Fitness Defined
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You should be familiar with the concepts of genotype, phenotype, and the three modes of selection (directional, stabilising, disruptive) covered in the previous lecture. You must also understand basic Mendelian inheritance and how allele frequencies are calculated in a diploid population.
Why this matters
Fitness is the quantitative engine that drives natural selection, translating phenotypic differences into changes in allele frequencies.
In the previous lecture, we described the *shape of selection—how it pushes traits toward a mean, away from it, or toward an extreme. However, description alone is insufficient for prediction. To understand *how fast a population evolves, we must define fitness precisely. Fitness is not a measure of strength, speed, or survival in isolation; it is a measure of relative reproductive success. It quantifies the contribution of a specific genotype to the next generation relative to other genotypes. Without a rigorous definition of fitness, natural selection remains a qualitative narrative rather than a predictive mathematical framework. This lecture bridges the gap between observable phenotypic variation and the genetic changes observed over generations, establishing the foundational equations used in population genetics.
Fitness in Plain Language
Imagine a population of beetles where some have green shells and others have brown shells. If the green beetles are better at hiding from birds, they are more likely to survive to adulthood. However, survival is only half the story. If the green beetles survive but fail to find mates or produce viable offspring, their genes will not be passed on. Fitness, in evolutionary biology, is strictly about the number of viable, fertile offspring that an individual produces relative to other individuals in the population. It is a relative measure, not an absolute one. If all beetles in a population produce exactly ten offspring, their fitness is equal, regardless of how fast they run. If one genotype produces twelve offspring and another produces ten, the first has a fitness advantage. This advantage is often denoted by the symbol \( w \). A genotype with \( w = 1.0 \) is the reference standard, while a genotype with \( w = 0.8 \) is less fit because it contributes 20% fewer offspring to the next generation. Crucially, fitness is context-dependent. A trait that is highly fit in one environment (e.g., thick fur in a cold climate) may be maladaptive in another (e.g., thick fur in a hot climate). Therefore, fitness is not an intrinsic property of a gene, but a relationship between a genotype and its specific environment. This relational nature means that as environments change, the fitness landscape changes, altering the direction and strength of natural selection. Understanding this allows us to move beyond static descriptions of adaptation and into dynamic models of evolutionary change.
Relative Fitness and Selection Coefficients
To quantify fitness, biologists often use relative fitness values, where the most successful genotype is assigned a value of 1.0. The fitness of other genotypes is expressed as a fraction of this maximum. For a diploid organism with two alleles, \( A \) and \( a \), we have three genotypes: \( AA \), \( Aa \), and \( aa \). Let \( w_{AA} \), \( w_{Aa} \), and \( w_{aa} \) represent their respective fitnesses. If \( AA \) is the most fit, we set \( w_{AA} = 1 \). The fitness of the heterozygote might be \( w_{Aa} = 1 - h s \), and the homozygous recessive \( w_{aa} = 1 - s \), where \( s \) is the selection coefficient. The selection coefficient \( s \) measures the strength of selection against a specific genotype. If \( s = 0.1 \), the \( aa \) genotype has 10% lower reproductive success than the \( AA \) genotype. This parameter \( s \) is central to evolutionary models because it directly determines the rate of allele frequency change. A small \( s \) implies weak selection, meaning allele frequencies change slowly. A large \( s \) implies strong selection, leading to rapid evolutionary change. It is important to note that fitness values are often estimated from field data by counting offspring or measuring survival rates, but these estimates can be biased by environmental fluctuations. Therefore, fitness is best understood as a long-term average over many generations and environments, rather than a snapshot of a single year.
The Breeder’s Equation and Heritability
While relative fitness describes the differential success of genotypes, the Breeder’s Equation provides a direct link between selection and the change in the mean phenotype of a population. The equation is expressed as \( R = h^2 S \), where \( R \) is the response to selection (the change in the mean phenotype from one generation to the next), \( S \) is the selection differential (the difference between the mean phenotype of selected parents and the mean phenotype of the whole population), and \( h^2 \) is the narrow-sense heritability. Heritability \( h^2 \) represents the proportion of phenotypic variance in a population that is due to additive genetic variance. If \( h^2 \) is high, the offspring will closely resemble their parents, and selection will be effective in shifting the population mean. If \( h^2 \) is low, most of the variation is due to environmental factors, and selection will have little effect on the next generation. For example, if farmers select for cows with higher milk yield, the increase in milk yield in the next generation depends on how much of that yield is genetically determined. This equation is powerful because it separates the strength of selection (\( S \)) from the genetic architecture of the trait (\( h^2 \)). It highlights that evolution requires both selection and heritable variation. Without heritability, selection cannot produce evolutionary change, no matter how strong the selection pressure is.
Allele Frequency Dynamics
To understand how selection changes allele frequencies over time, we can derive a recurrence relation for the frequency of an allele. Consider a simple case where the allele \( A \) has a fitness advantage over \( a \). Let \( p_t \) be the frequency of allele \( A \) in generation \( t \). The frequency of \( A \) in the next generation, \( p_{t+1} \), depends on the relative fitness of the genotypes. In the simplest case (haploid organisms, with \(A\) having fitness \(1+s\) relative to \(a\)) the recurrence is \( p_{t+1}=\frac{p_t(1+s)}{1+s\,p_t} \); for diploids the form depends on dominance, as in the worked example below. In the case of complete dominance, where the heterozygote has the same fitness as the dominant homozygote, the allele \( a \) is selected against. The frequency of the deleterious allele decreases over time, but the rate of decrease slows as the allele becomes rare. This is because in a heterozygote, the deleterious allele is "hidden" from selection. This phenomenon, known as the sheltering of recessive alleles, means that recessive deleterious alleles can persist in a population for many generations, even under strong selection. This has important implications for the maintenance of genetic variation and the risk of inbreeding depression in small populations. Understanding these dynamics allows us to predict the long-term evolutionary trajectory of populations and the persistence of genetic load.
The concept
Fitness and adaptation
Reproductive success shapes the traits of a population.
A common misconception is that fitness is an absolute value that can be measured in a vacuum. In reality, fitness is always relative to the specific population and environment. A genotype that is highly fit in one context may be maladaptive in another. Furthermore, fitness is not a fixed property of a gene; it is a dynamic relationship that changes as the environment fluctuates. This context-dependence means that evolutionary predictions must account for environmental variability and frequency-dependent selection, where the fitness of a genotype depends on its frequency in the population. Ignoring these factors can lead to incorrect predictions about the direction and rate of evolution. C
Worked example
Problem. In a population of 1,000 diploid beetles, the allele \( A \) has a frequency \( p = 0.6 \) and the allele \( a \) has a frequency \( q = 0.4 \). The fitness of the \( AA \) genotype is 1.0, the \( Aa \) genotype is 0.9, and the \( aa \) genotype is 0.8. Calculate the mean fitness of the population and the expected frequency of allele \( A \) in the next generation.
- Calculate the genotype frequencies using Hardy-Weinberg proportions: \( f(AA) = p^2 = 0.6^2 = 0.36 \), \( f(Aa) = 2pq = 2(0.6)(0.4) = 0.48 \), and \( f(aa) = q^2 = 0.4^2 = 0.16 \).
- Calculate the mean fitness \( \bar{w} \) of the population: \( \bar{w} = f(AA)w_{AA} + f(Aa)w_{Aa} + f(aa)w_{aa} = (0.36)(1.0) + (0.48)(0.9) + (0.16)(0.8) \).
- Compute the sum: \( \bar{w} = 0.36 + 0.432 + 0.128 = 0.92 \).
- Calculate the new frequency of allele \( A \), \( p' \), using the formula \( p' = \frac{p^2 w_{AA} + pq w_{Aa}}{\bar{w}} \). Here \(pq = 0.6 \times 0.4 = 0.24\) (half the heterozygote frequency, because half of a heterozygote's alleles are \(A\)). Substitute: \( p' = \frac{(0.36)(1.0) + (0.24)(0.9)}{0.92} \).
- Compute the numerator: \( 0.36 + 0.216 = 0.576 \). Then divide by the mean fitness: \( p' = \frac{0.576}{0.92} \approx 0.626 \), a rise of 0.026 from 0.600 in one generation.
Units check. The result is a dimensionless frequency, which is consistent with the definition of allele frequency as a proportion of the total allele pool.
Three quick tests
- If the selection coefficient \( s \) against the \( aa \) genotype is 0.2 and the heterozygote has the same fitness as \( AA \), what is the relative fitness of \( aa \)?
Answer
The relative fitness of \( aa \) is \( 1 - s = 1 - 0.2 = 0.8 \). - Why does the Breeder’s Equation include the term \( h^2 \)?
Answer
It accounts for the proportion of phenotypic variance that is additive genetic, determining how much of the selection differential is passed to the next generation. - What happens to the rate of allele frequency change as a deleterious recessive allele becomes rare?
Answer
The rate of change slows down because the allele is sheltered in heterozygotes, where it is not exposed to selection.
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Lecture notes checked line by line by the editor; every number in the worked example was recomputed.
Concepts cited: T-018 · Threads: evolution