Selection Coefficients and Relative Fitness Explained

In population genetics, relative fitness describes how well different genotypes or phenotypes contribute genes to the next generation compared with one another. The selection coefficient measures the reduction in relative fitness associated with natural selection against a particular type.

These concepts are closely related. If a genotype has relative fitness of 1, it is used as the reference. If another genotype has relative fitness of 0.8, its selection coefficient is 0.2. In simple terms, that genotype contributes about 20% fewer offspring to the next generation than the reference genotype under the conditions being studied.

Understanding the distinction matters because fitness and selection coefficient are not absolute properties of an organism. They are measures of reproductive success relative to other variants in a particular population and environment.

What relative fitness means

In evolutionary biology, fitness refers to an organism’s contribution to future generations. It is not simply a measure of physical strength, health, size, or survival.

For a particular genotype, relative fitness compares its reproductive contribution with that of other genotypes. Because the comparison is relative, the genotype with the highest fitness is commonly assigned a value of 1.

Suppose a population contains three genotypes with reproductive contributions of:

The raw numbers could represent surviving offspring, successful reproductive events, or another appropriate measure of genetic contribution. To calculate relative fitness, each value is divided by the highest value:$$w_i=\frac{W_i}{W_{\max}}$$

Here, $W_i$ is the reproductive contribution of genotype $i$, and $w_i$ is its relative fitness.

The resulting values tell us how each genotype compares with the reference genotype. They do not mean that an organism with a fitness of 0.8 is “80% healthy” or that it survives 80% of the time.

What the selection coefficient means

The selection coefficient, usually written $s$, describes the strength of selection against a genotype relative to a reference genotype.

It is calculated as:$$s=1-w$$

where $w$ is the genotype’s relative fitness.

For example, if a genotype has a relative fitness of 0.8:$$s=1-0.8=0.2$$

The selection coefficient is therefore 0.2, or 20%.

A selection coefficient of zero means that the genotype has the same relative fitness as the reference. A larger positive value means a greater reduction in relative fitness.

Using the previous example:

• AA: $w=1.00$, so $s=0$
• Aa: $w=0.80$, so $s=0.20$
• aa: $w=0.60$, so $s=0.40$

The selection coefficient is therefore best understood as a measure of fitness disadvantage, not as a direct measure of how common or rare an allele is.

Relative fitness and selection coefficient are two ways of describing the same comparison

The relationship is simple:$$w=1-s$$

If you know one quantity, you can calculate the other.

The word relative is important. If every genotype in a population experienced exactly the same proportional change in reproductive success, their relative fitnesses would not change, and that change alone would not produce selection among them.

How selection coefficients affect evolution

Natural selection changes allele frequencies when individuals with different heritable variants leave different numbers of descendants.

Imagine a population in which allele $A$ is associated with higher reproductive success than allele $a$. If that difference is caused by heritable genetic variation and persists across generations, $A$ can increase in frequency.

The selection coefficient helps quantify the size of the fitness difference that drives this process.

A small selection coefficient, such as $s=0.01$, represents a relatively small fitness difference. A much larger coefficient, such as $s=0.5$, represents a substantially greater disadvantage for the genotype in question.

However, the effect on allele frequencies cannot be inferred from $s$ alone. It also depends on genotype frequencies, dominance, mating patterns, population size, and other evolutionary forces.

For example, selection against a recessive allele can be much less effective when that allele is rare because most copies may occur in heterozygotes, where the disadvantage is not expressed.

Fitness is usually assigned to genotypes, not directly to alleles

A common source of confusion is assigning a selection coefficient directly to an allele without specifying how that allele behaves in different genotypes.

Consider a gene with two alleles, $A$ and $a$. The three diploid genotypes are:$$AA,\quad Aa,\quad aa$$

Each genotype can have its own relative fitness:$$w_{AA},\quad w_{Aa},\quad w_{aa}$$

For example:$$w_{AA}=1,\qquad w_{Aa}=1,\qquad w_{aa}=0.8$$

This represents a case in which $aa$ has a relative fitness of 0.8, while both $AA$ and $Aa$ have the highest fitness. The corresponding selection coefficient against $aa$ is 0.2.

This pattern is consistent with a recessive disadvantage: the deleterious effect is expressed in the homozygous genotype but not in the heterozygote.

By contrast:$$w_{AA}=1,\qquad w_{Aa}=0.9,\qquad w_{aa}=0.8$$

indicates that both copies and one copy of $a$ are associated with reduced fitness, although the heterozygote has an intermediate fitness.

The genotype-specific fitness values therefore provide more information than a single selection coefficient assigned to an allele.

Different fitness patterns describe different forms of selection

The arrangement of genotype fitnesses can reveal how selection acts.

Selection against a recessive allele

A simple model might be:$$w_{AA}=1,\qquad w_{Aa}=1,\qquad w_{aa}=1-s$$

Only the homozygous recessive genotype experiences the fitness reduction.

When the recessive allele is rare, relatively few individuals are homozygous for it. As a result, selection may have difficulty removing the allele rapidly because many copies remain hidden in heterozygotes.

Selection against a dominant allele

A simple model might instead be:$$w_{AA}=1-s,\qquad w_{Aa}=1-s,\qquad w_{aa}=1$$

Here, carrying the allele is sufficient for the fitness disadvantage to appear. Selection can therefore act on the allele even when it is relatively rare, because its effect is visible in heterozygotes.

Heterozygote advantage

Sometimes the heterozygote has the highest fitness:$$w_{AA}<w_{Aa}>w_{aa}$$

This is called heterozygote advantage or overdominance. Because both homozygotes have lower fitness than the heterozygote, selection can maintain both alleles in a population under suitable conditions.

The opposite pattern, in which the heterozygote has lower fitness than either homozygote, is called heterozygote disadvantage or underdominance. Its evolutionary behavior is quite different and can favor one allele becoming fixed, depending on starting frequencies and other conditions.

Relative fitness does not have to mean survival

Fitness is sometimes incorrectly treated as synonymous with survival.

An organism can survive to adulthood yet have low fitness if it produces few offspring. Conversely, an organism can have high reproductive success despite facing substantial mortality earlier in life.

Fitness can reflect multiple stages of the life cycle, including survival, mating success, fertility, offspring survival, and the reproductive success of descendants. What matters is the organism’s contribution to subsequent generations.

For this reason, a useful fitness estimate must be tied to the biological question being studied. A genotype might have an advantage at one life stage but a disadvantage at another, producing a different overall fitness when the entire life cycle is considered.

Fitness depends on the environment

There is no universal fitness ranking for genotypes independent of circumstances.

A genetic variant that improves survival in one environment may be neutral or harmful in another. Temperature, food availability, predators, pathogens, competitors, and many other environmental factors can change the relative reproductive success of genotypes.

Fitness can also depend on frequency. A variant may be advantageous when rare but less advantageous when common, or vice versa. This is one reason why simple constant-fitness models are useful for learning basic population genetics but do not describe every real population.

Consequently, saying that a genotype “has a fitness of 0.8” is incomplete without understanding what it is being compared with and under what conditions the measurement applies.

A simple example of selection coefficients in action

Suppose two genotypes have the following reproductive contributions:

• $AA$: 100 offspring
• $aa$: 80 offspring

Taking $AA$ as the reference gives:$$w_{AA}=1$$

and$$w_{aa}=\frac{80}{100}=0.8$$

The selection coefficient against $aa$ is:$$s=1-0.8=0.2$$

Thus, under this model, $aa$ has a 20% relative fitness disadvantage compared with $AA$.

It would be incorrect to conclude that exactly 20% of $aa$ individuals die, or that the $aa$ genotype must decline by exactly 20% in frequency every generation. Those statements require additional information. Selection acts on genotype frequencies and ultimately changes allele frequencies according to how the genotypes are distributed and reproduce.

Selection coefficient versus allele-frequency change

The distinction between these ideas is fundamental.

The selection coefficient describes a fitness difference.

The change in allele frequency describes the evolutionary outcome.

A selection coefficient can be known without knowing the current allele frequency. But to predict how quickly an allele changes in frequency, you generally need to know the frequencies of the relevant genotypes and how their fitnesses are related to the alleles.

For a simple diploid population with genotype frequencies $f_{AA}$, $f_{Aa}$, and $f_{aa}$, the mean fitness of the population is:$$\bar w=f_{AA}w_{AA}+f_{Aa}w_{Aa}+f_{aa}w_{aa}$$

Mean fitness represents the average relative reproductive contribution of the population under the specified fitness model. It provides the normalization needed when calculating genotype frequencies after selection.

This is why a selection coefficient should not be interpreted as a direct percentage change in allele frequency.

What a selection coefficient of zero does—and does not—mean

If $s=0$, then $w=1$ relative to the chosen reference. That means there is no fitness disadvantage in the model.

It does not necessarily mean that the allele’s frequency will remain constant.

An allele can change in frequency because of other evolutionary processes, including genetic drift, migration, mutation, or nonrandom mating. In a finite population, for example, an allele with no fitness difference can still rise or fall by chance.

Likewise, a positive selection coefficient does not guarantee that an allele will eventually reach fixation. Population size, genetic drift, dominance, initial frequency, and interactions with other variants can all influence its fate.

Why the reference genotype matters

Relative fitness is normalized, so the numerical values depend on the reference.

Suppose three genotypes have raw reproductive contributions of 100, 80, and 60. Relative to the genotype with contribution 100, their fitnesses are 1.0, 0.8, and 0.6.

If all raw values were instead expressed in another unit—say 10, 8, and 6—the relative fitnesses would remain exactly the same. Relative fitness deliberately removes the arbitrary scale of the original measurements.

The important information is the ratio between fitnesses, not the absolute numerical scale.

This also means that researchers can rescale fitness values without changing the underlying selection model, provided the ratios remain the same.

The key distinction to remember

Relative fitness and selection coefficient describe different sides of the same fitness comparison:$$\boxed{s=1-w}$$

Relative fitness (ww) tells you how a genotype’s reproductive contribution compares with the reference genotype.

Selection coefficient (ss) tells you how much lower that relative fitness is than the reference.

So if a genotype has $w=0.7$, its selection coefficient is $s=0.3$. That means it has a 30% relative disadvantage under the specified conditions—not that its frequency must fall by 30%, not that 30% of individuals necessarily die, and not that the associated allele will disappear.

That distinction is the foundation for using selection coefficients and relative fitness correctly in population genetics.