Figure 1.

Invasion probability of A₁ as a function of the recombination rate for a monomorphic continent. (A and B) Weighted average invasion probabilitiy $\overline{\pi }$ across the two genetic backgrounds B₁ and B₂ (Equations 2 and 4). For comparison, horizontal dashed lines give 10% of Haldane’s (1927) approximation 2a, valid for m = 0 and r = 0.5. (B) The optimal recombination rate r_opt, defined as the recombination rate at which $\overline{\pi }$ is maximized (red arrow), is nonzero. (C) Same as in B, but in addition to the weighted average, the invasion probabilities of A₁ conditional on initial occurrence on the B₁ or B₂ background are shown in blue or red, respectively. Note the difference in the scale of the vertical axis between B and C. In A–C, curves show exact numerical solutions to the branching process. Dots represent the point estimates across 10⁶ simulations under the branching-process assumptions (see Methods). Error bars span twice the standard error on each side of the point estimates, but are too short to be visible.