Figure 5. The long-term (fixed) allelic contribution to phenotypic adaptation.

We show the relative contribution of alleles as a function of effect size squared, based on the linear approximations and on simulations with the two shift sizes specified in the caption. (A) The Lande case. The theoretical prediction is described by the function $f(a)$ (Equations 13 and 20), and simulation results were generated using the single allele simulation, as detailed in Simulations and resources; error bars are not visible because they are smaller than the points. Our prediction for the long-term contribution (corresponding to $f(a)$ ) is always below the prediction for the rapid phase (corresponding to $v(a)$ ). The difference becomes substantial for $a^2⪆4$ , implying that the linear Lande approximation underestimates the fixed contribution when large effect alleles contribute markedly to the genetic variance at equilibrium. (B) The non-Lande case. Here, we assume an exponential distribution of effect sizes squared with $E(a^2)=16$ , which yields an amplification factor of $1+C\approx 2.2$ (Equation 22). The theoretical prediction for the joint contribution of standing variation and new mutations is described by the function ${\displaystyle (1+C)\cdot f(a)\mathrm{\Lambda }/V_A(0)}$ (Equation 28). Simulation results were generated using the all alleles simulation for the non-Lande case (see section on Simulations and resources). Specifically, we calculated the relative contribution of alleles in each effect size bin (between the gray gridlines), by dividing the contribution of all fixations in the bin by the mutation rate per generation corresponding to that bin. In both Lande and non-Lande cases, long-term stabilizing selection diminishes the contribution of alleles with large effects (red arrows). In the non-Lande case, long-term, weak directional selection greatly amplifies the contribution of alleles with small and moderate effects (blue arrow). See Appendix 3—figures 12–19 for other attributes of the long-term allelic response and for the nonlinear approximations.