Continuous models of population-level heterogeneity inform analysis of animal dispersal and migration

Behavioral heterogeneity among individuals is a universal feature of natural populations. Most diffusion-based models of animal dispersal, however, implicitly assume homogeneous movement parameters within a population. Recent attempts to consider the effect of heterogeneous populations on dispersal distributions have been somewhat limited by the high number of parameters required to subdivide a population into several groups. A solution to this problem is to characterize the value of a movement parameter as continuously distributed within a population. We present several cases in which this method is useful and tractable, applying the framework both to spatial distribution data and closely related first passage times. The resulting models allow ecologists to identify the extent to which the variability in dispersal distributions can be attributed to population-level heterogeneity as opposed to intrinsic randomness. We apply the formulation to two very different cases of dispersal: resident organisms in a stream (freshwater chub Nocomis leptocephalus) and migrating organisms (juvenile salmonids Oncorhynchus spp.). In both cases, the application of heterogeneity-explicit models provides insights into the behavioral mechanisms of movement.