Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T07:30:59.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Aspects of population genetics theory

Published online by Cambridge University Press:  14 July 2016

W. J. Ewens
Get access Rights & Permissions [Opens in a new window]

Abstract

Population genetics and evolution have long supplied a stimulus to mathematical and statistical research. In this note a brief survey of current theory is given, with special reference to the work of P. A. P. Moran. Finally, an analysis of various biometrical questions is presented in the spirit of Moran's contributions to mathematical genetics.

Keywords

EVOLUTIONGENOTYPEFITNESSSELECTIONMUTATIONQUASI-MARKOVIAN PROPERTIESCHARGE STATE MODELSCORRELATION BETWEEN RELATIVESLINKAGE
Type
Part 1 — Genetics
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 9 - 17
Copyright
Copyright © 1982 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cockerham, C. C. (1954) An extension of the concept of partitioning hereditary variance for analysis of covariances among relatives when epistasis is present. Genetics 39, 859–882.CrossRefGoogle ScholarPubMed
Eaves, L. J., Last, K., Martin, N. G. and Jinks, J. L. (1977) A progressive approach to non-additivity and genotype-environmental convariance in the analysis of human differences. Brit. J. Math. Statist. Psychol. 30, 1–42.Google Scholar
Fisher, R. A. (1918) The correlation between relatives on the supposition of Mendelian inheritance. Trans. R. Soc. Edinburgh 52, 399–433.Google Scholar
Fisher, R. A. (1958) The Genetical Theory of Natural Selection (2nd revised edn). Dover, New York.Google Scholar
Kingman, J. F. C. (1976) Coherent random walks arising in some genetical models. Proc. R. Soc. London A 351, 19–31.Google Scholar
Moran, P. A. P. (1958) Random processes in genetics. Proc. Camb. Phil. Soc. 54, 60–71.Google Scholar
Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar
Moran, P. A. P. (1964) On the nonexistence of adaptive topographies. Ann. Hum. Genet. 27, 383–393.CrossRefGoogle ScholarPubMed
Moran, P. A. P. (1973) A note on heritability and the correlation between relatives. Ann. Hum. Genet. 37, 217.Google Scholar
Moran, P. A. P. (1975) Wandering distribution and the electrophoretic profile. Theoret. Popn Biol. 8, 318–330.Google Scholar
Moran, P. A. P. (1976) Wandering distributions and the electrophoretic profile II. Theoret. Popn Biol. 10, 145–149.CrossRefGoogle ScholarPubMed
Nagylaki, T. (1976) The evolution of one- and two-locus systems. Genetics 83, 583–600.Google Scholar
Norman, M. F. (1975) Approximation of stochastic processes by Gaussian diffusions, and applications to Wright-Fisher genetic models. SIAM. J. Appl. Math. 29, 225–242.Google Scholar
Ohta, T. and Kimura, M. (1973) A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population. Genet. Res. Camb. 22, 201–204.Google Scholar
Watterson, G. A. (1962) Some theoretical aspect of diffusion theory in population genetics. Ann. Math. Statist. 33, 939–957.Google Scholar
Wilson, S. (1982) Heritability. J. Appl. Prob. 19A, 71–85.Google Scholar
Wright, S. (1931) Evolution in Mendelian populations. Genetics 16, 97–159.Google Scholar
Wright, S. (1969) Evolution and the Genetics of Populations , Vol. 2. The Theory of Gene Frequencies. University of Chicago Press, Chicago.Google Scholar