Figure 4.
Binary-splitting reproductive strategies are uniquely optimal under the effects of size with a single perturbation and threshold. (a) Optimal reproductive strategies under the effects of single advantageous size perturbations and thresholds. (b) Optimal reproductive strategies under the effects of single adverse size perturbations and thresholds. In (a,b), the perturbation only occurs at a single size at a time. The dark brown lines indicate the boundaries of optimal reproductive strategies observed under a single perturbation, threshold effects and both. Note that 7 + 1 is uniquely optimal under either a single perturbation or threshold effects. Reproductive strategies are multiple-optimal under the grey area. The white lines indicate the parameter space where we investigate the population growth rate in (c,d). (c,d) The population growth rates of reproductive strategies 1 + 3 and 3 + 5 under the effects of a size perturbation at n = 3, threshold and both, respectively. In (a,c), χn = 0.4. In (b,d), χn = 1.5. (e) The reproductive strategies that have been investigated for k ≤ 7 and N ≤ 8. The reproductive strategies in blue are uniquely optimal under the size effect of a single perturbation. The reproductive strategies in red are uniquely optimal under the threshold effects. The reproductive strategies in purple are newly emerged uniquely optimal strategies under both a single perturbation and the threshold effect. Parameters for all panels: w = 0.1, b = 10, c = 1, m = 0.01.