Effective population size is a key parameter in evolutionary and quantitative genetics because it measures the rate of genetic drift and inbreeding. Predictive equations of effective size under a range of circumstances and some of their implications are reviewed in this paper. Derivations are made for the simplest cases, and the inter-relations between different formulae and methods are discussed.
Avery, P J. 1984. The population genetics of haplo-diploids and X-linked genes. Genet Res, 44, 321–341.
Barton, N H. 1993. The probability of fixation of a favoured allele in a subdivided population. Genet Res, 62, 149–157.
Barton, N H, and Charlesworth, B. 1984. Genetic revolutions, founder effects and speciation. Ann Rev Ecol Syst, 15, 133–164.
Begon, M, Krimbas, C B, and Loukas, M. 1980. The genetics of Drosophila subobscura populations. XV. Effective size of a natural population estimated by three independent methods. Heredity, 45, 335–350.
Briscoe, D A, Malpica, J M, Robertson, A, Smith, G J, Frankham, R, Banks, R G, and Barker, J S F. 1992. Rapid loss of genetic variation in large captive populations of Drosophila flies. Implications for the genetic management of captive populations. Conserv Biol, 6, 416–425.
Bulmer, M G. 1980. The Mathematical Theory of Quantitative Genetics. Clarendon Press, Oxford.
Burrows, P M. 1984a. Inbreeding under selection from unrelated families. Biometrics, 40, 357–366.
Burrows, P M. 1984b. Inbreeding under selection from related families. Biometrics, 40, 895–906.
Caballero, A. 1994. On the effective size of populations with separate sexes, with particular reference to sex-linked genes. Genetics, (in press).
Caballero, A, and Hill, W G. 1992a. Effective size of non-random mating populations. Genetics, 130, 909–916.
Caballero, A, and Hill, W G. 1992b. A note on the inbreeding effective population size. Evolution, 46, 1969–1972.
Chesser, R K, Rhodes, O E, Sugg, D W, and Schnabel, A. 1993. Effective sizes for subdivided populations. Genetics, 135, 1221–1232.
Chia, A B, and Pollak, E. 1974. The inbreeding effective number and the effective number of alleles in a population that varies in size. Theor Pop Biol, 6, 149–172.
Choy, S C, and Weir, B S. 1978. Exact inbreeding coefficients in populations with overlapping generations. Genetics, 89, 591–614.
Cockerham, C C. 1969. Variance of gene frequencies. Evolution, 23, 72–84.
Crow, J F. 1954. Breeding structure of populations. II. Effective population number. In: Kempthorne, O., Bancroft, T. A., Gowen J. W., and Lush, J. L. (eds) Statistics and Mathematics in Biology, pp. 543–556. Iowa State College Press, Ames, IA.
Crow, J F, and Denniston, C. 1988. Inbreeding and variance effective population numbers. Evolution, 42, 482–495.
Crow, J F, and Kimura, M. 1970. An Introduction to Population Genetics Theory. Harper and Row, New York.
Crow, J F, and Morton, N E. 1955. Measurement of gene frequency drift in small populations. Evolution, 9, 202–214.
Emigh, T H, and Pollak, E. 1979. Fixation probabilities and effective population numbers in diploid populations with overlapping generations. Theor Pop Biol, 15, 86–107.
Ethier, S N, and Nagylaki, T. 1980. Diffusion approximations of Markov chains with two time scales and applications to population genetics. Adv Appl Prob, 12, 14–49.
Ewens, W J. 1979. Mathematical Population Genetics. Springer, Berlin.
Ewens, W J. 1982. On the concept of effective population size. Theor Pop Biol, 21, 373–378.
Falconer, D S. 1989. Introduction to Quantitative Genetics, 3rd edn. Longman, Harlow, Essex.
Felsenstein, J. 1971. Inbreeding and variance effective numbers in populations with overlapping generations. Genetics, 68, 581–597.
Fisher, R A. 1918. The correlation between relatives on the supposition of Mendelian inheritance. Trans R Soc Edinb, 52, 399–433.
Fisher, R A. 1930. The Genetical Theory of Natural Selection. Clarendon Press, Oxford.
Fisher, R A. 1939. Stage of development as a factor influencing the variance in the number of offspring, frequency of mutants and related quantities. Ann Eugen, 9, 406–408.
Frankham, R. 1994. Conservation of genetic diversity for animal improvement. Proc 5th World Cong Genet Applied to Lives Prod, 21, 385–392.
Gallego, A, and Caballero, A. 1990. The cumulative effect of artificial selection on the reduction of population effective size. Experimental and simulated data. J Anim Breed Genet, 107, 180–187.
Gallego, A, and Garcia-Dorado, A. 1986. Evolution de l'effectif génétique de lignées de Drosophila melanogaster soumises à une sélection artificielle. Génét Sél Évol, 18, 249–260.
Ghai, G L. 1969. Structure of populations under mixed random and sib mating. Theor Appl Genet, 39, 179–182.
Gowe, R S, Robertson, A, and Latter, B D H. 1959. Environment and poultry breeding problems. 5. The design of poultry control strains. Poultry Sci, 38, 462–471.
Gregorius, H-R. 1991. On the concept of effective number. Theor Pop Biol, 40, 269–283.
Haldane, J B S. 1924. A mathematical theory of natural and artificial selection. II. The influence of partial self-fertilisation, inbreeding, assortative mating, and selective fertilisation on the composition of Mendelian populations, and on natural selection. Proc Camb Phil Soc, (Biol Sci), (later Biol Rev), 1, 158–163.
Haldane, J B S. 1939. The equilibrium between mutation and random extinction. Ann Eugen, 9, 400–405.
Hedrick, P W, and Cockerham, C C. 1986. Partial inbreeding: equilibrium heterozygosity and the heterozygosity paradox. Evolution, 40, 856–861.
Hill, W G. 1972a. Estimation of genetic change. I. General theory and design of control populations. Anim Breed Abstr, 40, 1–15.
Hill, W G. 1972b. Effective size of populations with overlapping generations. Theor Pop Biol, 3, 278–289.
Hill, W G. 1979. A note on effective population size with overlapping generations. Genetics, 92, 317–322.
Hill, W G. 1985a. Effects of population size on response to short and long term selection. J Anim Breed Genet, 102, 161–173.
Hill, W G. 1985b. Fixation probabilities of mutant genes with artificial selection. Génét Sél Évol, 17, 351–358.
Hill, W G. 1986. Population size and design of breeding programmes. Proc 3rd World Cong Genet Applied to Lives Prod, 12, 245–256.
James, J W. 1962. The spread of genes in random mating control populations. Genet Res, 3, 1–19.
James, J W, and McBride, G. 1958. The spread of genes by natural and artificial selection in a closed poultry flock. J Genet, 56, 55–62.
Johnson, D L. 1977. Inbreeding in populations with overlapping generations. Genetics, 87, 581–591.
Jones, L P. 1969. Effect of artificial selection on rates of inbreeding in populations of Drosophila melanogaster. 1. Effect on early generations. Aust J Biol Sci, 22, 143–155.
Kimura, M. 1963. A probability method for treating inbreeding systems, especially with linked genes. Biometrics, 19, 1–17.
Kimura, M. 1983. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge.
Kimura, M, and Crow, J F. 1963a. The measurement of effective population number. Evolution, 17, 279–288.
Kimura, M, and Crow, J F. 1963b. On the maximum avoidance of inbreeding. Genet Res, 4, 399–415.
Latter, B D H. 1959. Genetic sampling in a random mating population of constant size and sex ratio. Aust J Biol Sci, 12, 500–505.
Lande, R, and Barrowclough, G F. 1987. Effective population size, genetic variation, and their use in population management. In: Soulé, M. E. (ed.) Viable Populations for Conservation, pp. 87–123. Cambridge University Press, Cambridge.
Li, C C. 1976. First Course in Population Genetics. Boxwood, Pacific Grove, CA.
Lush, J L. 1947. Family merit and individual merit as bases for selection. Am Nat, 81, 241–261, 362–379.
Malécot, G. 1948. Les Mathématiques de l'Hérédité. Masson et Cie, Paris.
Malécot, G. 1951. Un traitment stochastique des problémes linéaires (mutation, linkage, migration) en génétique de population. Ann Univ Lyon, Sci, Sec, A, 14, 79–117.
Milkman, R. 1978. Selection differentials and selection coefficients. Genetics, 88, 391–403.
Moran, P A P. 1962. The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.
Moran, P A P, and Watterson, G A. 1959. The genetic effects of family structure in natural populations. Aust J Biol Sci, 12, 1–15.
Motro, U, and Thompson, G. 1982. On heterozygosity and the effective size of populations subject to size changes. Evolution, 36, 1059–1066.
Nagylaki, T. 1981. The inbreeding effective population number and the expected homozygosity for an X-linked locus. Genetics, 97, 731–737.
Nagylaki, T. 1992. Theoretical Population Genetics. Springer, Berlin.
Nei, M, and Murata, M. 1966. Effective population size when fertility is inherited. Genet Res, 8, 257–260.
Nei, M, and Tajima, F. 1981. Genetic drift and estimation of effective population size. Genetics, 110, 495–511.
Nunney, L. 1991. The influence of age structure and fecundity on effective population size. Proc R Soc B, 246, 71–76.
Nunney, L. 1993. The influence of mating system and overlapping generations on effective population size. Evolution, 47, 1329–1341.
Nunney, L, and Campbell, K A. 1993. Assessing minimum viable population size: demography meets population genetics. Trends Ecol Evol, 8, 234–239.
Nunney, L, and Elam, D R. 1994. Estimating the effective size of conserved populations. Conserv Biol, 8, 175–184.
Orive, M E. 1993. Effective population size in organisms with complex life-histories. Theor Pop Biol, 44, 316–340.
Pérez-Enciso, M, Fernando, R L, and Gianola, D. 1992. The use of the uncertain relationship matrix for computing inbreeding effective population size. Proceedings of the 43rd Meeting of the European Association of Animal Production, p. 264. Madrid.
Pollak, E. 1977. Effective population numbers and their interrelations. Proceedings of the Washington State University Conference on Biomathematics and Biostatistics, pp. 115–144. Department of Pure and Applied Mathematics, Washington State University, Spokane, WA.
Pollak, E. 1980. Effective population numbers and mean times to extinction in dioecious populations with overlapping generations. Math Biosci, 52, 1–25.
Pollak, E. 1987. On the theory of partially inbreeding finite populations. I. Partial selfing. Genetics, 117, 353–360.
Pollak, E. 1988. On the theory of partially inbreeding finite populations. II. Partial sib mating. Genetics, 120, 303–311.
Pollak, E. 1990. The effective population size of an age-structured population with a sex-linked locus. Math Biosci, 101, 121–130.
Robertson, A. 1961. Inbreeding in artificial selection programmes. Genet Res, 2, 189–194.
Robertson, A. 1964. The effect of nonrandom mating within inbred lines on the rate of inbreeding. Genet Res, 5, 164–167.
Robertson, A. 1965. The interpretation of genotypic ratios in domestic animal populations. Anim Prod, 7, 319–324.
Santiago, E, and Caballero, A. 1994. Effective size of populations under selection. Genetics (in press).
Templeton, A R. 1980. The theory of speciation via the founder principle. Genetics, 94, 1011–1038.
Ugarte, E, Gallego, A, and Caballero, A. 1990. The prediction of effective size in selected populations. Investigación Agraria: Productión y Sanidad Animales, 5, 17–23.
Waples, R S. 1989. A generalized approach for estimating effective population size from changes in allele frequency. Genetics, 121, 379–391.
Woolliams, J A, Wray, N R, and Thompson, R. 1993. Prediction of long-term contributions and inbreeding in populations undergoing mass selection. Genet Res, 62, 231–242.
Wray, N R, and Thompson, R. 1990. Predictions of rates of inbreeding in selected populations. Genet Res, 55, 41–54.
Wray, N, Woolliams, J A, and Thompson, R. 1990. Methods for predicting rates of inbreeding in selected populations. Theor Appl Genet, 80, 503–512.
Wray, N R, Woolliams, J A, and Thompson, R. 1994. Prediction of rates of inbreeding in populations undergoing index selection. Theor Appl Genet, 87, 878–892.
Wright, S. 1922. Coefficient of inbreeding and relationship. Am Nat, 56, 330–338.
Wright, S. 1931. Evolution in Mendelian populations. Genetics, 16, 97–159.
Wright, S. 1933. Inbreeding and homozygosis. Proc Natl Acad Sci USA, 19, 411–420.
Wright, S. 1938. Size of population and breeding structure in relation to evolution. Science, 87, 430–431.
Wright, S. 1939. Statistical genetics in relation to evolution. Exposés de Biométrie et de Statistique Biologique. Herman & Cie, Paris, France.
Wright, S. 1969. Evolution and the Genetics of Populations, vol 2, The Theory of Gene Frequencies. The University of Chicago Press, Chicago, IL.
Yoo, B H. 1980. Long-term selection for a quantitative character on large replicate populations of Drosophila melanogaster. 5. The inbreeding effect of selection. Aust J Biol Sci, 33, 713–723.
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Caballero, A. Developments in the prediction of effective population size. Heredity 73, 657–679 (1994). https://doi.org/10.1038/hdy.1994.174
- nonrandom mating
- population numbers
- random genetic drift
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