Wright–Fisher allele-frequency variance

The formula Var(p′|p) = p(1−p)/(2Ne) summarizes how In the diploid Wright–Fisher model, the variance quantifies random allele-frequency change from finite gamete sampling per generation. To calculate it, first identify each quantity and its unit in the problem. For p=0.40 and Ne=100, Var(p′|p)=0.40·0.60/(2·100)=0.0012. The one-generation standard deviation is √0.0012≈0.0346 in allele-frequency units. Check: at p=0 or 1 the model variance is zero because an allele is fixed or lost. The calculation is interpretable only when denominators, factors and reference describe the same population, sample or time interval. Read the value with its unit and scale: a proportion is not a rate, a rate is not a probability, and a model output is not by itself a biological explanation.

The formula is useful only under specific conditions. This relation assumes independent random sampling of 2Ne allele copies without selection, mutation or migration in the idealized diploid model. Real Ne summarizes reproductive variance, sex ratio and demography and need not equal census size. Neutral drift leaves the expected p unchanged but creates variance; smaller Ne produces larger fluctuations. Across multiple generations, variance accumulates over time. Before substituting values, check that the population, measurement method, period and comparison group fit the question. Frequency variance dimensionless squared · Ne is effective diploid population size Even correctly calculated values can mislead when observations are dependent, data are missing or the reference is unsuitable. State the main model assumptions and uncertainty alongside the result; the equation does not replace study design or data-quality checks.

In practice, this metric helps to Estimate random allele-frequency fluctuation over one model generation. A good report also states which people or samples were included, how quantities were measured and what limits the claim has. In the diploid Wright–Fisher model, the variance quantifies random allele-frequency change from finite gamete sampling per generation. Interpret comparisons cautiously when populations, periods or measurement protocols differ. Separate a descriptive summary from a causal claim and report spread or uncertainty intervals for sample estimates. Also report the comparison unit and any exclusions.

Reproduce the example calculation: For p=0.40 and Ne=100, Var(p′|p)=0.40·0.60/(2·100)=0.0012. Wright–Fisher allele-frequency variance uses Var(p′|p) = p(1−p)/(2Ne). In plain terms, in the diploid Wright–Fisher model, the variance quantifies random allele-frequency change from finite gamete sampling per generation. Unit check: Frequency variance dimensionless squared · Ne is effective diploid population size. This relation assumes independent random sampling of 2Ne allele copies without selection, mutation or migration in the idealized diploid model. 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 Wright–Fisher allele-frequency variance is this: This relation assumes independent random sampling of 2Ne allele copies without selection, mutation or migration in the idealized diploid model. Do not use the metric without its reference; it is useful for Estimate random allele-frequency fluctuation over one model generation. In the diploid Wright–Fisher model, the variance quantifies random allele-frequency change from finite gamete sampling per generation. 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.