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28 March 2024
 
  » arxiv » q-bio.PE/0508025

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Self-optimization, community stability, and fluctuations in a class of individual-based models of biological coevolution
Per Arne Rikvold ;
Date 19 Aug 2005
Subject Populations and Evolution; Statistical Mechanics; Adaptation and Self-Organizing Systems | q-bio.PE cond-mat.stat-mech nlin.AO
AffiliationFlorida State Univ.
AbstractWe study a class of individual-based models of biological coevolution. These are multispecies, stochastic population-dynamics models in which the reproduction probability for individuals of a particular species depends nonlinearly on the population sizes of all the species present in the community. New species are introduced through a small probability of mutation during reproduction. For a subclass of simplified models we are able to perform linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations. Based on this analysis, we present a phase diagram for the total population size. Over time, the models are found to self-optimize through mutation and selection to maximize a community fitness function, subject only to constraints internal to the model. If the off-diagonal elements of the matrix that defines the interspecies interactions are distributed independently on an interval that includes positive values, the model evolves toward mutualistic communities, in which the population is self-sustaining. In contrast, for predator/prey models the interaction matrix is antisymmetric, and the community is constrained to a region of the phase diagram where a nonzero population size can only be sustained by an external resource. Time series of the diversity and total population size for the different models show 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator/prey model. The difference is probably due to a greater resilience of the predator/prey model toward mass extinctions.
Source arXiv, q-bio.PE/0508025
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