Details of mate finding drive dynamics of sex-structured invasions
The rate at which a population grows and spreads can depend on individual behavior and interactions. In many dioecious species, males and females differ in key life history traits (e.g. growth, survival, dispersal), which can scale up to affect population rates of growth and spread. Furthermore, in sexually reproducing species, the mechanics of locating mates and reproducing successfully (which can change non-linearly with density) introduce further complications for predicting the invasion speed (spread rate). Here we review existing approaches for modeling invasions with two sexes, which primarily rely on either entirely population-level or individual-level models. We then present a novel hybrid approach, which links individual-level mating behavior (in an individual-based model) to population level dynamics (in an integrodifference equation model). We compare the results from our hybrid approach to past population-level results.
We show that details of individuals mating behavior can profoundly impact the rate of population spread. A mechanistic mate-finding Allee effect (difficulty finding mates at low densities) that leads to a demographic Allee effect can slow, delay or even prevent an invasion, compared to a model with a mechanistic but no demographic Allee effect. However, we also find that sex-biased searching for mates can exacerbate these impacts, leading to a failed invasion when equal searching for mates by both males and females would have been succesful. In contrast, allowing individuals to mate multiply mediates mate-finding Allee effects. The extent to which the mate-finding Allee effect influences invasion speed also depends on the degree of sex bias in dispersal and the sex ratio at birth. Finally, our simulations exhibit fluctuations in invasion speed over time, which appear to be caused by the mate-finding Allee effect. Although models with a population-level approximation of mating behavior can reproduce some of our findings (slowed, delayed invasions) they do not generate fluctuations in invasion speed.