maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2024-2-142-151mais-1850Research ArticleAlgorithms in Computer ScienceМатематические свойства агентной модели вымирания — реколонизации для популяционной генетикиMathematical properties of the agent-based model of extinction — recolonization for population geneticshttps://orcid.org/0009-0001-0522-6856ГаяновНикита ВладимировичGaianovNikita V.nvgayanov@edu.hse.ruНациональный исследовательский университет «Высшая школа экономики»РоссияNational Research University Higher School of EconomicsRussian Federation202413062024312142151Copyright © Гаянов Н.В., 20242024Гаянов Н.В.Gaianov N.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1850

Агентная модель описывает динамику генетического разнообразия непрерывно распределенной популяции в случае конечного числа особей. В событии вымирания в некоторой области умирает часть популяции, после чего в ходе реколонизации рождаются новые особи с генотипом родителя. Мы рассматриваем модель, а также её модификацию, и получаем свойства, связанные с популяционными параметрами. В работе показано, что время жизни особей имеет экспоненциальное распределение, вероятности аллелей сохраняются во времени, средняя гетерозиготность при ограничении, связанном с числом особей при вымирании и реколонизации, равна аналогичной величине в модели Морана. Совместное распределение аллелей обобщено на случай популяций, непрерывно расположенных в пространстве. Совместное распределение аллелей и гетерозиготность посчитаны на симуляциях.

The individual-based model describes the dynamics of genetic diversity of a population scattered on a spatial continuum in the case of a finite number of individuals. During extinction events in a certain area, a portion of the population dies, after which new individuals with the genotype of the parent are born during recolonization event. In this paper we examine the model, as well as its modification, and derive properties related to population parameters. The study demonstrates that the lifespan of individuals follows an exponential distribution, allele probabilities remain constant over time, and the average heterozygosity, constrained by the number of individuals during extinction and recolonization, equals a similar quantity in the Moran model. The joint distribution of alleles is generalized for populations continuously scattered in space. Joint allele distribution and heterozygosity are computed through simulations.

популяционная модельреколонизациянепрерывное пространствомодель Моранаpopulation modelrecolonisationspatial continuumMoran modelРоссийский научный фонд (проект No 22-71-10056).Russian Science Foundation (Project no. 22-71-10056).ReferencesR. Durrett and R. Durrett, Probability models for DNA sequence evolution. Springer, 2008.R. Durrett and R. Durrett, Probability models for DNA sequence evolution. Springer, 2008.J. Felsenstein, “A pain in the torus: some difficulties with models of isolation by distance,” The American Naturalist, vol. 109, no. 967, pp. 359–368, 1975.J. Felsenstein, “A pain in the torus: some difficulties with models of isolation by distance,” The American Naturalist, vol. 109, no. 967, pp. 359–368, 1975.A. M. Etheridge, “Survival and extinction in a locally regulated population,” The Annals of Applied Probability, vol. 14, no. 1, pp. 188–214, 2004.A. M. Etheridge, “Survival and extinction in a locally regulated population,” The Annals of Applied Probability, vol. 14, no. 1, pp. 188–214, 2004.A. Etheridge, Some Mathematical Models from Population Genetics: 'Ecole D''Et'e de Probabilit'es de Saint-Flour XXXIX-2009. Springer Science & Business Media, 2011.A. Etheridge, Some Mathematical Models from Population Genetics: 'Ecole D''Et'e de Probabilit'es de Saint-Flour XXXIX-2009. Springer Science & Business Media, 2011.N. Barton, A. Etheridge, and A. V'eber, “A New Model for Evolution in a Spatial Continuum,” Electronic Journal of Probability, vol. 15, pp. 162–216, 2010, doi: 10.1214/EJP.v15-741.N. Barton, A. Etheridge, and A. V'eber, “A New Model for Evolution in a Spatial Continuum,” Electronic Journal of Probability, vol. 15, pp. 162–216, 2010, doi: 10.1214/EJP.v15-741.N. Biswas, A. Etheridge, and A. Klimek, “The spatial Lambda-Fleming-Viot process with fluctuating selection,” Electronic Journal of Probability, vol. 26, pp. 1–51, 2021, doi: 10.1214/21-EJP593.N. Biswas, A. Etheridge, and A. Klimek, “The spatial Lambda-Fleming-Viot process with fluctuating selection,” Electronic Journal of Probability, vol. 26, pp. 1–51, 2021, doi: 10.1214/21-EJP593.A. M. Etheridge, A. V'eber, and F. Yu, “Rescaling limits of the spatial Lambda-Fleming-Viot process with selection,” Electronic Journal of Probability, vol. 25, pp. 1–89, 2020, doi: 10.1214/20-EJP523.A. M. Etheridge, A. V'eber, and F. Yu, “Rescaling limits of the spatial Lambda-Fleming-Viot process with selection,” Electronic Journal of Probability, vol. 25, pp. 1–89, 2020, doi: 10.1214/20-EJP523.S. Guindon, H. Guo, and D. Welch, “Demographic inference under the coalescent in a spatial continuum,” Theoretical population biology, vol. 111, pp. 43–50, 2016.S. Guindon, H. Guo, and D. Welch, “Demographic inference under the coalescent in a spatial continuum,” Theoretical population biology, vol. 111, pp. 43–50, 2016.T. A. Joseph, M. J. Hickerson, and D. F. Alvarado-Serrano, “Demographic inference under a spatially continuous coalescent model,” Heredity, vol. 117, no. 2, pp. 94–99, 2016.T. A. Joseph, M. J. Hickerson, and D. F. Alvarado-Serrano, “Demographic inference under a spatially continuous coalescent model,” Heredity, vol. 117, no. 2, pp. 94–99, 2016.R. L. Streit and R. L. Streit, The Poisson point process. Springer, 2010.R. L. Streit and R. L. Streit, The Poisson point process. Springer, 2010.J. Wakely, Coalescent Theory: An Introduction. Macmillan Learning, 2016.J. Wakely, Coalescent Theory: An Introduction. Macmillan Learning, 2016.

The authors declare that there are no conflicts of interest present.