User`s Manual for the LCDMV Software (Calculation
Contents
1. a normal distribution of the distance Inf Di D u JVar D and Sup D u JVar D with u the Z value by the normal standard table for a chosen probability level a If the collection of OTUs to be analyzed is solely made up of pure line varieties ie homozygous for all the loci in all the lines and if we assume that the loci are independent and unlinked the Rogers distribution follows the binomal distribution B L In this case the exact boundaries of the Squared Modified Rogers distance confidence interval is calculated according to Collett 1991 Inf D T and LD n D 1 a a 22 1 122 1 1 up D LD E 1 m Di m 1 If the varieties are pure lines and the CHROMO and POS CHR variables of the MARKERS file have been given for at least a part of the locus Cf B 3 the program estimates in addition to the Squared Modified Rogers distance the BLUE Best Linear Unbiaised Estimator of the Squared Modified Rogers distance Dillmann et al 1997 estimated from the mapped loci Di ry av Where 7 is the dimension identity of the vector L 1 Dj 0 1 the Squared Modified Rogers distance vector estimated for L individual locus between the i and j varieties and V is the variance covariance of the Squared Modified Rogers distance for the individual locus estimated by the map distance between locus 11 The Di variance2. matrix and the method chosen by the user and calculate the robustness of the dendrogram by bootstrapping if requested by the user e Create a chart of mapped loci that differ between two pure lines Generate a report file showing the polymorphic markers in the study including information such as allele richness and diversity as well as the estimated distances between every pair of OTUs and the confidence interval associated with those estimates B Input file format The LCDMV program uses 3 files saved in a text format a The CULTIVARS file giving a description of the OTUs b The MARKERS file giving the description of the markers c The FRQUENCY file with the matrix of allele frequencies for each OTU B 1 The CULTIVARS file The CULTIVARS file describes the observations characterized in the FREQUENCES file and contains 3 columns of variables e Statut e var e echant without accent Note These variables must be declared at the top of the file on the first line separated by at least one space or a tab Spelling and case of the names must be consistent The STATUT variable is an alpha numeric variable allowing the precise specification of the cultivars 1e reference or candidate In the default version the program does not use this variable but it can be used in response to the future needs of the users who will choose to restrict the genetic distance calculations to the pairs reference reference and reference candi
3. using the values observed following repeated sampling with replacement the bootstrap procedure This method is recommended as the analytical estimation can become very imprecise for small sample sizes 3 Heterogenous varieties locus allele markers Two types of distances can be used by the program Squared Modified Rogers distance 1972 and Sanghvi Foulley and Hill 1999 The Squared Modified Rogers distance estimate is calculated by E l 1 1 1 1 a 1 a gt a Where L is equal to the number of loci characterizing the varieties i and j 1s the estimated frequency of allele a at the locus in the variety i 7 and M is the number of individuals in the variety i 7 The confidence interval is estimated using the values observed following repeated sampling with replacement the bootstrap procedure To remove bias from the estimation of the distance which can occur in this resampling of individuals within varieties the distance is recalculated as 1 1 ul AL ne 1 AAPP PIP Pipi pi pr Di al a l al a l ab al 5 2 225 1 N 1 NE E Where Pi Bj is the estimated frequency allele a has at the locus in the bootstrap values of i j for the variety i f 13 The Sanghvi distance estimate is calculated by 1 1 4 Bi P Di 29 m E db se Where A is equal to the total number of alleles on the sample of the loci analy
4. you the same format using other options may give random results and you will need to check the settings on your printer However by Exporting the file you will have different options for saving the graphics To verify the results of the analyses performed by the program check the file created by the program it will be named prefix out where prefix is the name of your input file You will find 3 to 4 text files corresponding to the files specifying variety type of the cultivars analyzed and the type of marker used The prefix you use in naming the files is followed by a number in order of their creation ie RAPD 1 RAPD 2 Without exiting the SAS program you can recall the program Lcdmv sas Local menu Recall text command which will place you in the PROGRAM EDITOR window This will relaunch the execution of the program Because files are edited progressively as you work and saved sequentially in the folder WORK GSEG that already contains the graphs created in the first session you will soon have many files in this folder However these files are automatically destroyed the moment you exit the SAS program You must remember to print or save the graphs you wish to keep using the Print or Export commands from the Spins menu 20 F References Bouroche JM et G Saporta 1980 L analyse des donn es Que sais je PUF Collet D 1991 Modeling binary data London Chapman amp Hall pp 23 25 Dillmann C A Charcos
5. 7 C10 H B 3 543 C10 H C 3 543 C10 H A 3 543 C102 E 1 3 61 4 C102 E 2 3 61 4 C102 E 3 3 61 4 C102 E 4 3 61 4 C102 E 5 3 61 4 Unknown map position locus allele Name of the variables in file head ADH2 H 1 ADH2 H ADH2 H ADH2 H ADH2 H ADH2 H ADH2 H ADH2 H C10 H B C10 H C C10 H C102 E 1 C102 E 2 3 4 5 L XQ N A C102 E C102 E C102 E Example 2 A MARKERS file describing the columns indicated in the FREQUENCES file given in Example 2 above and assuming dominant loci 1 e allelic relationships between bands do not exist or are not known locus allele AFLP Marker name Gen01 Gen02 Gen03 Gen04 Gen05 Gen06 108 Molecular weight of the bands Bar29 277 Bar30 280 Bar31 284 Bar32 289 B 3 The FREQUENCES file The FREQUENCY file contains as many observations lines as there are individuals OTUs analyzed to characterize a population as described in the CULTIVARS file This value will be one if it is a pure line cultivar or single cross hybrid It also contains as many variables columns as the number of markers described in the MARKERS file characterizing these OTUS Each line corresponds to the frequency profile of the markers of each given individual Notice that these frequencies are discrete 0 0 5 or 1 in each diploid individual 0 0 25 0 5 0 75 or 1 in each tetraploid individual etc for higher ploidy levels Note The data must be separated by a space or a tab and missing da
6. P LL LL o A d dk od 1 1 1 0 1 1 1 1 0 H1 1 1 1 1 1 1 1 1 0 1 1 1 0 I 0 O0 1 1 1 1 0 1 1 1 I 0 0 1 1 1 0 1 1 1I 0 0 1 1 0 IT 1 0 1 1 1 O0 1 1 1 1I 1 1 0 1 I 1 1 1 1 I 1 1 0 OI 1 1 1 0 1 The data is separated 1 1 1 0 by tabs C Analyses performed by the program C 1 Genetic diversity measurements Regardless of the type of OTU the program estimates 1 in the case that the molecular information can be classified as lt lt locus allele gt gt e The number of alleles per locus in this study e Nei s diversity index for populations in panmixis over all loci in the study Ss y i H 1 Y Nei 1973 a 1 Where 4 equals the total number of alleles for locus and b the estimated frequency of allele a at locus in the current study 2 in the case that molecular information can be classified as bands e frequency of the markers bands in the study e The PIC Polymorphism Information Content of the markers which is equivalent to Nei diversity estimate for biallelic loci PIC 2p 1 p Where b is the estimated frequency of the marker m in the study If the collection is composed of heterogeneous varieties the program estimates e The average number of individuals characterized by locus and by variety e The mean number of alleles within each variety over all loci in the stu
7. cal menu or by clicking the following icon When the program has finished running successfully you should see the FILES window appear within a few seconds ves FICHIERS Indicate the following 1 The complete path under which you saved the three files necessary to run the software for example C logiciel lcdmv files ma s RAPD 2 the name ofthe 3 entry files for example V_rapd dat dat and P rapd dat 3 The complete path under which you wish the resulting files to be stored for example C logiciel lcdmv results mais RAPD and 4 the prefix that you wish to give the results file to distinguish them from the input file for example RAPD 18 Upon successful completion of this step you will see the following OPTIONS window appear OPTIONS AGE Command MODIFICATION DES PARAMETRES PAR DEFAUT ENTER pour valider Nombre d axes ACP examiner P entre 0 et 51 M thode de classification UPGMR Upgma Ward Minimum Maximum MEE 1 entre 0 et 11 Nombre de bootstrap 0 0 100 200 500 ou 10001 Confiance souhait e pour l IC de la distance 1 95 190 95 ou 99 You then can validate the data using the default options or continue to modify the data by the following e Perform a PCA while specifying the number of axes that you wish to examine up to five e Chan
8. choice you must open the program Lcdmv sas menu Spins orders Open in interactive method the windows PROGRAM EDITOR OUTPUT and LOG must be accessible as below and replace MONREP by the name of the path and folder under which you have saved the four elements of the LCDMV program formerly C logiciel Lcdmv Note Modifying any other part of this file could result in errors or loss of function SAS 0 x File Edit View Locals Globals Options Window Help 7 z3 Delal alal sel 19 alale 8 LOG Untitled lof x Ri OUTPUT Untitled S PROGRAM EDITOR LCDMV c sas Ft RRRRRRRRRRRRRRRRRRRRRRRRRRRRBRRRRRRRBRRRRX EE EEE EEE EES options nosource Mstored sasmstore logiciel libname logiciel MONREP libname gdeviced MONREP 4global DdisP DdisL DimpP DimpL 4let DdisP WINdisP let DdisL WINdisL zlet DimpP CLJPSAYP zilet DimpL CLJPSAJL XProg P AREER EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE Et MEM PR options nosource Mstored sasmstore logiciel Libname logiciel C logiciel ledmv Libname logiciel C logiciel lcdmv global DdisP DdisL DimpP DimpL let DdisP WINdisP let DdisL WINdisL let DimpP CLJPSA4P let DimpL CLJPSA4L 17 Prog_P PRE Save the modification that you have made menu Spins orders Knows or by clicking the save button and run the program with the Submit command from the Lo
9. date for example to limit the program s execution time and to reduce the number of given results The NOM VAR variable is an alpha numeric variable used to identify the cultivars OTUs for analysis either by commercial denomination or by a code specified by the user This variable is essential and must not be left blank The name of an OTU may appear more than once in the file In this case the program treats each repetition as the same cultivar or of the same data of a given cultivar and the index automatically follows the order of this declaration In example 1 below the cultivar L3 is observed twice in the file lines 4 and 7 Therefore the first observation line 4 will be given the suffix 1 while the second line 7 will be given the suffix 2 The ECHANT variable is a numeric variable allowing the user to specify the number of individuals analyzed to characterize a heterogeneous cultivar If the number of observations in the CULTIVARS file is equal to the number of observations in the FREQUENCES file this variable is not required and left at the default and the program automatically begins a chain of calculations suitable for homogenous varieties pure lines or single cross hybrids If on the other hand the number of observations in the CULTIVARS file is less than to the number of observations in the FREQUENCES file then the ECHANT variable is used to notify the program of the number of individuals to be analyzed for each of the cu
10. dy e The Nei diversity index markers locus alleles or PIC value markers bands within each variety in the study 1 _1 2n Si Y Hi DE uf y Nei 1978 Where L is the total number of loci characterized for variety i n is the number of individuals characterized for locus and b is the estimated frequency of allele a at locus for variety i C 2 Principal Components Analyses PCA 1 Homogenous Varieties The program will perform a PCA on the matrix of genetic distances calculated from the frequencies of the markers alleles or bands stored in the FREQUENCES file Missing data is replaced by the frequency of the markers within all varieties in the study The quality of the graphical representation of an OTU is estimated by the square of the cosine of the angle between the original vector in the space represented by the centered and reduced variables bands or alleles and its projection on the principal axis under 2 spatial dimensions This approaches one as the area between the 2 vectors becomes very small 0 1 when 0 Itis graphically symbolized by a circle centered on the variety 2 Heterogenous Varieties The program performs two different Principal Components Analyses for heterogeneous varieties on the correlation matrix of the frequencies of the markers alleles or bands estimated within each population The graphical output is calc
11. following repeated sampling with replacement the bootstrap procedure To remove bias from the estimation of the distance that can occur in this resampling of individuals within varieties the distance 1s recalculated as m m 1 per 1 er ry 18 aha a Ner N N 1 Ni 1 i Where M is equal to the total number of markers Pi Pl is the estimated frequency of the marker m in the initial sample of the variety i and bi E the frequency of the marker m in the resampling of the variety 7 C 4 Hierarchical Classification To visualize the results of the distances in the matrices the program will perform a hierarchical classification using four different methods for the user to choose from Details of the methods can be found in Bouroche and Saporta 1980 Formulas to calculate the distances between groups formed in the preceding steps and any given element k using the following four methods e UPGMA Unweighted Pair Group Average Method dk GO 40 0 where p n n n weights assigned to group i and p 7n n weights assigned to group j e Ward minimum variance within groups d k GO pa p MG 7 pdi j where p n n n n weights assigned to group k p n n n n weights assigned to group i and p n n n n weights assigned to group j e Minimum nearest neighbor d k G o j min a amp i a am
12. ge the classification method to something other that UPGMA Ward for example e Display the varieties on a different scale for example to show them grouped more closely together by specifying a larger distance threshold e Calculate a confidence interval on the genetic distance estimates or test the robustness or stability of the join points of the dendrogram by performing a bootstrap analysis and specifying the number of resampling to use e Choose the confidence level of the confidence interval of the estimated genetic distances Upon choosing one of these analysis options the program begins calculations and progressive editing of the output The output graphic will depend on the analysis chosen and the combination of variety type and marker type as identified by the program and specified by your input files During the execution of the program you may wish to move to the GRAPH window to see the output If you wish to examine in detail or to modify an output graph for example to change the legend you can use the command Edit Graph from the Edit menu or by clicking on following icon x 19 The End command of the Spins menu graphic editor allows you to return to the GRAPH window You then can decide to print the graph or to save it to a file To do so go to the Spins menu and chose the Print command Export the file to be printed by default the graphs are in a postscript ps format Only printed postscript copies can guarantee
13. i CIMMYT User s Manual for the LCDMV Software Calculation Software of Molecular Distances between Varieties For Fingerprinting and Genetic Diversity Studies Dubreuil Dillmann a M Warburton J Crossa A 4 J Franco and C Baril fipril 2003 First Edition TABLE OF CONTENTS O ON 1 A General Presentation and Organization of the 1 B Input file A er E ER RR PU ARE C 2 Dd The COLE IIo da DO rca nie dome 2 BeZ dh MARKERS TIO A S IEEE VE AR ERA RS 4 Dod The PREOUENCES I sn esters ORAR AAA 7 C Analyses performed by the program 8 C Genetic diversity measurements seeds seal de dae A Regu e 8 C 2 Principal Components Analyses PCA 9 C 3 Estimation of the genetic distances and precision of the estimates 10 C 4 HierarohicalClassificaliQnus su AR der en este tn LES 15 D Installation of LCDMV and practice session 16 Es Referentes erorii e nero 21 Introduction LCDMV in English known as the Calculation Software of Molecular Distances between Varieties is a computer program developed in the SAS language SAS Institute Inc version 6 12 with the help of the modules SAS STAT and SAS IML It was written to analyze biochemical markers isozymes or molecular markers RFLP STS SSR RAPD AFLP obtained on hom
14. is estimated by wv The approximate boundaries of the confidence intervals of the Squared Modified Rogers distances observed are estimated under the normality hypothesis of D Inf Di D u Var D and Sup D D eu 2 Homogenous variety band markers This distance estimator used in this case is that of Nei and Li 1979 2N 1 ds N Where V is the number of common bands between varieties i andj N M the number of bands for the variety i 7 For information only the distance of Jaccard 1900 1908 is deducted from the distance of Nei amp Li j M Snijders et al 1990 J 14 Di Snij The variance of the Nei and Li distance is estimated by h ni N2 E i Im XN Oitmann 1999 pers com Var D 4 m Where m is the average and v is the variance of the total number of bands present within every pair of varieties within the study ny ra N and c i l j i My My cu cpi WR e nj i l j gt i Where ny equals the number of varieties in the study This estimate assumes that follows a binomial distribution with N and P calculated as E N EN e M pE NT 2N 2 is N m N The approximate confidence interval of the Nei and Li distance is estimated as Inf D D u JVar D and Sup D2 D u JVar D If requested by the user the program will estimate the confidence interval
15. ltivars see example 2 This structure supposes that only one individual will suffice to correctly characterize the molecular profile of a homogenous variety even if in practice such homogenous varieties are generally characterized using several individuals separately or bulked Note The data must be separated by at least one space or tab Example 1 A CULTIVARS file describing the observations of the FREQUENCES file statut nom var echant Name of the variables in file head r L1 1 r L2 1 r L3 1 r L4 1 r LS 1 r L3 1 r L7 1 r L10 1 Example 2 The CULTIVARS file describing the observations in the FREQUENCES file given in Example 2 Statut nom_var echant Barlet 10 Barpolo 8 Barylou 6 The variable statut must be specified If you do not wish to specify this variable use periods as shown in the examnle here B 2 The MARKERS file The MARKERS file describes the markers corresponding to those in the FREQUENCES file and up to but no more than 4 variables e locus e allele e chromo specifying chromosome e pos chr specifying the position on the chromosome As in the case of the CULTIVARS file these variables must be declared in the first line of the file separated by at least one space or tab They must remain consistent for spelling including case sensitivity and spaces The LOCUS and ALLELE variables are necessary and must not be left blank The CHROMO and POS_CHR variables are optional and sh
16. ogenous or heterogeneous varieties Its main function is to estimate genetic distances between varieties and to analyze the structure of the genetic makeup of a given collection of OTU s Operational Taxonomic Units A General Presentation and Organization of the Manual The structure of the OTUs and the type of markers used are the main determining factors of the analysis method used by the program We define two types of OTU structure homogenous varieties represented by clonal varieties inbred lines and single cross hybrids and heterogeneous varieties including double cross hybrids three way crosses and synthetic and traditional populations The markers were also classified into two distinct types co dominant markers isoenzymes RFLPs and SSRs and dominant markers RAPD and AFLP In the first case the marker bands can be defined to specific alleles while in the second case the allelic relationship between the markers is unknown This program is designed to most efficiently use the information provided by each marker type in order to calculate distances most correctly However in order to standardize analyses as much as possible dominant markers have been assumed in some cases to be co dominant In these cases each marker band is assumed to be a dominant allele of a bi allelic locus Data entry for this program uses three structured files Two of the files describe the OTUs cultivars and the markers while the third file c
17. ontains the marker data in a matrix of N lines and P columns N being the individuals or populations OTUs analyzed and P the number of genetic markers run on the collection of OTUs Each line of the matrix consists of allelic frequencies of the markers of a given individual The program realizes a pre determined series of calculations depending on type of OTU and marker dominant vs co dominant In the case that markers are mixed both dominant and co dominant all will be treated as dominant The program can then be used to e Analyze the frequencies of alleles or bands in the collection of OTUs e Perform Principal Components Analysis PCA This will display the OTUs graphically either as populations or if the populations were characterized with several individuals analyzed separately they can be displayed individually on the graph e Choose the most appropriate estimator of genetic distance based on OTU marker type combination e Estimate genetic distance between every pair of OTU in the study and the confidence interval for every estimate using either an analytic approach or an empirical approach using re sampling bootstrapping if an analytical calculation is not possible e Display the histogram of genetic distances between all pairs of OTUs in the study and a graph representing only pairs of OTUs for which the distance is lower than a threshold distance as defined by the user e Perform a cluster analysis using the distance
18. ould only be declared if the map data is available The LOCUS variable is alpha numeric and identifies the locus of various markers bands or alleles In cases where the allele relationship between the markers is known the identifier of a given locus should appear in the first column as many times as there are indexed alleles In Example 1 below the locus header ADH2 H is repeated 8 times to indicate each of its alleles named through 8 In cases where the allelic relationships between markers are unknown each individual marker is identified by the locus variable as if it were a separate locus see Example 2 below The variable ALLELE identifies the alleles at each locus by a number a letter or by molecular welght see Example 2 The variable CHROMO is a numeric variable used to identify the linkage group or chromosome of the analyzed locus The variable POS_CHR is also numeric and indicates the position of the locus on the linkage group or chromosome in centimorgans compared to neighboring loci Note The data must be separated by at least one space or tab Example 1 A MARKERS file describing the columns indicated in the FREQUENCES file given in Example 1 above and assuming co dominant loci with defined alleles Known map position locus allele chromo pos chr lt Name of the variables in file head ADH2 H 1 4 9 7 ADH2 H 2 4 9 7 ADH2 H 3 4 9 7 ADH2 H 4 4 9 7 ADH2 H 5 4 9 7 ADH2 H 6 4 9 7 ADH2 H 7 4 9 7 ADH2 H 8 4 9
19. p j e Maximum furthest neighbor d k i o j max d k i d k 7 If the user requests it a bootstrap procedure will be used by the program to test the stability of the junctions in the original dendrogram The stability of these junctions or join points is estimated by the percentage of times where the varieties joined by this junction in the original dendrogram are grouped together in the dendrograms calculated by each resample during the bootstrap procedure 15 100 rol r N d Where R is the stability of the junction c in the original dendrogram d N is the number of times where junction c is preserved among the trees produced in each resample and N y 15 the total number of resampling done in the bootstrap Note the calculations of stability of the junctions are considered only for dendrograms constructed using Rogers and Nei and Li distances D Installation of LCDMV and practice session To use LCDMV you must have a recent version of SAS later than version 6 10 running on a PC or Unix installed with the IML Interactive Matrix Language The complete LCDMV software package contains 1 A catalog of macros called Sasmacro Sc2 2 A catalog of devices called Devices Sc2 3 A permanent SAS file called Varstore Sd2 4 ASAS program called Lcdmv sas These four elements are required and must be stored in the same folder for example c logiciel Lcdmv When these elements have been copied to the folder of your
20. set Goffinet JSC Smith et Y Datt e 1997 Best linear unbiased estimator of the molecular genetic distance between inbred lines Advances in Biometrical Genetics Proceedings of the Tenth Meeting of EUCARPIA Section Biometrics in plant Breeding Posnan 14 16 May 1997 P Krajewski and Z Kaczmarek eds pp 105 110 Foulley JL et WG Hill 1999 A propos de l estimation de la pr cision d estimation de la distance g n tique XXXI Journ es de Statistiques 17 21 Mai 1999 Grenoble Session Biom trie et G nome Gh rardi Mangin Goffinet D Bonnet Huguet 1998 A method to measure genetic distance between allogamous populations of alfalfa Medicago sativa using RAPD markers Theor Appl Genet 96 406 412 Jaccard 1900 Contribution au probl me de l immigration post glaciaire de la flore alpine Bulletin de la Soci t Vaudoise des Sciences Naturelles 37 547 579 Jaccard P 1908 Nouvelles recherches sur la distribution florale Bulletin de la Soci t Vaudoise des Sciences Naturelles 44 223 270 Nei M 1973 Analysis of gene diversity in subdivided populations Proc Natl Acad Sci USA 70 3321 3323 Nei M 1978 Estimation of average heterozygosity and genetic distance from a small number of individuals Genetics 89 583 590 Nei M et WH Li 1979 Mathematical model for studying genetic variation in terms of restriction endonucleases Proc Natl Acad Sci USA 76 3269 3273 Rogers JS 1972 Meas
21. ta indicated by a period The first record should start on the second line and the first line is reserved for a description of the file origin and type of data written as a SAS comment that is beginning with the symbols and ending with the symbols Example 1 FREQUENCES file of 10 homogenous varieties 10 pure line OTUs characterized by 3 loci having 8 3 and 5 alleles each with a total of 16 variables Note that the frequencies of the alleles at each locus within an individual must sum to 1 Because these are pure lines only homozygous states 0 or 1 are recorded in this example Line reserved for comments 1000000000100001 0010000000100010 1000000001001000 00000101 00100 0000100001000010 1000000001001000 1000000010001000 0001000000100010 The frequencies are 0100000000100010 separated by one or 0000001001010000 The fourth sample has not been characterized for Locus 2 more tabs or spaces Locus 1 Locus 3 Locus 2 Example 2 FREQUENCES file for 3 heterogeneous varieties characterized by 10 AFLP markers numbers of individuals lines per population were defined in the CULTIVARS file showed in example 2 Line reserved for comments 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 I 0 1 1 0 1 0 1 1 1 1 0 1 1 0 101 0 1 1 I 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 0 D
22. ulated and represented as in C 2 1 homogenous varieties APCA on the correlation matrix of the frequencies of the markers with the individuals of each population analyzed separately individual data of the FREQUENCES file The missing data are estimated as in C 2 1 The Euclidian center of the cloud of points formed by the individuals in each population is calculated and represented in a graphic with together all of the individual points C 3 Estimation of the genetic distances and precision of the estimates 1 Homogenous variety locus allele markers Squared Modified Rogers 1972 distance estimator is used by the program A 1 Where L is the total number of loci characterizing the i and j varieties being compared 4 is the number of observed alleles at locus in the collection and P the frequency of allele of locus in the variety 7 In the case where i and j are pure lines the Squared Modified Rogers distance estimates the percentage of the loci for which the lines differ The sampling variance of the Squared Modified Rogers distance is estimated by D 1 Di Var D1 m Dillmann 1997 If the collection of OTUs is made up of simple hybrids or the varieties are incompletely fixed lines 1e residual heterozygosity for at least one locus in at least one line the approximate boundaries of the Squared Modified Rogers distance confidence intervals are estimated by assuming
23. ures of similarities and genetic distances Studies in genetics VII Univ Texas Publ 7213 145 153 Snijders TAB M Dormaar WH van Schuur C Dijkman Caes et G Driessen 1990 Distribution of some similarity coefficients for dyadic binary data in the case of associated attributes J Clas 7 5 31 21 il CIMMYT INTERNATIONAL MAIZE AND WHEAT IMPROVEMENT CENTER Apdo Postal 6 641 CP 06600 Mexico D F MEXICO www cinmytorg
24. zed and the estimated frequency of allele a at the locus in the variety sampled The variance of the Sanghvi distance estimate is calculated according to Foulley and Hill 1999 Var D 100 1 Ny Where e is the estimated Sanghvi distance for locus between the varieties i and j and N is the harmonic average of the number of individuals in the varieties i andj Nis calculated by TU X zx N WN 4 Heterogenous varieties band markers N These distances are calculated using Rogers 1972 calculation which estimates distance as Di SP ij EE al EA Gh rardi and al 1998 m 1 m 1 Where M is equal to the total number of markers bands Pi Pi is the estimated frequency of the marker m within the variety i 7 and N IV is the number of individuals in the variety i 7 Note this distance 1s estimated under the hypothesis that every marker band is a dominant allele of a biallelic locus This hypothesis is acceptable in the case of dominant marker types such as RAPD or AFLP Use of this distance estimator will be incorrect in the cases of codominant markers scored merely as present or absent because knowledge of the genetic relationships among alleles will be missing from the program In these cases the Squared Modified Rogers distance calculated here will overestimate the distance between varieties The confidence interval is estimated using the values observed
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