Dispersal distance of heterogeneous populations

Abstract

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 Ϫ 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).

Variation in individual walking behavior creates the impression of a Lévy flight

“…Although it is no surprise that mobile phone movement is different from that of insects, it is interesting to observe that superdiffusive movement in both cases could be explained by population-level variation. This is also supported by a number of other studies in which considerable variation in movement parameters between individuals was observed, with distributions that resemble power laws with cutoffs, even though it was not always established whether individuals move diffusively (23)(24)(25)(26)(27). These observations, combined with our finding that individual movement has diffusive characteristics, raise the question in how far the behavior of other animals truly has fractal properties, or whether this is a result of the pooling of data across individuals together with individual variation (14,15).…”

Microbial dispersal in unsaturated porous media: Characteristics of motile bacterial cell motions in unsaturated angular pore networks

“…In practice, Yamamura [2002] has shown that the travel time distribution of organisms, due to the fat-tailed dispersal kernels, is described reasonably well by the gamma distribution (a specific form of the inverse Gaussian distribution). Of available statistical distributions, the gamma distribution is well known and facilitates parametric and analytical modeling [e.g., Thom, 1958;Jury and Gruber, 1989;Husak et al, 2007;Haghighi and Or, 2013].…”

Anomalous diffusion of heterogeneous populations characterized by normal diffusion at the individual level

“…On the other hand, heterogeneity among individuals in a population has proven to be another important factor that can influence population dispersal. To incorporate population heterogeneity into dispersal rate, some studies assume that the movement of individuals is Brownian, but the travelling durations of organisms vary following an inverse-gamma distribution (Clark et al 1999) or a gamma distribution (Yamamura 2002) leading to fat-tailed dispersal kernels. Another way to integrate population heterogeneity into dispersal models is to assume that populations consist of several subgroups with different diffusion coefficients (Skalski & Gilliam 2000Okubo & Levin 2002).…”