Dispersal heterogeneity is increasingly being observed in ecological populations and has long been suspected as an explanation for observations of non-Gaussian dispersal. Recent empirical and theoretical studies have begun to confirm this. Using an integro-difference model, we allow an individual’s diffusivity to be drawn from a trait distribution and derive a general relationship between the dispersal kernel’s moments and those of the underlying heterogeneous trait distribution. We show that dispersal heterogeneity causes dispersal kernels to appear leptokurtic, increases the population’s spread rate, and lowers the critical reproductive rate required for persistence in the face of advection. Wavespeed has been shown previously to be determined largely by the form of the dispersal kernel tail. We qualify this by showing that when reproduction is low, the precise shape of the tail is less important than the first few dispersal moments such as variance and kurtosis. If the reproductive rate is large, a dispersal kernel’s asymptotic tail has a greater influence over wavespeed, implying that estimating the prevalence of traits which correlate with long-range dispersal is critical. The presence of multiple dispersal behaviors has previously been characterized in terms of long-range versus short-range dispersal, and it has been found that rare long-range dispersal essentially determines wavespeed. We discuss this finding and place it within a general context of dispersal heterogeneity showing that the dispersal behavior with the highest average dispersal distance does not always determine wavespeed.

Behavioral syndromes are widely recognized as important for ecology and evolution, but most predictions about ecological impacts are based on conceptual models and are therefore imprecise. Borrowing insights from the theory of demographic heterogeneity, we derived insights about the population-dynamic effects of behavioral syndromes. If some individuals are consistently more aggressive than others, not just in interspecific contests, but also in foraging, mating, and antipredator behavior, then population dynamics could be affected by the resulting heterogeneity in demographic rates. We modeled a population with a boldness-aggressiveness syndrome (with the individual's trait constant through life), showing that the mortality cost of boldness causes aggressive individuals to die earlier, on average, than their nonaggressive siblings. The equilibrium frequency of the aggressive type is strongly affected by the mortality cost of boldness, but not directly by the reproductive benefit of aggressiveness. Introducing aggressive types into a homogeneous nonaggressive population increases the average per-capita mortality rate at equilibrium; under many conditions, this reduces the equilibrium density. One such condition is that the reproductive benefit of aggression is frequency dependent and the population has evolved to equalize the expected fitness of the two types. Finally, if the intensity of aggressiveness can evolve, then the population is likely to evolve to an evolutionarily stable trait value under biologically reasonable assumptions. This analysis shows how a formal model can predict both how a syndrome affects population dynamics and how the population processes constrain evolution of the trait.