dorsal/arxiv
View SchemaSelf-optimization, community stability, and fluctuations in two individual-based models of biological coevolution
| Authors | Per Arne Rikvold |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0508025 |
| URL | https://arxiv.org/abs/q-bio/0508025 |
| DOI | 10.1007/s00285-007-0101-y |
| Journal | J. Math. Biol. 55, 653-677 (2007) |
Abstract
We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community fitness function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator-prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 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 greater resilience toward mass extinctions in the food-web like communities produced by the predator-prey model.
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"abstract": "We compare and contrast the long-time dynamical properties of two\nindividual-based models of biological coevolution. Selection occurs via\nmultispecies, stochastic population dynamics with reproduction probabilities\nthat depend nonlinearly on the population densities of all species resident in\nthe community. New species are introduced through mutation. Both models are\namenable to exact linear stability analysis, and we compare the analytic\nresults with large-scale kinetic Monte Carlo simulations, obtaining the\npopulation size as a function of an average interspecies interaction strength.\nOver time, the models self-optimize through mutation and selection to\napproximately maximize a community fitness function, subject only to\nconstraints internal to the particular model. If the interspecies interactions\nare randomly distributed on an interval including positive values, the system\nevolves toward self-sustaining, mutualistic communities. In contrast, for the\npredator-prey case the matrix of interactions is antisymmetric, and a nonzero\npopulation size must be sustained by an external resource. Time series of the\ndiversity and population size for both models show approximate 1/f noise and\npower-law distributions for the lifetimes of communities and species. For the\nmutualistic model, these two lifetime distributions have the same exponent,\nwhile their exponents are different for the predator-prey model. The difference\nis probably due to greater resilience toward mass extinctions in the food-web\nlike communities produced by the predator-prey model.",
"arxiv_id": "q-bio/0508025",
"authors": [
"Per Arne Rikvold"
],
"categories": [
"q-bio.PE",
"cond-mat.stat-mech",
"nlin.AO"
],
"doi": "10.1007/s00285-007-0101-y",
"journal_ref": "J. Math. Biol. 55, 653-677 (2007)",
"title": "Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution",
"url": "https://arxiv.org/abs/q-bio/0508025"
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