# 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?

• Welcome to Biology.SE. Your question is a possible duplicate of How does Natural Selection shape Genetic Variation?. You might also have a look at this post to understand Fisher's Fundamental Theorem of Natural Selection Jul 14, 2016 at 9:35
• Thanks for point that out! I will read with more attention, but I still think that it is not clear in that post whether, given only the mean fitness and fitness variance of a population, one could predict the future mean fitness and how. One of my conditions is saying that the G matrix is unknown (population composition is unknown). Jul 14, 2016 at 9:47
• The evolution of the G-matrix is exactly what you are interested in if I understand your post correctly. Once you read the other post, you might want to ask your question in reference to this particular post. Jul 14, 2016 at 9:50
• Although I understand the point of the G-matrix, what I was looking for was a way to predict mean fitness without direct access to the G-matrix... Given only the measured fitness variance of the population and assuming no new mutation, no recombination, no migration, can we predict future fitness variance (and by the FFTNS the mean fitness) of the population. Jul 14, 2016 at 10:08
• 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