Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 104
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Gallet, Romain Froissart, Rémy and Ravigné, Virginie 2018. Experimental demonstration of the impact of hard and soft selection regimes on polymorphism maintenance in spatially heterogeneous environments†. Evolution, Vol. 72, Issue. 8, p. 1677.
    Baquero, Fernando and Cantón, Rafael 2017. Antimicrobial Drug Resistance. p. 9.
    Leroy, Thibault Caffier, Valérie Celton, Jean-Marc Anger, Nicolas Durel, Charles-Eric Lemaire, Christophe and Le Cam, Bruno 2016. When virulence originates from nonagricultural hosts: evolutionary and epidemiological consequences of introgressions following secondary contacts inVenturia inaequalis. New Phytologist, Vol. 210, Issue. 4, p. 1443.
    Frankenhuis, Willem E. Panchanathan, Karthik and Belsky, Jay 2016. A mathematical model of the evolution of individual differences in developmental plasticity arising through parental bet-hedging. Developmental Science, Vol. 19, Issue. 2, p. 251.
    Holmes, Christopher J. Pantel, Jelena H. Schulz, Kimberly L. and Cáceres, Carla E. 2016. Initial genetic diversity enhances population establishment and alters genetic structuring of a newly establishedDaphniametapopulation. Molecular Ecology, Vol. 25, Issue. 14, p. 3299.
    Bono, Lisa M. Gensel, Catharine L. Pfennig, David W. and Burch, Christina L. 2015. Evolutionary rescue and the coexistence of generalist and specialist competitors: an experimental test. Proceedings of the Royal Society B: Biological Sciences, Vol. 282, Issue. 1821, p. 20151932.
    Dia, A. Guillou, L. Mauger, S. Bigeard, E. Marie, D. Valero, M. and Destombe, C. 2014. Spatiotemporal changes in the genetic diversity of harmful algal blooms caused by the toxic dinoflagellateAlexandrium minutum. Molecular Ecology, Vol. 23, Issue. 3, p. 549.
    Cayetano, L. and Vorburger, C. 2013. Genotype-by-genotype specificity remains robust to average temperature variation in an aphid/endosymbiont/parasitoid system. Journal of Evolutionary Biology, Vol. 26, Issue. 7, p. 1603.
    Friman, Ville-Petri Buckling, Angus and Grover, James 2013. Effects of predation on real-time host-parasite coevolutionary dynamics. Ecology Letters, Vol. 16, Issue. 1, p. 39.
    Zakas, Christina and Hall, David W. 2012. Asymmetric Dispersal Can Maintain Larval Polymorphism: A Model Motivated by Streblospio benedicti. Integrative and Comparative Biology, Vol. 52, Issue. 1, p. 197.
    Gsell, Alena S. de Senerpont Domis, Lisette N. Przytulska-Bartosiewicz, Anna Mooij, Wolf M. van Donk, Ellen and Ibelings, Bas W. 2012. GENOTYPE-BY-TEMPERATURE INTERACTIONS MAY HELP TO MAINTAIN CLONAL DIVERSITY INASTERIONELLA FORMOSA(BACILLARIOPHYCEAE). Journal of Phycology, Vol. 48, Issue. 5, p. 1197.
    Débarre, Florence and Gandon, Sylvain 2011. Evolution in Heterogeneous Environments: Between Soft and Hard Selection. The American Naturalist, Vol. 177, Issue. 3, p. E84.
    Traxler, Christian and Spichtig, Mathias 2011. Social norms and the indirect evolution of conditional cooperation. Journal of Economics, Vol. 102, Issue. 3, p. 237.
    VORBURGER, CHRISTOPH EUGSTER, BETTINA VILLIGER, JÖRG and WIMMER, CORINNE 2010. Host genotype affects the relative success of competing lines of aphid parasitoids under superparasitism. Ecological Entomology, Vol. 35, Issue. 1, p. 77.
    Barton, N. H. 2010. What role does natural selection play in speciation?. Philosophical Transactions of the Royal Society B: Biological Sciences, Vol. 365, Issue. 1547, p. 1825.
    Bierne, Nicolas 2010. THE DISTINCTIVE FOOTPRINTS OF LOCAL HITCHHIKING IN A VARIED ENVIRONMENT AND GLOBAL HITCHHIKING IN A SUBDIVIDED POPULATION. Evolution, Vol. 64, Issue. 11, p. 3254.
    FORMICA, V. A. and TUTTLE, E. M. 2009. Examining the social landscapes of alternative reproductive strategies. Journal of Evolutionary Biology, Vol. 22, Issue. 12, p. 2395.
    Vale, P F and Little, T J 2009. Measuring parasite fitness under genetic and thermal variation. Heredity, Vol. 103, Issue. 2, p. 102.
    Lazzaro, Brian P and Little, Tom J 2009. Immunity in a variable world. Philosophical Transactions of the Royal Society B: Biological Sciences, Vol. 364, Issue. 1513, p. 15.
    Novembre, John and Di Rienzo, Anna 2009. Spatial patterns of variation due to natural selection in humans. Nature Reviews Genetics, Vol. 10, Issue. 11, p. 745.
    Download full list
    ×

  • Access

Polymorphism in a varied environment: how robust are the models?

  • J. Maynard Smith (a1) and R. Hoekstra (a2)

Summary

This paper shows that a number of models of the maintenance of polymorphism in a heterogeneous environment, including those of Levene and Dempster, can be derived from a simple assumption about the way in which the numbers and kinds of individuals emerging from a niche depend on the number of eggs laid in it. It is shown that for such models, unless selective advantages per locus are large, protected polymorphism requires that the relative niche sizes lie in a narrow range. This lack of robustness applies also to models of stable polymorphism proposed by Clarke and by Stewart & Levin. Excluding models relaying on habitat selection or restricted migration, the only models which may escape this criticism are diploid models with partial dominance with respect to fitness, such as one proposed by Gillespie, in which in all niches the fitness of heterozygotes is higher than the arithmetic mean of the homozygotes.

    •

      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Polymorphism in a varied environment: how robust are the models?
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Polymorphism in a varied environment: how robust are the models?
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Polymorphism in a varied environment: how robust are the models?
      Available formats
      ×

Copyright

COPYRIGHT: © Cambridge University Press 1980

References

Hide All
Clarke, B. (1972). Density-dependent selection. American Naturalist 106, 1–13.
Clarke, B. (1979). The evolution of genetic diversity. Proceedings of the Royal Society B 206, 453–474.
Clarke, B. & Allendorf, F. W. (1979). Frequency-dependent selection due to kinetic differences between allozymes. Nature 279, 732–734.
Crow, J. F. & Temust, R. G. (1964). Evidence for the partial dominance of recessive lethal genes in natural populations of Drosophila. American Naturalist 98, 21–33.
de Jong, G. (1976). A model of competition for food. I. Frequency-dependent viabilities. American Naturalist 110, 1013–1027.
Dempster, E. R. (1955). Maintenance of genetic heterogeneity. Cold Spring Harbor Symposia on Quantitative Biology 20, 25–32.
Gillespie, J. H. (1976). A general model to account for enzyme variation in natural populations. II. Characterization of the fitness functions. American Naturalist 110, 809–821.
Gillespie, J. H. (1977). A general model to account for enzyme variation in natural populations. IV. The quantitative genetics of viability mutants. In Measuring Selection in Natural Populations (ed. Christiansen, F. B. and Fenchel, T. M.), pp. 301–314. Berlin: Springer-Verlag.
Hoekstra, R. F. (1978). Sufficient conditions for polymorphism with cyclical selection in a subdivided population. Genetical Research 31, 67–73.
Levene, H. (1953). Genetic equilibrium when more than one ecological niche is available. American Naturalist 87, 331–333.
Levins, R. (1962). Theory of fitness in a heterogeneous environment. I. The fitness set and adaptive function. American Naturalist 96, 361–373.
Lotka, A. J. (1932). The growth of mixed populations: Two species competing for a common food supply. Journal of the Washington Academy of Sciences 21, 461–469.
Maynard Smith, J. (1966). Sympatric speciation. American Naturalist 100, 637–650.
Mukai, T., Chigusa, S. T., Mettler, L. E. & Crow, J. F. (1972). Mutation rate and dominance of genes affecting viability in Drosophila melanogaster. Genetics 72, 335–355.
Stewart, F. M. & Levin, B. R. (1973). Partitioning of resources and the outcome of interspecific competition: a model and some general considerations. American Naturalist 107, 171–198.
Volterra, V. (1927). Variations and fluctuations in the numbers of coexisting animal species. Translation in The Golden Age of Theoretical Ecology (ed. Scudo, F. M. and Ziegler, J. R.). Berlin: Springer-Verlag.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed

Cancel
Confirm
×