What limits the efficiency of natural selection? Slide 1 of 10 Nick Barton 2 Simons 2014 II.nb Complex genomes that code for complex organisms have evolved 9 8 Slide 2 of 10 Human genome: 3 µ 10 bases, > 10 maintained by selection Particular changes have happened quickly: - insecticide resistance in Drosophila (Karasov et al, 2010) - rapid morphological change (Gingerich, 1983) Is the rate of evolution limited by mutation, selection, pop’ln size…? Simons 2014 II.nb 3 Population genetics: Slide 3 of 10 - genotype X!, genotype frequency g@XD, allele frequency p = E@XD Quantitative genetics: - traits Z, mean & covariance z, v In sexual populations, the infinitesimal model is accurate: - offspring are normally distributed around the mid-parent - covariance within families independent of selection - increased by mutation, decreased by inbreeding n Consistent with additive model: Z = ⁄i=1 ai Xi, n >> 1 4 Simons 2014 II.nb Selection experiments fit the predicted response after 50 generations Slide 4 of 10 Weber & Diggins, 1990 The infinitesimal model is locally accurate, even though Z = f@XD is complex Simons 2014 II.nb 5 What limits the efficiency of selection? Slide 5 of 10 “Genetic load”: loss of fitness relative to some ideal: 1 - W Wmax This leads to simple constraints: mutation load ~ U (Haldane, 1937) substitution load ~ logB 1 F (Haldane, 1957; Kimura, 1961) p0 1 drift load ~ 4 N per allele or trait (Kimura & Ohta,1970; Lande, 1976) However, these constraints become weaker when genes interact 6 Simons 2014 II.nb Mutation load Slide 6 of 10 With asexual reproduction, mean fitness is reduced by the chance of producing offspring with no deleterious mutations: W ~ ‰-U Wmax 8 In humans, m ~ 10 per base per generation fl U ~ 60 per diploid genome. Udel ~ 2 per diploid genome per generation (??) ¶ HW L U = log In a sexual population, the # of bad mutations ~ s , where s ¶k The mutation load is greatly reduced by negative epistasis The variance in fitness is U s, which equals the rate of decline in fitness due to mutation. Simons 2014 II.nb 7 Substitution load W * W * * W * Slide 7 of 10 1 2 Wt pt t i = _!! _!! _!! \ B F = B _!! F pt p0 … log p ⁄i=1 log = “load” W 1 W 2 W t 0 W i This is true for asexuals, and with sex & multiplicative fitnesses 1 With sex, and selecting the best q of the population, all rare variants will increase by q per generation. Substitutions at rate L require variance in fitness ~Ls For given fitness variance, weak selection, N s~1, maximises L 8 Simons 2014 II.nb Drift load Slide 8 of 10 Wright’s (1937) distribution of allele frequencies: n 2 N 4 Nmi-1 4 Nni-1 P@pD ~ W ‰ pi qi i=1 assuming free recombination, allowing arbitrary interactions fl distribution of trait means and covariance: 2 N P@z, vD ~ W@z, vD y0@z, vD Focus on the mean of a single trait, around an optimum at z = 0: A- S 2E fl 2 N @- 2D W ~ exp 2 z W ~ exp N Sz fl 1 fl EA S z2E 1 var[z] ~ 2 N S 2 ~ 4 N variance in fitness is 1 fl # of traits < 8 N2 8 N2 Simons 2014 II.nb 9 Fitness flux limits accumulation of information Slide 9 of 10 Mustonen and Lassig (2010), Jarzynski (1997) Xexp@-2 N F + DHD\ = 1 T P dpi H ª logB F F ª ‡ ‚si „ t P0 0 i dt 2 N XF \ ¥ < DH > T T 2 ‡ ‚si Hsi pi qi +mut' n +driftL „t § ‡ ‚Isi pi qiM „t 0 i 0 i Total variance in fitness bounds the increase in information? T 2 N ‡ var HWL „ t ¥ < DH > 0 10 Simons 2014 II.nb Summary Slide 10 of 10 Quantitative genetics describes trait evolution: - the infinitesimal model is remarkably accurate The genetic load appears to constrain genome size, rate of substitution, # of functional traits … If genes interact in the right way, constraints are relaxed: - variance in fitness limits rate of substitution, # of traits Why should genes interact in this way?.