commas you will need and save you considerable time For the next formatting step we recommend using TextPad editor It is a shareware program available at www textpad com in a
4. HHH HHHH HHHH HHHH HH HARE etc Maximum number of frequency cells is 250 Frequency cell midpoints MUST represent a size range that begins at 0 e g 0 5 1 5 of 2 5 5 0 etc Increment records Increment records The record input format for increment set then initial size then increment then start day of the year then end day of the year is HHHHHH HEHEHE HHHHHH HHEHHH HEHEHE Maximum number of increments is 800 For proper and efficient performance increment records MUST be sorted by set number then initial size then increment Day O MUST be 31 Dec of the year prior to those years for which increment data have been obtained Note objective function fs 2 Infikelhoodf As you can see we have already loaded one of the size frequency data files This is a good time to pull out your size frequency diagrams We will be referring to it For our example data we are going to choose the following options Age of 1 smallest age class 1 This allows you to adjust the starting point of your data Years between age classes 1 This allows you to set the intervals between what you believe are age classes for your data Introductory User Manual Number of frequency series 1 This allows you to evaluate up to 8 frequency series at once Warning more than one series can more than double the calculation time First frequency cell evaluated 1 If you do not consider the first few cells of data to be reliabl
5. Multi Distribution Annually Pulsed Size Frequency Data and Growth Increment Data Model Introductory User Manual By Alison Meynert Co op Student Pacific Biological Station July 1999 Table of Contents ICO TC Lt A E aia Sees 1 LA A E a a a T 2 O A is 3 Initializing the model susan ninia diia ias 4 Loading saving and editing algorithm dala oononnnccnnnninoccnonnnonncnonnnnnnnonnnnnnn nono nc conc nnnncnnnnons 7 One f ncton Call 426 CL REE ie Oi REE Ls Cea 8 WET ZA OM Lay il llas id 9 Resulis SUMAN A A ds 11 Calculatine COD 12 Using both increment and size frequency data ooooconnocccnnnccconocononononononcnnnoncnnnnncnnnccnnnnnnnno 13 Appendix A Parameter Descriptions oooooonnncccnnnoccnnnnnnnnnacononacononacononacononanononacononacnnnnannon 14 Introductory User Manual Introduction This manual is intended for use as an introductory guide to Barry Smith s Age Model program AgeFrequencyModel exe It is not intended to serve as a resource for actual data analysis rather its goal is to guide a new user through the functions of the program they are most likely to use We will follow an example data set through analysis starting from raw data Introductory User Manual Required Data This program takes two types of input data raw size frequency and growth increment data therefore we will be using both types of data in our example This data is for red sea urchins sampled at Site 3 in the Queen Cha
6. all zeroes You will be told what the time date based name of the algorithm file is This is a temporary name as we will be saving it under a more descriptive name later on Choose Edit Algorithm Data from the main menu You will see the following dialog al Algorithm data file name is 07191447 alg Doublechoh to edia Value or Sea ar daw amp le alick the column heading ta change tem all Absolute tolerance fi OO0E 06 Step Parameter description null value 1 0000E 01 Mean of L infinity von Bertalanffy 0 Marquardt maximum iterations 1000 2 0 1 0000E 01 SD of L infinity von Bertalanffy 0 Simplex maximum function calls 3 0 1 0000E 01 Mean of k von Bertalanffy 0 4 0 1 0000 01 SD of k von Bertalanffy 0 Terminal display frequency fio la 0 1 0000E 01 Amplitude of annual cycle in k 0 6 0 1 0000 01 Day of maximum in annual cycle of k 0 Stee eee redaction hacton JP 7 0 1 0000E 01 Amplitude of annual cycle in L 0 8 0 1 0000E 01 Day of maximum in annual cycle of L 0 g 0 1 0000E 01 SE of measurement 100 units SE 0 Open ose Log file name 10 0 1 0000E 01 Mean size for Gaussian selectivity 0 11 0 1 0000E 01 SD for Gaussian selectivity 0 12 0 1 0000E 01 Parameter b for size dependent k 0 is 0 1 0000E 01 von Bertalanffy s t0 the age in years at which size is zero 0 14 0 1 0000E 01 Value of Weibull
7. e you can skip them with this option Frequency values are zero beyond the extremes of the sampled distribution If you believe you may not have sampled the population extensively enough you can choose the truncation option Usually it is best to choose the zero beyond extremes option Number of young identifiable age classes in the series 2 This is when you look at your size frequency diagram How many age modes can you identify before they become blended Number of blended unidentifiable age classes in the series 99 Your options here are 0 5 10 20 50 and 99 The idea is to choose the amount which will take your population to zero by the end of the distribution Choose age modes to be a gamma distribution Combination of L and k is extremely slow Gaussian and gamma are much faster with the penalty of slightly less accuracy If you are using increment data ignore the Seasonality in Growth box for the time being and start by choosing your increment error distribution to be Gaussian as it is less complicated You can always come back later and switch to gamma We will work with size frequency data for now The idea is the same for increment data and it is possible to work with both at the same time Introductory User Manual Loading saving and editing algorithm data Once you have loaded the size frequency data choose Load Algorithm Data from the main menu When asked choose No to load the default values
8. eibull function scale parameter Psi 0 Proportion age for age class 1 of frequency series 1 0 Proportion age for age class 2 of frequency series 1 0 Marquardt is slower than Simplex but can obtain a lower minimum value In the current example I found that the mean size and standard deviation for Gaussian selectivity were not changing very much so I froze those parameter values by interrupting the minimization and changing their step sizes to 0 in the Edit Algorithm Data window I then set their values to be 5 and 2 5 respectively You can interrupt the minimization process at any time by hitting the Interrupt bar at the top of the window 10 Introductory User Manual Results Summary When the program has identified a minimum save your algorithm data Next choose Results Summary from the main menu It will run One Function Call then ask if you would like to see the plots as well as the summary If you choose yes a plotting window will come up Choose drop lines from the Plot Options box on the left then hit Clear Plot amp Re Set Axes Double click on Observed aggregate frequencies in the top right hand box Your original size frequency data will plot Choose lines from the Plot Options box then double click on Predicted aggregate frequencies in the top right hand box You can double click repeatedly to change the plot colour The following is a plot done before the minimization was com
9. ested in the ones for which you have visible age modes in the data Wi i Pal Ve 178 5 You can save your output as a sso file 11 Introductory User Manual Calculating Covariances Once you have looked at your results you can look at the covariances Choose Calculate Covariances from the main menu You will be asked about something called grid factors The defaults are good so I don t recommend changing them Just agree with the program until it asks you to Enter the constant W HICH WILL MAKE the objective function the In likelihood Cancel m Always enter 0 5 as the objective function is 2 In likelihood as you will recall from the screen shot of the model initialization on page 5 With a little luck you will end up after a moment of calculations by the program with output similar to the following Covariance constant 0 5 Factors 1 1 0000000E 00 2 1 0000000E 01 3 1 0000000E 02 Likelihood function value summary Mean 1 4557005E 02 1 2819633E 02 1 2802132E 02 Std Dev 2 5565022E 01 3 3888996E 01 2 1380607E 02 Coef of Var 0 1756201 0 0026435 0 0001670 The closer the means are for each column the better You can save your covariance calculations as a cov file 12 Introductory User Manual Using both increment and size frequency data Increment data can help to offset variation in size frequency data By loading both inc
10. f L 0 09 0 0000000E 00 SE of measurement 100 units SE 0 10 1 0000000E 01 Mean size for Gaussian selectivity 0 11 1 0000000E 01 SD for Gaussian selectivity 0 12 0 0000000E 00 Parameter b for size dependent k 0 13 5 0000000E 01 von Bertalanffy s t0 the age in years at which size is zero 0 14 5 0000000E 02 Value of Weibull function scale parameter Psi 0 15 1 0000000E 00 Value of Weibull function power parameter Phi 1 16 0 0000000E 00 Size above which the fishing mortality rate applies 0 17 0 0000000E 00 Instantaneous rate of fishing mortality 0 17 1 0000000E 01 Proportion age for age class 1 of frequency series 1 0 18 3 0000000E 01 Proportion age for age class 2 of frequency series 1 0 19 1 5000000E 02 Day relative to 1 January when series 1 was sampled 0 Note One function call requires 0 55 seconds Introductory User Manual Minimization There are two methods with which you can minimize your model Simplex and Marquardt Itis recommended that you use both methods when analysing data We will start by using Simplex To run the minimization click the Minimize with Simplex button on the main menu While the Simplex minimization is running you should see a window like the following E Simplex minimization uses geometry works best for models whose behaviour is markedly non linear progress is sensitive to step size EQ Interrupt Initial Simplex Starting f
11. function scale parameter Psi 0 Wiite frequency to log file po 15 0 1 0000E 01 Value of Weibull function power parameter Phi 1 16 0 1 0000E 01 Size above which the fishing mortality rate applies 0 17 0 1 0000E 01 Instantaneous rate of fishing mortality 0 y 4 Einish editing Note A sian size of 2era heezes the walkie af he CONes condi y DErIMNE er To start off set the maximum number of function calls to 99 999 This will save you the trouble of interrupted calculations later on Now double click on the word Value and choose Change all values and step sizes This will allow you to enter your first guesses at the function parameters See Appendix A for a list of the parameters For this example we will enter the following guesses Mean of L infinity 130 SD of L infinity 15 Mean of k 0 15 SD of k 0 015 Mean size for Gaussian selectivity 10 SD for Gaussian selectivity 10 von Bertalanffy s t0 0 5 Weibull function parameter Phi 0 05 Weibull function parameter Psi 1 Proportion age for age class 1 of frequency series 0 10 Proportion age for age class 2 of frequency series 0 30 Day relative to 1 January when series 1 was sampled 150 Introductory User Manual You will notice that as you set these parameters their corresponding step size is changed proportionately For all the parameters that you do not set and which you do not wish to estimate set their step size to O by double clic
12. it Merqueral lt Lose Aigoritan Wate Bait Again Wate Seve AGO in Wate mary Calcula sGyanances Introductory User Manual Choose Initialize Model from the menu You will see the following dialog all Initialize age modal size frequency and growth increment model Frequency data file EO pa as eee Ee Load Frequencies Seasonality in growth Set the seasonal lag in L equal OK Cancel step size for that lag parameter 8 MUST be set to zero Choose increment error distribution Wo C Yes l Gaussian ib Ganna b gt 1 Increment data file Load Increments to that fork If so then the m Describe frequency data Age of 1st smallest age class fi Number of frequency series o y Years between age classes fi First frequency cell evaluated fi y Frequency values are zero beyond the extremes of the sampled distribution The frequency distribution has been truncated at its extremes Number of young identifiable age classes not cohorts in the series o y Number of blended unidentifiable and older age classes whose proportions are determined by a Weibull mortality rate function o Choose age modes to be the joint distribution of L and k V Choose age modes to be a Gaussian distribution Choose age modes to be a gamma distribution Frequency records The record input format for the size frequency midpoint then frequency is HHHHHH HHHH
13. king on that cell We will also set the step size for Day relative to 1 January to be 0 because we know that it was May 30 and thus 150 days after 1 January Again set the step size to be O for the Weibull function parameter Psi We wish to estimate natural mortality and when Psi is 1 the parameter Phi is the estimate we are looking for Choose the big Finish editing button You will now be back at the main menu Choose Save Algorithm Data and save your algorithm It is recommended that you keep all the files of one analysis in the same folder or give them all the same filename just with different extensions One function call Now choose 1 Function Call from the main menu This will give you an idea of how long it will take the program to find the best parameters for your model Hopefully your time will be under 1 second as in this example Current minimum of 202 10703 found at the following parameter values 01 1 3000000E 02 Mean of L infinity von Bertalanffy 0 02 1 5000000E 01 SD of L infinity von Bertalanffy 0 03 1 5000000E 01 Mean of k von Bertalanffy 0 04 1 5000000E 02 SD of k von Bertalanffy 0 05 0 0000000E 00 Amplitude of annual cycle in k 0 06 0 0000000E 00 Day of maximum in annual cycle of k 0 07 0 0000000E 00 Amplitude of annual cycle in L 0 08 0 0000000E 00 Day of maximum in annual cycle o
14. n evaluation version Open your data in csv form in a text editor such as TextPad or NotePad and save it with the same filename but with extension dat This step is a pain to do Each column of your data must be right aligned using spaces not tabs The following is an example of correctly formatted data Size Frequency Data Sample Growth Increment Data Sample 0 5 0 1 8 620 8 336 152 516 135 0 1 9 009 8 179 152 516 LD 1 1 9 339 7 896 152 516 3255 0 1 9 688 11 076 152 516 4 5 2 1 9 832 9 004 152 516 Disc 3 1 9 908 7 420 152 516 6 5 T 1 10 042 9 272 152 516 Poy 12 1 10 070 5 326 152 516 8 3 13 1 10 432 8 643 152 516 975 19 1 10 803 6 524 152 516 LO ios 20 1 11 028 11 461 152 516 11 5 16 1 11 2607 9 595 152 516 LLO 18 111 356 T623 152 516 1335 18 1 11 407 6 483 152 516 14 5 15 1 LL 510 8 5745 152 516 TextPad gives you an advantage when doing this part of the formatting It has an option under the Configure menu that allows selection and copy and paste of vertical blocks of text Ensure your data is correctly formatted as 1t can cause you headaches later on if it is not Introductory User Manual Initializing the model Now we are ready to start the program It should be in your Start Menu if you are running Windows 95 or higher under Age Model You will see a screen that looks like the following xt Main menu HS rada all DEJESIan IAIOTE f tT ST meem
15. pleted for this data set PT jj w a j r i Data and prediction plots zaa x Y variate Observed aggregate frequencies Frequency Cell MidPoint Observed aggregate frequencies Predicted aggregate frequencies Predicted frequencies for age class 1 Predicted frequencies for age class 2 Predicted frequencies for age class 2 Predicted frequencies for age class 3 Predicted frequencies for age class 3 Y Predicted frequencies for age class 4 Y Predicted aqaregate frequencies Predicted frequencies for age class 1 IV Lines lt gt J Lines gt 7 Lines lt FT Drop lines P 10x10 Grid 8x8 Grid Clear Plot amp Reset Axes Set Min Max Y Min Y Max 50 Y Min 0 Plots are automatically scaled to the range of the data unless the model includes a scaling function To override a scaling function set the maximum or minimum of x or Y to 0 i Next Plot Page Quit plots When you are done looking at your plots click the Quit Plots button in the bottom left hand corner You will be asked how many parameters were estimated in this model In the example data there are nine You will also be asked how many chi square calculations you want done 1000 is a good round number and is usually fairly accurate You will then be asked how many age classes you want detailed reports for For the example choose 2 You will usually only be inter
16. rement and size frequency data as in the following example your calculations will often be more accurate at Initialize age modal size frequency and growth increment model x D 14MeynertiB arrySmith examples szf 1mm dat D 14MeynertiB arryS mithhexamplestinc dat Everything else is done exactly as in the size frequency only example 13 Introductory User Manual Appendix A Parameter Descriptions Mean of L infinity von Bertalanffy Standard deviation of L infinity von Bertalanffy Mean of k von Bertalanffy Standard deviation of k von Bertalanffy Amplitude of annual cycle in k Day of maximum in annual cycle of k Amplitude of annual cycle in L infinity Day of maximum in annual cycle of L infinity Standard error of measurement 100 units percent standard error Mean size for Gaussian selectivity Ria Ziawojeljojaju alu n Standard deviation for Gaussian selectivity na N Parameter b for size dependent k W Von Bertalanffy s to the age in years at which size is zero P Value of Weibull function scale parameter Psi Nn Value of Weibull function power parameter Phi jaa nN Size above which the fishing mortality rate applies Instantaneous rate of fishing mortality NO co Proportion age for age class 1 of frequency series 1 Proportion age for age class 2 of frequency series 1 N
17. rlotte Islands in 1998 Size Frequency Data Sample Increment Data Sample 0 5 0 1 8 620 8 336 152 516 1 5 0 1 9 009 8 179 152 516 2 5 1 1 9 339 7 896 152 516 3 5 0 1 9 688 11 076 152 516 4 5 2 1 9 832 9 004 152 516 5 5 3 1 9 908 7 420 152 516 6 5 7 1 10 042 9 272 152 516 7 5 12 1 10 070 5 326 152 516 8 5 13 1 10 432 8 643 152 516 9 5 19 1 10 803 6 524 152 516 10 5 20 1 11 028 11 461 152 516 11 5 16 1 11 267 9 595 152 516 12 5 18 1 11 356 7 623 152 516 13 5 18 1 11 407 6 483 152 516 14 5 15 The size frequency data is in pairs with the first column being the midpoint of the size interval and the second being the number of animals found in that interval The growth increment data is somewhat more complicated The first column is called the set number and is usually set to 1 for a single data set The second column is the initial size and the third is the growth increment The fourth column is the date of initial measurement in days from January 1 of that year Jan 1 day 1 The fifth column is the date of final measurement in days from January 1 of the year the initial measurements were done Note If you do not have growth increment data but you do have size at age data you can use this data as growth increment data Assign the set number column to the age of the animal the initial size to zero the growth increment to the measured size the initial date to zero and the final date to 365 times the animal s age If you
18. unction value gt 202 10703 Max gt 28358661 55116 Min gt 190 52534 Initial parameter values 01 02 03 04 10 11 13 14 18 19 3000000E 02 Mean of L infinity von Bertalanffy 0 5000000E 01 SD of L infinity von Bertalanffy 0 SODOOODE 01 Mean of k von Bertalanffy 0 5000000E 02 SD of k von Bertalanffy 0 QOOO0000E 01 Mean size for Gaussian selectivity 0 DOOOOODE 01 SD for Gaussian selectivity 0 OO00000E 01 von Bertalanffy s tO the age in years at which size is zero 0 0000000E 02 Value of Weibull function scale parameter Psi 0 DODOOODE 01 Proportion age for age class 1 of frequency series 1 0 DOOOOOOE 01 Proportion age for age class 2 of frequency series 1 0 OrRMMRPRRRHEEH Note 41 iterations 65 function calls and O restarts Current Min gt 95 13572 Max gt 101 53751 Abs TC gt 6 4018E 00 Current minimum found at these adjusted parameter values 01 02 03 04 10 11 13 14 18 19 11421585E4 02 Mean of L infinity von Bertalanffy 0 6161563E 01 SD of L infinity von Bertalanffy 0 1971387E 01 Mean of k von Bertalanffy 0 63394087E 02 SD of k von Bertalanffy 0 0140458E 01 Mean size for Gaussian selectivity 0 0571741E 01 SD for Gaussian selectivity 0 4162900E 01 von Bertalanffy s tO the age in years at which size is zero 0 9453860E 02 Value of Weibull function scale parameter Psi 0 1321671E 01 Proportion age for age class 1
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