Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems
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...
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/128470 |
| _version_ | 1811088174159495168 |
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| author | Wang, Juven |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Wang, Juven |
| author_sort | Wang, Juven |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:57:25Z |
| format | Article |
| id | mit-1721.1/128470 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:57:25Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
| record_format | dspace |
| spelling | mit-1721.1/1284702022-09-28T17:22:51Z Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems Wang, Juven Massachusetts Institute of Technology. Department of Physics 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. NSF (Grants DMS-1607871, DMR-1005541 and NSFC 11274192) 2020-11-12T22:50:13Z 2020-11-12T22:50:13Z 2020-02 2019-07 2020-09-24T21:05:39Z Article http://purl.org/eprint/type/JournalArticle 1431-7613 1611-7530 https://hdl.handle.net/1721.1/128470 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 en https://doi.org/10.1007/s12064-020-00308-4 Theory in Biosciences Article 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. Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Science and Business Media LLC Springer Berlin Heidelberg |
| spellingShingle | Wang, Juven Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title | Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title_full | Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title_fullStr | Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title_full_unstemmed | Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title_short | Gene-mating dynamic evolution theory II: global stability of N-gender-mating polyploid systems |
| title_sort | gene mating dynamic evolution theory ii global stability of n gender mating polyploid systems |
| url | https://hdl.handle.net/1721.1/128470 |
| work_keys_str_mv | AT wangjuven genematingdynamicevolutiontheoryiiglobalstabilityofngendermatingpolyploidsystems |