# Adaptation by standing genetic variation and fitness variance [duplicate]

I've read a couple of paper on Fisher's Fundamental Theory of Natural selection that states: $W(t+1) = W(t) + Var_{W}(t)$

Given a population with some degree of genetic variability, and assuming that no new mutations can appear, eventually the most fit strain will be fixed (discarding the effect of drift). The FFTNS allows to predict, given the mean fitness at any point and the fitness variance, the mean fitness of the population in the next generation. However, can we predict the variance on fitness for the new population?

Given the possible complexity of the problem, the situation I'm focus have specific conditions, but I would also like to know the general answer. But in my case:

• Individuals reproduce asexually
• Random mating
• Diploids
• Expanding population with recurrent bottlenecks (we can approximate to Wrigth-Fisher population with certain effective population size)

More generally, given only the initial mean fitness and variance of the fitness can we predict the trajectory of the mean fitness during adaptation? If not, what do we need more? Number of strains present? Or only the full composition of the population allow for such prediction?

• Given the measured fitness variance of the population you can construct a G-matrix (if you have sex-specific variance and cross sex covariance estimated, it would be a 2 x 2 matrix) and perform the prediction using the multivariate breeders eq. $\Delta \bar{z} = G \beta$ where $\Delta \bar{z}$ would be the change in fitness, $G$ is a 2 x 2 matrix as above, and $\beta$ is the sex-specific selection coefficient, thus fitness after selection would be $z + \Delta \bar{z}$. Price equation is also likely very useful. Jul 14, 2016 at 10:30