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Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems

Author(s)
Wang, Juven
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Abstract
Extending the previous 2-gender dioecious diploid gene-mating evolution model, we attempt to answer “whether the Hardy–Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender N-polyploid gene-mating system with arbitrary number of alleles?” For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring. Each of the pair contributes one inherited character, the allele, to combine into the genotype of their offspring. Hence, for an N-gender N-polypoid gene-mating model, each of N different genders contributes one allele to combine into the genotype of their offspring. We exactly solve the analytic solution of N-gender-mating $(n+1)$-alleles governing highly nonlinear coupled differential equations in the genotype frequency parameter space for any positive integer N and $n$. For an analogy, the 2-gender to N-gender gene-mating equation generalization is analogs to the 2-body collision to the N-body collision Boltzmann equations with continuous distribution functions of discretized variables instead of continuous variables. We find their globally stable solution as a continuous manifold and find no chaos. Our solution implies that the Laws of Nature, under our assumptions, provide no obstruction and no chaos to support an N-gender gene-mating stable system.
Date issued
2020-02
URI
https://hdl.handle.net/1721.1/128470
Department
Massachusetts Institute of Technology. Department of Physics
Journal
Theory in Biosciences
Publisher
Springer Science and Business Media LLC
Citation
Wang, Juven C. "Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems." Theory in Biosciences 139, 2 (February 2020): 135–144 © 2020 Springer-Verlag
Version: Author's final manuscript
ISSN
1431-7613
1611-7530

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