Lewontin The Meaning Of Stability Pdf Download
Kenneth Calimlim
I apologize for the delay in passing a decision due to one of the reviewers being sick and, unfortunately, eventually unable to send in the review. At the latest news the reviewer had to stay a short while at the hospital but is now feeling better. Fortunately, the other reviewer did a very thorough job and I will be happy to recommend the preprint after you have taken into account the minor changes that the reviewer suggested.
I am grateful to the authors for taking my previous comments seriously. I think that the manuscript is much improved and remains interesting. Nevertheless, looking at the new Figure S7, I still have concerns about the legitimacy of estimating Ne from S_bar. If the authors agree, I think that the concerns should be emphasized more strongly. I also think that the authors could do more to show that the results could in principle be real. They need to show e.g. that a past bottleneck could lead to very large differences in the Ne values that apply to different statistics. Neither of these suggestions would require large changes.
Currently, it is suggested that the reader can skip sections 1-3 of the discussion, but, unless the authors think my comments above are mistaken, I think that sections 4-5 need to clearly acknowledge the possibility that S_bar does not provide a meaningful estimate of Ne.
The simulations.
The simulations should prove to the reader that non-equilibrium demography could lead to very large differences in the range Ne values as estimated from piS and Sbar. Currently, this is not very explicit from Figure 4. Also, I could not find a description of the bottleneck depth at generation 15,000.
In my previous comment 2.3, I asked whether the authors might attempt to estimate s_bar (i.e the mean selection coefficient unscaled by Ne). I think that previous authors have done this, and it relates to the interesting discussion in lines 631-635.
Three reviewers have now read your manuscript "How much does Ne vary among species?". All three reviewers find the manuscript very interesting but all three think that the manuscript could be improved by clarifying its main aim. In particular, they would like you to (i) clarify what is being measured by the two estimates of Ne, (ii) improve the comparison of the different DFE models, (ii) extend the simulations. Once this is done it should be easier to present the different aims of the paper (compare different estimates of Ne, testing Lewontin paradox, assess the stability of the DFE across species) in a clearer way or refocus the manuscript.
The effective size of a population is the census size of a Wright-Fisher population that would give the same value of some statistic, related to drift. When the Wright-Fisher assumptions are violated, different statistics can imply different values of Ne. Differences between different methods of estimating Ne (e.g. from mean time to pairwise coalescence, vs. total genealogy length) are interesting, because they tell us about violations of the Wright-Fisher assumptions, and because the different Ne values might affect different things (e.g. total neutral diversity vs. current efficacy of purifying selection).
This preprint compares the extent of differences in Ne, estimated in two ways. First, it uses piS, the mean pairwise differences at synonymous sites, where E(piS)=4Nemu. Second, it estimates S=4Nes using the non-synonymous and synonymous SFS. Estimates are obtained for a wide variety of animal species, but focussing on primates vs. Drosophila. Results show that S/min(S) is 1-2 orders of magnitude more variable than piS/min(piS). This is a surprising result, especially if the DFE is identical between species.
The authors relate their finding to Lewontin's paradox: the finding that genetic diversity between species varies much less than would be expected under an equilibrium neutral model, assuming that effective population sizes are proportional to current census sizes. The authors implicate non-equilibrium demography, because piS is strongly influenced by past periods of low population size, while piN/pi_S equilibrates more rapidly, and so should be less influenced by past demography. This point is illustrated with simulations.
This preprint compares two different types of Ne, but I think the authors could be much clearer about what they measure.
In the equation E(pi_S)=4Nemu, 2Ne describes the average time to coalescence of two randomly chosen sequences.
The method of Galtier (2016) estimates Ne in two different ways, via the compound parameters theta=4Nemu and S=4Ne*s. Only the second measure is reported, and I could not tell when/whether the two Ne values are expected to differ from each other, and whether the second measure (which is the only one reported) is a valid measure of Ne.
From eqs. 6 and 10 of Galtier 2016 with r1=1, it looks like 4Ne estimated from theta/mu measures the mean length of the terminal branches on the genealogy. With non-equilibrium demography, this could differ from the mean time to pairwise coalescence. The lengths of the internal branches are fit via the nuisance parameters (ri).
I found the other Ne (estimated from S/4s) much more difficult to interpret. S is estimated from the complete SFS of non-synonymous mutations. But it does not use existing results for the SFS with selection and non-equilibrium demography or linkage effects (e.g. Evans et al 2007 TPB; Good et al 2014 PLoS Genet). Instead, it uses the standard equilibrium formula for the population allele frequency (eq. 4 of Galtier 2016), while also allowing for non-equilibrium effects on the shape of the underlying genealogy, by allowing for arbitrary variation in the r_i.
For this reason, I struggled to understand what these Ne estimates meant, and whether all of the possible variation in the non-synonymous SFS could be modelled via variation in Ne, even assuming that the gamma+method DFE is accurate.
Estimates of S are highly model-dependent, and the authors present some suggestive evidence that the standard gamma model underfits the SFS data. They use a gamma+lethal model and show that the extra parameter has a substantial influence on the estimates.
This is an interesting result, but I think that the authors might be too quick to assume that the gamma+lethal model solves the problem of model adequacy, and to conclude that there is little difference in the DFE across their data sets.
Previous authors have examined the adequacy of the gamma model, with different sorts of data, including Nielsen & Yang (2003, MBE) and Loewe and Charlesworth (2006, Biol Lett). Nielsen and Yang also used a gamma+lethal model (and a normal + lethal model), while Loewe and Charlesworth argued for a lognormal model. Other authors have combined a gamma distribution with a class of purely neutral mutations (Loewe et al 2006, Genetics; Betancourt et al. 2012 Evolution). It would be useful to know if results are robust to using other distributions like this. While Table 2 contains many good robustness analyses, I think more formal work on model adequacy could be presented to make the headline results really convincing.
Second, the authors argue that their estimated likelihood surface "suggests that the DFE perhaps does not differ so dramatically between primates and fruit flies", but doesn't this flat likelihood surface suggest instead that the parameters are non-identifiable with data of this kind?
Third, as the authors say, the results for Ne depend heavily on the very strong assumption that s_bar has the same value for one set of genes in Drosophila and a different set of genes in primates. Chen et al. 2017 and Loewe et al. 2006 present methods for estimating the strength of selection directly. Could these be used to test this strong assumption?
Figure 4 presents simulation runs, aiming to show that piN/piS is less affected by demographic events than pi_S. This is an important part of the paper, but I was not sure how well the simulations related to the results reported.
First, the S estimates used the full SFS for non-synonymous and synonymous polymorphisms, while the simulations report piN/piS. These quantities might equilibrate differently (as is evident from Tajima's D).
Second, if I have understood correctly, the "recovery phase" shows a gain in genetic diversity starting from a large but genetically uniform population. Is this realistic? Why did the authors not explicitly simulate the recovery from a bottleneck?
Third, to place their results in context, the authors cite Brandvain and Wright 2016 regarding the different equilibration times of piN and piS. But I think the explanation of the simulation results might be that ratios of pairwise diversity equilibrate more rapidly than raw diversity measurements. This is seen in neutral Fst, for example (Pannell and Charlesworth 2002).
Finally, if the authors suspect that non-equilibrium effects explain some of their results, why do they not test for these effects directly in their data (e.g. by reporting the r_i from Galtier 2016, or Tajima's D for synonymous sites etc.)?
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Here, then, is my question: Are you and I machines? Are we analyzable without remainder into a collection of mechanisms whose operation can be fully explained by the causal operation of physical and chemical laws, starting from the parts and proceeding to the whole? It might seem so, judging from the insistent testimony of those whose work is to understand life.
Think first of a living dog, then of a decomposing corpse. At the moment of death, all the living processes normally studied by the biologist rapidly disintegrate. The corpse remains subject to the same laws of physics and chemistry as the live dog, but now, with the cessation of life, we see those laws strictly in their own terms, without anything the life scientist is distinctively concerned about. The dramatic change in his descriptive language as he moves between the living and the dead tells us just about everything we need to know.
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