Breeder's Equation

The breeder's equation, R = h²S, predicts how much a trait will change in one generation of selection. R is the response to selection, S is the selection differential, and h² is the narrow-sense heritability of the trait. It was formulated in animal breeding by Jay Lush in the 1930s.

The selection differential is the difference between the average trait value of the individuals chosen as parents and the average of the whole population. If farmers pick cows that give 10 liters more milk than the herd average, and the heritability is 0.3, the next generation is expected to average 3 liters more than the previous one. The equation shows that selection works only on the part of variation that is passed on genetically.

Russell Lande applied the equation to natural selection in 1979, writing the response in terms of the selection gradient and genetic variance. The approach lets biologists predict the speed of evolution, for example the changes in beak size of Darwin's finches after a drought. It rests on the work of Ronald Fisher on the decomposition of variance.

The equation is a short-term approximation and assumes a stable heritability, and it ignores correlations among traits, which can make a trait evolve in unexpected directions. Heritability itself can change as selection uses up variation, and environmental effects can mask the response. It is the basis for improving crops and livestock such as cattle and domestic chickens, and a topic in population genetics and the study of fitness.

• Heritability — the term h² in the equation
• Natural Selection — the process it quantifies
• Population Genetics — the wider field