Genetics - A. V. Sivolob 2008

Population Genetics
Factors of the Dynamics of Population Genetic Structure
Selection

Selection can be defined as the differential reproduction of individuals with different genotypes within a population. Under METABOLISM/18.html">The Influence of selection, allele and genotype frequencies will shift in a specific direction; selection may lead to either the loss or fixation of an allele.

The differential contribution of individuals with different genotypes to the reproduction of the next generation can be quantified using their relative reproductive success, or relative fitness w₁, which is The ratio of the fitness of individuals with a given genotype to the fitness of the optimal variant present in the population (Table 8.3).

The selection coefficient s is simply related to relative fitness and indicates the degree to which the fitness of individuals with a given genotype falls short of the fitness of the optimal variant:

Class="center">s_i = w_max - w_i.

Obviously, the relative fitness of the optimal variant equals one, and its selection coefficient is zero.

Table 8.3. Example of determining the relative fitness w of three genotypes

Because individuals with different genotypes possess varying fitness, the ratios of genotypes and Gene frequencies will change over successive generations until one of the alleles is completely eliminated or until gene frequencies reach an equilibrium. The change in allele frequency over a single generation under the action of selection is generally illustrated in Table 8.4.

Table 8.4. Change in gene frequency under the action of selection over a single generation

The average fitness of a population w is calculated as the sum of the contributions of different genotypes to the next generation:

w = p² w₁+ 2pq w₂ + q² w₃.      (8.2)

After normalizing the genotype frequencies, we determine the new frequency q' of allele a in the population, which is the frequency following selection

The difference in allele frequencies before and after selection allows us to determine how the allele frequency changed under the influence of selection during a single generation:

After substituting the expression for into the numerator (Eq. 8.2) and performing elementary algebraic transformations (taking into account, in particular, that 1 - q = p and 1 - 2q = p - q), we find that over a single generation, the allele frequency changes under the influence of selection by an amount equal to

The sign of ∆q, which characterizes the direction of selection, depends on the relative fitness of the different genotypes w₁, w₂, and w₃ (since p, q, and the denominator of the fraction are always positive numbers). Meanwhile, The rate of selection—in other words, the magnitude of ∆q—is influenced by both the fitness values and the initial gene frequencies. When ∆q = 0, genetic equilibrium is established:

This equilibrium equation has two trivial solutions (p = 0 or q = 0) as well as a third solution corresponding to the condition p(w₂ - w₁) = q(w₂ - w₃). From this, we obtain the allele frequency ratio corresponding to The equilibrium state:

The ratio p/q is always positive, and therefore two cases are possible: (1) w₂ > w₃ and w₂ > w₁, or (2) w₂ < w₃ and w₂ < w₁.

Thus, under the action of selection, gene frequency will continue to change until it reaches one of the stationary states. A single diallelic locus can have three such states.

1. p = 1, q = 0: allele a is lost under the influence of selection (selection against allele a). According to Equation 8.3, this situation occurs when the fitness relationships are w₁ = w₂ > w₃ (complete dominance) and w₁ > w₂ > w₃ (incomplete dominance, where the fitness of the heterozygote is intermediate between the fitnesses of the homozygotes).

2. p = 0, q = 1 - under the influence of selection, allele a becomes fixed (selection in favor of allele a) when w₁ = w₂ < w₃ or w₁ < w₂ < w₃.

- selection leads to a genetic equilibrium according to equation 8.4. In the case of overdominance (w₁ < w₂ > w₃), neither allele is eliminated, as both have an advantage in the heterozygous state. The initial direction of selection is determined by the relative fitnesses of the two homozygotes, after which a stable equilibrium is established where allele frequencies remain unchanged. If the heterozygote is characterized by reduced fitness (underdominance, w₁ > w₂ < w₃), an unstable equilibrium is reached: allele frequencies remain constant until the equilibrium is perturbed by various evolutionary factors, in which case the equilibrium is disrupted and one of the alleles eventually becomes fixed.

Similar to changes in gene frequency under selection, the average population fitness w will also change. The value ∆w - the change in the average population fitness due to selection over one generation - is always positive. Therefore, As a result of selection, the average fitness of a population cannot decrease; it can either remain constant or increase. According to Fisher's fundamental theorem of natural selection (Ronald Aylmer Fisher), the rate of its increase is higher when its initial value is lower and the difference in fitness among individuals with different genotypes is greater. At equilibrium points (∆q = 0), the value of ∆w will be zero. Under conditions of stable equilibrium at a given point, the average fitness of the population will be at its maximum.

Most traits subject to selection are quantitative, meaning they depend on multiple gene loci (see Chapter 3). Selection can alter the distribution of individuals in a population regarding the value of a quantitative trait in three different ways. If selection favors trait values at one of the distribution extremes, a gradual shift of the distribution occurs in that direction - directional selection (Fig. 8.9, a). In nature, this occurs when environmental conditions change in a specific direction, forcing the population to adapt to these changes.

If selection favors values at both extremes of the distribution, disruptive selection takes place: practically speaking, this is directional selection acting in both directions (Fig. 8.9, b). Typically, disruptive selection occurs either under conditions of assortative mating (crosses predominantly occur between individuals with similar extreme manifestations of the trait) or as a result of ecological or geographical isolation of subpopulations.

Selection can also favor the conservation of average distribution values by "pruning" extreme variants - stabilizing selection (Fig. 8.9, c). Such a process occurs when individuals with intermediate trait expressions are characterized by enhanced fitness.

Fig. 8.9. Changes in the distribution of individuals by quantitative trait (ordinate axis represents frequency) under the action of Three types of selection: directional (a), disruptive (b), and stabilizing (c)