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Natural Selection, Adaptation, and Fitness

Natural selection acts on differences in phenotypes, producing differential survival and reproductive success, i.e., fitness. Adaptation is the outcome: traits that improve survival and reproduction in a given environment. Adaptation can be structural (morphology), physiological (chemistry/metabolism), or behavioral, and all arise through natural selection.

Fitness and Selection

Fitness, as Darwin described, is the ability to survive, find a mate, and reproduce. It is the contribution of a genotype to the gene pool of the next generation. In quantitative terms, fitness is the average number of offspring produced by individuals with a given genotype, relative to others. The fittest genotype has relative fitness 1; others have w < 1. The selection coefficient s is the reduction in fitness relative to the fittest genotype, with s = 1 − w. Equivalently, w = 1 − s for the genotype being considered. The fittest genotype has s = 0, and higher s means stronger selection against that genotype.

General Selection Model (GSM)

The GSM predicts changes in allele frequencies from one generation to the next due to natural selection, assuming no mutation, no genetic drift, and no migration. It tracks how differential survival translates to changes in allele frequencies across generations.

Fitness notation and two-allele system

Assume a single locus with two alleles (A and a). Fitness values are assigned to the three genotypes: wAA, wAa, and w_aa, with the highest fitness set as the reference (w = 1). The relative fitness of each genotype is used to determine selection dynamics. The selection coefficient s relates to the genotype with the highest fitness by w = 1 for the fittest genotype and w < 1 for others.

Selection Coefficient and relative change

The selection coefficient s is the reduction in fitness relative to the fittest genotype: s = 1 − w. Higher s corresponds to stronger selection and a lower w; the fittest genotype has s = 0.

General Models of Natural Selection

General Model #1: Selection Against Recessive Allele

AA Aa aa
Relative fitness, w: 1, 1, 1 − s
Allele a is deleterious only in homozygotes, so a remains at low frequency but is not driven to zero; allele A remains more common and typically not fixed.

General Model #2: Selection Against Dominant Allele

AA Aa aa
Relative fitness, w: 1 − s, 1, 1 − s
Deleterious allele is exposed in both homozygotes and heterozygotes differ in fitness. The greater the s, the faster allele frequencies change. If s = 1 (lethal), the deleterious allele p can be driven to zero in a single generation.

General Model #3: Heterozygote has Intermediate Fitness

AA Aa aa
Relative fitness, w: 1 − s, 1, 1 − s/2 (or equivalently wAA = 1, wAa = 1 − s, w_aa = 1 − s/2)
Heterozygotes have fitness between the two homozygotes; selection acts against one or both homozygotes, altering allele frequencies more slowly than complete dominance.

General Model #4: Heterozygote Advantage (Overdominance)

AA Aa aa
Relative fitness, w: 1 − s, 1, 1 − t
Heterozygotes have the highest fitness; both homozygotes are selected against. This creates a stable polymorphism where both alleles are maintained.

General Model #5: Selection Against Heterozygote

AA Aa aa
Relative fitness patterns vary, but in this model the heterozygote is less fit than either homozygote, promoting fixation of one homozygous genotype depending on the relative fitness values.

Heterozygote Advantage: Equilibria and Example

When heterozygotes have the highest fitness (Aa with w = 1) and both homozygotes are reduced in fitness (wAA = 1 − s, waa = 1 − t), a stable equilibrium is reached where
$p^{<em>} = \frac{t}{s + t}, \qquad q^{</em>} = \frac{s}{s + t}$
where p is the frequency of A and q is the frequency of a in the population.

Example: with "s = 0.1" and "t = 0.2":
$p^{<em>} = \frac{0.2}{0.1+0.2} = 0.667, \quad q^{</em>} = \frac{0.1}{0.1+0.2} = 0.333$
This yields a stable polymorphism, with both alleles present at equilibrium frequencies.

In-Class Question (illustrative): with t = 0.1 and s = 0.3, the equilibrium frequency for A is
$p^{*} = \frac{t}{s+t} = \frac{0.1}{0.3+0.1} = 0.25.$ Therefore, the population maintains a polymorphic state with p around 0.25 at equilibrium.

Sickle-Cell Anemia: Heterozygote Advantage in Humans

In malaria-endemic regions, individuals heterozygous for sickle-cell: AS have resistance to malaria and higher overall fitness than the two homozygotes. Homozygous recessive (SS) suffer sickle-cell disease, while homozygous dominant (AA) are susceptible to malaria. This is a classic case of balanced polymorphism maintained by heterozygote advantage, illustrating natural selection maintaining multiple alleles at a locus.