Computer modeling of spatial dynamics and primary genetic divergence for a population system in a ring areal

   One of the main goals of modern evolutionary biology is to understand the mechanisms that lead to the initial differentiation (primary divergence) of populations into groups with genetic traits.

   This divergence requires reproductive isolation, which prevents or hinders contact and the exchange of genetic material between populations. This study explores the potential for isolation based not on obvious geographical barriers, population distance, or ecological specialization, but rather on hereditary mechanisms, such as gene drift and flow and selection against heterozygous individuals. To this end, we propose and investigate a dynamic discrete-time model that describes the dynamics of frequencies and numbers in a system of limited populations coupled by migrations. We consider a panmictic population with Mendelian inheritance rules, one-locus selection, and density-dependent factors limiting population growth. Individuals freely mate and randomly move around a one-dimensional ring-shaped habitat. The model was verified using data from an experiment on the box population system of Drosophila melanogaster performed by Yu.P. Altukhov et al. With rather simple assumptions, the model explains some mechanisms for the emergence and preservation of significant genetic differences between subpopulations (primary genetic divergence), accompanied by heterogeneity in allele frequencies and abundances within a homogeneous area. In this scenario, several large groups of genetically homogeneous subpopulations form and independently develop. Hybridization occurs at contact sites, and polymorphism is maintained through migration from genetically homogeneous nearby sites. It was found that only disruptive selection, directed against heterozygous individuals, can sustainably maintain such a spatial distribution. Under directional selection, divergence may occur for a short time as part of the transitional evolutionary process towards the best-adapted genotype. Because of the reduced adaptability of heterozygous (hybrid) individuals and low growth rates in these sites (hybrid zones), gene flow between adjacent sites with opposite genotypes (phenotypes) is significantly impeded. As a result, the hybrid zones can become effective geographical barriers that prevent the genetic flow between coupled subpopulations.

1. Aguillon S.M., Rohwer V.G. Revisiting a classic hybrid zone: movement of the northern flicker hybrid zone in contemporary times. Evolution. 2022;76(5):1082­1090. doi: 10.1111/evo.14474

2. Allee W.C. The Social Life of Animals. Beacon Press, 1958

3. Altukhov Yu.P. Genetic Processes in Populations. Moscow: Akadem kniga Publ., 2003 (in Russian)

4. Altukhov Yu.P., Bernashevskaya A.G. Experimental modeling of genetic processes in a population system of Drosophila melanogaster corresponding to a circular stepping­stone model: 2. Stability of al­lelic composition and periodic relationship of allele frequency with distance. Soviet Genetics. 1981;17(6):1052­1059 (in Russian)

5. Altukhov Yu.P., Bernashevskaya A.G., Milishnikov A.N. Experimen­tal modeling of genetic processes in the population system of Drosophila melanogaster corresponding to the ring step model. Soviet Genetics. 1979;15(4):646­655 (in Russian)

6. Bazykin A.D. Reduced fitness of heterozygotes in a system of adjacent populations. Soviet Genetics. 1972;8(11):155­161 (in Russian)

7. Blair W.F. Mating call and stage of speciation in the Microhyla olivacea–M. carolinensis complex. Evolution. 1955a;9(4):469­480. doi: 10.1111/j.1558­5646.1955.tb01556

8. Blair W.F. Size difference as a possible isolation mechanism in Micro­hyla. Am Nat. 1955b;89(848):297­301. doi: 10.1086/281894

9. Blinov V.N., Zheleznova T.K. Black Corvus corone and grey C. cornix crows: controversial issues about status (races, semispecies or species?), origin (allo­ or sympatric?) and the phenomenon of stable hybrid zones. Russkiy Ornitologicheskiy Zhurnal = Russian Ornithological Journal. 2020;29(1958):3596­3601 (in Russian)

10. Dey S., Joshi A. Stability via asynchrony in Drosophila metapopulations with low migration rates. Science. 2006;312(5772):434­436. doi: 10.1126/science.1125317

11. Filchak K., Roethele J., Feder J. Natural selection and sympatric divergence in the apple maggot Rhagoletis pomonella. Nature. 2000; 407(6805):739­742. doi: 10.1038/35037578

12. Frisman E.Y. Primary Genetic Divergence (Theoretical analysis and modeling). Vladivostok, 1986 (in Russian)

13. Haring E., Däubl B., Pinsker W., Kryukov A., Gamauf A. Genetic divergences and intraspecific variation in corvids of the genus Corvus (Aves: Passeriformes: Corvidae) – a first survey based on museum specimens. J Zool Syst Evol Res. 2012;50(3):230­246. doi: 10.1111/j.1439­0469.2012.00664.x

14. Kapitonova L.V., Formozov N.A., Fedorov V.V., Kerimov A.B., Seliva­nova D.S. Peculiarities of behavior and ecology of the Great tit Parus major Linneus, 1758 and Japanese tit P. minor Temmink et Schlegel, 1848 as possible factors of maintaining the stability of speciesspecific phenotypes in the area of sympatry and local hybridi zation in the Amur Region. Dal’nevostochnyy Ornitologicheskiy Zhurnal = Far Eastern Journal of Ornithology. 2012;3:37­46 (in Russian)

15. Keymer J.E., Galajda P., Muldoon C., Park S., Austin R.H. Bacterial metapopulations in nanofabricated landscapes. Proc Natl Acad Sci USA. 2006;103(46):17290­17295. doi: 10.1073/pnas.0607971103

16. Kryukov A.P. Phylogeography and hybridization of corvid birds in the Palearctic Region. Vavilov J Genet Breed. 2019;23(2):232­238. doi: 10.18699/VJ19.487

17. Kulakov M., Frisman E.Ya. Primary genetic divergence in a system of limited population coupled by migration in a ring habitat. Маthematical Biology and Bioinformatics. 2025;20(1):1­30. doi: 10.17537/2025.20.1 (in Russian)

18. Láruson Á.J., Reed F.A. Stability of underdominant genetic polymorphisms in population networks. J Theor Biol. 2016;390:156­163. doi: 10.1016/j.jtbi.2015.11.023

19. Littlejohn M.J. Premating isolation in the Hyla ewingi complex (Anura: Hylidae). Evolution. 1965;19(2):234­243. doi: 10.2307/2406376

20. Matsumoto M., Nishimura T. Mersenne twister: a 623­dimensionally equidistributed uniform pseudorandom number generator. ACM Trans Model Comput Simul. 1998;8(1):3­30. doi: 10.1145/272991.272995

21. Murphy M.A., Dezzani R., Pilliod D.S., Storfer A. Landscape genet­ics of high mountain frogmetapopulations. Mol Ecol. 2010;19(17): 3634­3649. doi: 10.1111/j.1365­294X.2010.04723.x

22. Orsini L., Corander J., Alasentie A., Hanski I. Genetic spatial structure in a butterfly metapopulation correlates better with past than present demographic structure. Mol Ecol. 2008;17(11):2629­2642. doi: 10.1111/j.1365­294X.2008.03782.x

23. Poelstra J.W., Vijay N., Bossu C.M., Lantz H., Ryll B., Müller I., Baglione V., Unneberg P., Wikelski M., Grabherr M.G., Wolf J.B.W. The genomic landscape underlying phenotypic integrity in the face of gene flow in crows. Science. 2014;344(6190):1410­1414. doi: 10.1126/science.1253226

24. Smith M.J., Osborne W., Hunter D. Geographic variation in the advertisement call structure of Litoria verreauxii (Anura: Hylidae). Copeia. 2003;4:750­758. doi: 10.1643/HA02­133.1

25. Sundqvist L., Keenan K., Zackrisson M., Prodöhl P., Kleinhans D. Directional genetic differentiation and relative migration. Ecol Evol. 2016;6(11):3461­3475. doi: 10.1002/ece3.2096

26. Tait C., Kharva H., Schubert M., Kritsch D., Sombke A., Rybak J., Feder J.L., Olsson S.B. A reversal in sensory processing accom­panies ongoing ecological divergence and speciation in Rhagoletis pomonella. Proc Biol Sci. 2021;288(1947):20210192. doi: 10.1098/rspb.2021.0192

27. Yeaman S., Otto S.P. Establishment and maintenance of adaptive genetic divergence under migration, selection, and drift. Evolution. 2011;65(7):2123­2129. doi: 10.1111/j.1558­5646.2011.01277.x

28. Yee W.L., Goughnour R.B. Mating frequencies and production of hy­brids by Rhagoletis pomonella and Rhagoletis zephyria (Diptera: Tephritidae) in the laboratory. Can Entomol. 2011;143(1):82­90. doi: 10.4039/n10­047

29. Zhdanova O.L., Frisman E.Y. On the genetic divergence of migration-coupled populations: modern modeling based on the experimental results of Yu.P. Altukhov et al. Russ J Genet. 2023;59:614­622. doi: 10.1134/S1022795423060133