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Days post-treatment

Figure 6.2 Allele frequencies at the protease locus over time in the HIV populations in two patients undergoing protease inhibitor (ritonavir) treatment (Doukhan & Delwart 2001). Alleles found at very low frequencies before drug treatment come to predominate in the HIV population after drug treatment, due to natural selection among HIV genotypes for drug resistance. Alleles are bands observed in denaturing-gradient gel electrophoresis (DGGE), a technique that is capable of discriminating single-base-pair differences among different DNA fragments. DGGE was used to identify the number of different protease locus DNA sequences present in a sample of HIV particles. Protease inhibitor treatment began on day 0. Dr. E. Delwart kindly provided the original data used to draw this figure.

### Natural selection with sexual reproduction

The model of natural selection with clonal reproduction leaves out a critical part of the biology of many organisms, namely sexual reproduction. To build a model of natural selection for sexual reproduction, we can combine the Hardy-Weinberg model of genotype frequencies with genotype-specific growth rates to get a general model of natural selection operating on the three genotypes produced by a single locus with two alleles. The blending of these two models leads to a number of assumptions that are listed in Table 6.2 (compare with the assumptions of Hardy-Weinberg alone given in Chapter 2). For now, let's utilize the assumptions that yield expected genotype frequencies. The consequences of many of the other assumptions are explored throughout the chapter.

Imagine a population of N diploid individuals formed by random mating among the parents and then random fusion of gametes to produce zygotes.

Table 6.2 Assumptions of the basic natural selection model with a diallelic locus.

Genetic

Diploid individuals One locus with two alleles Obligate sexual reproduction Reproduction

Generations do not overlap Mating is random Natural selection

Mechanism of natural selection is genotype-specific differences in survivorship (fitness) that lead to variable genotype-specific growth rates, termed viability selection

Fitness values are constants that do not vary with time, over space, or in the two sexes Population

Infinite population size so there is no genetic drift No population structure No gene flow No mutation

When the N zygotes have just formed, before any natural selection, the genotypes are in Hardy-Weinberg expected frequencies. If the total population size at this time is Nt, then the number of zygotes of each genotype is

which defines the initial number of each of the three genotypes analogously to NA(0) and NB(0) used in the case of clonal reproduction.

After the initial population of zygotes is formed, natural selection will then operate on the three genotypes. The mechanism of natural selection takes a particular form under the assumptions of the one locus selection model. Each genotype is assumed to experience genotype-specific survival and reproduction during the course of a single generation as diagrammed in Fig. 6.3. This leads to a possible reduction in the number of zygotes of each genotype present in the population at the very beginning of the life cycle of a single generation. For the time being let's assume that any reduction in the numbers of individuals of any genotype comes exclusively from failure to survive to reproductive age but that all adults reproduce equally regardless of genotype. In this situation the fitness values of each genotype specify the probability of survival to reproduction, termed viability. Natural selection then takes the form of viability selection.

Generation t

Viability

Fecundity

Zygotes

Reproductive adults

Mating pairs

Generation t + 1

Mating success

### Gamete compatibility Meiotic drive

Figure 6.3 A diagram of the life cycle of organisms showing some points where differential survival and reproduction among genotypes can result in natural selection. Viability is the probability of survival from zygote to adult, mating success encompasses those traits influencing the chances of mating and the number of mates, and fecundity is the number of gametes and progeny zygotes produced by each mating pair. Gametic compatibility is the probability that gametes can successfully fuse to form a zygote whereas meiotic drive is any mechanism that causes bias in the frequency of alleles found in gametes. Most models of natural selection assume a single fitness component such as viability. In reality, all of these components of fitness can influence genotype frequencies simultaneously.

Viability selection A form of natural selection where fitness is equivalent to the probability that individuals of given genotype survive to reproductive age but all surviving individuals have equal rates of reproduction. Marginal fitness The frequency-weighted and allele-copy-weighted sum of the relative fitness values of genotypes that contain a specific allele; a special case of the average fitness for only those genotypes that contain a certain allele.

Frequency of a allele in gametes

In each of these equations the number of heterozygote individuals after selection is multiplied by one-half since a heterozygote contributes one copy of a given allele to the gamete pool for every two copies of that same allele contributed by a homozygote. These expressions simplify to:

As an analog of X used for clonal reproduction, let € (the cursive letter l ) represent the genotype-specific probability of survival to reproductive age. The numbers of individuals of each genotype after viability selection at the point of reproduction is then

These are the numbers of individuals of each genotype that will engage in random mating to form the next generation. The total number of individuals in the population after selection is then

This is a quantity that can be used to determine the frequency of a genotype or allele in the population after selection. For example, the proportion of the total population made up of individuals with an AA genotype after selection is

Frequency of AA genotype

V P2Nt

Frequency of A allele in gametes -Aa pq

and:

Frequency of a allele in gametes €aag2 + €Aa pq €AA p2 + €Aa2pq + €aaq2

because Nt can be factored out of each term in the numerator and denominator and then cancelled, and the constants of 1/2 and 2 cancel in the numerator.

As in the case of clonal reproduction, we can utilize relative fitness values for each genotype rather than absolute values of survivorship to reproductive age. We can then replace the €AA, €Aa, and €aa values with the relative fitness values wAA, wAa, and waa to give w pt+1 =

Since there are fewer alleles than genotypes, the results of natural selection are often summarized in terms of allele frequencies rather than in terms of genotype frequencies. The allele frequencies in the gametes made by surviving individuals (under the assumptions in Table 6.2) are:

Frequency of A allele in gametes €aa p2N + 2(£Aa2pqNt) €AA p2N + € Aa2pqNt +

Notice that the denominator in both expressions is the sum of the fitness-weighted genotype frequencies, or the mean relative fitness w. Making this substitution gives even more compact expressions for the allele frequencies:

Table 6.3 The expected frequencies of three genotypes after natural selection for a diallelic locus with sexual reproduction and random mating. The absolute fitness of the AA genotype is used as the standard of comparison when determining relative fitness. | |||||

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