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The selection coefficient s expresses a genotype’s relative fitness disadvantage; h specifies how much of it appears in a heterozygote.
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Formula
Relative fitness w, s and h are dimensionless
| Symbol | Meaning | Unit |
|---|---|---|
| Selection coefficient against genotype aa relative to AA | dimensionless | |
| Dominance parameter for the heterozygote effect | dimensionless, usually from 0 to 1 | |
| Relative fitnesses of genotypes AA, Aa and aa | dimensionless |
w_{AA}=1,\quad w_{Aa}=1-hs,\quad w_{aa}=1-sFor p=f(A) and q=1−p, mean fitness is wbar=p2wAA+2pqwAa+q2waa and p′=(p2wAA+pqwAa)/wbar. This is a one-locus diploid model with constant fitness values. Dominance, environment, drift, migration and mating structure can change the trajectory. Fitness is expected relative reproductive contribution in a context, not an absolute or moral property. State the reference genotype and generation model.
One-locus diploid model with constant fitnesses normalized to a reference genotype and a defined generation.
Fitness weights genotype frequencies before the next generation.
Mean fitness
p+q=1.
Given p=0.8, q=0.2, s=0.1, h=0.5, find wbar.
wAa=0.95, waa=0.9 and wbar=0.98.
Reading fitness as absolute survival probability.
Relative fitness summarizes reproductive contribution relative to a reference.
Formula cluster
Fitness describes selection direction, not its cause alone.
For p=0.8, q=0.2, s=0.1 and h=0.5, wAA=1, wAa=0.95 and waa=0.9; wbar=0.98. Then p′=(0.64+0.8·0.2·0.95)/0.98≈0.8082, a one-generation increase of about 0.0082 under this model.
Analyzing how differences in survival or reproductive success change allele frequencies across generations
Here is how to work through a typical Selection Coefficient and Relative Fitness (wAA=1; wAa=1−hs; waa=1−s) task step by step:
Task
Given p=0.8, q=0.2, s=0.1, h=0.5, find wbar.
Solution path
wAa=0.95, waa=0.9 and wbar=0.98.
Under this parameterization, genotype aa has relative fitness 1−s=0.9 compared with reference genotype AA at fitness 1. This describes a 10% relative disadvantage in expected reproductive contribution, not automatically a 10% lower survival probability. The measured fitness component must match the life cycle. s depends on population and environment; it is not an invariant value of a variant in every condition. State the reference genotype, fitness component and generation. This keeps s interpretable as a relative measure for a specific population and environment. Sampling error, drift and environmental change can also explain observed frequency shifts, so fitness differences should not be inferred from one population step alone.
h specifies what fraction of the recessive fitness cost appears in heterozygote Aa: wAa=1−hs. At h=0 the deleterious effect is fully recessive, at h=1 fully dominant, and at h=0.5 additive in this simplified sense. These categories refer to fitness, not necessarily visible traits or molecular action. Real genotypes can show different effective h values across environments and fitness components. State the reference genotype, fitness component and generation. This keeps s interpretable as a relative measure for a specific population and environment. Sampling error, drift and environmental change can also explain observed frequency shifts, so fitness differences should not be inferred from one population step alone.
For p=f(A) and q=1−p, first calculate mean fitness w̄=p2wAA+2pqwAa+q2waa. Then p′=(p2wAA+pqwAa)/w̄. With p=0.8, s=0.1 and h=0.5, genotype fitnesses are 1, 0.95 and 0.9; w̄=0.98 and p′≈0.808. The calculation assumes Hardy–Weinberg genotype frequencies before selection and a one-locus model; drift and migration are omitted. State the reference genotype, fitness component and generation. This keeps s interpretable as a relative measure for a specific population and environment. Sampling error, drift and environmental change can also explain observed frequency shifts, so fitness differences should not be inferred from one population step alone.
Reproduce the example calculation: For p=0.8, q=0.2, s=0.1 and h=0.5, wAA=1, wAa=0.95 and waa=0.9; wbar=0.98. Selection Coefficient and Relative Fitness uses wAA=1; wAa=1−hs; waa=1−s. In plain terms, the selection coefficient s expresses a genotype’s relative fitness disadvantage; h specifies how much of it appears in a heterozygote. Unit check: Relative fitness w, s and h are dimensionless. One-locus diploid model with constant fitnesses normalized to a reference genotype and a defined generation. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.
A key limit of Selection Coefficient and Relative Fitness is this: One-locus diploid model with constant fitnesses normalized to a reference genotype and a defined generation. Do not use the metric without its reference; it is useful for Analyzing how differences in survival or reproductive success change allele frequencies across generations. The selection coefficient s expresses a genotype’s relative fitness disadvantage; h specifies how much of it appears in a heterozygote. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.
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