9. Sex Linkage and Other Sex Differences. Extensions to the HWC model to allow for differences between the sexes

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1 9. Sex Linkage and Other Sex Dierences Extensions to the HWC odel to allow or dierences between the sexes. Unequal allele requences or eales & ales: I, in the current generation, the two sexes have dierent allele requencies (e.g., due to igrations aong populations o only ales, or o only eales), what happens in subsequent generations? call the allele requencies in the current generation and, respectively; assue locus, 2 alleles (A, A 2 ); the allele requencies or eales are and 2 ; the allele requencies or ales are and 2 ; Punnett square: A A 2 2 A 2 A genotype requencies o ospring: P = req(a A ): P 2 = req(a A 2 ): P 22 = req(a 2 A 2 ): 2 2 allele requencies o ospring: P = req(a ): ( ) ( ) ( ) ( ) ( ) P = + + [ ] = + + = + + = P = thus, allele requencies or eales and ales becoe equal (i.e., are averaged) in one generation; however, the population is not necessarily in HWC equilibriu ater one generation.

2 9. Sex linkage 2 Second generation achieves HWC genotype proportions. A A 2 P P 2 A P 2 p p p 2 A 2 P 2 p p 2 2 p 2 Exaple: A ish biologist collects a series o ale sunish ro one lake and an equal nuber o eale sunish ro a dierent lake, and discovers the ollowing genotype requencies at a particular autosoal locus: A A A A 2 A 2 A 2 Feales. Males She randoly puts together pairs o ales and eales into separate aquaria, lets the breed, and then puts all o their progeny into a single pool. Allele requencies o the parents: = 2 = = 2 = Expected genotype requencies o the progeny: P = = ()() = 4 P 2 = = ()() + ()() = 2 P 22 = 2 2 = ()() = 4 Expected allele requencies o the progeny: p = (4) + ½ (2) = p 2 = (4) + ½ (2) = Note that, under the HWC odel, the genotype requencies o the progeny (given their allele requencies) should be [ 5,, 5 ]. The irst-generation progeny are not in HWC equilibriu.

3 9. Sex linkage 3 One interesting result: i eales and ales dier in their allele requencies, total heterozygosity (genetic diversity) ust be less than i they have identical requencies; thereore genetic diversity increases ro the initial generation to the subsequent generation, and stabilizes under HWC equilibriu. general principle: any kind o population subdivision results in less genetic diversity than would be present with rando ating. Exaples: Het (H) and allele (,) requencies. H 2 3 =. =. = = H. Het (H) and allele (,) requencies 2 3 Het (H) and allele (,) requencies. H =. = 2 3

4 9. Sex linkage 4 2. Sex-linked traits Now let s add a coplication: a sex-linked trait; Assue the aalian sex-chroosoe syste, in which ales are the heterogaetic sex; assue locus, 2 alleles; then there are 3 eale genotypes but only 2 ale genotypes: Males AY ay Feales AA Aa aa i.e., eales are diploids but ales are haploids (actually, they re onoploids) at this locus. Returning to the irst case above, assue that eales and ales have dierent allele requencies: - in generation t, the allele requencies area: t t = req o the a allele in ales = requency o the a allele in eales We can now ask: what are the allele requencies in the current generation (t), based on the allele requencies in the previous generation (t )? - since eales are diploids, receiving one allele each ro both ather and other, the allele requency in the current generation is the ean o the eale and ale requencies o the previous generation; - since ales receive their single allele ro their others, the allele requency o ales in the current generation is the requency o eales in the previous generation; t = t ( ) = + t 2 t t - this is an iterative (recursive) odel: - beginning with initial allele requencies in generation t =, we can calculate the requencies in the next generation, t = ; - ro the requencies o generation t = we can calculate those o generation t = 2; - and so on.

5 9. Sex linkage 5 Assue, or exaple, the extree condition in which the a allele is ixed in ales ( = ) but absent in eales ( = ): Male Feale requency requency /2 2 /2 /4 3 /4 3/8 4 3/8 5/6 Allele requency. M Popl F Note, or this exaple, several things: ) Ater the initial generation, ale requencies lag eale requencies by one generation. 2) The eale requencies in each generation is the average (idpoint) o the ale and eale requencies o the preceding generation. 3) The ale and eale requencies do not becoe equal ater one generation, as beore, but rather gradually becoe ore equal over generations; - i.e., the odel asyptotically approaches equilibriu, but actually never attains it.

6 9. Sex linkage 6 4) The ale and eale requencies gradually approach the population ean requency (dotted line), which never changes its value; i.e., although ale and eale requencies change draatically ro generation to generation, the population as a whole is in equilibriu. This can be shown by considering that, during any generation, the population ean requency is the weighted average o the diploid eale requency and the onoploid ale requency: 2 q = + t 3 t 3 t expressing the population requency o the current generation in ters o the previous generation: 2 q = + t 3 t 3 t [ ] 2 ( t ) 3 2 ( t t ) = + + = + + = + = q 3 3 t 3 t 3 t 3 t t 2 3 t thus, the population requency at each generation is identical to that in the previous generation; i.e., the population as a whole is in genetic equilibriu, asking the changes in the separate sexes. general principle: the act that a population appears to be in genetic equilibriu does not ean that its coponents (whatever they ight be) are in genetic equilibriu. M Allele requency Popl Allele requency F Popl M F