%0 Journal Article %1 neubert1995dispersal %A Neubert, M.G. %A Kot, M. %A Lewis, M.A. %D 1995 %J Theoretical Population Biology %K Turing_bifurcation dispersal ecology integro-difference population_dynamics predator-prey spatial_structure %N 1 %P 7 - 43 %R http://dx.doi.org/10.1006/tpbi.1995.1020 %T Dispersal and Pattern Formation in a Discrete-Time Predator-Prey Model %U http://www.sciencedirect.com/science/article/pii/S0040580985710209 %V 48 %X We investigate the dispersal-driven instabilities that arise in a discrete-time predator-prey model formulated as a system of integrodifference equations. Integrodifference equations contain two components: (1) difference equations, which model growth and interactions during a sedentary stage, and (2) redistribution kernels, which characterize the distribution of dispersal distances that arise during a vagile stage. Redistribution kernels have been measured for a tremendous number of organisms. We derive a number of redistribution kernels from first principles. Integrodifference equations generate pattern under a far broader set of ecological conditions than do reaction-diffusion models. We delineate the necessary conditions for dispersal-driven instability for two-species systems and follow this with a detailed analysis of a particular predator-prey model.

@article{neubert1995dispersal, abstract = {We investigate the dispersal-driven instabilities that arise in a discrete-time predator-prey model formulated as a system of integrodifference equations. Integrodifference equations contain two components: (1) difference equations, which model growth and interactions during a sedentary stage, and (2) redistribution kernels, which characterize the distribution of dispersal distances that arise during a vagile stage. Redistribution kernels have been measured for a tremendous number of organisms. We derive a number of redistribution kernels from first principles. Integrodifference equations generate pattern under a far broader set of ecological conditions than do reaction-diffusion models. We delineate the necessary conditions for dispersal-driven instability for two-species systems and follow this with a detailed analysis of a particular predator-prey model. }, added-at = {2014-12-05T01:33:15.000+0100}, author = {Neubert, M.G. and Kot, M. and Lewis, M.A.}, biburl = {https://www.bibsonomy.org/bibtex/2f73350804210fec175e8be444809d877/peter.ralph}, doi = {http://dx.doi.org/10.1006/tpbi.1995.1020}, interhash = {e045e46c6e1fa1e072445cd03b2400e0}, intrahash = {f73350804210fec175e8be444809d877}, issn = {0040-5809}, journal = {Theoretical Population Biology }, keywords = {Turing_bifurcation dispersal ecology integro-difference population_dynamics predator-prey spatial_structure}, number = 1, pages = {7 - 43}, timestamp = {2014-12-05T01:33:15.000+0100}, title = {Dispersal and Pattern Formation in a Discrete-Time Predator-Prey Model }, url = {http://www.sciencedirect.com/science/article/pii/S0040580985710209}, volume = 48, year = 1995 }