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1971 Population genetic theory of density-dependent natural selection
CHAPTER THIRTY FOUR
1971 Population genetic theory of density-dependent natural selection The concept MacArthur’s ideas about r- and K-selection, as he called it were only semi-quantitative (MacArthur, 1962; MacArthur and Wilson, 1967). While the logistic equation was referenced in MacArthur’s 1962 paper, his 1967 book with E.O. Wilson developed verbal theories of r- and K-selection. This verbal theory discusses repeated reproduction as a K-selected strategy even though the logistic model has no age-structure (Pianka, 1970, 1972). Roughgarden (1971) developed explicit single locus population genetic models and then made predictions for the outcome of evolution at high and low densities which could then be subject to experimental tests.
The explanation Roughgarden (1971) developed an explicit genetic model in which he assumed fitness was equivalent to per-capita rates of population growth. Accordingly, when growth rates are assumed to be density dependent and they decline linearly with population size, the fitness of genotype AiAj is 1þrij(rijN/Kij), where rij and Kij are the genotype specific intrinsic rate of increase and carrying capacity of the logistic equation. Roughgarden goes on to analyze the outcome of evolution in stable environments that allow the population to approach carrying capacity. In that case she shows the genotype with the highest K is favored. Roughgarden also analyzes seasonal environments that keep the population size below carrying capacity. In that case, depending on the severity of the environment, the genotype with the highest r can be favored. A detailed stability analysis of these models was also carried out by Charlesworth (1971). Roughgarden suggests that a possible test of this theory would be to compare the r and K values of Drosophila melanogaster taken from low and high latitude environments, the reasoning being that in higher latitudes Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00034-X
© 2020 Elsevier Inc. All rights reserved.
79
j
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Conceptual Breakthroughs in Evolutionary Ecology
there is more seasonality (and hence higher r-values should be at a premium). To my knowledge those measurements have never been made. However, environments with and without extreme “seasonality” were created in the lab specifically to test these ideas (Mueller and Ayala, 1981, Chapter 46).
Impact: 8 Roughgarden’s work was the first to link the standard models of population genetics with ecological theory. This work then marks the true union of evolutionary and ecological theory.
References Charlesworth, B., 1971. Selection in density-regulated environments. Ecology 52, 469e474. MacArthur, R.H., 1962. Some generalized theorems of natural selection. Proc. Natl. Acad. Sci. U.S.A. 48, 1893e1897. MacArthur, R.H., Wilson, E.O., 1967. Island Biogeography. Princeton Univ. Press, Princeton. Mueller, L.D., Ayala, F.J., 1981. Trade-off between r-selection and K-selection in Drosophila populations. Proc. Natl. Acad. Sci. U.S.A. 78, 1303e1305. Pianka, E.R., 1970. On r and K selection. Am. Nat. 104, 592e597. Pianka, E.R., 1972. r and K selection or b and d selection? Am. Nat. 106, 581e588. Roughgarden, J., 1971. Density-dependent natural selection. Ecology 52, 453e468.
1971 Population genetic theory of density-dependent natural selection The concept MacArthur’s ideas about r- and K-selection, as he called it were only semi-quantitative (MacArthur, 1962; MacArthur and Wilson, 1967). While the logistic equation was referenced in MacArthur’s 1962 paper, his 1967 book with E.O. Wilson developed verbal theories of r- and K-selection. This verbal theory discusses repeated reproduction as a K-selected strategy even though the logistic model has no age-structure (Pianka, 1970, 1972). Roughgarden (1971) developed explicit single locus population genetic models and then made predictions for the outcome of evolution at high and low densities which could then be subject to experimental tests.
The explanation Roughgarden (1971) developed an explicit genetic model in which he assumed fitness was equivalent to per-capita rates of population growth. Accordingly, when growth rates are assumed to be density dependent and they decline linearly with population size, the fitness of genotype AiAj is 1þrij(rijN/Kij), where rij and Kij are the genotype specific intrinsic rate of increase and carrying capacity of the logistic equation. Roughgarden goes on to analyze the outcome of evolution in stable environments that allow the population to approach carrying capacity. In that case she shows the genotype with the highest K is favored. Roughgarden also analyzes seasonal environments that keep the population size below carrying capacity. In that case, depending on the severity of the environment, the genotype with the highest r can be favored. A detailed stability analysis of these models was also carried out by Charlesworth (1971). Roughgarden suggests that a possible test of this theory would be to compare the r and K values of Drosophila melanogaster taken from low and high latitude environments, the reasoning being that in higher latitudes Conceptual Breakthroughs in Evolutionary Ecology ISBN: 978-0-12-816013-8 https://doi.org/10.1016/B978-0-12-816013-8.00034-X
© 2020 Elsevier Inc. All rights reserved.
79
j
80
Conceptual Breakthroughs in Evolutionary Ecology
there is more seasonality (and hence higher r-values should be at a premium). To my knowledge those measurements have never been made. However, environments with and without extreme “seasonality” were created in the lab specifically to test these ideas (Mueller and Ayala, 1981, Chapter 46).
Impact: 8 Roughgarden’s work was the first to link the standard models of population genetics with ecological theory. This work then marks the true union of evolutionary and ecological theory.
References Charlesworth, B., 1971. Selection in density-regulated environments. Ecology 52, 469e474. MacArthur, R.H., 1962. Some generalized theorems of natural selection. Proc. Natl. Acad. Sci. U.S.A. 48, 1893e1897. MacArthur, R.H., Wilson, E.O., 1967. Island Biogeography. Princeton Univ. Press, Princeton. Mueller, L.D., Ayala, F.J., 1981. Trade-off between r-selection and K-selection in Drosophila populations. Proc. Natl. Acad. Sci. U.S.A. 78, 1303e1305. Pianka, E.R., 1970. On r and K selection. Am. Nat. 104, 592e597. Pianka, E.R., 1972. r and K selection or b and d selection? Am. Nat. 106, 581e588. Roughgarden, J., 1971. Density-dependent natural selection. Ecology 52, 453e468.