Lotka–Volterra approximations for evolutionary trait-substitution processes

16483 10 90390 2 261688 document 90390 Ito2020_Article_LotkaVolterraApproximationsFor.pdf application/pdf 4f31d468d0ce802bcdccdc9dc17b5847 MD5 1242983 2020-05-25 03:45:26 https://pure.iiasa.ac.at/id/eprint/16483/1/Ito2020_Article_LotkaVolterraApproximationsFor.pdf 16483 1 1 application/pdf text en public cc_by_4

Ito2020_Article_LotkaVolterraApproximationsFor.pdf

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/90390 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/90390 http://eprints.org/relation/issmallThumbnailVersionOf https://pure.iiasa.ac.at/id/document/90390 archive 353 disk0/00/01/64/83 2020-05-25 03:46:12 2021-08-27 17:33:03 2020-05-25 03:46:12 article show Ito H.C. 8079 Dieckmann U. 1668 0000-0001-7089-0393 Metz H. 7506 Lotka–Volterra approximations for evolutionary trait-substitution processes pub prog_eep prog_esp Adaptive dynamics; Attractor inheritance; Lotka–Volterra approximations; Lotka–Volterra models. A set of axioms is formulated characterizing ecologically plausible community dynamics. Using these axioms, it is proved that the transients following an invasion into a sufficiently stable equilibrium community by a mutant phenotype similar to one of the community's finitely many resident phenotypes can always be approximated by means of an appropriately chosen Lotka-Volterra model. To this end, the assumption is made that similar phenotypes in the community form clusters that are well-separated from each other, as is expected to be generally the case when evolution proceeds through small mutational steps. Each phenotypic cluster is represented by a single phenotype, which we call an approximate phenotype and assign the cluster's total population density. We present our results in three steps. First, for a set of approximate phenotypes with arbitrary equilibrium population densities before the invasion, the Lotka-Volterra approximation is proved to apply if the changes of the population densities of these phenotypes are sufficiently small during the transient following the invasion. Second, quantitative conditions for such small changes of population densities are derived as a relationship between within-cluster differences and the leading eigenvalue of the community's Jacobian matrix evaluated at the equilibrium population densities before the invasion. Third, to demonstrate the utility of our results, the 'invasion implies substitution' result for monomorphic populations is extended to arbitrarily polymorphic populations consisting of well-recognizable and -separated clusters. 2020-05-21 published Springer 10.1007/s00285-020-01493-y 1342 66 206 public Journal of Mathematical Biology 80 2141-2226 TRUE 1432-1416 FALSE no info:eu-repo/semantics/article