Probabilities of extinction, weak extinction permanence, and mutual exclusion in discrete, competitive, Lotka-Volterra systems
The probabilities of extinction, weak extinction, permanence, and mutual exclusion are calculated for models with up to five species by examining one million randomly chosen discrete, competitive, Lotka-Volterra systems. The probability of permanence drops off very rapidly with the increase in the number of species. It drops to less than 1% with five species. The probability that at least one species will die out increases with the number of species. It reaches 95% with five species. When a group of species weakly dominates another species, the dominated species goes extinct. The probability that at least one species is weakly dominated is close to 50%. Mutual exclusion happens between 10% and 20% of the time when there are at least three species. (C) 2004 Elsevier Ltd. All rights reserved.
probabilities lotka-volterra population dynamics dynamical systems