Figure 1.

One-dimensional simulations. Differential movement patterns between sexes enhance the probability of mating encounters over a certain lifespan t_max (n_m = n_f = 1; d = 10; 10 000 000 replicates). Because males and females are completely interchangeable in our simulations, we show only the results for the combinations where a Lévy exponent μ_m ≥ μ_f. (a) Effect of combination of movement patterns on the probabilities of encounters over different lifespans. (b) Probabilities of encounter as derived analytically; these results were qualitatively consistent with those of our simulations. SW and BW approximated a Lévy walker with μ = 1.1 and μ = 3.0, respectively. (c) Most efficient combinations of movement patterns. The solid line indicates μ_m and dashed line μ_f. Circles in each square indicate the most efficient combinations of μ_f and μ_m. Darkness of squares represents the degree of difference between sexes. (d) Rates of encounter under different combinations of movement patterns across lifespans of several lengths.