Figure 1.

Population outcomes with zero migration. (a) Scaled critical selection threshold Ks_c, above which populations are metastable, as a function of the scaled mutation target 2LU = 2L(u/r₀) for different values of Ku (different colours) for nearly recessive (h = 0.02; solid lines) and additive (h = 0.5; dashed lines) alleles. A non-zero equilibrium population size $N_{\ast }=1-\mathbb{E}[R_g|N_{\ast }]$ exists for Ks > Ks_c but not for Ks < Ks_c. This selection threshold is calculated using equation (2.3) by neglecting demographic stochasticity, and thus strictly provides a criterion for stable populations in the limit ζ = r₀ K → ∞. (b) The scaled extinction half-time T_1/2 = r₀ t_1/2 (see text for definition) as a function of 2LU for various K (different colours) for nearly recessive (h = 0.02; main plot) and additive alleles (inset). (c) The average scaled population size N = n/K of metastable populations versus 2LU for various K (different colours) along with the semi-deterministic prediction $N_{\ast }=1-\mathbb{E}[R_g|N_{\ast }]$ (dashed black line) for nearly recessive (h = 0.02; main plot) and additive alleles (inset). In both (b) and (c), the carrying capacity is increased while proportionately decreasing s, u and increasing L, such that Ks = 25, Ku = 0.01 and 2LU = 2L(u/r₀) remain unchanged; increasing K thus has the sole effect of weakening demographic stochasticity. Extinction times and the average population sizes in the metastable state are computed from allele frequency simulations (under LE and IE) of 1000 replicates with r₀ = 0.1.