Coexistence and Survival in Conservative Lotka-Volterra Networks

2013/03/28 by Johannes Knebel, Torben Krüger, Markus F. Weber +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #q-bio.PE #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.110.168106

published as Phys. Rev. Lett. 110, 168106 (2013) · 5 pages, 3 figures

arxiv created 2013/03/28 · arxiv updated 2013/04/26

Abstract

Analyzing coexistence and survival scenarios of Lotka-Volterra (LV) networks in which the total biomass is conserved is of vital importance for the characterization of long-term dynamics of ecological communities. Here, we introduce a classification scheme for coexistence scenarios in these conservative LV models and quantify the extinction process by employing the Pfaffian of the network's interaction matrix. We illustrate our findings on global stability properties for general systems of four and five species and find a generalized scaling law for the extinction time.

Cited by

• On Coexistence of Conservative Replicator Dynamics with Four Strategies
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields

Related

• Extinction dynamics of Lotka-Volterra ecosystems on evolving networks
• Stable coexistence in indefinitely large systems of competing species
• Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities
• Exploring the Dynamics of Lotka-Volterra Systems: Efficiency, Extinction Order, and Predictive Machine Learning
• The persistence of bipartite ecological communities with Lotka-Volterra dynamics