GENETIC DIVERGENCE IN THE SYSTEM OF ADJACENT POPULATIONS WITH DENSITY-DEPENDENT LIMITATION OF GAMETE PRODUCTION

M.P. Kulakov, E.Ya. Frisman

Аннотация


The paper studies the mechanisms leading to the emergence of genetic divergence (stable genetic differences) between two populations coupled by migration. We considered the classical system of panmictic populations with Mendelian rules of inheritance and monolocus selection directed against heterozygotes. In order to limit the growth of populations, we propose to assume that gamete production and total fertility (birth) decreases with population growth due to limited resources. We have proposed a non-linear discrete time model that describes the concentration dynamics of one of the alleles and each population abundance. To calculate the coordinates of all fixed points corresponding to different types of the limiting genetic structure and the abundance ratio, we have proposed a method for calculating their coordinates. It is shown that with a density-dependent birth limitation in the model, a set of fixed points corresponding to a homogeneous and heterogeneous distribution is possible. At a homogeneous distribution, both populations are monomorphic, with individuals belonging to only one genotype. At this, the limiting values of population abundance do not always coincide. With a non-homogeneous distribution, adjacent populations are polymorphic with individuals of different genotypes, but they differ significantly in the frequencies of alternative alleles and asymptotic population abundance. Bifurcations of the fixed points birth corresponding to heterogeneous distribution and genetic divergence are described. It is found that the movement towards one of the possible limiting genetic structures is accompanied by a change in the reproductive capabilities of populations.It is shown that a reduced fitness of heterozygotes in monomorphic populations results in a higher birth rate as compared to polymorphic populations obviously containing individuals with different reproductive capabilities. As a result, monomorphic and polymorphic populations correspond to different limiting abundances and cycles with different periods and oscillation phases after the loss of stability, even if the populations are completely identical. 

Ключевые слова


genetic divergence; population; dynamics; migration; bifurcations; multistability

Литература


REFERENCES:Kulakov M.P., Frisman E.Ya. Genetic divergence in the system of adjacent populations with density-dependent limitation of gamete production. Regional’nye problemy, 2023, vol. 26, no. 1, pp. 9–11. (In Russ.). DOI: 10.31433/2618-9593-2023-26-1-9-11.

Bezruchko B.P., Prokhorov M.D., Seleznev Ye.P. Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, no. 4, pp. 47–67. (In Russ.).

Kuznetsov A.P., Sedova J.V., Sataev I.R. Structure of control parameters space of nonidentical coupled systems with period- doublings. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, no. 5, pp. 46–57. (In Russ.).

Kuznetsov A.P., Kuznetsov S.P. Critical dynamics of coupled map lattices at the onset of chaos. Izvestiya vysshikh uchebnykh zavedenii. Radiofizika, 1991, vol. 34, no. 10–12, pp. 1079–1115. (In Russ.).

Kulakov M.P., Axenovich T.I., Frisman E.Ya. Approaches to the description of spatial dynamics of migration-related populations. Regional problems, 2013, vol. 16, no. 1, pp. 5–14. (In Russ.).

Kulakov M.P., Frisman E.Ya. Simple and complex dynamics in the model of evolution of two populations coupled by migration with non-overlapping generations. Izvestiya VUZ. Applied Nonlinear Dynamics, 2022, vol. 30, no. 2, pp. 208–232. (In Russ.). DOI: 10.18500/0869-6632-2022-30-2-208-232.

Kulakov M.P., Frisman E.Y. Synchronizing the period-2 cycle in the system of symmetrical coupled populations with stock–recruitment based on the Ricker population model. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, no. 6, pp. 25–41. (In Russ.). DOI: 10.18500/0869-6632-2010-18-6-25-41.

Pozdnyakov M.V., Savin A.V. Multistable regimes in asymmetrically coupled period-­doubling systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, no. 5, pp. 44–53. (In Russ.). DOI: 10.18500/0869-6632-2010-18-5-44-53.

Salmenkova E.A., Gordeeva N.V., Rubtsova G.A., Omel’chenko V.T., Romanov N.S., Radchenko O.A. Genetic divergence of chars of the genus salvelinus from kronotsky lake (kamchatka peninsula). Russian Journal of Genetics, 2005, vol. 41, no. 8. pp. 897–906. DOI: 10.1007/s11177-005-0178-6.

Svirezhev Yu.M., Pasekov V.P. Osnovy matematicheskoi genetiki (Fundamentals of mathematical genetics). Moscow: Nauka Publ., 1982. 512 p. (In Russ.).

Frisman E.Y., Kulakov M.P. On the genetic divergence of two adjacent populations living in a homogeneous habitat. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, no. 5, pp. 706–726. (In Russ.). DOI: 10.18500/0869-6632-2021-29-5-706-726.

Frisman E.Y. Pervichnaya geneticheskaya divergentsiya (Teoreticheskii analiz i modelirovanie) (Primary genetic divergence (Theoretical analysis and modeling)). Vladivostok: FESC AS USSR, 1986. 160 p. (In Russ.).

Bertram J., Masel J. Different mechanisms drive the maintenance of polymorphism at loci subject to strong versus weak fluctuating selection. Evolution, 2019, vol. 73. pp. 883–896. DOI: 10.1111/evo.13719.

Bürger R. A survey of migration-selection mo-

dels in population genetics. Discrete & Continuous Dynamical Systems – B, 2014, vol. 19, no 4, pp. 883–959. DOI: 10.3934/dcdsb.2014.19.883.

Carroll S.P., Hendry A.P., Reznick D.N., Fox C.W. Evolution on ecological time-scales. Functional Ecology, 2007, vol. 21, pp. 387–393. DOI: 10.1111/j.1365-2435.2007.01289.x.

Fisher R.A. The genetical theory of natural selection. Oxford: Clarendon Press, 1930. 272 p. DOI: 10.5962/bhl.title.27468.

Fussmann G.F., Loreau M., Abrams P.A. Eco-evolutionary dynamics of communities and ecosystems. Functional Ecology, 2007, vol. 21, pp. 465–477. DOI: 10.1111/j.1365-2435.2007.01275.x.

Gaines M.S., McClenaghan Jr L.R., Rose R.K. Temporal patterns of allozymic variation in fluctuating populations of Microtus ochrogaster. Evolution, 1978, vo1. 32, no. 4, pp. 723–739. DOI: 10.2307/2407488.

Gottlieb L.D. Genetic stability in a peripheral isolate of Stephanomeria exigua ssp. coronaria that fluctuates in population size. Genetics, 1974, vol. 76, no. 3, pp. 551–556. DOI: 10.1093/genetics/76.3.551.

Haldane J.B.S. A mathematical theory of natural and artificial selection. Part II. The influence of partial self-fertilisation, inbreeding, assortative mating, and selective fertilisation on the composition of Mendelian populations, and on natural selection. Biological Reviews, 1924, no. 1, pp. 158–163. DOI: 10.1111/j.1469-185X.1924.tb00546.x.

Neverova G.P., Zhdanova O.L., Frisman E.Y. Effects of natural selection by fertility on the evolution of the dynamic modes of population number: bistability and multistability. Nonlinear Dynamics, 2020, vol. 101, pp. 687–709. DOI: 10.1007/s11071-020-05745-w.

Pelletier F., Garant D., Hendry A.P. Eco-evolutionary dynamics. Philosophical Transactions of the Royal Society B, 2009, vol. 364, no. 1523, pp. 1483–1489. DOI:10.1098/rstb.2009.0027.

Sato S., Urawa S. Genetic variation of Japanese pink salmon populations inferred from nucleotide sequence analysis of the mitochondrial DNA control region. Environmental biology of fishes, 2017, vol. 100, pp. 1355–1372. DOI: 10.1007/s10641-017-0648-4.

Smith W.H., Wooten J.A., Camp C.D., Stevenson D.J., Jensen J.B., Turner M., Reed N.A. Genetic divergence correlates with the contemporary landscape in populations of Slimy Salamander (Plethodon glutinosus) species complex across the lower Piedmont and Coastal Plain of the southeastern United States. Canadian Journal of Zoology, 2018, vol. 96, no. 11, pp. 1244–1254. DOI: 10.1139/cjz-2018-0050.

Tellier A., Brown J.K.M. Stability of genetic polymorphism in host–parasite interactions. Proceedings of the Royal Society B, 2007, vol. 274, pp. 809–817. DOI: 10.1098/rspb.2006.0281.

Telschow A., Hammerstein P., Werren J.H. The Effect of Wolbachia on Genetic Divergence between Populations: Models with Two-Way Migration. The American Naturalist, 2002, vol. 160, no. 4, pp. 54–66. DOI: 10.1086/342153.

Udwadia F.E., Raju N. Dynamics of Coupled Nonlinear Maps and Its Application to Ecological Modeling. Applied mathematic and computation, 1997, vol. 82, no. 2–3, pp. 137–179. DOI: 10.1016/S0096-3003(96)00027-6.

Yeaman S., Otto S.P. Establishment and maintenance of adaptive genetic divergence under migration, selection, and drift. Evolution, 2011, vol. 65, no. 7, pp. 2123–2129. DOI: 10.1111/j.1558-5646.2011.01277.x.

Zhdanova O.L., Frisman E.Ya. Genetic polymorphism under cyclical selection in long-lived species: The complex effect of age structure and maternal selection. Journal of Theoretical Biology, 2021, vol. 512, no. 110564. DOI: 10.1016/j.jtbi.2020.110564.


Ссылки

  • Ссылки не определены.