Dispersal distance of heterogeneous populations

Heterogeneity among individuals in a population is one of the important factors that influence the rate of population spread. To incorporate the population heterogeneity into dispersal rate, we assume that the traveling duration varies following a gamma distribution with a shape parameter k , where (1/ k ) indicates the heterogeneity in the traveling duration. The resultant distribution of the traveling distance, which is called dispersal function, is then expressed by using a modified Bessel function of the second kind of order ( k − 1). It is shown that the front of the distribution spreads with time in an accelerated manner during an early phase of expansion if the heterogeneity is sufficiently large, which is consistent with the results from previous studies of biological invasions. By using the data obtained from mark–recapture experiments using traps, we can obtain the maximum likelihood estimates of three parameters: heterogeneity in the traveling duration, which is defined by (1/ k ); the mean dispersal ability, which is defined by the product of the diffusion coefficient and the mean traveling duration; and the trap efficiency. The usefulness of this model is shown by using the data of mark–recapture experiments with the common cutworm, Spodoptera litura (Fabricius) (Lepidoptera: Noctuidae).