Group selection on the boundary of a stable population.

A model of group selection is constructed for the case of differential extinction acting on small boundary populations of a large, fixed population. Consideration is restricted to extinction operators acting at or near to carrying capacity. Under the assumption that the extinction rate is large relative to individual genetic parameters affecting gene frequencies in boundary populations, we discuss the conditions under which differential extinction is most likely to produce a significant effect. In particular, a condition for bimodality in the distribution of gene frequencies in boundary populations (population polymorphism) is that there be some critical allele frequency at which the extinction rate jumps from high to low. An extinction operator linear in allele frequency produces no qualitative effect of this kind. In consequence, we are able to make precise rather limited circumstances under which group selection is likely to have a significant effect.

[1]  George C. Williams,et al.  Adaptation and Natural Selection , 2018 .

[2]  S. Wright.  Tempo and Mode in Evolution: A Critical Review , 1945 .

[3]  L. Cook.  The Edge Effect in Population Genetics , 1961, The American Naturalist.

[4]  W. Hamilton.  The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[5]  E. Mayr.  Animal Species and Evolution , 1964 .

[6]  V. Gelder,et al.  The Serengeti Lion , 1973 .

[7]  R. Lewontin.  The Units of Selection , 1970, The Structure and Confirmation of Evolutionary Theory.

[8]  E. Wilson.  The Insect Societies , 1974 .

[9]  P. Moran,et al.  The statistical processes of evolutionary theory. , 1963 .

[10]  T. Ohta,et al.  Theoretical aspects of population genetics. , 1972, Monographs in population biology.

[11]  R. Levins.  Theory of Fitness in a Heterogeneous Environment. I. The Fitness Set and Adaptive Function , 1962, The American Naturalist.

[12]  E. Wilson.  The species equilibrium. , 1969, Brookhaven symposia in biology.

[13]  M. Kimura,et al.  An introduction to population genetics theory , 1971 .

[14]  Nathan Keyfitz,et al.  Introduction to the mathematics of population , 1968 .

[15]  R. Lewontin,et al.  Interdeme Selection Controlling a Polymorphism in the House Mouse , 1962, The American Naturalist.

[16]  R. Estes,et al.  Prey selection and hunting behavior of the African wild dog. , 1967 .

[17]  G. Schaller,et al.  The Relevance of Carnivore Behavior to the Study of Early Hominids , 1969, Southwestern Journal of Anthropology.

[18]  R. Levins.  Fitness and Optimization , 1970 .

[19]  L. Slobodkin.  Growth and regulation of animal populations , 1962 .

[20]  V. Wynne-Edwards.  Animal dispersion in relation to social behaviour , 1962 .

[21]  Edward O. Wilson,et al.  Experimental Zoogeography of Islands: Defaunation and Monitoring Techniques , 1969 .

[22]  S. Wright,et al.  Evolution and the Genetics of Populations: Volume 2, The Theory of Gene Frequencies , 1968 .

[23]  P. Darlington.  Interconnected patterns of biogeography and evolution. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Motoo Kimura,et al.  Diffusion models in population genetics , 1964, Journal of Applied Probability.

[25]  George C. Homans.  Sentiments and activities , 1962 .

[26]  Edward O. Wilson,et al.  The Ergonomics of Caste in the Social Insects , 1968, The American Naturalist.

[27]  A. Robertson.  A Theory of Limits in Artificial Selection with Many Linked Loci , 1970 .

[28]  David Pimentel,et al.  Animal Population Regulation by the Genetic Feed-Back Mechanism , 1961, The American Naturalist.

[29]  Holling Cs,et al.  Stability in ecological and social systems. , 1969 .

[30]  J. M. Smith.  Group Selection and Kin Selection , 1964, Nature.

[31]  R. Macarthur,et al.  The Theory of Island Biogeography , 1969 .

[32]  L. V. Valen.  GROUP SELECTION AND THE EVOLUTION OF DISPERSAL. , 1971 .

[33]  R. Levins.  Evolution in Changing Environments , 1968 .

[34]  Edward O. Wilson,et al.  Experimental Zoogeography of Islands: The Colonization of Empty Islands , 1969 .

[35]  A. Lomnicki.  Animal Population Regulation by the Genetic Feedback Mechanism: A Critique of the Theoretical Model , 1971, The American Naturalist.