Regensburg 2013 – scientific programme

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BP: Fachverband Biologische Physik

BP 3: Statistical Physics in Biological Systems I (joint with DY)

BP 3.7: Talk

Monday, March 11, 2013, 11:00–11:15, H47

Coexistence and survival in conservative Lotka-Volterra networks — •Johannes Knebel¹, Torben Krüger², Markus Weber¹, and Erwin Frey¹ — ¹Arnold-Sommerfeld Center for Theoretical Physics and Center for NanoScience, Theresienstraße 37, 80333 München — ²Department of Mathematics, Ludwig-Maximilians-Universität München, Theresienstraße 38, 80333 München

Conservative Lotka-Volterra (LV) models play a fundamental role in many fields of science such as population dynamics. New insights into the maintenance of biodiversity can be gained by understanding the long-term behavior of complex LV interaction networks and by revealing their coexistence and survival scenarios.

Here we present a classification scheme for coexistence scenarios in well-mixed, conservative LV networks. Our theoretical approach to study global stability properties builds on a deterministic analysis by using the Pfaffian of the interaction matrix, a simpler form of the determinant for skew-symmetric matrices. We find that the classification of conservative LV dynamics on the basis of their interaction topology is incomplete and that non-cyclic networks can also maintain coexistence of all species. The deterministic analysis also leads to a deeper understanding of the stability of ecological networks in finite populations as is reflected by a generalized scaling law for the extinction time in the vicinity of critical reaction rates. Our general results are illustrated for systems composed of four and five species.