Selection Coefficient Calculator

The selection coefficient, written as s, measures how strongly natural selection acts against a genotype relative to the most-fit reference genotype in a population. It is one of the central parameters of population genetics and evolutionary biology, quantifying the relative fitness disadvantage of an allele or genotype in a single number that ranges from -1 to 1. A value of s = 0 means the variant is selectively neutral; a positive s means the mutant suffers a fitness cost (deleterious), and a negative s means the mutant enjoys a fitness advantage (beneficial).

This selection coefficient calculator converts raw fitness or survival data into s, then propagates an allele's frequency forward through many generations so you can watch selection sweep, purge, or balance a variant. Researchers in evolutionary biology, conservation genetics, and quantitative genetics use the selection coefficient to compare the strength of selection across loci, predict how fast an adaptive mutation spreads, and estimate how long a harmful allele persists before it is removed. Because fitness is always measured relative to a reference, the wildtype is conventionally assigned a fitness of 1, and every other genotype is scaled against it.

In Wright-Fisher and Hardy-Weinberg frameworks, the selection coefficient links directly to the relative fitnesses of the three diploid genotypes at a single locus: the homozygous reference (AA), the heterozygote (Aa), and the homozygous variant (aa). Whether you start from laboratory survival percentages or from estimated fitness values, the calculator returns the same evolutionary currency, s, and the genotype fitness schedule that drives the dynamics.

The calculator derives the selection coefficient from the ratio of mutant fitness to wildtype fitness. In fitness mode, you supply absolute or relative fitness values; in survival mode, you supply survival percentages. Both reduce to the same definition of s:

Fitness mode: s = 1 − (w_mutant / w_wildtype)

Survival mode: s = 1 − (survival_mutant / survival_wildtype)

Once s is known, the calculator builds the relative fitnesses of the three genotypes using the dominance coefficient h, which controls how the heterozygote's fitness sits between the two homozygotes. In survival mode the schedule is the textbook form w_AA = 1, w_Aa = 1 − h·s, w_aa = 1 − s. In fitness mode the wildtype value is kept on its original scale: w_AA = w_wildtype, w_Aa = w_wildtype·(1 − h·s), and w_aa = w_mutant.

The dominance coefficient ranges from h = 0 (the variant is fully recessive, so heterozygotes carry no fitness cost) through h = 0.5 (additive or codominant, the heterozygote is exactly intermediate) to h = 1 (the variant is fully dominant, so one copy already carries the full effect). This single locus, biallelic model is the workhorse of deterministic selection theory and underlies every projection the calculator makes.

Knowing s tells you the direction of selection, but the allele frequency trajectory tells you how fast and how far it goes. The calculator iterates the standard deterministic selection recursion for a diploid population in Hardy-Weinberg proportions. Let p be the frequency of the reference allele A and q = 1 − p the frequency of the variant allele a. Each generation the population's mean fitness is the weighted average of the three genotype fitnesses:

w̄ = p²·w_AA + 2pq·w_Aa + q²·w_aa

The frequency of A in the next generation is the share of A alleles that survive and reproduce, normalized by mean fitness:

p' = (p²·w_AA + pq·w_Aa) / w̄

The calculator applies this recursion for the number of generations you enter (capped internally at 500 steps for the displayed trajectory) and reports the final allele frequency. Because selection always increases mean fitness in this constant-fitness model, the trajectory marches monotonically toward fixation of the fitter allele unless heterozygotes are favored. When you set h outside the 0-to-1 interval to model overdominance or underdominance, the calculator also reports the internal equilibrium frequency where the two opposing selection pressures balance, giving a stable polymorphism in the overdominant case.

Beyond the deterministic sweep, the calculator reports two diffusion-style timescales that summarize the long-run fate of the variant in a finite population. These estimates assume an effective population size of N_e = 1000, a common reference value for illustrating selection strength.

For a beneficial variant (s < 0, meaning the mutant is fitter than wildtype), the calculator estimates the time to fixation as roughly (2 / |s|) · ln(2 N_e) generations. Stronger selection (larger |s|) drives the favored allele to fixation faster, while weaker selection stretches the sweep over many more generations.

For a deleterious variant (s > 0), the calculator estimates the time to loss as roughly (1 / s) · ln(1 / p₀) generations, where p₀ is the initial frequency of the variant. A harmful allele starting at higher frequency takes longer to purge, and weaker selection again prolongs its persistence. These are order-of-magnitude approximations, not exact stochastic expectations, but they are extremely useful for intuiting how the strength of natural selection translates into evolutionary time.

The magnitude of s tells you whether selection is strong or subtle. As a rough guide used widely in evolutionary biology and population genetics, an s on the order of 0.1 or greater is considered strong selection that can change allele frequencies noticeably within a handful of generations. A value near 0.01 represents moderate selection, and values below about 0.001 are weak enough that genetic drift can overwhelm selection in small populations, especially when N_e · s is less than 1.

The dominance coefficient profoundly affects how visible selection is. Fully recessive deleterious alleles (h = 0) hide from selection in heterozygotes, so they persist far longer and are purged slowly because selection only "sees" the rare homozygotes. Dominant variants (h = 1) are exposed to selection in every carrier and respond quickly. This is why recessive disease alleles linger in human populations at low frequency while strongly dominant deleterious alleles are rare. When you report a final frequency from this selection coefficient calculator, always note the dominance assumption alongside s, because the same s produces very different trajectories depending on h.

Finally, remember that this model is deterministic: it ignores mutation, migration, and the random sampling of genetic drift. In real finite populations, a beneficial allele can still be lost by chance early in its sweep, and a slightly deleterious allele can drift to fixation. Use the calculator's projections as expectations under strong, consistent selection rather than guarantees for any single population.