ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Frisman E. Y., Zhdanova O. L. The dynamic behavior of genetic structure and population size in the evolution models of limited population. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 1, pp. 98-112. DOI: 10.18500/0869-6632-2006-14-1-98-112

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text:
(downloads: 134)
Language: 
Russian
Article type: 
Article
UDC: 
574.3

The dynamic behavior of genetic structure and population size in the evolution models of limited population

Autors: 
Frisman Efim Yakovlevich, Institute for Complex Analysis of Regional Problems of Russian Academy of Sciences, Far Eastern Branch
Zhdanova Oksana Leonidovna, Institute of Automation and Control Processes, FEB RAS (IASP FEB RAS)
Abstract: 

It has been shown in this work how the evolutionary change of alleles’ frequencies, which is accompanied by the growth of average population fitness, leads to chaotic and cyclic dynamics of population size. Then the possible mechanisms of appearance of complicate temporal organization of genetic biodiversity have been considered.

Key words: 
Reference: 
  1. Roulier KF. Animal life in relation to external conditions. Moscow: Nauka; 1952. 121 p. (In Russian).
  2. Pianka E. Evolutionary ecology. Moscow: Mir; 1981. 400 p. (In Russian).
  3. Davis DE, Christian J. Population reflection in mammals. Ecology. 1976;1:15–31.
  4. Chitty D. The natural selection of self-regulatory behavior in animal populations. Proc. Ecol. Soc. Australia. 1967;2:51–78.
  5. Shapiro AP. To the question of cycles in return sequences. Management and information. Iss. 3. Vladivostok: FEB AS USSR; 1972. P. 96. (In Russian).
  6. Shapiro AP, Luppov SP. Recurved equations in the theory of population biology. Moscow: Nauka; 1983. 132 p. (In Russian).
  7. May RM. Biological populations obeying difference equations: stable points, stable cycles, and chaos. J Theor Biol. 1975;51(2):511–524. DOI: 10.1016/0022-5193(75)90078-8.
  8. Ricker WE. Stock and recruitment. Theor. J. Fish. Res. Bard. Can. 1954;11(5):559–623. DOI: 10.1139/F54-039.
  9. Fisher RA. The genetical theory of natural selection. Oxford: Clarendon Press; 1930. 308 p.
  10. Ratner VA. Mathematical population genetics. Novosibirsk: Nauka; 1977. 126 p. (In Russian).
  11. Gottlieb LD. Genetic stability in a peripheral isolate of Stephanomeria exigua spp. coronaria that fluctuates in population size. Genetics. 1974;76(3):551–556.
  12. Graines MS, McClenaghay LR, Rose RR. Temporal patterns of allozymic variation in fluctuating populations in Microtus ochrogaster. Evolution. 1978;32(4):723–739. DOI: 10.1111/j.1558-5646.1978.tb04626.x.
  13. Kingman JFC. A mathematical problem in population genetics. Proc. Can. Phill. Soc. 1961;57(3):574–582. DOI: 10.1017/S0305004100035635.
  14. Witten M. Fitness and survival in logistic models. J Theor Biol. 1978;74(1):23–32. DOI: 10.1016/0022-5193(78)90287-4.
  15. Frisman EY, Skaletskaya EI. Strange attractors in the simplest models of the dynamics of biological populations. Vestnik of Far Eastern Branch of Russian Academy of Sciences. 1994;5/6:97.
  16. Evdokimov EV. Problems of regular behavior and deterministic chaos in the main models of population dynamics (Theory and experiment). Autoreferat dissertation Doctor of Biological Sciences. Krasnoyarsk. 1999. 39 p. (In Russian).
  17. Pianka ER. On r- and K-selection. Amer. Natur. 1970;104:592–597. DOI: 10.1086/282697.
  18. Pianka ER. Evolution ecology. New York: Harper and Row; 1974. 356 p.
  19. Pianka E.R. On r- and K-selection. San Francisco: Reading Sociobiol; 1978. P. 45.
  20. Graham J. Reproductive effect and r- and K-selection in two species of Lacuna (Gastropods: Prosobranchia). Mar. Biol. 1977;40(3):217–224. DOI: 10.1007/BF00390877.
  21. Long T, Long G. The effects of r- and K-selection on components of variance for two quantitative traits. Genetics. 1974;76(3):567–573. DOI: 10.1093/genetics/76.3.567.
  22. MacNaughton SJ. r- and K-selection in Tipha. Amer. Natur. 1975;109(961):251–261.
  23. Rougharden J. Density dependent natural selection. Ecology. 1971;52(3):453–468. DOI: 10.2307/1937628.
  24. Charlesworth B. Selection in density-regulated populations. Ecology. 1971;52:469–474. DOI: 10.2307/1937629.
  25. Asmussen MA. Regular and chaotic cycling in models of ecological genetics. Theor Popul Biol. 1979;16(2):172–190. DOI: 10.1016/0040-5809(79)90012-1.
  26. Birch LC. Selection in Drosophila pseudob. in relat. to crow. Evol. 1955;9(4):160.
  27. Chitty D. Population processes in the vole and their relevance to general theory. Canad. J. Zool. 1960;38(1):99–113.
  28. Farmer J. Doyne, Ott Edward, Yorke James A. The dimension of chaotic attractors. Physica D7, North-Holland Publishing Company; 1983. P. 153.
  29. Zhdanova OL, Frisman EYa. The investigation of the model dynamics of the Mendelian one-locus poly-allelic population under the exponential density-dependent natural selection. Dal'nevost. Mat. Zh. 2004;5(2):250–262.
Received: 
06.06.2005
Accepted: 
22.01.2006
Published: 
28.04.2006
Short text (in English):
(downloads: 59)