User's guide
Contents
1. IF CONSTANT If evenly 0 Integer Number of dams per sire Endif Integer If evenly Number of dams per sire for all nt sires that are selected Endif IF CONSTANT Integer If evenly 0 Number of dams per sire in generation i To be repeated on time2 lines Endif Integer If evenly Number of dams per sire for all nt sires that are To be repeated on time2 lines selected in generation i Endif ENDIF ENDIF OffSire Integer Attribution of the number of offspring per sire Oifthe parameters are provided by the user 1 ifthis should be random uniformity constant2 offspPerSire 1 1 1 Integer Integer IF OFFSIRE Oifall sires have the same number of offspring lelse Oifthe number of offspring per sire is kept On the same line as uniformity constant over the generation lelse IF CONSTANT2 Integer If uniformity 0 Number of offspring per sire Endif 28 offspPerSire 1 nt 1 1 offspPerSire 1 1 1 If uniformity 1 Integer Number of offspring for each of the nt sires that are selected Endif ENDIF IF CONSTANT2 Integer If uniformity 0 Number of offspring per sire in generation 7 Endif If uniformity 1 To be repeated on time2 lines offspPerSire 1 nt 1 1 Integer Number of offspring for each of the nt sires that are To be repeated on time2 lines selected2. 0 if completely at random 1 if the number of each type of interacting pairs is defined by the user 2 if the type of interaction is defined by the user for each pair of QTL If typ_interac n_interacl Integer Number of pairs of QTL with a multiplicative interaction If typ_interac typ_inter 1 Integer Kind of interaction in the th pair of associated QTL Repeated as many times as there are pairs of associated QTL Endif ENDIF typ_map Integer Kind of genetic map 1 if the map is constructed at random 2 if all the positions of the markers and QTL are provided by the user 35 IF TYP_MAP 1 lgth chr Integer if the length is the same for all chromosomes 2 if the length of each chromosome is given by the user Iflgth chr 2 lg chrom Real Length of each chromosome in Morgans Length of all chromosomes on the same line Endif typ_density Integer 1 if there should be the same number of markers on each chromosome 2 else Iftyp_density 2 nloc k Integer Number of loci on chromosome k Repeated as many times as nchrom Endif evenly Integer 1 if the markers are evenly spaced on the chromosomes 2 else IF TYP_MAP max_loc Integer Maximum number of loci QTL markers on one chromosome nloc k Integer Number of loci on chromosome k Repeat pos_loc k i Real Position of locus 7 on chromosome k pides ed as typ_loc k 1 Integer Kind of locus on chromosome k 1 for a QTL 0 for a Same line as P tj ma
3. 2 F F parents according to the formula Ooi Fat 5 where Obay is the polygenic variance in the founder generation and F resp F is the inbreeding coefficient of the sire resp dam of the offspring i Residual effects are normally distributed with mean 0 and a variance constant over time QTL effects can be simulated as additive dominance and 2 locus epistasic effects In the case of random effects the dominance effects are computed as the additive effect times a random number drawn from a uniform distribution between 0 and 1 5 This enables having overdominance cases Two kinds of epistatic effects described at the molecular level were considered multiplicative effects the effects of the genotypes at both loci are multiplied Cordell 2002 The loci A and B have no direct additive effect but their effect on the phenotype is the product of the overall direct effect of each locus within an individual 12 compositional epistasis Phillips 2008 The QTL genotype at a locus A is only expressed if the individual has at least one allele with a positive effect at locus B Biologically this could correspond to the role of a suppressor known for instance for qualitative traits such as the blood group Different allelic effects can be wished They are described in the genomic information part of this manual Phenotypes are computed in the historical part as soon as selection is applied Otherwise they are compute
4. http jblevins org mirror amiller taus88 f90 L Ecuyer s 1996 random number generator Fortran version by Alan Miller vic cmis csiro au N B This version is compatible with Lahey s ELF90 http www ozemail com au milleraj Latest revision 30 March 1999 57
5. time2 Cross gene ped gene_typ gene_perf Integer IF TYP_POP 0 OR TYP_POP Number of generations Integer If nbpop Crossing scheme Oifthe population 2 should be introgressed in the 1 population or used or paternal line 1ifthe population 1 should be introgressed in the 2 population or used or paternal line Endif Integer Integer Integer Number of generations with pedigree Number of generations with genotypes Number of generations with phenotypes ENDIF Allon the same line These values cannot exceed time2 1 orig sel 1 2 0 1 IF TYP_POP Integer If nbpop 2 Type of population 0 for a Fn population 1 fora random mating population Endif Real Proportion of males and females of the last historical generation selected to produce the first generation of the pedigree known part 22 mode _sel 0 1 2 n 1 2 1 sel 1 2 1 1 mode _sel 1 1 2 accur g 1 2 DamSire Integer Integer Real Integer Type of selection for each sex in the 1 historical generation 0 for a phenotypic selection 1 fora selection with a given accuracy of the true breeding values TBV polygene additive QTL value 2 for a selection on BLUP estimated breeding values EBV Number of males and females in generation i 1 comprised between 1 and time2 Proportion of males and females selected in generation i to produce the next generation Type of sele
6. Character Name of the file containing the founder numbers for the population pop Character Name of the file containing the phenotypes and true polygenic values for the population pop Integer 0 if the numerator relationship matrix between the individuals in the population pop is unknown 1 else IF LECT_NRM Character Name of the file containing the values of the numerator relationship matrix for the population pop ENDIF ELSE IF STORE_COP 0 Character Name of the file containing the haplotypes for the population pop Character Name of the file containing the phenotypes and true polygenic values for the population pop Integer 0 if the numerator relationship matrix between the individuals in the population pop is unknown 1 else IF LECT NRM Character Name of the file containing the values of the numerator relationship matrix for the population pop ENDIF On the same line as haplo_file pop On the same line as haplo_file pop On the same line as haplo_file pop On the same line as haplo_file pop On the same line as haplo_file pop As many times as there are populations As many times as there are populations 38 Optional files If and which optional output files should be created must be provided in the file files These files provide information on different parameters during the evolution of the historical population The considered parameters are LD between all loci simld only between th
7. Number of generations studied Generation numbers Length of the bin in M to compute the statistics Endif f dl sum Character J Integer gener eval 8 1 3 Integer bin Real f ibd Character yifthe file containing the length of all founder segments should be created nelse J Integer gener eval 2 1 3 Integer Iff ibd y Number of generations studied Generation numbers Endif f ibdq Character y 1fthe file containing the length of the founder segments containing the QTL should be created nelse On the same line as j On the same line as j On the same line as j On the same line as j 40 j gener eval 3 1 3 f csg j gener eval 4 1 3 f hPIC J gener_eval 5 1 j f fqall J gener_eval 6 1 j f fqcop J gener eval 7 1 Integer Integer Iff ibdq y Number of generations studied Generation numbers On the same line as j Endif Character Integer Integer y 1fthe file containing the average inbreeding at each locus should be created nelse Iff csg y Number of generations studied Generation numbers On the same line as j Endif Character yifthe file containing the PIC values of the QTL should be created nelse Integer Integer Iff hPIC y Number of generations studied Generation numbers On the same line as j Endif Character y 1fthe file containing the allele frequencies at all loci should be created ne
8. Number of QTL model Integer Model for the QTL effects 1 if the effects are drawn from a gamma distribution 2 if the effects are provided by the user n_qtl_dom Integer Number of QTL with a dominance effect ncpl qtl interac Integer Number of pairs of QTL having an epistatic interaction Same line as n_qtl_dom store_cop Integer 1 if the founder origin of each allele should be recorded 2 else lect_map Integer 0 if a new genetic map should be created if a previously created genetic map should be read lect_gen Integer 0 if the population should be completely created Same line as ect_map 1 if the genotypes phenotypes and true polygenic values are available further_use Integer 0 if the numerator relationship matrix should not be Same line as ect_map printed at the end of the simulation 1 else IF LECT_MAP IF MODEL alpha Real Shape parameter of the gamma distribution beta Real Scale parameter of the gamma distribution Same line as alpha ENDIF 34 IF MODEL Ifn_qtl dom gt 0 eff 1 Real Additive effect genotypic value Falconer 1996 of QTL i Repeated as many times eff dom i Real Dominance effect genotypic value Falconer 1996 of Same line as eff i for QTL i as there are QTL QTL i Ifn qtl dom eff 1 Real Additive effect genotypic value Falconer 1996 of Repeated as many times as there are QTL QTLi Endif ENDIF IF NCPL_QTL_INTERAC gt 0 typ_interac Integer Type of interactions
9. occurs n2 i Integer Number of individuals in the 2 population after the change in the population size t2 1 Integer Number of generations between the 2 changes in the population size soud 1 Integer Type of change in the population size e Oe sane ne Tot DOE ind aS i tar eden nee e Repeat as many times as nb_bott g 2 fora progressive change sel i 2 1 2 Real Proportion of the population kept to be parents of the next generation during the i change in the population size nb infusion Integer Number of introgressions from external individuals in the currently simulated population 16 introg 1 time_introg 1 nb_infus 1 Integer integer IF NB_INFUSION gt 0 Number of individuals that should be used as parents for the introgression i Generations at which individuals should be introgressed Repeater as many fimes as ND AUSIN ENDIF ENDIF IF LECT_GEN all_ frq all fix fq_init i 1 nball ij j Integer Initial distribution of the allele frequencies 0 fora uniform distribution 1 ifall allele frequencies are provided by the user 2if the allele frequencies are drawn at random from a uniform distribution Integer IF ALL_FRQ Oifall loci are fixed lelse Real Ifall fix 1 Frequency of all alleles except the last one at locus i first for all Provide all allele frequencies for the 1 markers and then for the QTL in population j population and then if
10. parameter equals 0 2 and the expected distribution should be U shaped For the second population size 4Ne u 1 and the expected frequency should follow a uniform distribution The results for 50 replicates are presented in Figure 3 06 1 Ne 1000 0 6 1 Ne 200 Generation 1000 05 Generation 1000 05 Generation 2000 Generation 2000 04 04 e Generation 5000 Generation 5000 Frequency 03 L Frequency 0 3 ee lp II a E A a e Lo 0 4 0 0 0 0 0 0 0 0 0 e T T T T T T T T T T 02 04 0 6 08 1 0 02 04 0 6 08 1 0 Allele frequency interval Allele frequency interval Figure 3 Frequencies of the different allele frequency classes after 1000 2000 and 5000 generations for populations of effective size 200 and 1000 54 REFERENCES Boitard S Abdallah J de Rochambeau H Cierco Ayrolles C Mangin B 2006 Linkage disequilibrium interval mapping of quantitative trait loci BMC 7 54 Botstein D White R L Skolnick M Davis R W 1980 Construction of a genetic map in man using restriction fragment length polymorphisms Am J Hum Genet 32 314 331 Cordell H J 2002 Epistatis what it means what it doesn t mean and statistical methods to detect it in humans Human Molecular Genetics 11 2463 2468 Fan B Du Z Q Gorbach D M Rotschild M F 2010 Development and application of high density SNP arrays in genomic studies of domestic animal
11. populations and that the alleles have divergent effects the most favourable allele being fixed in the second population Genotyping errors and missing genotypes are allowed The real alleles are provided in the file genotype_err Example 4 A random mating population The initial population is composed of 200 individuals The population size remains constant over 500 generations The final population is composed over 8 generations by 500 males and 1000 females Only 50 males and 500 females are selected to reproduce The selected males have between 127 and 1 descendant The number of offspring per selected dam is chosen at random All individuals were selected on the basis of their phenotypic value The genetic map is composed of 1000 markers and 100 QTL All loci are initially fixed The maximum number of alleles per locus that can be achieved is 2 Neither dominance nor epistatic effects are assumed 50 Example 5 According to an existing pedigree The historical part consists of 1000 generations with 2000 individuals The simulated trait has an initial heritability of 0 5 which is for 30 due to a polygenic component The genetic map is composed by 100 markers located on 3 chromosomes having different length 0 15 0 1 and 0 05 M There are 10 QTL segregating 1 of them having a dominance effect and 1 pair of QTL showing epistatic interactions All QTL are biallelic and all loci are initially fixed The mutation rate for the biall
12. the 2 population selected to be crossed with the females of the 1 population Type of selection for each sex in the historical generation i 0 for a phenotypic selection 1 fora selection with a given accuracy of the TBV polygene additive QTL value 2 fora selection on BLUP EBV Real IF MAXVAL mode sel g Accuracy of the estimation of the TBV in the males 1 and females 2 in generation g ENDIF Integer Integer Integer Integer Number of generations where males of the od population should be mated to females of the 1 population Generation of the i th admixture Number of individuals resulting from the i th admixture For the attribution of the number of dams per sire Oifthe parameters are provided by the user 1 ifthe attribution should be random On the same line as n 1 2 1 To be repeated on time2 lines On the same line as n 1 2 1 If one of the sexes is selected with a given accuracy in generation g To be repeated on as many lines as there are generations selected with a given accuracy On the same line as genelntrog 1 To be repeated on nb_introg lines constant evenly Integer Integer IF DAMSIRE 0 if the number of dams per sire is kept constant over the generations lelse Oifall sires have the same number of dams lelse On the same line as evenly 27 damPerSire 1 1 1 damPerSire 1 nt 1 1 damPerSire 1 i 1 damPerSire 1 nt 1 1
13. the case arises for the second population Endif ENDIF ENDIF 17 direct_fin Integer 0 if an historical population should be simulated 1 else IF DIRECT_FIN 1 old_ped pop Integer 0 if no pedigree is available If two populations are simulated the 1 else values should be on the same line IF ANY OLD_PED fic_ped pop Character Name of the file where the pedigree for the population pop is If two populations are simulated the recorded values should be on the same line indPed pop Integer Number of individuals in the pedigree Iftwo populations are simulated the values should be on the same line On the same line as fic_ped pop last ind Integer Number of the last individual in the pedigree s ENDIF ENDIF 18 Recent population The recent population may be an admixture of the two previous populations or the continuation of the history of the first population when only one has been simulated previously LDSO should enable mimicking a wide range of situations going from natural populations to classical experimental ones Options typ_pop 0 1 or 2 correspond to simulated populations whereas typ_pop 3 and 4 enables following the familiar structure of a known population When two populations are simulated there are two kinds of situations the population are admixed only once Fn populations or random mating or the second population continue to evolve as a pure breed and there are repetit
14. values computed with the 1 as a function of the distance for the generations 100 200 500 and 1000 S 7 Generation 100 To toa ta _ wer e e Sooo te 24 e T T T T 0 00 0 05 0 10 0 15 Distance between loci M S 7 Generation 500 Y SS 54 3 Y e F 24 0 00 0 05 0 10 0 15 Distance between loci M Figure 2 LD 1 between all pairs of loci in generations 100 200 500 and 1000 0 6 05 04 03 0 2 0 0 06 05 04 03 0 1 Generation 200 T T 0 05 0 10 Distance between loci M 0 15 Generation 1000 Study of the mutation drift equilibrium 0 05 0 10 Distance between loci M 0 15 The files required to simulate the scenario with 200 individuals are in the directory EX8 Two effective population sizes were considered 200 or 1000 individuals The populations 53 evolved over 5 000 generations in total and the allele frequencies were recorded in generations 1 000 2000 and 5 000 The genetic map comprised 10 000 markers and 100 QTL All loci were fixed at the beginning of the simulation The mutation rate u of the loci all bi allelic and thus following a recurrent mutation model was set to 2 5 10 According to Wright 1931 the distribution of the allele frequencies at the mutation drift equilibrium depends on the value of 4Ne w In the case of the smallest population size this
15. IF OffSire Integer Attribution of the number of offspring per sire Oifthe parameters are provided by the user 1 ifthis should be random IF OFFSIRE uniformity Integer 0 ifall sires have the same number of offspring 1 else constant2 Integer 0 if the number of offspring per sire is kept On the same line as uniformity constant over the generation lelse 24 offspPerSire 1 1 1 IF CONSTANT2 Integer If uniformity 0 Number of offspring per sire Endif If uniformity offspPerSire 1 nt 1 1 Integer Number of offspring for each of the nt sires that are selected Endif ENDIF IF CONSTANT2 If uniformity offspPerSire 1 i 1 Integer Number of offspring per sire in generation i To be repeated on time2 lines Endif If uniformity 1 offspPerSire 1 nt 1 1 Integer Number of offspring for each of the nt sires that are To be repeated on time2 lines selected in generation i Endif ENDIF constant3 Integer 0ifthe number of offspring per dam is constant within a sire lelse ENDIF ENDIF IF TYP_POP ngpm Integer Number of maternal grand sires nt Integer Number of sires nf Integer Number of dams per sire selection 1 1 1 2 Real Proportion of males and females of the last historical generation selected to create the 1 generation of the grand daughter design 25 mode _sel 1 1 2 accur 1 1 2 Integer IF MINVAL SELECTION 1 1 lt 1 Type of select
16. SO has the possibility of reading information haplotypes phenotypes genetic map or even pedigrees and to simulate the evolution from this information on Mutation and genetic drift are classically considered in all simulation programs in the historical generations but not selection It seems however a reasonable hypothesis to think that selection may have been applied in livestock since domestication at least on some production reproduction and behavioural traits LDSO enables simulating phenotypic selection at any time of the population history In the historical population as well as in the recent generations the population size can be increased population expansion or reduced bottleneck in each generation In the section pedigree known population LDSO enables simulating natural and experimental livestock populations submitted to different evolutionary histories First three methods of evaluation of the breeding values are available for the recent generations in LDSO phenotypic evaluation BLUP or in accordance to a given accuracy defined by the user for each generation The method used to select the individuals can be varied over the generations LDSO accounts for the different population structures between species e g number of offspring per dam and may thus be adapted to the species one want to simulate Furthermore the experimental populations also differ the grand daughter design is classical in cattle or small rumina
17. User s guide Version 1 02 Last update December 05 2011 Disclaimer This guide describes the use and outcomes of LDSO software The authors accept no responsibility for the accuracy or inaccuracy of the results obtained with this software Please notify fytourn gwdg de upon the discovery of bugs Comments and suggestions are welcome The bibliographical reference for this software is Ytournel F 2008 Linkage disequilibrium and QTL fine mapping in a selected population PhD thesis Station de G n tique Quantitative et Appliqu e INRA SUMMARY INTRODUCTION EA 5 INFIEES O O 9 A ve csestyevaeacter ysasedexseaducenst teas ou eb aeecteons Soeustseaummeraees 9 Historical generations ii 9 Initial allele frequencies vit A as 9 A A A eatememedieeradee 10 Changes in O A ea cl dd 11 S 12 Simulation from previous data ooconnocionicanoni nncononc nac naccnnac na ccoo cona non ncdnn conc sona cono rcanend ss 13 TN A eeoa oiai eu eyelet es ental end ata Mats aa 19 Genetcmiormati ud 32 Optional TA REA 39 QUITE SA A Sa ede 42 A see scares e a ie Seuss a goes Ca A ISS 42 E 42 SAA A A a eae ew cea 42 SUT AD INGO Esa ias 42 SINCOD ec E ents Fae tas Nats lau ns aac E aS dna ae niall ae Sd ccc uns tases E aca 43 A sonia cds cues a a ye cancteas A A A A A 43 SP att E A E EE 43 hetero y TN 44 genotyp efine ar E E E a a a e e 44 O EN T tac ely 44 EXAMPLES 0 A A A a A as 48 Example 1 A grand daughter desir tices dan
18. al size 500 individuals are simulated over 100 generations The first population evolves without any change in its size and with a light selection pressure only in 48 the last 10 generations On the other hand the y population gets progressively to a size of 300 between the generations 3 and 82 and its size decreases even more drastically between the generations 83 and 100 by getting from 300 to 90 In generation 83 the males start to be selected with a low intensity Population 2 is introgressed in population 1 in generation 95 by producing 20 Fl products The final population is a F10 cross with the sires of the F1 being chosen in the historical second population and the dams being chosen in the historical first population All 10 generations consist of 200 individuals 100 females and 100 males with 10 of the sires and 80 of the dams being chosen to have offspring in the next generation The number of sires per dam and how many offspring a sire and thus a dam has are randomly chosen The 10 best percents of the sires are selected in the generations 1 and 2 the individuals in the last historical generation are unselected according to their phenotypes and afterwards on their breeding values with accuracies of 0 7 to create the 3 and 4 generation and 0 8 latter The females are selected from the 1 generation on with 80 of them being selectable They are selected until generation 4 included on their phenotype and latter on an estimated bre
19. bles simulating populations with additive dominance and epistatic effects between two loci Dominance and epistatic effects are restricted to QTL with only 2 alleles The kind of epistatic effects must be defined in the file general by means of the option typ inter which takes the value 1 for the multiplicative effects Cordell 2002 and 2 for the compositional epistasis Phillips 2008 To establish a mutation drift equilibrium the loci are allowed to mutate according to two models 32 the recurrent mutation model in which the transition probabilities from one allele to the other are equal This applies to bi allelic loci the stepwise mutational model Kimura and Ohta 1978 which applies to multi allelic loci such as microsatellites The transition probability from the current allele to the allele with one less repetition or one more repetition are assumed to be the same whereas the transition probability to any other allele is null Finally we supposed that the mutation probability at the QTL loci can be different from those at marker loci because for instance they correspond to coding regions Thus a further mutation rate is required for these loci 33 Table 3 Description of the input parameters in the file general Name Type Meaning Comment tot_length Real Total length of the genome nchrom Integer Number of chromosomes Same line as tot_length nmq Integer Number of markers nqtl Integer
20. cdackaveieaiss se taaasaeoacesadesdnased 48 Example 2 An F2 popula Othiscciey ti jsasein cur Ga ninii E E cleans 48 Example 3 AUB COPIA O 50 Example 4 A random mating population ii did 50 Example 5 According to an existing pedigree ccecccesscesscescecssecesecseeeeesceceeceeeseeeenaees 51 Example 6 Extending an existing pedigree with new families ooooonocnnccnncnoncnoconocononcnncnnnons 51 Example 7 Extending an existing pedigree with new individuals in the families 52 Example 8 Using previous dai tad 52 ED analysis a data it la 52 Study of the mutation drift equilibrium oooonnoninccnoncnoncconnnconncconocono nono nconnccono cono cono ccon nono ncnnns 53 REFERENCE Se E E E EAE A A EAE A 55 License for theta lt a taphannettaavuanas ee A a iia 57 INTRODUCTION The use of Linkage Disequilibrium LD greatly increased over the last decades It has become a classical tool for the detection of QTL by using fine mapping methods Meuwissen and Goddard 2000 Boitard et al 2006 or genome wide association studies Hayes et al 2009 Pausch et al 2011 LD is also the key point of the genomic selection Meuwissen et al 2001 Finally LD is also used for studying the population histories for instance to evaluate the evolution of the population sizes over the time Hayes et al 2003 or the effects of natural and artificial selection through the identification of selective sweeps Fan et al 2010 Simulations are necessa
21. ction for each sex in the historical generation i 0 for a phenotypic selection 1 fora selection with a given accuracy of the TBV polygene additive QTL value 2 fora selection on BLUP EBV Real IF MAXVAL mode sel g Accuracy of the estimation of the TBV in the males 1 and females 2 in generation g ENDIF Integer For the attribution of the number of dams per sire Oifthe parameters are provided by the user lif the attribution should be random On the same line as n 1 2 1 To be repeated on time2 lines If one of the sexes is selected with a given accuracy in generation g To be repeated on as many lines as there are generations selected with a given accuracy constant Integer IF DAMSIRE 0 if the number of dams per sire is kept constant over the generations lelse 23 evenly Integer 0ifall sires have the same number of dams On the same line as evenly lelse IF CONSTANT If evenly damPerSire 1 1 1 Integer Number of dams per sire Endif If evenly damPerSire 1 nt 1 1 Integer Number of dams per sire for all nt sires that are selected Endif IF CONSTANT 1 If evenly damPersSire 1 1 1 Integer Number of dams per sire in generation i To be repeated on time2 lines Endif If evenly 1 damPerSire 1 nt 1 1 Integer Number of dams per sire for all nt sires that are To be repeated on time lines selected in generation i Endif ENDIF END
22. d only in the final populations The computation of the inbreeding between individuals starts in the first generation even if no selection is applied at that moment The simulated populations can be submitted to selection by truncation The real number seized by the user between 0 and 1 corresponds to the proportion of the individuals having the best phenotypes in generation T that may become parents of the generation 7 When there is simultaneously a progressive change in the population size the number of potential parents is calculated with the population size at generation 7 Simulation from previous data Since the version 1 02 of LDSO it is possible to simulate the evolution historic and or only in the last generation of one or two population s for which some information is already known Three possibilities are available only the genetic map and the effects of the QTL are known ect_map 1 The whole population is then simulated conventionally This enables simulating several populations from the exact initial situation the genotypes phenotypes and polygenic values of the individuals are already known lect_gen 1 In combination to an already known map this option enables making a population diverge into several populations evolving independently This also enables 13 modelling the mixture of more than two populations if one of the populations is already an admixed population The genotypes phenotypes and poly
23. e QTL and all loci markers and QTL simldg or as a summary for bins of a user defined length simld_sum the allele frequencies at all loci simfgall the frequencies of the founder numbers at all loci simfqcop the average inbreeding at each locus derived form the founder numbers consang the length of the founder segments for all loci ibd or only the segments containing the QTL ibdgqtl the Polymorphism Information Content PIC Botstein et al 1980 haplo PIC For a description of the outputs see the part optional files in the section Outputs 39 Table 4 Description of the input parameters in the file files Name Type Meaning Comment max_gener_ eval Integer Maximum number of generations for which statistics should be provided outfiles Integer Oifno optional file should be On the same line as created max_gener_eval lelse IF OUTFILES 0 f dl Character y ifthe file containing the LD between all loci should be created nelse Iff dl y Integer Number of generations studied gener eval 1 1 3 Integer Generation numbers Endif f dlq Character yifthe file containing the LD between the QTL and all the loci should be created nelse J Integer gener eval 10 1 j Integer Iff dlq y Number of generations studied Generation numbers Endif y 1fthe file containing the summary of the LD for intervals bins should be created nelse Iff dl sum y
24. eding value with an accuracy of 0 5 The genetic map consists of 201 genetic markers and 5 QTL All loci are placed by the user The QTL have between 5 and 10 alleles in the first population and between 4 and 12 alleles in population 2 The allele frequencies are determined at random The outputs consist of the pedigree of the F population over the last 10 generations the molecular information alleles and founder origin for the last 3 generations the phenotypes of the last 9 generations the length of the founder segments containing the QTL in the last historical generation and the last generation of the recent history 49 the LD between the QTL and any other locus at the creation of the population in the last historical generation and in the last generation of the recent history the allele frequencies at all loci in the 50 and in the last generation of the historical part and in last generation of the recent history Example 3 A BC population The evolution of the historical populations is the same as in Example 2 The F2 population is also simulated as previously After this F2 generation 4 generations of back crossing are added with the male parents being chosen in the second population and the female ones in the admixed population The genetic map differs from that of the F2 population as 2 fixed QTL are simulated in each population with the option altern 2 implying that the 2 QTL fixed are the same in both
25. eger Minimum number of sires per dam Integer Maximum number of sires per dam Integer Minimum number of offspring per sire Integer Maximum number of offspring per sire Endif ENDIF IF PEDIG Integer 1 ifthe males are taken from the real population and the females from the simulated one 2ifthe females are taken from the real population and the males from the simulated one 3 ifall individuals are taken from the real pedigree On the same line as ntotped1 On the same line as nt_hs On the same line as nt_hs On the same line as ndmin_hs On the same line as nt_hf2 On the same line as nt_hf2 On the same line as ndmin_hf2 30 nsires datafile8 datafile9 datafile10 datafile 1 ntotped1 nbport nt_hs nfmin_hs nfmax_hs ndmin_hs ndmax_hs nt hf2 nfmin_hf2 nfmax_hf2 ndmin_hf2 ndmax_hf2 Integer String Number of sires Name of the file containing the genotypes of the real population String Name of the file containing the pedigree of the real population String Name of the file containing the phenotypes of the real population String Name of the file containing the polygenic breeding values of the real population Integer Number of animals in the real pedigree Integer 1 if paternal half sibs should be simulated 2 if maternal half sibs should be simulated If nbport Integer Number of sires Integer Minimum number of dams per sire Integer Maximum number of dams per sire Integer Minimum number o
26. elic loci was set to 10 LD was recorded in generations 100 200 300 400 500 600 700 800 900 and 1000 The results are presented in the section LD analysis in a data set The final population follows the pedigree provided in the file pedig It is composed of 1216 individuals 610 of them being founders and two animals having an unknown parent Example 6 Extending an existing pedigree with new families The historical population is composed of two populations evolving in total over 100 generations The first one is subjected to 3 changes in its size reducing it from 1000 to 68 individuals A bottleneck also happens in the second population reducing its size from 500 to 100 The first population receives recursive introgressions from individuals of the 2 population between the generations 15 and 24 A single QTL is assumed having only an additive effect and 5 alleles The genetic map is composed of 500 markers which positions are given by the user The allele frequencies are initially uniformly distributed In the recent part new populations are added to an existing pedigree The initial pedigree is stored in fic genea It contains 8000 individuals whose genotypes are provided in fic geno Their phenotypes and breeding values are respectively in fic perf and 51 fic _gind The extension is done by creating new paternal half sibs from 4 sires of the last historical generation having each 3 dams fo
27. erator Then for each historical generation the programme determines the parents of the next generation If selection applies the parents are drawn at random among the best individuals individuals with the best phenotypic value A different selection rate can be applied to the males and the females If no selection is applied all individuals can become parents Then the haplotypes of the chosen parents are transmitted to the new generation which completely replaces the parental one with possible recombinations and mutations For these generations LDSO can provide optional information about some indicators on the population such as allelic frequencies inbreeding coefficients or the LD in the population For the estimation of the inbreeding coefficients the founder origin of each locus is recorded and a new number is created each time a mutation occurs This enables also estimating the length of each founder segment for each chromosome of each individual After all historical generations have been simulated the programme reads the file popfin which provides information on the recent part of the simulation pedigree known generations structure of the population selection rates eventually number of generations etc The populations are then simulated according to the same rules as before selection transmission of the haplotypes but they now can have a given structure For instance one can decide to simulate a grand daughter populat
28. estock Genet Sel Evol 33 3 209 229 Hedrick P 1987 Gametic disequilibrium measures proceed with caution Genetics 117 331 341 Kimura M and Ohta T 1978 Stepwise mutation model and distribution of allelic frequencies in a finite population Proc Natl Acad Sci USA 75 6 2868 2872 55 Lewontin R C 1964 On measures of gametic disequilibrium Genetics 49 49 67 MacCluer J W VandeBerg J L Read B Ryder O A 1986 Pedigree analysis by computer simulation Zoo Biol 5 147 160 Meuwissen T H E Hayes B J Goddard M E 2001 Prediction of total genetic value using genome wide dense marker maps Genetics 157 1819 1829 Meuwissen T H E Goddard M E 2000 Fine mapping of quantitative trait loci using linkage disequilibria with closely linked marker loci Genetics 155 421 430 Phillips P C 2008 Epistasis the essential role of gene interactions in the structure and evolution of genetic systems Nature Reviews 9 855 867 Pausch H Flisikowski K Jung S Emmerling R Edel C G tz K U Fries R 2011 Genome Wide Association Study Identifies Two Major Loci Affecting Calving Ease and Growth Related Traits in Cattle Genetics 187 289 297 Yamazaki T 1977 The effects of overdominance on linkage in a multilocus system Genetics 86 227 236 56 License for the random generator The random number generator incorporated in LDSO is based on a code from L Ecuyer downloaded from
29. f offspring per dam Integer Maximum number of offspring per dam Endif If nbport 2 Integer Number of sires Integer Minimum number of sires per dam Integer Maximum number of sires per dam Integer Minimum number of offspring per sire Integer Maximum number of offspring per sire Endif ENDIF ENDIF On the same line as ntotped1 On the same line as nt_hs On the same line as nt_hs On the same line as ndmin_hs 31 Genetic information All information needed to create the general genetic map is provided in a file called general This map i e the location of the loci is common to both populations The number of a loci and QTL b QTL with dominance effects c pairs of QTL with epistatic effects has to be defined by the user LDSO allows the user to simulate several QTLs located on different chromosomal regions which can be unlinked Two situations are possible The user provides a completely defined map with the marker positions given in Morgans typ_map 2 The map should be random To enable keeping the same map for different replicates the randomness of the map and initial genotypes relies on the 1 seed provided in the file parameter In this case the user needs to specify if the markers should be equally or unequally spaced In any of the cases the map is then provided in the file map see output files The effects of the QTL are also defined by the parameters in this file LDSO ena
30. g to the favourable allele population size generation number 47 EXAMPLES The parameter files corresponding to the following examples are provided in the directory EXAMPLES of the zip file Example 1 A grand daughter design A population of an initial size 100 evolves over 100 generations with no change in the population size this happens because even if one bottleneck is stated the number of individuals remains constant Note that in such a case it is preferable to require a progressive change in the population size The male population is selected with a low intensity over the two first generations proportion selected 0 8 The trait has an heritability of 0 3 with relies on half on the QTL and on the second half on the polygene The genetic map is entirely provided by the user with 200 genetic markers and one QTL in position 61 All genetic markers are biallelic and the QTL initially has five alleles All alleles initially have the same frequency within a locus After these 100 generations a grand daughter design is simulated Fifty sires are mated to 100 dams each to provide thus 100 offspring per sire The dams are originating from 30 maternal grand sires The sires and dams are selected relatively to their breeding values estimated with accuracies of 0 9 and 0 5 respectively Ten and fifty percents of the sires and dams respectively can be selected as parents Example 2 An F2 population Two populations of initi
31. genic values should only be provided for the individuals still alive the pedigree is also known The simulation then directly goes to the pedigree known part of the simulation An example of such a simulation is provided in the example 9 14 Table 1 Description of the input parameters in the file pop1 Name Type Meaning Comment nbpop Integer Number of populations l or2 nb_bott Integer Number of changes in the number of individuals in the 1 Should at least be 1 population IF NBPOP nb_bott2 Integer Number of changes in the number of individuals in the 2 Should at least be 1 population On the same line as nb_bott ENDIF n1 0 Integer Number of founders of the 1 population t1 0 Integer Number of generations before the 1 change in the population size occurs All on the same line sel 0 1 1 2 Real Proportion of the population kept to be parents of the next generation before the 1 bottleneck occurs n1 1 Integer Number of individuals in the 1 population after the change in the population size t1 1 Integer Number of generations between the population changes i and 1 soud 1 i Integer Type of change in the population size All on the same line for botteleneck 7 1 fora sudden change 2 fora progressive change sel 1 1 1 2 Real Proportion of each sex kept to be parents of the next generation during the i change in the population size qtl_mute 1 nbpop Integer Number of initially fixed QTL in each populatio
32. i The genotypes at all marker loci are written in this file The alleles are coded as numbers simcop This file can only be written if the founder numbers are recorded Each line is composed the following way i j Mi Mij Mai Moai Mmmq nqthji with i the individual s number j the haplotype number for the individual 7 Mi the founder number at locus k on the ga haplotype of individual i The founder numbers at all loci are written in this file They are coded as numbers simcopNoQTL This file can only be written if the founder numbers are recorded Each line is composed the following way i j Mii Mii Moi Mai Mamgji with i the individual s number j the haplotype number for the individual i Mii the founder number at locus k on the j haplotype of individual i The founder numbers at all marker loci are written in this file They are coded as numbers simperf The phenotypes are printed in this file The lines give the following information Individual s number phenotype of the individual polygenic value of the individual 43 heterozygotes This file is only printed in the case of a grand daughter design It contains the number of sires that are heterozygous at the QTL loci The provided information is QTL number number of sires heterozygous at this QTL frequency of the allele of the QTL affecting the phenotype calculated only among the sires genotyp_err This file is only produced if genotyping err
33. in generation i Endif ENDIF constant3 Integer 0 ifthe number of offspring per dam is constant within a sire lelse ENDIF ENDIF IF TYP_POP 4 pedig Integer 1 to create new families 2 to extend existing families IF PEDIG lect Integer 1 if the males are taken from the real population and the females from the simulated one 2ifthe females are taken from the real population and the males from the simulated one 3 if all individuals are taken from the real pedigree 4ifall individuals are taken from the simulated pedigree 29 datafile8 datafile9 datafile10 datafile 1 ntotped1 nbport nt_hs nfmin_hs nfmax_hs ndmin_hs ndmax_hs nt hf2 nfmin_hf2 nfmax_hf2 ndmin_hf2 ndmax_hf2 lect String Name of the file containing the genotypes of the real population String Name of the file containing the pedigree of the real population String Name of the file containing the phenotypes of the real population String Name of the file containing the polygenic breeding valeus of the real population Integer Number of animals in the real pedigree Integer 1 if paternal half sibs should be simulated 2 if maternal half sibs should be simulated If nbport 1 Integer Number of sires Integer Minimum number of dams per sire Integer Maximum number of dams per sire Integer Minimum number of offspring per dam Integer Maximum number of offspring per dam Endif If nbport 2 Integer Number of dams Int
34. ion for each sex in the historical generation i 0 for a phenotypic selection 1 fora selection with a given accuracy of the TBV polygene additive QTL value 2 for a selection on BLUP EBV Real If maxval mode_sel 1 1 Accuracy of the estimation of the TBV in the males 1 and females 2 in generation g Endif ENDIF ENDIF If one of the sexes is selected with a given accuracy in generation g sel 1 4 0 1 mode _sel 0 1 4 Real Integer IF TYP_POP Proportion of males positions 1 and 3 and females positions 2 and 4 of the last historical generation in the two populations selected to produce the first generation of the pedigree known part Type of selection for each sex in each population in the 1 historical generation 0 for a phenotypic selection 1 fora selection with a given accuracy of the TBV polygene additive QTL 2 for a selection on BLUP EBV In this part the 1 population is defined as the population where admixture happens i e the 1 historical population if cross 0 or the 2 if cross 1 26 n 1 4 1 sel 1 5 1 1 mode _sel 1 1 2 accur g 1 2 nb_introg genelntrog 1 indIntrog genelntrog 1 DamSire Integer Real Integer Number of males and females in generation i i comprised between 1 and time2 Proportion of males and females selected in generation i to produce the next generation The 5 element is the proportion of males from
35. ion or any real population for which one has the pedigree During these generations in addition to all optional files possible in the historical part LDSO prints the phenotypes genotypes and pedigree of the simulated population INFILES Population information The populations are simulated in a forward process following the gene dropping method MacCluer et al 1986 One or two populations can be simulated The parameters to describe the populations and the historical generations have to be provided in a file called pop1 Both populations are thus independent for all of these parameters but they have the same genetic map information provided in the file general The randomness of the population creation and evolution relies on the 2 seed provided in the file parameter The information to simulate the recent generations pedigree known population should be contained in a file called popfin The random elements of this part rely on the 3 seed in the file param A particularity of LDSO compared to other publically available simulation programs is that it enables getting in a single run the genotypes with the alleles allelic state and optionally the founder origin of each locus For the latter at the beginning of the simulation each locus in the founders is given a number corresponding to the number of the founder individual it belongs to These numbers are independent of the allelic state Hi
36. ive admixtures of individuals of the second population into the first one repetitive introgression or BC populations These two situations correspond respectively to the options typ_pop 0 or typ_pop 2 For both of them the user must provide on how many generations the pedigree genotyping and founder numbers if this has been stated previously and phenotypes should be recorded The information of the last historical generation can also be included The user must strictly define how many males and females are in the population and which proportion of them is kept with the possibility of having a different selection intensity for the males in the second population when used for breeding with the females of the 1 or the 2 population if typ_pop 2 Concerning the family structure it can be completely user provided through the definition of the number of females per male and offspring per male or it may occur at random If only one population has been simulated there are two options Under typ_pop 0 the user has the possibility of having a random mating population with the same features as previously Under the option typ_pop 1 the family structure is a grand daughter design with the possibility of having dams related to each other by specifying the number of maternal 19 grand sires The new population can also be submitted to selection with a new selection rate defined as previously The recorded pedigree is composed of the grand parent
37. lse Integer Integer Iff fqall y Number of generations studied Generation numbers On the same line as j Endif Character y 1fthe file containing the frequencies of the founder numbers at all loci should be created nelse Integer Integer If f_fqcop y Number of generations studied Generation numbers On the same line as j Endif Endif 41 OUTFILES Standard outfiles simped This file provides the pedigree for the last generation which is printed as follows individual number sire number dam number generation still alive sex For the founders individuals appearing 1 in the pedigree in the case they have neither phenotypes nor molecular information the sire and dam numbers are coded as 0 The file is structured by population if typ_pop equals 0 or 2 and the population is written at the end of each line and by sire family if typ_pop equals 1 simhaplo Each line is composed the following way i j Mi Mai Maj Moai M amg nqtbji with i the individual s number j the haplotype number for the individual 7 Mi the allele at locus k on the j haplotype of individual i The genotypes at all loci are written in this file The alleles are coded as numbers simhaploNoQTL Each line is composed the following way i j Mii Mii Moi Mai Mamgji with i the individual s number j the haplotype number for the individual i 42 Mii the allele at locus k on the j haplotype of individual
38. n IF AT LEAST ONE QTL IS INITIALLY FIXED altern Integer Combination of the fixed QTL see initial allele frequency part 0 randomly chosen in 1 or 2 populations chosen at random in both populations with divergent effects 2 same loci in both populations with divergent effects 3 same loci in both populations with identical effects ENDIF Repeat as many times as nb_bott 15 IF TYP MK mut j Integer 1 if the marker is allowed to mutate Repeat as many times as nmq 0 else ENDIF IF TYP_MK nball j 1 Integer Number of alleles at each marker locus Repeat as many times as nmq mut j Integer 1 if the marker is allowed to mutate e Repeat as many times as nmq 0 else e On the same line as nball j 1 ENDIF nball nmq j 1 Integer Number of alleles at each QTL Repeat as many times as ngtl mut nmqtj Integer 1 if the QTL is allowed to mutate e Repeat as many times as nqil 0 else e On the same line as nball nmq j 1 h2 Real Heritability to be simulated On one line one value per population ratio polQTL Real Ratio between the polygenic variance and the additive variance On one line one value per population when the phenotypes are generated IF NBPOP n2 0 Integer Number of founders of the 2 population t2 0 Integer Number of generations before the 1 change in the population size EE EE E sel 0 2 1 2 Real Proportion of each sex kept to be parents of the next generation before the 1 bottleneck
39. n the initial population The rest of the haplotype is attributed at random for all other loci The haplotype composed of all the makers but not the QTL may not be unique while the whole haplotype including the QTL is Such a situation classically corresponds to a mutation in one of the individuals of a population Changes in population size As many changes as wished can be simulated Two different ways of changing the population size are possible It occurs on one generation and afterwards the population size remains constant It takes place over more than one generation The change is then linear over the generations During the last generation before the reduction or increase of the number of individuals the population size is Ne at the end it is Ns The change takes place over Ts generations leading to the equation at the generation t N t Ne Ns Ne t The two possibilities can be summarized by the following scheme 11 Ne individuals 1 generation ts generations SS Progressive change Sudden change Ns individuals Selection Phenotypes are simulated from the initial founding generation as the sum of the QTL additive effects eventual dominant and epistatic effects an infinitesimal additive polygenic effect and an environmental effect Polygenic Mendelian sampling effects are normally distributed with mean 0 and a variance corrected for each offspring i by the inbreeding coefficients of both
40. nts especially for mapping studies whereas crosses are preferentially used in pigs Finally many breeds have herdbooks where the pedigree is recorded over even more than 15 generations in some cases Simulating populations as close as possible to the real ones is of great interest The genetic map is also a key parameter Depending on the objective of a study one may need to simulate a whole genome or only a small part Several kinds of genetic maps can thus be simulated While genomic selection or genome wide scans require simulating complete genomes with a very large number of markers that can be placed randomly fine mapping methods are classically used on smaller regions where one may want to place the markers to mimic a concrete situation Both situations are possible with LDSO Generally in each generation the individuals are first subject to selection if s lt 1 Once the potential parents have been identified the actual ones are arbitrarily chosen and mated at random The principle of gene dropping MacCluer et al 1986 makes it possible to apply selection in each generation contrary to a coalescent process Each generation is created by transmitting the parental gametes to the offspring following the Mendelian rules A gamete is formed under the assumption of Haldane s mapping function a the number of recombinations is drawn from a Poisson distribution with parameter the length of the chromosome and b the crossing overs to f
41. ny marker pos_loc k i for the T pean times same i and k moco as nchrom ENDIF typ_mk Integer if all markers are SNP 2 else ELSE IF LECT_MAP 1 typ_mk Integer if all markers are SNP 2 else file map Character Name of the file where the map is stored 36 file _eff Character Name of the file where the additive and dominant effects are stored max_loc Integer Maximum number of loci QTL markers on one chromosome ENDIF tmutSNP Real Mutation rate of SNP tmutMST Real Mutation rate of microsatellites Same line as tmutSNP tmutQTL Real Mutation rate at the QTL loci Same line as tmutSNP deseq Integer Type of initial Linkage Disequilibrium 1 if the causal mutations should be unique 0 else typing err Integer 1 if genotyping errors should be assumed IF TYPING_ERR errSNP Real Error rate in the genotyping of bi allelic loci errMST Real Error rate in the genotyping of multi allelic loci Same line as errSNP ENDIF IF LECT_MAP 1 inter_mute pop Character For each population name of the file where the If two populations are simulated the two names interacting and initially fixed QTL are stored ENDIF should be on the same line 37 IF LECT_GEN haplo_file pop copy_file pop perf file pop lect_nrm pop app_file pop haplo_file pop perf file pop lect_nrm pop app_file pop IF STORE_COP 1 Character Name of the file containing the haplotypes for the population pop
42. ollowing structures The genotype file should have one line per individual The first element is the animal number followed by the complete first haplotype of the individual QTL included and then the whole second haplotype The pedigree file should also consist of one line per individual with its first element being the individual s number followed by the corresponding sire number and the dam number Finally the files containing the phenotypes and breeding values have the same 20 structure They should have two columns the first one showing the individual s numbers and the second one the phenotype or breeding value For the final populations corresponding to the types 0 to 2 it is possible to select the parents on a phenotypic base on their true breeding value computed as the sum of the polygenic value and the additive QTL effects corrected or not to have a given accuracy which may be different for both sexes or on BLUP estimated breeding values Moreover in the types 0 and 2 the mode of selection can be chosen independently for all generations 21 Table 2 Description of the input parameters in the file popfin Name Type Meaning Comment typ_pop Integer Type of final population to be simulated 0 for an F population or a population with random mating 1 fora grand daughter desing 2 fora BC population or repetitive introgressions 3 for areal pedigree 4 fora full or half sibs design
43. orm the gamete that will be transmitted to one descendant are then positioned at random on the chromosome i e assuming no interference Then mutation can occur Each locus marker or QTL can be allowed to mutate at any time of the simulation historical and recent generations Mutation can occur following a stepwise mutational model Kimura and Ohta 1978 or a recurrent mutation model to establish a mutation drift equilibrium in the historical generations The stepwise mutational model corresponds to microsatellite markers the DNA Polymerase adding or suppressing a repetition of the repeated sequence creating an allele different from the parental one The recurrent mutation model corresponds to the Single Nucleotide Polymorphisms SNP where only 2 alleles are coexisting and mutation makes one allele alter into the other Mutation is follows a binomial distribution at each locus and the haplotypes where mutation happens are drawn at random in the population A replicate starts by providing the simulation programme the description of the historical population file pop1 and the genetic map file general In the historical population file are specified among other the size of the population the selection rates in the population the number of generations etc The number of markers QTL the kind of map etc should be provided in the genetic map file A further file param is required to provide the seeds to the random number gen
44. ors are assumed Each line is composed the following way Locus number individual s number chromosome true allele This option is not available for the extension of the population size typ_pop 4 Optional files Two measures of the LD are computed and recorded in some of the following files the D Lewontin 1964 Hedrick 1987 and the y Yamazaki 1978 NB The files containing information relying on the copy numbers cannot be computed if the situation typ_pop 4 is used extension of existing populations with simulated individuals 44 Table 5 Description of the output of the optional files Name of the read variable Name of the output file Contains fdl simld two loci between which LD is computed D value y value population size generation number is locus 1 a QTL 1 if yes is locus 2 a QTL 1 if yes distance between the 2 loci 50 means that the 2 loci are on different chromosomes f_dlq simldq QTL and locus between which LD is computed the QTL can be either in the 1 or 2 place D value x value population size generation number distance between the 2 loci 50 means that the 2 loci are on different chromosomes f dl sum simld_sum Intra within one chromosome or Inter between chromosomes Number of the chromosome If intra then number of the bin if inter number of the second chromosome Measure of the LD D or x S
45. rm the real pedigree and 1 offspring per dam Example 7 Extending an existing pedigree with new individuals in the families The same historical population and genetic map were taken to extend the families of a population with a real pedigree Ten sires are taken for that purpose from the real pedigree and the females are issued from the historical population As previously the extension is done by creating new paternal half sibs from 4 sires of the last historical generation having each 3 dams form the real pedigree and 1 offspring per dam Example 8 Using previous data The files containing the haplotypes copy numbers and phenotypes consisted of the data from 200 individuals The pedigree was composed of 1 100 individuals from 5 generations The genetic map had 1037 markers and 15 QTL on one chromosome all QTL having dominance effects The population derived from this known population consisted in 5 generations of random admixture LD analysis in a data set The files required to simulate this dataset are provided where the same as those for the example 5 Three chromosomes were simulated with different lengths 0 15 0 1 and 0 05 M In total 110 loci were simulated with the same number of markers on each chromosome Initially all markers were fixed 52 The LD between all pairs of loci was recorded at generations 100 200 300 400 500 600 700 800 900 and 1000 Figure 2 represents the overall distribution of the LD
46. ry to evaluate the new methods that can be developed for any method using LD LD is created over the generations by different evolutionary forces as mutation genetic drift or selection It has been shown that the LD structure in small regions is the result of the history of the population a long time ago while the recent history has an impact on LD at longer distances Hayes et al 2003 It is thus necessary to subdivide the simulations into two parts called historical population a long time ago and pedigree known population recent generations Random mating is assumed all over the evolution of the population One or two populations can be simulated simultaneously and then joined at some points of the population history in the case of admixed populations or experimental crosses This particularly applies for populations that diverged a long time ago as it may be the case in pig where there seem to have been several different domestication centres Larson et al 2005 LDSO is intended for simulating livestock experimental populations which are mainly pure bred or one way crosses Following up on the pig example a classical experimental cross generally a F2 or a BC population results from the mating of a European population Large White or Landrace population with a Chinese one Meishan for instance However one may also wish to simulate populations diverging from a common initial one or 4 way crosses For that purpose LD
47. s Asian Australian Journal of Animal Science 23 7 833 847 Farnir F Grisart B Coppieters W Riquet J Berzi P Cambisano N Karim L Mni M Moisio S Simon P Wagenaar D Vilkki J Georges M 2002 Simultaneous mining of linkage and linkage disequilibrium to fine map quantitative trait loci in outbred half sib pedigrees revisiting the location of a quantitative trait locus with major effect on milk productionon bovine chromosome 14 Genetics 161 275 287 Larson G Dobney K Albarella U Fang M Matisoo Smith E Robins J Lowden S Finlayson H Brand T Willerslev E Rowley Conwy P Andersson L Cooper A 2005 Worldwide Phylogeography of Wild Boar Reveals Multiple Centers of Pig Domestication Science 307 1618 1621 L Ecuyer P 1996 Maximally equidistributed combined Tausworthe generators Math of Comput 65 203 213 available at http jblevins org mirror amiller taus88 f90 Hayes B J Bowman P J Chamberlain A J van Tassell K S C P Sonstegard T S Goddard M E 2009 A Validated Genome Wide Association Study to Breed Cattle Adapted to an Environment Altered by Climate Change PLoS ONE 4 8 e6676 Hayes B J Visscher P M McPartlan H C Goddard M E 2003 Novel Multilocus Measure of Linkage Disequilibrium to Estimate Past Effective Population Size Genome Research 13 635 643 Hayes B and Goddard M E 2001 The distribution of the effects of genes affecting quantitative traits in liv
48. s and the parents the recorded phenotypes being the parental ones The haplotypes and genotypes from the individuals of the 2 last generations or the number of heterozygous sires are also provided A known pedigree can be used to keep the structure as close as possible to a real one when using the option typ_pop 3 It must be stored in a file called pedig In this file the individuals should be listed with continuously increasing numbers the oldest animals having the lowest numbers Finally one can also make use of a real pedigree to determine the optimal experimental size typ_pop 4 There are two options simulate news families or add offspring to the current family The individuals that will be selected as parents could come from the animals in the simulated historical population and or from the real pedigree The total number of animals in the simulated population and in the pedigree must be provided Concerning the family structure the user can choose between paternal half sibs or maternal half sibs It is then possible to vary the number of dams and descendant per family for instance if you are simulating two families in a population you may want to have one family with 10 dams and 50 offspring by sire and the other one with 20 dams and 30 offspring by sire One can also have mixtures of full and half sib families if a dam has more than 1 offspring and the sire more than 1 dam The input files from the real pedigree must have the f
49. storical generations Initial allele frequencies Three different possibilities are offered The first one all frg 0 corresponds to the equifrequency for all alleles of a locus For the second one all_frg 1 the user should provide the frequencies of all alleles except the last one which is computed In the last case all_frq 2 the allele frequencies are drawn at random from a uniform distribution All these options can be supplanted by the combination of the options qtl_ mute and altern The table qt mute contains the number of fixed QTL at the beginning of the simulation in each population If this number is greater than 0 in any of the simulated populations then it is possible to decide which kind of situation should be considered In the case of a single simulated population the fixed QTL are chosen at random altern 0 The allele present at the beginning of the simulation is then a neutral or the deleterious one This situation can also be chosen when two populations are simulated When two populations are simulated e The fixed QTL can be different in both populations The fixed allele is chosen at random for each population altern 1 It may be any allele e The fixed QTL are monomorphic in both populations However the alleles are different alleles in both populations altern 2 the second population presents the favourable allele while the first population has either an intermediate or the deleterious allele This would be
50. suited for modelling the introgression of a gene in a population e The QTL can randomly be chosen to be fixed for the same allele in both populations altern 3 The allele present at the beginning is then an intermediate or the deleterious one When initially fixed QTL are assumed then the number of alleles initially provided for each of them is only used as a limit for the number of alleles the QTL may have Initial disequilibrium The populations may be created in different ways depending on the type of initial disequilibrium wished at least for the genetic markers For the QTL the situation will be influenced by the presence of fixed QTL or not Some fine mapping methods rely on the hypothesis of a unique allele or causal mutation at the QTL in the founder population e g 10 Farnir et al 2002 Boitard et al 2006 whereas other methods suppose that all alleles are initially equifrequent e g Meuwissen and Goddard 2000 No initial disequilibrium deseg 0 All alleles are present more than once in the population according to the initial frequencies wished The alleles are attributed at random to each individual at each locus The initial situation is therefore exactly the same for all the simulated populations from an allelic point of view but not for the generated haplotypes as alleles are associated at random Complete disequilibrium deseq 1 One of the alleles at the QTL position s is represented by only one copy i
51. um of the LD in the bin Sum of the squared LD in the bin Frequency of the LD values in classes 0 0 lt LD lt 0 1 0 1 lt LD lt 0 2 0 9 lt LD lt 1 LD 1 Generation f ibd ibd number of the individual haplotype number of the segment length of the segment in cM 45 J ibdq ibd_qtl number of the individual haplotype QTL number length of the segment in cM frequency of the QTL allele carried by the individual at the current QTL f_csg consang locus number average inbreeding at this locus variance of the inbreeding for this locus population size generation F hPIC haplo PIC population size generation locus number number of haplotypes in the population haplotypes defined without considering the QTL loci proportion of remaining haplotypes relatively to the initial number of haplotypes defined without considering the QTL loci number of haplotypes in the population haplotypes defined considering the QTL loci proportion of remaining haplotypes relatively to the initial number of haplotypes defined considering the QTL loci indicator 1 if the locus is a QTL PIC of the locus f faall simfqall locus number allele allele frequency population size generation number 46 Ffacop simfqcop locus number founder number number of founder numbers remaining at the current lous founder number frequency if the locus is a QTL number of copies correspondin
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