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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?

sterid
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  • Fitness is unidimensional (for an individual, it is a single point, not a matrix). Phenotype and environment are typically highly multidimensional. – Remi.b Nov 29 '16 at 17:43
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    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. – Remi.b Nov 29 '16 at 17:46
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    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? – sterid Nov 29 '16 at 17:54
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    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. – Remi.b Nov 29 '16 at 17:59
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    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). – Remi.b Nov 29 '16 at 18:01
  • This isn't my area of expertise, so excuse my ignorance if necessary, but I feel like your question might be more straightforward if you remove the "dimension of fitness" terminology unless this terminology is standard in the field. Perhaps your question is "How does variability of selection pressures between generations influence the evolution of relevant traits?" I am assuming you are looking for a semi-quantitative comparison of the rates of change in genotypes when selection pressures are variable vs. static across generations. – Bryan Krause Nov 29 '16 at 18:04
  • And it looks like Remi.b beat me to it - I would reiterate that a case study or explanation like in your comment would improve the question and help solicit quality answers. – Bryan Krause Nov 29 '16 at 18:06
  • Thank you, Remi. Yes Bryan, but not just the selection pressure upon a whole genotype, the selection pressure upon individual traits. – sterid Nov 29 '16 at 18:06
  • I think a case study will be rather elaborate. I'll work on it. Thank you. – sterid Nov 29 '16 at 18:08
  • When I said genotypes what I really meant was allele frequencies that lead to particular distributions of genotypes in the population, sorry for the imprecise terminology - I think this fits what you are asking. – Bryan Krause Nov 29 '16 at 19:27

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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 ...

Ben Bolker
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  • 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. – Remi.b Nov 30 '16 at 05:26
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    fair enough, but what else would "low in some generations, high in others" mean? – Ben Bolker Nov 30 '16 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). – Remi.b Nov 30 '16 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. – Bryan Krause Nov 30 '16 at 22:30
  • Ben Bolker, I thank you very much for that answer. Remi, this is the kind of analysis I was looking for. Makes me wonder what you thought I was looking for. Yes, I'm looking for selection pressures upon a trait varying from generation to generation (though not necessarily varying within a generation). I've tried reading Dempster's article, but I'm stuck because I don't see how this answer was obtained: "The change in p in one generation of selection is spq/(1--sq) in the haploid case and spq/(1--2sq) in the diploid." – sterid Dec 01 '16 at 09:18
  • I haven't looked at it carefully, but this is presumably what you get if you go through the algebraic steps of computing the expected number of each genotype (p^2, q^2, and 2pq in the diploid case or p and q in the haploid case), the relative number of offspring for each genotype, and then scaling by the total number of offspring - i.e. this should be found in any standard population genetics book ... – Ben Bolker Dec 01 '16 at 13:00
  • if this answers your question, you can click on the check-mark to accept it ... – Ben Bolker Dec 01 '16 at 13:01
  • Ben, I sincerely apologize. I did not get notification about your comments. It actually appears that the formula given (spq/(1-sq)) is the same as the one Remi referenced in this post (http://biology.stackexchange.com/questions/15984/how-do-i-calculate-the-change-in-allele-frequency-in-a-haploid-population-under?rq=1). The derivation is there too. Now I understand it. I appreciate your helpful answer, but I don't feel it answers my question completely (maybe I have to better understand Kimura 1954). If I click the check mark, does it discourage future replies? Do you still get credit? – sterid Dec 04 '16 at 19:09
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    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 ... – Ben Bolker Dec 05 '16 at 02:13