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# Class Note for Biol 519 at WSU 04

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Date Created: 02/06/15

Coarse Notes Population Genetics NONRANDOM MATING amp GENETIC DRIFT NONRANDOM MATINGINBREEDING READING Hedrick pp 479 482 237 279 OWill distinguish two types of nonrandom mating 1 Assortative mating mating between individuals with similar phenotypes or among individuals that occur in a particular location 2 Inbreeding mating between related individuals Both types of nonrandom mating may have similar consequences since individuals with similar phenotypes often have similar genotypes It is often difficult to separate cause from effect Eg individuals with similar phenotypes may mate because a phenotypic assortative mating occurs b mating with relatives is preferred c matings are primarily based on proximity I Population subdivision The Wahlund Effect It turns out that population subdivision per 38 can effect the distribution of genotypes in the entire population Consider a locus with 2 alleles A and a and a collection of isolated subpopulations numbered 1 2 3 Let the frequencies of A and a in subpopulation i be pi and q Assuming random mating within each isolated subpopulation FreqAA in subpopulation i pi2 FreqAa in subpopulation i ZpIqi Freqaa in subpopulation i q Let 7 Av g pi average freq of A across all subpopulations Likewise let a Avgqi 1 1 7 What is the average frequency of each genotype over all the subpopulations II l Coarse Notes Population Genetics 0 Consider AA homozygotes first From Fun Facts VarX EX2 EX2 so EX2 VarX So AYgp2 17 172 Varp Similarly for ad homozygotes Avgqi2 q2 2 Varq C72 Varp since Varq Var1 p Varp Finally for Ad heterozygotes AYg2pqi1 p2 q2 1 172 C72 2Varp 217C 2Varp A Thought Experiment 0 Suppose genotypes were randomly sampled from a population whose substructure was unknown The frequencies of A and a in sample would be 1 7 and q With random mating would then expect to find genotypes in proportions 2 2 AAAaaa 2p 2pqq But the genotype frequencies observed would be AA Aa ad 2 I 2 pq 1 72 Varp Z g 2Varp z Varp Ie would find an excess of homozygotes and a deficit of heterozygotes compared to expectations Why Simply because of population subdivision and in particular variance in allele frequencies across subpopulations Given across subpopulations differences in allele frequencies the apparent excess in homozygotes and deficit of heterozygotes from what is expected were the entire population to mate at random defines what is called the Wahlund E 39ect The Wahlund effect is a common cause of non conformity to Hardy Weinberg expectations in population samples I INBREEDING Will now consider the genetic consequences of mating between relatives inbreeding e g 11 2 Coarse Notes Population Genetics In 192039s Sewall Wright invented an ingenious B 9 D approach to tracking genotypes through pedigrees based on the probability that allele copies are identical by descent G 0 Will follow the French geneticist Malecot39s re working of Wright39s method here Q Q G 0 Identity by descent IBD Two alleles are identical by descent if 1 both are descended from the same allele in a common ancestor or 2 one allele is descended from the other 0 Will mean IBD relative to a specific base population whose alleles are deemed to be not IBD Definition The inbreeding coefficient f 1 of an individual J is the probability that its two gene copies at a locus are identical by descent Once f I is known it s not hard to find the probabilities that J is AA Act or ad Consider a randomly chosen individual 0 With probability f 1 both gene copies in that individual are IBD Then both will be A if the allele they were copied from in the base population were A 0 But A occurs with frequency p in the base population so the probability of being an AA given both genes are IBD is p gt the probability of getting two A alleles that are IBD is f I p Likewise the probability of being ad with both genes are IBD is f I 1 p 0 With probability 1 f 1 the two genes in an individual will not be IBD Must have descended from different allele copies in the base population Assuming the copies are made independently then with probability p X p p2 the copied alleles are both A genotype AA etc 0 Putting this all together have 13 1 fp2 12p 13 1 f2p1 p 11 3 Coarse Notes Population Genetics 12m1 1p2 f11 p Great So now only need to determine f 1 Thanks to Wright this is very easy to do Eg Let39s find f in the pedigree above 0 c C Need only concentrate on the central part of the pedigree E G f Probe E c X Probc E c X Probc E g 639 39 g 12 x 12 x 12 18 So the expected genotype frequencies for this pedigree are R 782 1812 BM 782p1 17 PM 781 p2 181 p ASIDE What is the average frequency of A among individuals with inbreeding coefficient f1 FreqA PAA 1139PA4 1 f1p2 f1p 391 f12p1 17 1f1p2 p p2f1p1f1p p 17 Inbreeding does not affect allele frequencies on average but does affect the probabilities that 2 A s or 2 as co occur in an individual Computing Inbreeding Coefficients in general Say we want to find f in the pedigree at right Rupcs 1 Enumerate each loop 2 Each loop must a go through each individual no more than once b only change from up to down once II 4 Coarse Notes Population Genetics 3 Multiply by Z for each passage through an individual D If the passage through an individual involves a change of direction updown l multiply l J lt9 by 1 f2 instead of 12 where f is the inbreeding coefficient for that individual 4 Add the probabilities of each loop 0 For the above example f H K0 30 Km xv H Kn O lt N Kt KN ys4 K 732 1 84X54 Some forbidden loops IGECBDEGI goes through G twice IJDBCEGIalready counted IGECBDEJI loop ECBDE already accounted for in fE Evolutionary Application Kin Selection 0 Probability that M individuals share an allele descended from a common ancestor is called the kinship coef cient or coefficient of consanguinity Kinship coefficient between individuals A and B is denoted F AB 0 What is Fa in the last example Clearly it is the inbreeding coefficient of their offspring I f 732 0 The connection between f and F The kinship coefficient of two individuals is equal to the inbreeding coefficient of their perhaps hypothetical offspring 11 5 Coarse Notes Population Genetics 0 e g Fmotherydaughter 14 assuming unrelated non inbred parents Kinship coefficients useful in studying evolution of social especially quotaltruisticquot traits In 1964 W D Hamilton proposed a rule of thumb to determine whether a rare allele will be favored by selection 0 A rare mutation which affects the fitness of its carrier and others will spread if br gt c where b quotbenefitquot 2 increase in fitness to recipients of action 0 2 quotcostquot 2 loss in fitness to actor r 2 quotdegree of relatednessquot can use above rules to find r r 2F Another view of f I 0 f I is the proportion by which heterozygosity is reduced relative to a random mating group with the same allele frequencies If f I 0 the population is in Hardy Weinberg proportions If f I 1 all individuals are homozygous In general Het 1 fHet0 where Het0 2p1 p 217g 0 Consider e g the Wahlund effect Overall frequencies of A and a are 17 and a If individuals from all subpopulations mate at random expect to find 21 a heterozygotes Would actually observe 217 2Varp heterozygotes Thus in this case 21 2Varp1 f217 In order for this to be true f Var 17 Suggested exercise show this Note f 0 even though there is no deficit of heterozygotes within subpopulations 99 I and no obvious inbreeding II 6

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