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A problem in determining fitness differences

A problem in determining fitness differences FRANK B. LIVINGSTONE Department of Anthropology, University of Michigan, Ann Arbor, M I 48109 Although differential contributions to the next generation have frequently been used to measure differences in fitness, a t genetic equilibrium there will be no such differences among genotypes with balanced polymorphism. For a single locus the frequencies, after selection, of , where the three genotypes, AA, A a , aa,will be: qlp2/K2W,,pq/W and W ,q2/v, v = w,, + 2W,, pq + p2 tyz2 pa. To estimate the contribution of any genotype to the next generation, the average fitness of the offspring can be calculated from the frequencies of possible matings for that genotype and the average fitness of the offspring of each mating. For the AA genotype the average fitness of the offspring will be (K1p2/W) + (2W,,pdP) (0.5 K + 0 . 5 % ~ ) (%2 W,, + a2/WK2 or ~-1(w,l~rw,l~+w,,crl+w,2arw,2~+w,241). At genetic equilibrium, W ,p + 4,q = q 2 p+ W ,q = , , so that average fitness will be simply For the A a genotype, the average fitness of the offspring will be w. w, (qlp2/v) (0.5q1+0-5W,,) + ( 2 & 2 p 4 / v ) (0.25q1+0.5K2+0.25W,2) + (b2Q2/v) (0'5K2+0'5%,), which also reduces to p; and similarly for the aa genotype. This conclusion is only valid when selection occurs as early mortality. However, the sickle cell gene appears to be close to equilibrium in many populations in Africa ;and since most selection due to either sickle-cell anaemia or cerebral malaria occurs in early childhood, this inay explain the inconclusive nature of the data on differences in the average number of surviving offspring for sicklers and non-sicklers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Human Genetics Wiley

A problem in determining fitness differences

Annals of Human Genetics , Volume 40 (3) – Jan 1, 1977

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Publisher
Wiley
Copyright
Copyright © 1977 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0003-4800
eISSN
1469-1809
DOI
10.1111/j.1469-1809.1977.tb00201.x
Publisher site
See Article on Publisher Site

Abstract

FRANK B. LIVINGSTONE Department of Anthropology, University of Michigan, Ann Arbor, M I 48109 Although differential contributions to the next generation have frequently been used to measure differences in fitness, a t genetic equilibrium there will be no such differences among genotypes with balanced polymorphism. For a single locus the frequencies, after selection, of , where the three genotypes, AA, A a , aa,will be: qlp2/K2W,,pq/W and W ,q2/v, v = w,, + 2W,, pq + p2 tyz2 pa. To estimate the contribution of any genotype to the next generation, the average fitness of the offspring can be calculated from the frequencies of possible matings for that genotype and the average fitness of the offspring of each mating. For the AA genotype the average fitness of the offspring will be (K1p2/W) + (2W,,pdP) (0.5 K + 0 . 5 % ~ ) (%2 W,, + a2/WK2 or ~-1(w,l~rw,l~+w,,crl+w,2arw,2~+w,241). At genetic equilibrium, W ,p + 4,q = q 2 p+ W ,q = , , so that average fitness will be simply For the A a genotype, the average fitness of the offspring will be w. w, (qlp2/v) (0.5q1+0-5W,,) + ( 2 & 2 p 4 / v ) (0.25q1+0.5K2+0.25W,2) + (b2Q2/v) (0'5K2+0'5%,), which also reduces to p; and similarly for the aa genotype. This conclusion is only valid when selection occurs as early mortality. However, the sickle cell gene appears to be close to equilibrium in many populations in Africa ;and since most selection due to either sickle-cell anaemia or cerebral malaria occurs in early childhood, this inay explain the inconclusive nature of the data on differences in the average number of surviving offspring for sicklers and non-sicklers.

Journal

Annals of Human GeneticsWiley

Published: Jan 1, 1977

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