Skip to main content
PMC home page
Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1980 Dec;77(12):7501–7505. doi: 10.1073/pnas.77.12.7501

Density-dependent selection in a random environment: An evolutionary process that can maintain stable population dynamics

Michael Turelli 1, Doug Petry 1
PMCID: PMC350533  PMID: 16592939

Abstract

A theoretical analysis of natural selection is presented in which fitnesses depend on population density and randomly varying environmental processes. The theory is based on a general, heuristic analysis of a pair of coupled, nonlinear, stochastic difference equations that describe the joint dynamics of allele frequencies and population size. Four main conclusions emerge from the investigation of a particular class of models: (i) growth rates at low population densities tend to increase; (ii) individual selection, given sufficient genetic flexibility, will mold growth rates at higher densities so that in spite of i, stable deterministic population dynamics are maintained; (iii) “more fit” genotypes cannot be simply characterized—in particular, the mean population size need not be increased; and (iv) genetic polymorphisms can be maintained in both haploid and diploid organisms.

Keywords: ecological genetics, r-selection, chaos, stochastic approximations

Full text

PDF
7502

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Armstrong R. A., Gilpin M. E. Evolution in a time-varying environment. Science. 1977 Feb 11;195(4278):591–592. doi: 10.1126/science.835017. [DOI] [PubMed] [Google Scholar]
  2. Asmussen M. A., Feldman M. W. Density dependent selection 1: A stable feasible equilibrium may not be attainable. J Theor Biol. 1977 Feb 21;64(4):603–618. doi: 10.1016/0022-5193(77)90263-6. [DOI] [PubMed] [Google Scholar]
  3. Asmussen M. A. Regular and chaotic cycling in models of ecological genetics. Theor Popul Biol. 1979 Oct;16(2):172–190. doi: 10.1016/0040-5809(79)90012-1. [DOI] [PubMed] [Google Scholar]
  4. Felsenstein J. The theoretical population genetics of variable selection and migration. Annu Rev Genet. 1976;10:253–280. doi: 10.1146/annurev.ge.10.120176.001345. [DOI] [PubMed] [Google Scholar]
  5. Gilpin M. E., Ayala F. J. Global models of growth and competition. Proc Natl Acad Sci U S A. 1973 Dec;70(12):3590–3593. doi: 10.1073/pnas.70.12.3590. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Heckel D. G., Roughgarden J. A species near its equilibrium size in a fluctuating environment can evolve a lower intrinsic rate of increase. Proc Natl Acad Sci U S A. 1980 Dec;77(12):7497–7500. doi: 10.1073/pnas.77.12.7497. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Karlin S., Carmelli D. Numerical studies on two-loci selection models with general viabilities. Theor Popul Biol. 1975 Jun;7(3):399–421. doi: 10.1016/0040-5809(75)90026-x. [DOI] [PubMed] [Google Scholar]
  8. Macarthur R. H. SOME GENERALIZED THEOREMS OF NATURAL SELECTION. Proc Natl Acad Sci U S A. 1962 Nov;48(11):1893–1897. doi: 10.1073/pnas.48.11.1893. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. May R. M. Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos. Science. 1974 Nov 15;186(4164):645–647. doi: 10.1126/science.186.4164.645. [DOI] [PubMed] [Google Scholar]
  10. May R. M., MacArthur R. H. Niche overlap as a function of environmental variability. Proc Natl Acad Sci U S A. 1972 May;69(5):1109–1113. doi: 10.1073/pnas.69.5.1109. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Roughgarden J. Resource partitioning among competing species--a coevolutionary approach. Theor Popul Biol. 1976 Jun;9(3):388–424. doi: 10.1016/0040-5809(76)90054-x. [DOI] [PubMed] [Google Scholar]
  12. Schoener T. W. Effects of density-restricted food encounter on some single-level competition models. Theor Popul Biol. 1978 Jun;13(3):365–381. doi: 10.1016/0040-5809(78)90052-7. [DOI] [PubMed] [Google Scholar]
  13. Turelli M. Does environmental variability limit niche overlap? Proc Natl Acad Sci U S A. 1978 Oct;75(10):5085–5089. doi: 10.1073/pnas.75.10.5085. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Turelli M., Gillespie J. H. Conditions for the existence of stationary densities for some two-dimensional diffusion processes with applications in population biology. Theor Popul Biol. 1980 Apr;17(2):167–189. doi: 10.1016/0040-5809(80)90004-0. [DOI] [PubMed] [Google Scholar]

Articles from Proceedings of the National Academy of Sciences of the United States of America are provided here courtesy of National Academy of Sciences

RESOURCES