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Substituting the mean fitness from Haldane's result above and recalling that wmax = 1, the genetic load under complete dominance is L = 1 - (1 -p) = p and under incomplete dominance L = 1 - (1 - 2p) = 2p. The straightforward conclusion is that higher mutations rates lead to higher genetic loads because a larger number of deleterious mutations must be purged by natural selection to remain at selection/ mutation equilibrium. This translates into some proportion of homozygous individuals that must die or fail to reproduce each generation. The load never disappears because while selection removes deleterious alleles from a population, mutation continually supplies new ones.

Later, Haldane (1957) used a mutational-load argument to estimate the rate of substitutions. His goal in this analysis was to understand the rate of phenotypic evolution, perceived at that time to be relatively slow, consistent with Darwinian emphasis on gradual change. Haldane concluded that natural selection could accomplish no more than about one beneficial substitution every 300 generations and that this would require the deaths of 30 times the population size present in one generation. This result made a major impact on some researchers in population genetics. Haldane's conclusion was often applied very generally as a fundamental limit on the rate of natural selection. As shown later by Ewens (2004), Haldane's result implicitly assumed that demographic excess in humans is limited to 10% of the population size and so was not as general as some had originally thought.

Segregational load The decrease in the mean fitness in a population caused by individuals with low-fitness genotypes that are introduced in a population by each generation of Mendelian segregation. Substitutional load The decrease in the mean fitness in a population caused by the introduction of deleterious mutations or the culling of lower-fitness genotypes required for the eventual substitution of beneficial mutations.

To understand the segregational load, assume a standard diallelic locus model of overdominance for fitness where relative fitness values are 1 - s for the AA genotype, 1 for the Aa genotype, and 1 - t for the aa genotype, where s and t are selection coefficients. As shown in Chapter 6, the expected equilibrium allele frequencies for this model of natural selection are t

Using these equilibrium allele frequencies, it is possible to express the equilibrium frequency of heterozygotes expected under balancing selection as

eq req^eq

eq req^eq

/ \ t

( \ s

1s+t J

This shows that the frequency of heterozygotes in a population depends on the magnitude of the selection coefficients against the homozygous genotypes.

For example, if both homozygotes have 10% lower viability than the heterozygote, s = t = 0.1 and at equilibrium half of the population is composed of heterozygotes (H = 2(0.1)(0.1) = 0.5). Weaker eq (0.1 + 0.1)2

selection results in less heterozygosity at equilibrium while stronger selection results in more equilibrium heterozygosity.

We can combine the expected frequency of heterozygotes at equilibrium and the mean fitness to get an expression for the genetic load at equilibrium under balancing selection in terms of the homozygote selection coefficients:

as worked out in Math box 11.1. This population mean fitness can also be expressed in terms of the heterozygosity maintained by balancing selection by utilizing the equilibrium frequency of heterozygotes given in equation 11.6. Notice that so that the mean fitness

st =

' 2st ^

/ \ s + t

s + t

[(s + t)2 J

12 J

so that the mean fitness for one locus can be written as for one locus can be written as w = 1 - H

This equation has the biological interpretation that the mean fitness at equilibrium in a population under balancing selection is one minus the product of the equilibrium heterozygosity and the mean selection coefficient. A population experiencing balancing selection therefore always has at least some genetic load since the mean fitness will never reach the maximum fitness of one (mating among heterozygotes will generate additional lower-fitness homozygotes every generation).

Let's use some data on heterozygosity and selection coefficients similar to those available in the 1960s to compute the segregational load caused by balancing selection. Allozyme surveys in Drosophila of the time estimated that average heterozygosity was around 0.3. A homozygote disadvantage of 10% was considered reasonable under the balance hypothesis, giving a selection coefficient of s = 0.10. Putting these two values into equation 11.7 gives the mean fitness as s

Math box 11.1

Mean fitness in a population at equilibrium for balancing selection

To solve the equation for the mean fitness in terms of the selection coefficients s and t on the homozygous genotypes, start with the standard expression for the mean fitness:

w = P2wAA + 2PqWAa + q2Wa and then substitute the fitness values for each genotype:

Then express the genotype frequencies as equilibrium allele frequencies given in terms of the selection coefficients (equations 11.3 and 11.4):

and then multiply through to give

Expanding the numerators of the first and last terms gives t2 -12s + 2st + s2 - s2t

Notice that s2t + t2s = st(s + t) and t2 + 2st + s2 = (t + s)(t + s) in the numerator, and so making these substitutions:

which on simplifying gives

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