Long-range interactions and evolutionary stability in a predator-prey system.
Evolving ecosystems often are dominated by spatially local dynamics, but many also include long-range transport that mixes spatially separated groups. The existence of such mixing may be of critical importance since research shows spatial separation may be responsible for long-term stability of predator-prey systems. Complete mixing results in rapid global extinction, while spatial systems achive long term stability due to an inhomogeneous spatial pattern of local extinctions. We consider the robustness of a generic evolving predator-prey or host-pathogen model to long-range mixing and find a transition to global extinction at nontrivial values implying that even if significant mixing already exists, a small amount of additional mixing may cause extinction. Our results are relevant to the global mixing of species due to human intervention and to global transport of infectious disease.
Rauch
Erik M
EM
MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, Massachusetts 02139, USA.
Bar-Yam
Yaneer
Y
D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D017753:Ecosystem; D020387:Food Chain; D005716:Game Theory; D014644:Genetic Variation; D005828:Genetics, Population; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D015996:Survival Rate; D013997:Time Factors