Diffusion models for animals in complex landscapes: incorporating heterogeneity among substrates, individuals and edge behaviours

1. Animals move commonly through a variety of landscape elements and edges in search of food, mates and other resources. We developed a diffusion model for the movement of an insect herbivore, the planthopper Prokelisia crocea, that inhabits a landscape composed of patches of its host plant, prairie cordgrass Spartina pectinata, embedded in a matrix of mudflat or smooth brome Bromus inermis. 2. We used mark-release-resight experiments to quantify planthopper movements within cordgrass-brome and cordgrass-mudflat arenas. A diffusion model was then fitted that included varying diffusion rates for cordgrass and matrix, edge behaviour in the form of a biased random walk and heterogeneity among planthoppers (sessile vs. mobile). The model parameters were estimated by maximum likelihood using the numerical solution of the diffusion model as a probability density. Akaike's information criterion (AIC) values were used to compare models with different subsets of features. 3. There was clear support for models incorporating edge behaviour and both sessile and mobile insects. The most striking difference between the cordgrass-brome and cordgrass-mudflat experiments involved edge behaviour. Planthoppers crossed the cordgrass-brome edge readily in either direction, but traversed the cordgrass-mudflat edge primarily in one direction (mudflat to cordgrass). Diffusion rates were also significantly higher on mudflat than for cordgrass and brome. 4. The differences in behaviour for cordgrass-brome vs. cordgrass-mudflat edges have implications for the connectivity of cordgrass patches as well as their persistence. Higher dispersal rates are expected between cordgrass patches separated by brome relative to mudflat, but patches surrounded by mudflat appear more likely to persist through time. 5. The experimental design and diffusion models used here could potentially be extended to any organism where mass mark-recapture experiments are feasible, as well as complex natural landscapes.