Without selection, the variance m 2 converges to (N − 1 ) μ σ 2. As long as the selection gradient does not vanish (w 1 ≠ 0 ), the mean trait value changes according to Equation 9a, which is a standard result of population genetics (Ewens 2004) and corresponds to the canonical equation in adaptive dynamics theory (Dieckmann and Law 1996; Champagnat et al. 2006).
In quantitative genetics, a population's response to selection at a single trait (i.e. how the mean value of a trait changes across generations in response to selection) is measured using the breeder's equation: R = h S, where R is the per generation response to selection, h is the heritability and S is the selection differential (Lynch and Walsh 1998).
In some cases, evolutionary changes in mean trait values and/or plasticity differed among the three populations (Tables 1– 3, Year × Population and Treatment × Year × Population effects).
We have, necessarily, used particular prior distributions for the change in mean trait value caused by the PTVs.
For example, with n = 50, the data correspond to a rather small change in mean trait values.
Specifically, the breeder's equation R = h S expresses the response to selection (change in mean trait) R as the product of the trait heritability h and the selection differential S.
This result has very great significance for predicting the reaction to selection in natural populations if heterozygotes are not distinguished and we only measure additive variance, we are very likely to overestimate the expected change in mean trait values between generations.
This enables investigating how the direction of selection on g changes with increasing mean trait values of the population and to analyze how the ESS in g depends on angling intensity.
A significant intercept slope interaction indicates that an individual's mean trait level is related to the way the trait changes with age.
Selection differentials measure the change of a population's mean trait value before and after selection (Fig. 1; Falconer and Mackay 1996).
