Breeders Equation Guide
Meaning
The breeder’s equation is a compact model for predicting change in a quantitative trait after selection. It connects three ideas. Heritability describes how much observed variation is passed through additive genetic effects. The selection differential measures how far chosen parents differ from the whole population. The response predicts the expected shift in the next generation.
Calculator Purpose
This calculator helps students and breeders test those relationships quickly. It supports direct input of heritability and selection differential. It also calculates heritability from additive genetic variance and phenotypic variance. It can calculate selection differential from the selected mean and population mean. That makes the tool useful when different forms of data are available.
Core Method
The central equation is R = h²S. R is the response to selection. h² is narrow sense heritability. S is the selection differential. When the trait mean of the base population is known, the predicted next generation mean is found by adding R to that base mean. For repeated generations, the simple projection adds the same response each generation. Real breeding programs may change because selection intensity, environment, and variance can shift over time.
Input Steps
Use the calculator by entering a population mean and selected parent mean, or by entering a direct selection differential. Then enter heritability directly, or provide additive and phenotypic variances. Add an optional observed response to compare prediction error. Choose units and decimal places for clear reporting. Submit the form to see results above the inputs. Use the export buttons to save the calculation.
Interpreting Results
The results should be read as a prediction, not a guarantee. High heritability means selection can cause faster progress, but it does not remove environmental influence. A large selection differential can increase response, yet it may reduce diversity if applied too strongly. Negative values are also meaningful. They show selection toward a lower trait value.
Best Use
This page is designed for math practice, genetics lessons, plant breeding examples, animal breeding planning, and simple quantitative genetics checks. Always confirm biological assumptions before applying results to costly decisions. Because the inputs are transparent, learners can change one number and observe the effect. This supports sensitivity testing. It also shows why precise measurement and balanced sampling matter in breeding calculations. Keep records for every scenario compared during each review.