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1928 Selection in age-structured populations
CHAPTER FOUR
1928 Selection in age-structured populations The concept In 1918, R. A. Fisher settled an important debate in population genetics when he showed how biometrical measurements like correlations between relatives could be derived from standard Mendelian genetic models. However, Fisher’s work treated populations with discrete generation life-histories. Future research on life-history evolution would require some understanding of how natural selection works in populations with age-structure. H. T. J. Norton’s seminal paper in 1928 (Norton, 1928) developed many of the basic results for selection in age-structured populations. Serious work in this area would not begin again Charlesworth, 1970). Norton’s most important result was to show that the outcome of selection at a single-locus could be predicted from the genotypic intrinsic rates of increase.
The explanation Genetic variation for survival and fertility of genotype (AiAj) at a single locus can be described by the survival function lij(x) and the fertility function mij(x) which describe the chance of surviving to age-x and number of offspring produced at age-x, respectively. This formulation assumes no differences between the sexes and a maximum possible lifespan of d. Then the intrinsic rate of increase for AiAj is rij which is given as the real, positive root, Z d z, of, ezx lij ðxÞmij ðxÞdx ¼ 1. Norton showed that if A1 carrying geno0
types were inferior and possibly recessive ðr11 r12 < r22 Þ or possibly dominant ðr11 < r12 r22 Þ then selection would result in the frequency of A1 going to 0. In the case of overdominance Norton concluded there might be a stable equilibrium or cycles. The possibility of cycles was ruled out by Charlesworth (1994).
Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00004-1
© 2020 Elsevier Inc. All rights reserved.
9
j
10
Conceptual Breakthroughs in Evolutionary Ecology
Impact: 8 Norton was far ahead of his time but his early work solved some of the very difficult mathematical problems concerning age-structured population genetics. This work was eventually largely completed and tied into modern problems of life-history evolution by Charlesworth (1994). According to Haldane (1927), Norton started his work in this paper in 1910 and was mostly completed by 1922.
References Charlesworth, B., 1970. Selection in populations with overlapping generations. I. The use of Malthusian parameters in population genetics. Theor. Popul. Biol. 1, 352e370. Charlesworth, B., 1994. Evolution in Age-Structured Populations. Cambridge University Press, Cambridge. Haldane, J.B.S., 1927. A mathematical theory of natural and artificial selection. Part IV. Math. Proc. Camb. Philos. Soc. 23, 607e615. Norton, H.T.J., 1928. Natural selection and Mendelian variation. Proc. Lond. Math. Soc. 28, 1e45.
1928 Selection in age-structured populations The concept In 1918, R. A. Fisher settled an important debate in population genetics when he showed how biometrical measurements like correlations between relatives could be derived from standard Mendelian genetic models. However, Fisher’s work treated populations with discrete generation life-histories. Future research on life-history evolution would require some understanding of how natural selection works in populations with age-structure. H. T. J. Norton’s seminal paper in 1928 (Norton, 1928) developed many of the basic results for selection in age-structured populations. Serious work in this area would not begin again Charlesworth, 1970). Norton’s most important result was to show that the outcome of selection at a single-locus could be predicted from the genotypic intrinsic rates of increase.
The explanation Genetic variation for survival and fertility of genotype (AiAj) at a single locus can be described by the survival function lij(x) and the fertility function mij(x) which describe the chance of surviving to age-x and number of offspring produced at age-x, respectively. This formulation assumes no differences between the sexes and a maximum possible lifespan of d. Then the intrinsic rate of increase for AiAj is rij which is given as the real, positive root, Z d z, of, ezx lij ðxÞmij ðxÞdx ¼ 1. Norton showed that if A1 carrying geno0
types were inferior and possibly recessive ðr11 r12 < r22 Þ or possibly dominant ðr11 < r12 r22 Þ then selection would result in the frequency of A1 going to 0. In the case of overdominance Norton concluded there might be a stable equilibrium or cycles. The possibility of cycles was ruled out by Charlesworth (1994).
Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00004-1
© 2020 Elsevier Inc. All rights reserved.
9
j
10
Conceptual Breakthroughs in Evolutionary Ecology
Impact: 8 Norton was far ahead of his time but his early work solved some of the very difficult mathematical problems concerning age-structured population genetics. This work was eventually largely completed and tied into modern problems of life-history evolution by Charlesworth (1994). According to Haldane (1927), Norton started his work in this paper in 1910 and was mostly completed by 1922.
References Charlesworth, B., 1970. Selection in populations with overlapping generations. I. The use of Malthusian parameters in population genetics. Theor. Popul. Biol. 1, 352e370. Charlesworth, B., 1994. Evolution in Age-Structured Populations. Cambridge University Press, Cambridge. Haldane, J.B.S., 1927. A mathematical theory of natural and artificial selection. Part IV. Math. Proc. Camb. Philos. Soc. 23, 607e615. Norton, H.T.J., 1928. Natural selection and Mendelian variation. Proc. Lond. Math. Soc. 28, 1e45.