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CLASSICAL MODEL OF SELECTION AT A SINGLE LOCUS THE MODEL: Same conditions as Hardy-Weinberg, but with selection included. Genetic system: 1) diploid population 2) sexual reproduction 3) random mating Selection 1) identical selection in both sexes 2) viability selection 3) constant selection on each genotype Other factors 1) non-overlapping generations 2) infinite population size 3) no migration (gene flow) 4) no mutation Single locus with 2 alleles, A1 and A2, in frequencies p and q. RELATIVE FITNESS GENOTYPES A1 A1 A1 A2 A2 A2 FREQUENCY p2 2pq q2 FITNESS w11 w12 w22 Fitnesses are denoted as relative fitnesses: highest fitness is standardized to 1, others are denoted as a fraction less than 1 (see Table 3.5) Example: deleterious recessive GENOTYPES A1 A1 A1 A2, A2 A2 FITNESS 1 1 1-s Average fitness in the population: w _ = p2w11 + 2pqw12 + q2w22 CHANGE IN GENE FREQUENCIES Remember that the frequencies of the alleles in the population are (relative to genotype frequencies): p = P + 2H = p2 + pq, q = Q + 2H = q2 + pq To get frequencies of the alleles in the next generation, multiply each genotype frequen cy by its relative fitness and divide by the mean fitness: p' = [p2w11 + pqw12]/w _ similarly: q' = [q2w22 + pqw12]/w _ We can denote the change in gene frequency in terms of the change in gene frequency, w - p = [p2w11 + pqw12]/_ ∆p = p' - p = [p2w11 + pqw12]/_ w - p_ w/_ w (multiplied out) = {[p2w11 + pqw12] - p[p2w11 + 2pqw12 + q2w22]}/_ w = [p2w11 + pqw12 - p3w11 - 2p2qw12 - pq2w22]/_ w (gather "w" terms) = [p2w11(1 - p) + pqw12(1 - 2p) - pq2w22]/_ w (sub. q = 1 - p) = [p2qw11 + pqw12(q - p) - pq2w22]/_ w (factor out pq) = pq[pw 11 - pw12 + qw12 - qw22]/_ w THE BOTTOM LINE: ∆p = p' - p _ = pq[p(w11 - w12) + q( w12 - w22)]/w Note that ∆p is proportional to the gene frequencies, but also to the relative fitnesses of the genotypes. SHORTCUT Deleterious recessive alleles represent a special case, if we substitute w11, w12 = 1, w22 = 1 - s into the equations above: Mean fitness (_ w) = p2w11 + 2pqw12 + q2w22 = p2 + 2pq + q2 - sq2 = 1 - sq2 ∆p = p' - p = pq[p(w 11 - w12) + q(w12 - w22)]/_ w 2 = pq[q(1 - (1 - s))]/(1 - sq ) = spq2/(1 - sq2)