A difficulty in using diffusion models to predict large scale animal population dispersal is that individuals move differently based on local information (as opposed to gradients) in differing habitat types. This can be accommodated by using ecological diffusion. However, real environments are often spatially complex, limiting application of a direct approach. Homogenization for partial differential equations has long been applied to Fickian diffusion (in which average individual movement is organized along gradients of habitat and population density). We derive a homogenization procedure for ecological diffusion and apply it to a simple model for chronic wasting disease in mule deer. Homogenization allows us to determine the impact of small scale (10-100 m) habitat variability on large scale (10-100 km) movement. The procedure generates asymptotic equations for solutions on the large scale with parameters defined by small-scale variation. The simplicity of this homogenization procedure is striking when compared to the multi-dimensional homogenization procedure for Fickian diffusion,and the method will be equally straightforward for more complex models.

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Chronic wasting disease (CWD) is an infectious prion disease that affects mule deer, along with other Cervids. It is a slow-developing, fatal disease which is rare in the free-ranging deer population of Utah. We present a sex-structured, spatial model for the spread of CWD over heterogeneous landscapes, incorporating both horizontal and environmental transmission pathways. To connect the local movement of deer to the regional spread of CWD, we use ecological diffusion with motility coefficients estimated from mule deer movement data. Ecological diffusion allows for aggregation of populations in desirable habitats and therefore allows for an interaction between density dependent disease transmission and landscape structure. The major innovation presented is use of homogenization to accelerate simulations of disease spread in southeastern Utah, from the La Sal Mountains near Moab to the Abajo Mountains near Monticello. The homogenized model provides accuracy while maintaining fidelity to small-scale habitat effects on deer distribution, including differential aggregation in land cover types with high residence times, with errors comparable to the order parameter measuring separation of small and large scales ([Formula: see text] in this case). We use the averaged coefficients from the homogenized model to explore asymptotic invasion speed and the impact of current population size on disease spread in southeastern Utah.

3. To discriminate between the hypothesis of population spread versus independent eruption, a model of spot formation by dispersing beetles facing a local Allee effect is derived. The model gives rise to an inverse power distribution of travel times from existing outbreaks. Using landscape-level host density maps in three study areas, an independently calibrated model of landscape resistance depending on host density, and aerial detection surveys, we calculated yearly maps of travel time to previous beetle impact. Isolated beetle spots were sorted by travel time and compared with predictions. Random eruption of locally endemic populations was tested using artificially seeded spots. We also evaluated the relationship between number of new spots and length of the perimeter of previously infested areas.4. Spot distributions conformed strongly to predicted power-law behaviour. The spatially random eruption hypothesis was found to be highly improbable. Spot numbers grew consistently with perimeter of previously infested area, suggesting that MPB spread long distances from infestation boundaries via spots following an inverse power distribution.5. The Allee effect in MPB therefore accelerates, rather than limits, invasion rates, contributing to recent widespread landscape-scale mortality in western North America. K E Y W O R D Sbark beetle, Dendroctonus ponderosae, patchy spread, power-law, travel time

A suite of statistical methods are used to study animal movement. Most of these methods treat animal telemetry data in one of three ways: as discrete processes, as continuous processes, or as point processes. We briefly review each of these approaches and then focus in on the latter. In the context of point processes, so-called resource selection analyses are among the most common way to statistically treat animal telemetry data. However, most resource selection analyses provide inference based on approximations of point process models. The forms of these models have been limited to a few types of specifications that provide inference about relative resource use and, less commonly, probability of use. For more general spatio-temporal point process models, the most common type of analysis often proceeds with a data augmentation approach that is used to create a binary data set that can be analyzed with conditional logistic regression. We show that the conditional logistic regression likelihood can be generalized to accommodate a variety of alternative specifications related to resource selection. We then provide an example of a case where a spatio-temporal point process model coincides with that implied by a mechanistic model for movement expressed as a partial differential equation derived from first principles of movement. We demonstrate that inference from this form of point process model is intuitive (and could be useful for management and conservation) by analyzing a set of telemetry data from a mountain lion in Colorado, USA, to understand the effects of spatially explicit environmental conditions on movement behavior of this species.