Interspecific influence on mobility and Turing instability.
In this paper we formulate a multi-patch multi-species model in which the per-capita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly. In the case of competition a cross-emigration response promotes pattern formation by exercising a destabilizing influence; in particular, it may lead to diffusive instability provided that the response is sufficiently strong, which contrasts sharply with the well-known fact that the standard competition system does not exhibit Turing instability. In the case of prey-predator or activator-inhibitor interaction it acts against pattern formation by exerting a stabilizing effect; in particular, the diffusive instability, even though it may happen in a standard system, never occurs when the response is sufficiently strong. We conclude that the cross-emigration response is an important factor that should not be ignored when pattern formation is the issue.
Huang
Yunxin
Y
Mathematical Department, Utrecht University, 3508 TA Utrecht, The Netherlands. huang@math.uu.nl
Diekmann
Odo
O
D000818:Animals; D004641:Emigration and Immigration; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011156:Population Density; D011235:Predatory Behavior; D013045:Species Specificity