Quantitative genetics - the Breeder's Equation

Predicting response to selection for a quantitative trait is done with the Breeder's Equation, R = h²S.

• R is the amount of change in the mean value of a trait from one generation to another
• h² is the heritability of the trait
• S is the selection differential, which is the amount of difference between the mean of the parent population and the mean of the parents who actually breed

The app below shows a heritability estimation based on a linear regression of offspring body lengths against parent body lengths - the slope of the line is the narrow-sense heritability of the trait (this is in the graph to the left).

In the graph to the right of the heritability graph you'll see a curve representing the population of parents (blue curve) and a population of parents that are selected to breed (green curve) - the difference between their means is the selection differential, which you can set. By default it is set to 10. The range indicator above the curves labeled S shows the selection differential.

At first the offspring curve is hidden, but if you slide the "Visibility of offspring curve" slider to the right it will appear - the response to selection is the difference between the parent population and the offspring population (indicated by the R range indicator above the curves).

Changing the heritability or the selection differential changes the response. Note the following:

• If heritability is 0 there is no additive genetic variation for the trait, and all of the variation in body length is due to phenotypic plasticity
• The relationship between offspring and parent is a flat line, because offspring phenotypes can't be predicted from parent phenotypes
• There is no response to selection, no matter how big S is
• Higher heritability (up to a maximum of 1) means that more of the trait value is due to additive genetic variation
• The relationship between offspring and parent is a sloped line - if offspring are identical to parents the slope of the line is 1
• The offspring mean is equal to the mean of the breeders if heritability is 1, because the offspring are identical to their parents
• Larger selection differentials produce larger responses as long as the heritability is over 0