Evolution__3rd_Edition

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CHAPTER 5 / The Theory of Natural Selection 105
Table 5.3
(a) Algebraic calculation of genotype frequences after selection, with selection against a recessive genotype. (b) A numerical
illustration. See text for further explanation.
(a) (b)
Genotype Genotype
AA Aa aa AA Aa aa Total
Birth Birth
Frequency p 2 2pq q 2 Number 1 18 81 100
Fitness 1 1 1 − s Frequency 0.01 0.18 0.81
Fitness 1 1 0.9
Adult Adult
Relative frequency p 2 2pq q 2 (1 − s) Number 1 18 73 92
Frequency p 2 /(1 − sq 2 ) 2pq/(1 − sq 2 ) q 2 (1 − s)/(1 − sq 2 ) Frequency 1/92 18/92 73/92
We construct a model for the
change in gene frequency per
generation
“relative fitnesses.” However, biologists usually just say “fitness.” With the fitnesses
given above, selection will act to eliminate the a allele and fix the A allele. (To “fix” a
gene is genetic jargon for carry its frequency up to 1. When there is only one gene at a
locus, it is said to be “fixed” or in a state of “fixation.”) If s were 0, the model would
lapse back to the Hardy–Weinberg case and the gene fequencies would be stable.
Notice that alleles do not have any tendency to increase in frequency just because
they are dominant, or to decrease because they are recessive. Dominance and recessivity
only describe how the alleles at a locus interact to produce a phenotype. Changes in
gene frequency are set by the fitnesses. If the recessive homozygote has higher fitness,
the recessive allele will increase in frequency. If, as here, the recessive homozygote has
lower fitness, the recessive allele decreases in frequency.
How rapidly will the population change through time? To find out, we seek an
expression for the gene frequency of A (p′) in one generation in terms of its frequency
in the previous generation (p). The difference between the two, ∆p = p′ −p, is the
change in gene frequency between two successive generations. The model has the form
of Figure 5.3, and we shall work through both the general algebraic version and a
numerical example (Table 5.3).
To begin with, at birth the three genotypes have Hardy–Weinberg frequencies
as they are produced by random mating among adults of the previous generation.
Selection then operates; aa individuals have a lower chance of survival and their frequency
among the adults is reduced. As the numerical example shows (Table 5.3b), the
total number of adults is less than the number at birth and we have to divide the adult
numbers of each genotype by the total population size to express the adult numbers as
frequencies comparable to the frequencies at birth. In the algebraic case, the relative
frequencies after selection do not add up to 1, and we correct them by dividing by the
mean fitness.