## P

Allele frequency after selection

Figure 6.13 A graphical illustration of R.A. Fisher's fundamental theorem of natural selection. The curved lines represent the product of the homozygote frequencies (P = p2 andR = q2) as a constant proportion of the square of the product of the allele frequencies (Q = pq) orX= Q2/PR. Hardy-Weinberg genotype frequencies produced by random mating represent the special case of X = 1 (solid colored line). Mean fitness is represented by the grayscale gradient with darker tones representing higher mean fitness. In this illustration, genotype frequencies start out at z1. Suppose that natural selection over one generation changes genotype frequencies to point z 3 (under the conditions that genotype AA has the highest fitness and additive gene action, for example). This change in genotype frequencies can be decomposed into two distinct parts. One part is the change from 2j to 2, moving along the curve where X is constant but allele frequencies change fromp to p'. The other part is the change in the genotype frequencies (changing the value of X) that occurs by moving vertically on the De Finetti diagram from 2, to 2 3 but keeping allele frequencies constant. The fundamental theorem says that the change in the mean fitness by natural selection is proportional to the change in allele frequency alone. Processes other than natural selection, such as mating system, dictate the change in genotype frequencies. When natural selection moves the genotype frequencies along a curve of constant X, then the total change in mean fitness is completely due to changes in allele frequency and genetic variation in fitness is completely additive. Modified fromEdwards (2002).

in allele frequencies alone with everything else held constant. This partial change in the mean fitness due exclusively to the change in allele frequencies is exactly the same as the genie variance or the additive genetic variance that is present in the population at point zv The second part of the change in mean fitness is due to changes in genotype frequency and is therefore caused by factors such as mating patterns or physical linkage resulting in gametic disequilibrium that will change the value of X as allele frequencies change. The fundamental theorem says that natural selection will change mean fitness by an amount proportional to the additive genetic variance alone. If X is constant, the total change in mean fitness is just the change due to the variation in allele frequencies. When X is not constant, changes in genotype frequencies can either increase or decrease mean fitness and can be thought of as causing an average change of zero.

Genetic variation in phenotype due to the substitution of alleles (additive genetic variation) and due to the effects of genotypes is examined from a completely distinct perspective in Chapters 9 and 10 on quantitative genetics. Those chapters also demonstrate the distinction that is made in the fundamental theorem between genetic variation due to changes in allele frequencies and changes in genotype frequencies. Both approaches give the same result that additive genetic variation is the basis of changes in mean phenotype due to natural selection.

### Chapter 6 review

• For haploid organisms, natural selection is a population growth process where different genotypes vary in genotype-specific population growth rates. The ratio of genotype-specific growth rates is the relative fitness and it predicts the genotype that will approach fixation in an infinitely expanding population over time.

• Natural selection in diploid organisms also relies on the relative fitness to express genotype-specific growth rates with the addition of sexual reproduction such that pairs of parents can produce a predictable frequency of genotypes in their progeny under random mating.

• The outcomes of natural selection on viability for a diallelic locus can be generalized into directional selection (a homozygote most fit) that results in fixation and loss (or very nearly fixation and loss), balancing selection (heterozygote advantage) that maintains both alleles forever, and disruptive selection (heterozygote disadvantage) that results in fixation or loss depending on initial genotype frequencies.

• The fundamental theorem of natural selection shows us that the change in mean fitness by natural selection is proportional to the additive genetic variation in fitness.

• The degree of dominance and recessivity for viability phenotypes impacts the rate of change of genotype frequencies under natural selection because there is not a perfect relationship between genotype and phenotype. Natural selection changes genotype frequencies fastest when gene action is additive.

Further reading

Arguably the first comprehensive treatment of natural selection that came out of the modern synthesis and still a stimulating read today is:

Fisher RA. 1999. The Genetical Theory of Natural Selection: a Complete Variorum Edition. Oxford University Press, Oxford (originally published in 1930).

Another early classic of the modern synthesis that established the mathematical connections between Mendelian genetics and natural selection is:

Haldane JBS. 1990. The Causes of Evolution. Princeton University Press, Princeton, NJ (originally published in 1932).

Problem box answers

### Problem box 6.1 answer

To solve for relative fitness given initial and final allele frequencies and time elapsed, we need to rearrange equation 6.8 by taking the logarithm of both sides:

to remove the exponent. We will let p represent the frequency of the wild-type allele and q the combined frequency of the drug-resistant alleles. Based on 601 days between allele frequency estimates, t = 231 generations elapsed. Substituting these values gives log f \

Sl Pt

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