Consider a population of Heliconius butterflies - at a diploid and bi-allelic lo

Question

Consider a population of Heliconius butterflies - at a diploid and bi-allelic locus that governs wing pattern variation, there are two alleles A and B. Butterflies that are heterozygotes at this locus are twice as fit as either homozygotes. The population allele frequencies are P(A) = 0.8, P(B) = 0.2. The mutation rate of A alleles into B alleles is 10- 6 mutations per generation. Write a function in R and plot the frequency of the B allele in this population over 100 generations. What is the equilibrium frequency of the B allele?

Explanation / Answer

The comimetic Heliconius butterfly species pair, H. erato and H. melpomene, appear to use a conserved Mendelian switch locus to generate their matching red wing patterns.H. cydno and H. pachinus, species closely related to H. melpomene, use this same switch locus to generate their highly divergent red and brown color pattern elements. Using an F2 intercross between H. cydno and H. pachinus, first map the genomic positions of two novel red/brown wing pattern elements; the G locus, which controls the presence of red vs brown at the base of the ventral wings, and the Br locus, which controls the presence vs absence of a brown oval pattern on the ventral hind wing. The results reveal that the G locus is tightly linked to markers in the genomic interval that controls red wing pattern elements of H. erato and H. melpomene. Br is on the same linkage group but approximately 26 cM away. Next, we analyze fine-scale patterns of genetic differentiation and linkage disequilibrium throughout the G locus candidate interval in H. cydno, H. pachinus and H. melpomene, and find evidence for elevated differentiation between H. cydno and H. pachinus, but no localized signature of association. Overall, these results indicate that the G locus maps to the same interval as the locus controlling red patterning in H. melpomene and H. erato. This, in turn, suggests that the genes controlling red pattern elements may be homologous across Heliconius, supporting the hypothesis that Heliconius butterflies use a limited suite of conserved genetic switch loci to generate both convergent and divergent wing patterns.

Most speciation events probably occur gradually, without complete and immediate reproductive isolation, but the full extent of gene flow between diverging species has rarely been characterized on a genome-wide scale. Documenting the extent and timing of admixture between diverging species can clarify the role of geographic isolation in speciation. Here we use new methodology to quantify admixture at different stages of divergence in Heliconius butterflies, based on wholegenome sequences of 31 individuals. Comparisons between sympatric and allopatric populations of H. melpomene, H. cydno, and H. timareta revealed a genome-wide trend of increased shared variation in sympatry, indicative of pervasive interspecific gene flow. Up to 40% of 100-kb genomic windows clustered by geography rather than by species, demonstrating that a very substantial fraction of the genome has been shared between sympatric species. Analyses of genetic variation shared over different time intervals suggested that admixture between these species has continued since early in speciation. Alleles shared between species during recent time intervals displayed higher levels of linkage disequilibrium than those shared over longer time intervals, suggesting that this admixture took place at multiple points during divergence and is probably ongoing. The signal of admixture was significantly reduced around loci controlling divergent wing patterns, as well as throughout the Z chromosome, consistent with strong selection for Mu¨llerian mimicry and with known Z-linked hybrid incompatibility. Overall these results show that species divergence can occur in the face of persistent and genome-wide admixture over long periods of time.

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