Population dynamics play out in time and space. Understanding and predicting population trajectories in both dimensions are core objectives in the study of biological invasions, a term we use broadly to describe population expansion into an unoccupied region. Current theory for biological invasions is largely restricted to one-sex models, which may be well-suited to asexual or hermaphroditic species, including most plants. However, the application of one-sex invasion models to dioecious species, including most animals, requires the assumption that either females and males disperse equal distances, or that bias in the sex ratio (proportion female) has no effect on population growth. In nature, these assumptions are often violated. We therefore developed invasion theory - building upon integro-difference models and two-sex birth functions - that explicitly tracks both sexes through time and space. We used the model to ask how sex-biased dispersal and sex ratio-dependent population dynamics interact to influence the speed of biological invasions under different mating systems. To integrate the theory with data, we estimated two-sex demography and dispersal parameters for the bean beetle Callosobruchus maculatus. Finally, we tested model predictions using experimental beetle invasions in the laboratory.
Results/Conclusions
Our theoretical results reveal complex interactions between demography and dispersal in two-sex invasions. First, sex-biased dispersal can cause an invasion to fail. This occurs when the difference between female and male dispersal distance is sufficiently large to drive sex ratios at newly colonized locations beyond thresholds for population increase. Second, for invasions that spread, sex-biased dispersal can accelerate range expansion (relative to unbiased dispersal) if the farther travelling-sex is also the sex that most limits recruitment (determined by the mating system). This has the effect of pushing the invasion front sex ratio toward a value that maximizes local population growth. Conversely, dispersal bias in favor of the non-limiting sex decelerates range expansion. Experiments to estimate model parameters indicated that male bean beetles dispersed significantly farther than females, and that the local population growth rate was maximized under a strongly female-biased sex ratio (0.86); these results suggest that the mathematical components of the theory are biologically realistic. We conducted experimental invasions to test the prediction, generated by theory, that shifting dispersal bias in favor of females (but holding mean dispersal constant) would accelerate bean beetle invasions. Combined, our theoretical and empirical results provide novel insights into mechanisms and consequent patterns of spatial spread by populations with two sexes.
