I present an alternative method of generating movement matrices for complex, fragmented landscapes. Instead of applying a simple 'travel success' function to a matrix of inter-patch distances, between-patch movements follow a model of chemotaxis. For the movements out of a given patch, the matrix is filled with a density map generated by a diffusion process in which that patch acts as a constant source and the other patches as sinks. The result is a surface with local minima at the patches, and the destinations of organisms emigrating from the source patch are generated as the end-points of down-gradient trajectories from a sampling of points around the edge of the source. This model is proposed as a general approach than can also work for long-distance perception such as vision. In this case, the perceived attractiveness of patches is represented by the depth of their sinks. Large patches, for example might be given deeper sinks which therefore attract organisms from a wider radius. It is also to easy to add barriers and other features to the matrix. 

Results/Conclusions

This process generates very different-looking movement matrices from the traditional method. Patch shape becomes important. Also, most patch emigrants end up at one of a small number of adjacent patches, and long-distance movements occur mainly via a 'stepping stone' process. (As a side-effect, the perception-based matrices are very sparse, and therefore can be represented compactly and multiplied efficiently, making analysis of extremely complex landscapes feasible.) We show how such movement patterns affect our perception of the quality of fragmented landscapes, and of the relative value of specific fragments. Examples include forest fragments in Central America and the vegetation patches of New York City. In the latter case, the urban infrastructure is used to constrain inter-patch movement trajectories.