Breeder's Equation Calculator (Response to Selection)

How it works

R = h² × S · S = i × σ_P (i = selection intensity from the proportion kept: 50% → 0.80, 20% → 1.40, 10% → 1.75, 5% → 2.06, 1% → 2.67) · gain per year = R ÷ generation interval · realised h² = R ÷ S

When breeders keep only the best animals or plants as parents, the next generation moves toward them, but only by the share of the parents' superiority that is genetic rather than environmental — that share is the narrow-sense heritability, and the breeder's equation multiplies it by the selection differential to give the response. How far above average the chosen parents are depends on how few are kept: truncating a normal distribution at the top 20% gives parents 1.4 standard deviations above the mean, the top 1% about 2.7, with steeply diminishing returns that also shrink the breeding population and raise inbreeding. Dividing by the generation interval converts response to annual gain, which is why dairy and poultry programmes chase shorter generations as hard as higher intensity.

Worked example

A trait with mean 100, standard deviation 10 and heritability 0.3: keeping the top 20% as parents gives an intensity of 1.40, a selection differential of 14 and a response of 0.3 × 14 = 4.2 per generation — 1.68 per year with a 2.5-year interval. Reaching a mean of 120 would take about 4.8 generations (12 years). If the observed response had been only 2.8, the realised heritability would be 0.2.

Frequently asked questions