Effects of movement behavior, space and nonlinearity on interaction rates within and between populations

It is now generally accepted that spatial structure has a stabilizing effect on population dynamics for a variety of reasons. One key reason is related to the way that organisms move among locations and respond to density. For example, movement rates often increase when conditions in a patch become unsuitable, as for example, when the density of conspecifics becomes too high. This has important implications for survival and reproduction because high densities can lead to reductions in fecundity and increases in mortality, nonlinear responses to density. Other forms of nonlinearity lead to increases in survival and reproduction as density increases. These so-called Allee effects happen for example when individuals cannot find mates at low density. Increases in density then lead to increased mate-finding success, fecundity and population growth rate. Thus, nonlinearities in population density can interact with dispersal in a variety of ways. Furthermore, even when individuals disperse irrespective of density, interactions with antagonists can be strongly affected by the relative scales of dispersal distance and patch size. This work is concerned with interactions among all three of these variables as they are added to models of population dynamics to increase realism. In the first study, we find that, using a combination of field experiments and models, we can make inferences about nonlinear population processes from a two-dimensional time series. Specifically, we found that monarch butterflies avoid existing eggs while seeking oviposition sites and egg mortality increases with egg density suggesting that nonlinear interactions with predators may partially explain the oviposition behavior. In the second study, nonlinear population dynamics coupled with passive diffusion increase the time required for a random sequence of introductions to lead to successful invasion. We show that (1) frequency and magnitude of introductions are interchangeable except at extremely low values of either, (2) that wide dispersion of release sites slows invasion, in contrast to models of the process that do not include Allee effects and (3) interactions with habitat edges congregate invaders, making releases far from edges least likely to invade. In the third study, we model interactions between an insect host and its viral pathogen. We show that increased spatial clumping of disease, and decreased dispersal both lead to decreases in disease transmission. Furthermore, heterogeneity in movement rate leads to nonlinear transmission whereby the rate of infection increases at a decreasing rate as the density of the pathogen is increased in the environment. As these three studies show, nonlinearities, spatial patchiness and dispersal strategies can profoundly impact interaction rates within and among populations. Models that include these features are more complex, but yield new insights into the underlying processes.