Geodesic
Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals
Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024), pp. 293-303.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper studies an evolutionary model of natural selection in a two-stage population with autoregulation of the survival of adult individuals. The population breeds seasonally, and we assume that reproductive potential is determined genetically. The proposed ecological-genetic model is a combination of an ecological model of the dynamics of a stage-structured population and a microevolutionary model of the dynamics of its genetic structure when the adaptive trait of birth rate is controlled by a single diallelic autosomal locus with allelomorphs $A$ and $a$. We study the proposed model analytically and numerically and determine the parametric regions with different dynamic behaviors. We consider the possibility of changing the dynamic mode due to a variation in the genetic composition of the population. The study shows the genetic composition of the population, namely, whether will it be polymorphic or monomorphic, is mainly determined by the values of the reproductive potentials of heterozygotes and homozygotes. Reduced fitness of the heterozygotes leads to a “bistability trap” when both monomorphic fixed points are attractive, and the initial abundances of stage classes and allele frequencies determine the genotype that will be fixed in the population. However, with density-dependent regulation of the survival of adult individuals, displacement of one of the alleles can lead to the extinction of the population. In general, a change in the direction of evolution may be accompanied by a change in the population dynamics mode. 
@article{MBB_2024_19_a11,
     author = {G. P. Neverova and E. Ya. Frisman},
     title = {Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {293--303},
     publisher = {mathdoc},
     volume = {19},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2024_19_a11/}
}
TY  - JOUR
AU  - G. P. Neverova
AU  - E. Ya. Frisman
TI  - Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2024
SP  - 293
EP  - 303
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2024_19_a11/
LA  - ru
ID  - MBB_2024_19_a11
ER  - 
%0 Journal Article
%A G. P. Neverova
%A E. Ya. Frisman
%T Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals
%J Matematičeskaâ biologiâ i bioinformatika
%D 2024
%P 293-303
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2024_19_a11/
%G ru
%F MBB_2024_19_a11
G. P. Neverova; E. Ya. Frisman. Evolutionary dynamics of a two-stage population with density-dependent regulation of the survival of reproductive individuals. Matematičeskaâ biologiâ i bioinformatika, Tome 19 (2024), pp. 293-303. http://geodesic.mathdoc.fr/item/MBB_2024_19_a11/

[1] Haldone J. B.S., “Animal population and their regulation”, New Biology, 15 (1953), 9–24

[2] P. A.P. Moran, The statistical processes of evolutionary theory, Oxford University Press, London, 1962, 204 pp. <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0119.35901'>0119.35901</ext-link>

[3] L. C. Birch, “Stability and instability in natural populations”, Science Review. New Zealand, 20 (1962), 9–14

[4] Yu. M. Svirezhev, D. O. Logofet, Ustoichivost biologicheskikh soobschestv, Nauka, M., 1978, 352 pp. <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=537932'>537932</ext-link>

[5] A. D. Bazykin, Matematicheskaya biofizika vzaimodeistvuyuschikh populyatsii, Nauka, M., 1985, 181 pp.

[6] O. L. Zhdanova, E. Ya. Frisman, “Nelineinaya dinamika chislennosti populyatsii: vliyanie uslozhneniya vozrastnoi struktury na stsenarii perekhoda k khaosu”, Zhurnal obschei biologii, 72:3 (2011), 214–229

[7] E. Ya. Frisman, O. L. Zhdanova, “Evolyutsionnyi perekhod k slozhnym rezhimam dinamiki chislennosti dvukhvozrastnoi populyatsii”, Genetika, 45:9 (2009), 1277–1286

[8] E. Ya. Frisman, G. P. Neverova, O. L. Revutskaya, M. P. Kulakov, “Rezhimy dinamiki modeli dvukhvozrastnoi populyatsii”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya mekhanika, 18:2 (2010), 111–130

[9] G. P. Neverova, O. L. Zhdanova, E. Ya. Frisman, “Vozniknovenie slozhnykh rezhimov dinamiki chislennosti v khode evolyutsii strukturirovannoi limitirovannoi populyatsii”, Genetika, 56:7 (2020), 714–725 <ext-link ext-link-type='doi' href='https://doi.org/10.31857/S0016675820060065'>10.31857/S0016675820060065</ext-link>

[10] G. P. Neverova, O. L. Zhdanova, E. Y. Frisman, “Evolutionary dynamics of structured populations with density-dependent limitation of juvenile survival”, Communications in Nonlinear Science and Numerical Simulation, 109 (2022) <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.cnsns.2022.106272'>10.1016/j.cnsns.2022.106272</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4379793'>4379793</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1536.92080'>1536.92080</ext-link>

[11] M. Uilyamson, Analiz biologicheskikh populyatsii, Mir, M., 1975, 272 pp.

[12] Dazho R., Osnovy ekologii, Progress, M., 1975, 416 pp.

[13] Odum Yu., Osnovy ekologii, Mir, M., 1975, 740 pp.

[14] G. Yu. Riznichenko, A. B. Rubin, Biofizicheskaya dinamika produktsionnykh protsessov, Regulyarnaya i khaoticheskaya dinamika, Izhevskii institut kompyuternykh issledovanii, Moskva-Izhevsk, 2004, 464 pp.

[15] P. H. Leslie, “On the use of matrices in certain population mathematics”, Biometrika, 33:3 (1945), 183–212 <ext-link ext-link-type='doi' href='https://doi.org/10.1093/biomet/33.3.183'>10.1093/biomet/33.3.183</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=15760'>15760</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0060.31803'>0060.31803</ext-link>

[16] H. Caswell, Matrix Population Models: Construction, Analysis, and Interpretation, Sinauer Associates, Inc, Sunderland, MA, 2001

[17] L. P. Lefkovitch, “The study of population growth in organisms grouped by stages”, Biometrics, 21 (1965), 1–18 <ext-link ext-link-type='doi' href='https://doi.org/10.2307/2528348'>10.2307/2528348</ext-link>

[18] D. O. Logofet, I. N. Klochkova, “Matematika modeli Lefkovicha: reproduktivnyi potentsitsal i asimptoticheskie tsikly”, Matematicheskoe modelirovanie, 14:10 (2002), 116–126 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1989787'>1989787</ext-link><ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1011.92041'>1011.92041</ext-link>

[19] D. Logofet, “Convexity in projection matrices: Projection to a calibration problem”, Ecological Modelling, 216 (2008), 217–228 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.ecolmodel.2008.03.004'>10.1016/j.ecolmodel.2008.03.004</ext-link><ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=4478779'>4478779</ext-link>

[20] A. A. Gimmelfarb, L. R. Ginzburg, R. A. Poluektov, Yu. A. Pykh, V. A. Ratner, Dinamicheskaya teoriya biologicheskikh populyatsii, Nauka, M., 1974, 456 pp.

[21] E. Ya. Frisman, S. P. Luppov, I. N. Skokova, A. V. Tuzinkevich, “Slozhnye rezhimy dinamiki chislennosti populyatsii, predstavlennoi dvumya vozrastnymi klassami”, Matematicheskie issledovaniya v populyatsionnoi ekologii, DVO AN SSSR, Vladivostok, 1988, 4–18 <ext-link ext-link-type='mr-item-id' href='http://mathscinet.ams.org/mathscinet-getitem?mr=1033011'>1033011</ext-link>

[22] E. Ya. Frisman, E. I. Skaletskaya, “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti biologicheskikh populyatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 1:6 (1994), 988–1008 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0833.92011'>0833.92011</ext-link>

[23] E. Ya. Frisman, G. P. Neverova, O. L. Revutskaya, “Complex Dynamics of the Population with a Simple Age Structure”, Ecological Modelling, 222 (2011), 1943–1950 <ext-link ext-link-type='doi' href='https://doi.org/10.1016/j.ecolmodel.2016.09.005'>10.1016/j.ecolmodel.2016.09.005</ext-link>

[24] E. Ya. Frisman, “Strannye attraktory v prosteishikh modelyakh dinamiki chislennosti populyatsii s vozrastnoi strukturoi”, Doklady RAN, 338:2 (1994), 282–286 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:0900.92118'>0900.92118</ext-link>

[25] T. I. Axenovich, I. V. Zorkoltseva, I. R. Akberdin, S. V. Beketov, S. N. Kashtanov, I. A. Zakharov, P. M. Borodin, “Inheritance of litter size at birth in farmed arctic foxes (Alopex lagopus, Canidae, Carnivora)”, Heredity, 98:2 (2007), 99–105 <ext-link ext-link-type='doi' href='https://doi.org/10.1038/sj.hdy.6800908'>10.1038/sj.hdy.6800908</ext-link>

[26] A. P. Kuznetsov, Yu. V. Sedova, “Bifurkatsii trekhmernykh i chetyrekhmernykh otobrazhenii: Universalnye svoistva”, Izvestiya vysshikh uchebnykh zavedenii. Prikladnaya nelineinaya dinamika, 20:5 (2012), 26–43 <ext-link ext-link-type='zbl-item-id' href='https://zbmath.org/?q=an:1274.34117'>1274.34117</ext-link>

[27] O. L. Revutskaya, “Analiz izmeneniya chislennosti dikikh kopytnykh na osnove matematicheskoi modeli dinamiki populyatsii s polovoi strukturoi”, Regionalnye problemy, 27:2 (2024), 31–34