TRANSLATING FORAGING MOVEMENTS IN HETEROGENEOUS ENVIRONMENTS INTO THE SPATIAL-DISTRIBUTION OF FORAGERS

The relationship between movement and population dynamics in heterogeneous environments has been approached from two directions: theoretical analyses using diffusion models and empirical studies that often employ computer simulations. In this paper I am proposing a unified framework for studying individual movements that brings both of these approaches together. The proposed framework is based on the "diffusion-approximation" procedure developed by Patlak (1953a, b), which translates a probabilistic description of the pattern of individual movements (such as provided by simulation models) into a partial differential model describing the population redistribution in a patchy habitat. My first goal in this paper was to make Patlak's work accessible to ecologists interested in realistic movement models. Secondly, making some simplifying assumptions I solved Patlak's model to obtain the equilibrium distribution of organisms among patches in a heterogeneous environment. This led me to a definition of "residence index." The residence index of a patch is estimated by observing and recording movement trajectories of organisms within the patch. The pattern of variation in the residence index among different kinds of patches specifies the predicted equilibrium densities of organisms in each patch. I assessed the utility of the above approach by using data on movement tracks of Euphydryas anicia females to calculate butterfly residence indices in host-plant patches vs. nonhost environment. The predicted distribution of butterflies among host and nonhost areas differed by only 16% from the actual distribution, as documented by an independent data set. I also applied the model to data from three studies on insect movement and spatial distribution. The accuracy of model predictions varied from adequate to excellent. Finally, I argue that Patlak's model and its residence-index extension provides a general, and at the same time realistic, framework for quantifying individual movements, and for relating movement patterns to spatial population dynamics. Although this approach, as developed here, is explicitly concerned only with population redistribution within an area, birth/death or immigration/emigration terms can be added in a straightforward manner. Thus, this framework can be very useful in studies of consumer-resource (e.g., predator-prey or herbivore-host) spatial dynamics, since movement behaviors of consumers searching for prey, and prey attempting to avoid consumers, are known to be important in affecting the outcome of such population interactions.