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## Side Box 3.1. Heritability, Selection Differential, and Response to
Selection

The effects of truncation selection across generations
acts via heritable vaiation and we can visualize selection in terms of the
relationship between parents and offspring. Assume that only parents with
very large phenotypic values are allowed to breed. The selection differential,
**s**, is the difference in mean of the selected parents versus to unselected
parents (red vs red+blue distributions on the horizontal axis). The response
to selection, **R**, is the change in mean of the progeny distribution
relative to parents. Response to selection will always be less than the
selection differential because, h2, the slope of the line is less than one,
or the proportion of phenotypic variation explained by additive genetic
causes should be less than one. Another way to think about the relationship
between R, h2, and s is to predict R (the rise in the progeny generation)
as a function of the s (the run), where rise over run is the slope (h2).
The rise is a function of the the run times the slope or R = h2s.

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Sexual Selection