title: On the importance of dimensionality of space in models of space-mediated population persistence.
abstract: Spatially explicit models have become widely used in today's mathematical ecology to study persistence of populations. For the sake of simplicity, population dynamics is often analyzed with 1-D models. An important question is: how adequate is such 1-D simplification of 2-D (or 3-D) dynamics for predicting species persistence. Here we show that dimensionality of the environment can play a critical role in the persistence of predator-prey interactions. We consider 1-D and 2-D dynamics of a predator-prey model with the prey growth damped by the Allee effect. We show that adding a second space coordinate into the 1-D model results in a pronounced increase of size of the domain in the parametric space where predator-prey coexistence becomes possible. This result is due to the possibility of formation of a number of 2-D patterns, which is impossible in the 1-D model. The 1-D and the 2-D models exhibit different qualitative responses to variations of system parameters. We show that in ecosystems having a narrow width (e.g. mountain valleys, vegetation patterns along canals in dry areas, etc.), extinction of species is more probable compared to ecosystems having a pronounced second dimension. In particular, the width of a long narrow natural reserve should be large enough to guarantee nonextinction of species via interaction of 2-D population patches.
authors.affiliation: Ecological Complexity and Modeling Laboratory, University of California, Riverside, CA 92521-0124, USA. morozov_andrew@yahoo.com <morozov_andrew@yahoo.com>
authors.forename: Andrew
authors.initials: A
authors.lastname: Morozov
authors.forename: Bai-Lian
authors.initials: BL
authors.lastname: Li
mesh_terms: D000222:Adaptation, Physiological; D000818:Animals; D017753:Ecosystem; D008954:Models, Biological; D010933:Plankton / Q000145:classification / Q000502:physiology; D011156:Population Density; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D013037:Spatial Behavior / Q000502:physiology*; D013045:Species Specificity