In this chapter, we have presented a general diffusion model for animal movement, and demonstrated that it can be made complex enough to include many aspects of animal behavior and, especially, responses to environmental heterogeneity. As noted by Kareiva and Odell (1987) and Moorcroft and Lewis (2006), an advantage of working with mechanistic models in general is that it may be possible to extrapolate beyond observations, e.g., predicting responses to habitat alteration or asking how parameters might evolve in current or altered landscapes. In the context of the diffusion model, this was demonstrated by Ovaskainen et al. (2008a), who showed that a model parameterized with data from a reference landscape successfully predicted clouded apollo butterfly movements in a structurally dissimilar landscape. If behaviors are built phenomenologically into simulation models or purely statistical models, it is less reliable to predict how these behaviors would change if the landscape changes.
Given the advantages of diffusion models, why aren't they used more widely to describe animal movement? We speculate that one reason is that theoretical ecologists working with these models have tended to focus on general, analytically tractable examples as case studies, rather than working with the complexities of the interactions of behavior and environmental features. At the same time, animal ecologists collecting movement data have tended to be most interested in the complexities of environmental responses, so have used statistical, rather than mechanistic, models to relate animal movement or locations to the environment. Also, many ecologists may not be comfortable working with differential equations, or not familiar with numerical methods needed for solving them. Finding solutions to diffusion models with complex behaviors and environments is computationally intensive, which, in the short term, might limit application to data analysis. Finally, it is clear that all kinds of movement behaviors cannot be fruitfully described by diffusion. The main assumption of the basic diffusion model (4.1) is that of a pure Markov process. If the animal's past movement history is needed to predict its future behavior, diffusion may not be likely to be the most successful modeling approach. Examples of such behavior include autocorrelation at fine spatial scales, and learning from experience moving in a particular landscape.
So where to go from here? We encourage readers of this book to consider diffusion as a simple though biologically plausible framework for describing and especially analyzing animal movement. The most important area for future research is relating models to data. This flows naturally from using diffusion models to calculate probability densities of animal's location, but is not yet widely recognized. In tandem with developing such techniques, we can take advantage of the growing number of animal movement studies and advances in remote tracking technologies, such as radio and satellite tracking. Important conservation questions to address in this area include the effects of habitat loss and fragmentation on animal movement, the role of matrix habitat in determining among-site dispersal, and the effects of landscape alteration on encounters between animals, such as predators and prey, or human-wildlife conflicts. Basic ecological questions include the consequences of different foraging strategies, the evolution of dispersal under different landscape structures, and the interaction of movement behavior and landscape structure in shaping species interactions. We will only learn from case studies how well different mechanisms of movement can be distinguished for real populations in real landscapes.
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