An inequality in population genetics

Scheuer, P A G; Mandel, S. P. H.

doi:10.1038/hdy.1959.52

Cited by 61 publications

(24 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) i j (All summations, except where otherwise indicated, are over the integers 1,2, ...,m.) V will be called the mean viability in the first generation. The two equations, together…”

mentioning

confidence: 99%

A mathematical problem in population genetics

Kingmán

1961

Math. Proc. Camb. Phil. Soc.

128

View full text Add to dashboard Cite

1. Introduction. A genetical population in which different genotypes have different viabilities will undergo, by selection, changes in its genetical constitution which can be expressed in a simple mathematical form. We here consider a system of m alleles A lt A z , ...,A m segregating at one locus, and we assume that the genotype A^j has viability a ip where a it = a n ^ 0. We assume discrete, non-overlapping generations and random mating.In an infinite population there will be no random fluctuations, and, as in Mandel's paper (l), the frequencies p t , p' t of the gene A { in two successive generations will be connected by

show abstract

“…(2) i j (All summations, except where otherwise indicated, are over the integers 1,2, ...,m.) V will be called the mean viability in the first generation. The two equations, together…”

mentioning

confidence: 99%

A mathematical problem in population genetics

Kingmán

1961

Math. Proc. Camb. Phil. Soc.

128

View full text Add to dashboard Cite

show abstract

“…All the negative conclusions of this paper remain correct when fitnesses are time-dependent or in cases of selection that cannot be interpreted as viability selection. 9 This explicit result goes back at least toScheuer and Mandel (1959). They discuss all the other assumptions besides one-locus control that must hold for this result to be correct -these complications are left out here for the sake of expository simplicity.…”

mentioning

confidence: 89%

Maynard Smith, optimization, and evolution

Sarkar

2006

Biol Philos

View full text Add to dashboard Cite

Maynard Smith's defenses of adaptationism and of the value of optimization theory in evolutionary biology are both criticized. His defense does not adequately respond to the criticism of adaptationism by Gould and Lewontin. It is also argued here that natural selection cannot be interpreted as an optimization process if the objective function to be optimized is either (i) interpretable as a fitness, or (ii) correlated with the mean population fitness. This result holds even if fitnesses are frequency-independent; the problem is further exacerbated in the frequency-dependent context modeled by evolutionary game theory. However, Eshel and Feldman's new results on ''long-term'' evolution may provide some hope for the continuing relevance of the game-theoretic framework. These arguments also demonstrate the irrelevance of attempts by Intelligent Design creationists to use computational limits on optimization algorithms as evidence against evolutionary theory. It is pointed out that adaptation, natural selection, and optimization are not equivalent processes in the context of biological evolution.

show abstract

“…(12) The interesting matrix inequality (11) has been found or proved in [1], [14], [171, [19], [21].…”

mentioning

confidence: 98%

On the equilibrium states in certain selection models

Hadeler

1974

J. Math. Biology

View full text Add to dashboard Cite

SummaryThe Fisher-Wright-Haldane model describes the behavior of a diploid population with random mating and separated generations under selection. Similar models for overlapping generations have been investigated. The corresponding differential equations for gene frequencies are derived under the hypothesis that the population as a whole is in Hardy-Weinberg-equilibrium. This hypothesis cannot be satisfied in actual populations. A system of equations for the genotype frequencies is derived without this hypothesis. It can be shown that the equations for gene frequencies yield an appropriate description --at least in the neighborhood of an equilibrium --if the differences in fitness result from differences in fertility rather than mortality.

show abstract

An inequality in population genetics

Cited by 61 publications

References 7 publications

A mathematical problem in population genetics

A mathematical problem in population genetics

Maynard Smith, optimization, and evolution

On the equilibrium states in certain selection models

Contact Info

Product

Resources

About