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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?

Thanks in advance

Diogo Santos
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    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 – Remi.b Jul 14 '16 at 09:35
  • 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). – Diogo Santos Jul 14 '16 at 09:47
  • 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. – Remi.b Jul 14 '16 at 09:50
  • 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. – Diogo Santos Jul 14 '16 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. – rg255 Jul 14 '16 at 10:30
  • Thanks a lot!! Can you point out a reference for constructing the G-matrix from the variance in fitness alone? By the way, if the species is asexual, then G is a 1*1 matrix right? And how does G changes for every generation? – Diogo Santos Jul 14 '16 at 10:38
  • Asexual would be complicated, not something I've considered before, so I'm not sure how that would affect it off the top of my head. Just a note, you may also want to consider the effects of non-genetic variance in fitness and how that impacts selection (see Hansen and Houle's papers on the concept of evolvability) – rg255 Jul 14 '16 at 10:43
  • Sure! Although I want to start with a simple model, without external complications... It's funny, I had always the felling that asexual populations would be easier to model than sexual!! :) – Diogo Santos Jul 14 '16 at 10:44
  • Given the asexual condition in my question I think that the linked question does not answer it, so can the "This question may already have an answer here:" be removed? – Diogo Santos Jul 14 '16 at 16:47

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