# How to determine the evolution of a dimension of fitness that has high variability of selection intensity?

How can one determine the evolution of a dimension of fitness that has high variability of selection intensity (low in some generations, high in others) compared to other dimensions of fitness?

• Fitness is unidimensional (for an individual, it is a single point, not a matrix). Phenotype and environment are typically highly multidimensional. Nov 29, 2016 at 17:43
• The question is unclear to me. Are you talking about analysis of G-matrix (see Arnold et al. 2008 and this post)? Telling us what you've found for the moment would be helpful. Also, if you have a specific application in mind, you can let us know your end goal. Nov 29, 2016 at 17:46
• I mean, in a given generation, there may be stronger selection intensity upon an individual's ability to evade predators than upon an individual's ability to find territory. In another generation, selection on each of these abilities may be more modest. (I am referring to each of these abilities as a "dimension" of fitness.) Does this make sense? Nov 29, 2016 at 17:54
• Oh ok. That makes sense. I don't think anyone ever referred to the covariance between a given phenotypic trait and fitness (as this is what you are describing I think) as a dimension of fitness. Roff's book, as I recall offers a good semantic on the subject but I don't fully remember it by heart. Nov 29, 2016 at 17:59
• I think that a case-study example in your post would be helpful to understanding exactly your goal (I am removing my close vote in the meantime). Nov 29, 2016 at 18:01

It's complicated. The classic answer is from Dempster 1955 Cold Spring Harb Symp Quant Biol 1955. 20: 25-32 (doi:10.1101/SQB.1955.020.01.005), which has a whole section on "Selection Intensity Varying With Time". Summarizing:

• An example from Kimura (1954) with a mean selective coefficient of zero: "the variation of selection facilitates the loss or near loss of alleles thus tending, if anything, to decrease rather than maintain genetic heterogeneity".
• An example with haploid populations (approximately equal to the diploid case for weak selection) with a time-varying selection coefficient of $s_k$ shows that the behaviour of allele frequencies over time depends on the mean value of $m=\left\langle x_k \right\rangle= \left\langle\ln(1/(1-s_k) \right\rangle$, i.e. the geometric mean of the relative fitness; in general, the geometric mean is smaller than the arithmetic mean (i.e. variation in time would lower the fitness advantage of the more-fit allele). I believe the bottom line here (although it takes quite a bit of work to understand the whole story) is as given in the last sentence of the paper: "Selection pressures variable in space or time could act to maintain genetic variance of fitness ..."

On the other hand, Tănase-Nicola and Nemenman (2011), "Fitness in time-dependent environments includes a geometric phase contribution" (DOI: 10.1098/rsif.2011.0695) say it's still more complex:

the selection coefficient in infinitely slowly changing environments (we call this the adiabatic limit) is given by a time-average of static selection coefficients corresponding to each environment. This time-average is equivalent to the geometric mean result of Dempster [10]. It is independent of the order or the speed with which different environmental states are visited. However, for environments varying at a slow but finite rate, this time-average is not the whole story ...

All of the above is about the evolutionary dynamics of a single allele, not a comparison of the evolution multiple alleles/traits within the same genome. Things could get (much) more complicated in that case, even in the absence of explicit pleiotropy, linkage, etc. (e.g the Hill-Robertson effect). I doubt there's a simple answer; I would suggest heuristic guesses based on independent dynamics of alleles based on the single-allele phenomena described above, followed by simulation ...

• The question does not contain the term "time". Only in one comment did the OP said "in a given generation" and "In another generation" and I would suspect (s)he got lost in between several concepts in trying to clarify the question (but might be wrong). I am not sure the OP was interested about selection pressures varying through time. Nov 30, 2016 at 5:26
• fair enough, but what else would "low in some generations, high in others" mean? Nov 30, 2016 at 12:38
• I think it was a point where the OP got mixed up with two different concepts when writing his comment. But again, I might be wrong. It will be the OP's job to clarify it. (I am not saying the answer is bad, I just wanted to highlight the point that I find unclear in the post). Nov 30, 2016 at 15:56
• I also read the OP's original question to mean variability in time even if this wasn't mentioned explicitly (as opposed to variable pressure on different members of the species) - I think this is the more interesting question because variability across members of the species seems trivial. Nov 30, 2016 at 22:30
• If you don't feel your question is adequately answered, there's no pressure to accept an answer. However, if you think you can edit your question to clarify what you don't understand, or otherwise try to improve the chances that I or someone else will be able to answer in the future, that would be useful. You're also welcome to answer your own question, if and when you answer it to your own satisfaction ... Dec 5, 2016 at 2:13