Dispersal asymmetries and deleterious mutations influence metapopulation persistence and range dynamics

Abstract

Asymmetric dispersal within and between populations is more often the norm than the exception. For example, prevailing winds and currents can result in directional dispersal of many passively dispersed species and inter-individual variability in physical condition can generate asymmetric dispersal rates between individuals and populations. Despite this, very little theory incorporates asymmetric dispersal into spatial ecological or genetic models. We therefore present three illustrative scenarios incorporating asymmetric dispersal into spatially and genetically explicit individual based models. In the first, asymmetric dispersal due to environmental forces, such as wind or currents, interacts with the accumulation of mutation load across an environmental gradient, with consequences for range dynamics. In the second, asymmetric dispersal rates arise as individuals disperse according to their physical condition, such that individuals carrying more mutation load disperse less. We demonstrate that this condition-dependent asymmetric dispersal substantially reduces metapopulation persistence. Finally, we turn to the potential implications of condition-dependent dispersal for range expansions. Simulations demonstrate that asymmetric dispersal of individuals according to their load status can substantially slow the rate of range expansion. Taken together, these results highlight that overlooking asymmetric dispersal can result in major biases of our estimates of species persistence and range expansion dynamics.

Appendix

See Figs. 7 and 8.

Fig. 7

Scenario 2. a Mean genetic survival (w) and b mean population size through time of a metapopulation inhabiting a homogenous landscape. The different coloured lines compare the effects of no mutation load, mutation load (m _g  = 0.5) that doesn’t incur a dispersal distance penalty, and mutation load (m _g  = 0.5) that does incur a dispersal distance penalty. Standard deviation of the dispersal kernel (σ) = 0.1, fecundity (ʎ) = 3, carrying capacity (K) = 30, and the mutation effect size (s) = 0.005.  Lines represent the mean of 30 replicates and grey shading represents the standard deviation. (Color figure online)

Fig. 8

Scenario 2. Left hand column (a, c, e, g) is for simulations with mutation load evolving without incurring a dispersal penalty. Right hand column (b, d, f, h) is for simulations with mutation load evolving and incurring a penalty on the distance an individual disperses. The probability of extinction (a, b) was calculated as the number of replicates that went extinct divided by the total number of replicates. The mean time to extinction (c, d for those parameters that resulted in extinction), was calculated as the average time of extinction in the replicates. The mean genetic survival (e, f) represents the average genetic viability of all the individuals in the metapopulation over the 10 generations prior to extinction (or simulation end). Similarly the mean effective dispersal distance (g, h) represents the mean distance individuals dispersed in the 10 generations prior to extinction (or simulation end). Fecundity (ʎ) = 2, mutation effect size (s) = 0.005. Graphs were generated using the mean of 30 replicates