Dispersal distance of corn pollen under fluctuating diffusion coefficient

I develop a mechanistic model for pollen dispersal by a generalization of the Brownian motion model. This model provides an explanation as to why the distribution of the dispersal distance is leptokurtic in most organisms. The pollen is assumed to move in a period between and + to the circumference of a circle of radius r that has a center at the current position. The angle of movement is chosen at random. Unlike the conventional Brownian motion model, the step length, r, fluctuates in a stochastic manner, obeying a generalized gamma distribution. The convection flow, i.e., the directional movement of pollen, is also considered. I show that this model is identical to the diffusion model where the dispersal duration weighted by the diffusion coefficient obeys a gamma distribution. Hence, the model is called the gamma model. The solution is given in an explicit form. The model is fitted to six data sets obtained from the literature by maximizing the quasi-likelihood. Another model (the inverse gamma model), which is not a mechanistic model but a phenomenological model, is also fitted to the data to evaluate the validity of the gamma model.