Estimating the parameters for diffusion models of dispersal using mean occupancy time

Background/Question/Methods

One fundamental goal of ecology is to examine how dispersal affects the distribution and dynamics of organisms across natural landscapes. These landscapes are frequently divided into patches of habitat embedded in a matrix of several non-habitat regions, and dispersal behavior could vary within each landscape element as well as the edges between elements. Diffusion models are a common way of modeling dispersal in such landscapes, but to apply these models we also need methods of estimating the diffusion rate and any edge behavior parameters. We present a novel method of estimating the diffusion rate using the mean occupancy time for a circular region, derived from analytical solutions of the diffusion model. We also use mean occupancy time to estimate a parameter (the crossing probability) that governs one type of edge behavior often used in these models, a biased random walk.  The statistical properties of these estimators are then examined using simulated observations of the occupancy time (time spent within the circle) for individual organisms. 

Results/Conclusions

The mean occupancy time estimator for the diffusion rate is simple in form, and our simulations suggest it is an unbiased estimator of this parameter.  The estimation method derived for the crossing probability is more complex, but also shows minimal bias for biologically realistic values of this parameter.  We also demonstrate that bootstrapping yields valid confidence intervals for the parameter estimates.  These new methods have some advantages over other methods of estimating these parameters, including reduced computational cost and ease of use in the field. They also provide a method of estimating the diffusion rate for a particular location in space, compared to existing methods that represent averages over large areas. Methods for estimating mean occupancy time using field experiments are also discussed.