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- W2017221429 abstract "The author considers the gene spread of a certain diploid plant, one of whose gene loci has two alleles. A mathematical model is formulated as a system of integrodifference equations $[N^{(n + 1)} ,u^{(n + 1)} ] = Q[N^{(n)} ,u^{(n)} ]$, where Q is a system of nonlinear convolution integral operators. The dynamics of Q in the heterozygote intermediate case is considered in a one-dimensional habitat. When the initial disadvantageous gene is present only in a finite region of the habitat, the dynamics of Q tends to a constant equilibrium dominated by the advantageous gene. Under certain conditions, the system has traveling wave solutions with speed not less than a minimal wave speed. The method of the Laplace transform is used to determine the minimal wave speed explicitly. The Contraction Mapping Theorem is applied to prove the existence and the uniqueness of the traveling waves. Moreover, it is proved that the minimal wave speed is the asymptotic speed of propagation of the advantageous gene, and the dynamics of the model approaches the traveling waves from suitable initial generations." @default.
- W2017221429 created "2016-06-24" @default.
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- W2017221429 date "1995-01-01" @default.
- W2017221429 modified "2023-09-25" @default.
- W2017221429 title "On a System of Integrodifference Equations Modelling the Propagation of Genes" @default.
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- W2017221429 doi "https://doi.org/10.1137/s003614109223708x" @default.
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