Translating across scales: Simulating species distributions as the aggregate response of individuals to heterogeneity

The mechanistic linkage between movement responses of animals to heterogeneity and distribution of populations provides a useful framework for investigating the extent to which fine-scale ecological information can be extrapolated across scales to explain broad-scale phenomena. We developed a simple, spatially explicit simulation model to explore whether patterns of species distributions across landscapes emerge as the aggregate response of individuals to fine-scale heterogeneity. As an empirical basis for this modelling exercise, we studied two species of acridid grasshoppers (Orthoptera) in the shortgrass prairie in northcentral Colorado, USA. Grasshopper distributions were sampled in two pastures that had been subjected to different intensities of cattle grazing. A large species, Xanthippus corallipes (Haldeman) was patchily distributed across this grassland, whereas the smaller Psoloessa delicatula (Scudder) occurred as a random distribution in both pastures. We produced a grid map of each pasture, in which each grid cell was classified according to 3 habitat types representing a gradient of forage abundance for grasshoppers. During model simulations, individuals were randomly distributed across the pasture maps and allowed to redistribute according to habitat-specific movement probabilities — the rate that an individual would leave a particular cell (habitat) type. Movement probabilities were extrapolated from observed movement rates of each species within habitats. We were initially unable to simulate realistic levels of aggregation for the two grasshopper species when extrapolated rates of movement were applied to the model. Species distributions thus do not emerge as a linear function of fine-scale movement rates, presumably because movement is constrained by different processes operating at different scales. Fine-scale movement responses to heterogeneity can be used to provide qualitative predictions of speciesʹ distributional patterns in different landscapes, however. For example, P. delicatula exhibited faster rates of movement through habitats comprising 92% of one pasture; such a high rate of turnover should lead to a random distribution, which is what we observed for this species in this system. Xanthippus corallipes had reduced movement in 35% of this same landscape, but was able to move rapidly across the remainder. This may enable individuals to aggregate within a minor component of the landscape and produce the clumped distributions we observed. While the general pattern of distribution can be determined from individual movement responses to heterogeneity, such information is too coarse to quantify the exact location of individuals and other statistical properties of population distributions (e.g., density).