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dc.contributor.authorWang, Juven
dc.date.accessioned2020-11-12T22:50:13Z
dc.date.available2020-11-12T22:50:13Z
dc.date.issued2020-02
dc.date.submitted2019-07
dc.identifier.issn1431-7613
dc.identifier.issn1611-7530
dc.identifier.urihttps://hdl.handle.net/1721.1/128470
dc.description.abstractExtending 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.en_US
dc.description.sponsorshipNSF (Grants DMS-1607871, DMR-1005541 and NSFC 11274192)en_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.isversionofhttps://doi.org/10.1007/s12064-020-00308-4en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleGene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systemsen_US
dc.typeArticleen_US
dc.identifier.citationWang, 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-Verlagen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.relation.journalTheory in Biosciencesen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2020-09-24T21:05:39Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag GmbH Germany, part of Springer Nature
dspace.embargo.termsY
dspace.date.submission2020-09-24T21:05:39Z
mit.journal.volume139en_US
mit.journal.issue2en_US
mit.licensePUBLISHER_POLICY
mit.metadata.statusComplete


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