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  1. Reviewer #4 (Public Review):

    In this paper, the author uses an impressive comparative dataset of 172 species to investigate the relationship between intraspecific genetic diversity and census (actual) population size. They find that even when they use phylogenetic comparative methods, the relationship between neutral diversity and population size is much weaker than predicted by theory and that selection on linked sites is unlikely to explain this difference. The paper convincingly demonstrates that the paradox of variation first pointed out by Lewinton in the 70s remains paradoxical.

    This paper is exceptionally strong in multiple ways. First, it is statistically rigorous; this is particularly impressive given that the paper uses methods and data from multiple fields (genomics, macroecology, conservation biology, macroevolution). This is the most robust estimate of the relationship between diversity and population size that has been published to date. Second, it is conceptually rigorous: the paper clearly lays out the various hypotheses that have been put forth over the years for this pattern as well as the logic behind these. The author has done a great job at synthesizing some complex debates and different types of data that are potentially relevant to resolving it. Third, it is exceptionally well-written. I sincerely enjoyed reading it. Overall, I think this is a major contribution to this field and though the paper does not resolve the challenge laid down by Lewinton, I think these analyses (and curated data/computational scripts) will inspire other researchers to dig into this question.

    I do however, have some suggestions as to how this paper could be strengthened.

    First, in phylogenetic comparative methods (PCMs) there has been a persistent confusion as to what phylogenetic signal is relevant -- when applying a phylogenetic generalized linear model with a phylogenetically structured residual structure (which the author does here), one is estimating the phylogenetic structure in the errors and not the traits themselves. The comparative analysis are well-done and properly interpreted but at some points in the text, particularly when addressing Lynch's conjecture that PCMs are irrelevant for coalescent times and comments/analysis on the appropriateness of Brownian motion as a model of evolution, that there is some conceptual slippage and I suggest that author take a close look and make sure their language is consistent. Strictly speaking the PGLM approach doesn't assume that the underlying traits are purely BM -- only that the phylogenetic component of the error model is Brownian. As such running the node-height test on the both the predictors and the response variable separately -- while interesting and informative about the phylogenetic patterns in the data (including the shift points you have observed) isn't really a test of the assumptions of the phylogenetic regression model. It is at least theoretically plausible (if not biologically) that both Y and X have phylogenetic structure but that the estimated lambda = 0 (if for instance, Y and X were perfectly correlated because changes in Y were only the result of changes in X). To be clear, I am fine with the PGLM analysis you've done and with the node-height test; I just don't think that the latter justifies the former.

    One note about the ancestral character reconstruction: I think it is a fine visualization and realize you didn't put too much emphasis on it but strictly speaking the ASR's were done under a constant process model and therefore they wouldn't provide evidence for (a probably very real shift) between phyla. I think it was a good idea to run the analyses on the clade specific trees (particularly given how deep and uncertain the branches dividing the phyla are) but I just don't think you could have gotten there from the ASR.

    I am not convinced that the IUCN RedList analysis helps that much here and in my view, you might consider dropping this from the main text. This is for two reasons: 1) species may be of conservation concern both because they have low abundance in general and/or that their abundance is known to have experienced a recent decline -- distinguishing these two scenarios is impossible to do with the data at hand; and 2) there is of course a huge taxonomic bias in which species are considered; I don't think we can infer anything ecologically relevant from whether a species is listed on the RedList or not (as you suggest regarding the lynx, wolverine, and Massasauga rattlesnake) except that people care about it.

    This is not really a weakness but I find it notable that recombination map length is correlated with body size. I realize this is old news but I was left really curious as to a) why such a relationship exists; and b) whether the mechanism that generates this might help explain some of the patterns you've observed. I would be keen to read a bit more discussion on this point.

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  2. Reviewer #3 (Public Review):

    This study is quite directly a follow-up study of the recent work of Corbett-Detig et al (2015) and the commentary by Coop (2016) which aimed to understand the relation between population size and diversity, and the degree to which the shape of the relation could be explained by the action of linked selection. The analysis here scales up the sample size for a large-scale focus on comparative analyses of animals, and introduces the application of phylogenetic correction to control for relatedness.

    As the most comprehensive analysis of its type to date, and with the addition of phylogenetic correction, this work's strength primarily lies in confirming the conclusions laid out in the commentary by Coop, notably that linked selection is unable to fully explain the narrowness of the diversity across species with orders of magnitude variation in population sizes. Through an explicit model-fitting of the effects of linked selection, the main conclusions are essentially that Lewontin's Paradox remains unexplained. The Introduction and discussion provide a very nice accounting of the range of possible explanations. I also appreciated the connection of the population size inferences to IUCN status.

    I wasn't so convinced that the assessment of phylogenetic inertia (Lambda>0) really provides a way to assess Lynch's argument that coalescent times are too short to have a phylogenetic effect. For reasons outlined by the author in the discussion, it could well be that any phylogenetic inertia signal is due to inertia of life history traits correlated with effective population size rather than with diversity itself. The discussion raises this important point, but I think leaves us with the difficulty of really assessing how important that phylogenetic correction really is: if diversity has no direct phylogenetic non-independence, I am a bit unsure how much we have learned through this analysis alone (i.e. what is lambda telling us), without an explicit assessment of how often divergence times may actually truly be on the same order as coalescent times.

    That said, I think it's a very open question whether diversity actually has phylogenetic independence because of short split times relative to effective population sizes. The author mentions the possible effect of large Ne on causing this to be violated; but I also wondered whether many of the small Nc species are still retaining a fair bit of ancestral polymorphism, further homogenizing diversity levels.

    Overall a number of possible explanations (such as the effect of variable selected site densities, and variable recombination) were raised, and rather quickly rejected as 'unlikely to explain the qualitative patterns'. In a number of cases these statements were fairly brief, and I wondered whether in aggregate how likely a combination of these COULD explain the patterns. Looking at Figure 5B, it seems like the major effect of phylogeny (or correlated life history) is also apparent for the discrepancy between observed and predicted diversity- Chordates seem to have the largest discrepancy. With that in mind, I do wonder whether some feature of genome structure in Cordates, including a combination of the effects discussed in the paper that could account for the discrepancy (e.g. the effects of variable recombination rates/genome size and functional densities, variation in mutation rates, etc.) could collectively account for the paradox, even though individually the author rules them out as being able to explain the 'qualitative pattern'. Could the genome structure of chordates lead to a major difference in linked selection that's unaccounted for here?

    Mei et al (2018) (American Journal of Botany, Volume 105, Issue 1, p1-124) argued that species with larger genomes have greater 'functional space', implying a greater deleterious mutation rate in species with larger genomes. This could potentially be a factor driving those Chordates with intermediate Nc values furthest below the predicted line?

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  3. Reviewer #2 (Public Review):

    This manuscript presents a thorough reanalysis of estimates of genetic heterozygosity pi, its distribution among animals, and its relationship with the census population size, here estimated from organism body mass and species range. A significant phylogenetic effect on pi is uncovered, and a formal model of linked selection is shown to be insufficient to explain the so-called Lewontin's paradox.

    My first and maybe most important comment is that the introduction, discussion and overall writing of the manuscript are really excellent. This might be the most lucid, extensive, balanced overview of Lewontin's paradox and the associated literature I've ever read.

    My second comment, somehow counterbalancing the first one, is that the major point made here, that linked selection alone cannot explain Lewontin's paradox, has been made before, e.g. by Coop (2016) and Ellegren & Galtier (2016) commenting on Corbett-Detig et al (2015). The material presented here substantiates this point further, but is perhaps not a major advance per se, so that the manuscript lies somewhere between a review and research article.

    I have a few additional, more specific comments below. I think this is a great addition to the existing literature, which clarifies and synthetizes many aspects of a complex question.

    1. Phylogenetic inertia

      I am not sure I get the point of the phylogenetic inertia analysis. It seems to be intended as a response to Lynch 2011, who, responding to a criticism by Whitney & Garland, stated that the coalescence time is not inherited across the phylogeny. That quote from Lynch is mentioned several times, and as a motivation for performing this analysis. Yet the result reported here, i.e., that pi has some phylogenetic inertia, does not seem to contradict this specific statement, for at least two reasons. First pi might have some inertia via inertia on the mutation rate, not on coalescence time. Secondly, pi might have some inertia because it is in part determined by traits that have some inertia, such has body mass for instance. The text insightfully discusses these aspects (l399-407), but honestly I do think that this analysis invalidates Lynch's (somewhat trivial) point that coalescence time is not a trait that can be inherited.

      I still agree that the analysis is worth doing and publishing, but I would suggest putting less emphasis on the Garland/Lynch controversy. Also it might be fair to mention that Leffler et al (2012) and Romiguier et al. (2014) did attempt to correct for phylogenetic inertia when correlating pi to various traits, although they did not analyse the phylogenetic effect as thoroughly as it is done here.

    1. Range effect

      I was surprised to read that species range alone has a significant effect on pi. The reason is that I suspected species range varied at a shorter time scale than coalescence time - e.g. think of what ranges were 20,000 years ago, when pi was probably, I thought, very similar to current pi; maybe worth discussing?

    1. IUCN categories

      I found the result that endangered species have a lower estimated Nc and a lower pi than non-endangered species a bit trivial, knowing that lare body sized vertebrates are typically more threatened, and more of concern, than small body sized invertebrates. What would be more relevant to conservation biology is an analysis that controls for body size, e.g., are endangered large mammals less polymorphic than non-endangered large mammals. There is a fairly large amount of literature on this topic.

    1. The Methods section (l580-581) states that map length data are available in 41 species, but figure 5A shows a relationship with 131 data points; some clarification needed here
    1. abstract line 10: "vary two orders of magnitude", word missing
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  4. Reviewer #1 (Public Review):

    The standard neutral model, which is our null model for levels of genetic variation, predicts that they should be proportional to census population sizes. In reality census population sizes across metazoan species span several orders of magnitude more than the ~3 orders spanned by levels of genetic diversity. This discrepancy is referred to as Lewontin's paradox, and to resolve it would mean to explain how basic population genetic processes lead to the modest span of genetic diversity levels that we observe. This is a central question in population genetics (which is, after all, concerned with understanding patterns of genetic variation) and is of substantial general interest.

    The manuscript addresses Lewontin's paradox through three main analyses:

    1. It derives novel estimates of census population size across metazoans, which alongside previous estimates of neutral diversity levels, enables a revised quantification of the relationship between diversity levels (\pi) and census populations sizes (Nc).

    2. It quantifies the relationship between \pi and Nc controlling for phylogenetic relatedness.

    3. It revisits the question of whether this relationship can be accounted for by the effects of selection at linked loci (e.g., sweeps and background selection). I address each of these analyses in turn.

    Novel estimation of census population sizes in metazoans: The estimates are derived by: 1) estimating the density of individuals within their range, based on body size and a previously observed linear relationship between body size and density (Damuth 1981, 1987); 2) applying a geometric algorithm (finding the minimum alpha-shape computationally, sometimes adjusting alpha manually) to geographic occurrence data to estimate the area of the range; and 3) multiplying the two.

    The results are sometimes surprising. For example, Drosophila melanogaster is estimated to have a population size > 10^17 (Fig. 1); if the volume of an individual is 1 mm3, this implies a total volume > 1km x 1km x 100 m. Additionally, some species classified as endangered have census estimates > 10^8 (Fig. 3). The author compares his area estimates with estimates for species in the IUCN Red List (focused on endangered species) to find that they largely correlate (although this is not quantified). I think further investigation of the quality of the census size estimates is warranted. Are there are other estimates of census size or biomass that can be used for validation, e.g., for species of economic and biomedical importance (e.g., herring and anopheles)?

    If the proposed method proves to work well, I imagine that the estimates of census size may be of broad interest in other contexts. In the context of Lewontin's paradox, it may be interesting to quantify the difference in the relationship between \pi and Nc suggested by the new estimates vs the proxies used in previous work (e.g., Leffler et al. 2012).

    Quantifying the relationship between \pi and Nc controlling for phylogenetic relatedness: I am unclear about the motivation for this analysis. As Lynch argued (and the author describes), if TMRCAs of neutral loci within a species are smaller than the split time from another species in the sample, its genetic diversity level was shaped after the split, and it could be considered an independent sample for the relationship between \pi and Nc. There may be underlying factors shaping this relationship that are not phylogenetically independent (e.g., similar life history traits) but it is unclear why that would justify down-weighting a sample. In that sense, I am not convinced by the authors argument that finding a 'phylogenetic signal' justifies the correction. Stated differently, it is not obvious what is the 'true' relationship being estimated and why relatedness biases it. One could imagine that the 'true' relationship is the one across extant species, in which case the correction is not needed (with the possible exception of species in which TMRCAs are on the same order or greater than split times). I don't know what an alternative 'true' relationship would be.

    Moreover, I am not sure how a more precise 'quantification' of the relationship between diversity and census size serves us. Regardless of corrections, it is obvious that the null provided by the standard neutral model is off by orders of magnitude. Perhaps once we have alternative explanations for this relationship then testing them may require corrections, but presumably the corrections will depend on the explanations.

    One context in which phylogenetic considerations and quantification may be relevant is the comparison of the \pi - Nc relationship among clades. Notably, one could imagine that different population genetic processes are important in different clades (e.g., due to reproductive strategy) and a comparative analysis may highlight such differences. It is less clear whether the corrections that are applied here are the relevant ones. Separating clades makes sense in this regard, but it is unclear why to correct for non-independence within a clade. Furthermore, it seems that in order to point to different processes one would like to control for the distribution of census population sizes in comparisons between clades (to the extent possible). Otherwise, one can imagine the same process shaping the relationship in different clades, but having a non-linear (in log-log scale) functional dependence on census population size (as in the case of genetic draft studied next). In this regard, I am not sure I follow the argument attributed to Gillespie (1991) and specifically how the current analysis supports it.

    In summary, I find the ideas of clade level analyses and of using phylogenetic comparative methods (PCMs) to look at census population size (and possibly diversity levels) promising. For example, as the author alludes to in the Discussion (bottom of P. 13), PCMs may be informative about the hypothesis that species with large census sizes have a greater rate of speciation. Yet I find the current analyses difficult to interpret.

    Analysis of the effects of linked selection: The author investigates whether the effect of selection at linked sites (e.g., selective sweeps and background selection) can account for the observed relationship between diversity levels and census population size. To this end, he assumes that different species have the same sweeps and background selection parameters inferred in Drosophila melanogaster, but differ in census size and genetic map length.

    As justification for using selection parameters inferred in D. melanogaster, the author argues that this is a "generous" assumption in that the effects of linked selection in this species are on the high end. One issue with this argument is that among reasons for the strong effects in D. melanogaster is its short genetic map length. This is not a substantial caveat, given that the analysis is meant as an illustration and it can be resolved by using appropriate wording. Perhaps more troubling is that the author's estimate of the reduction in diversity level in D. melanogaster is much greater than the reduction estimated in the inference that he relies on (several orders of magnitude and less than one, respectively). This discrepancy is mentioned but should probably be addressed more substantially.

    The results of the analysis are intriguing. The effects of linked selection `shrink' the ~13 orders of magnitude of census population sizes to ~3 orders of magnitude of diversity levels. This massive effect is largely due to the genetic draft (Gillespie 2001) and to a lesser extent to the decrease in map length with increasing census size: when the census population size becomes very large (Nc~10^9) and coalescence rates due to genetic drift decrease accordingly (~1/2Nc), coalescence rates due to sweeps, which increase owing to the smaller map lengths (and would otherwise remain constant), become dominant. In hindsight this is quite intuitive and aligns with Gillespie's original argument, but this is in hindsight, and using this argument in conjunction with data, specifically with census population size and map length estimates, is novel.

    As the author points out, the resulting relationship between diversity levels and census population sizes does not fit the data well. Notably, predicted diversity levels are too high in the intermediate range of census population sizes. Nonetheless, their analysis suggests that linked selection may play a much greater role than previous studies suggested (i.e., the analyses of Corbett-Detig et al. (2015) and Coop (2016) suggests that it cannot account for more than 1 order of magnitude). Maybe the poor fit is due to the importance of other factors (e.g., bottlenecks) in species with intermediate census population sizes?

    I also wonder whether the potential role of linked selection may be clearer if the different effects are shown separately, and perhaps with less reliance on the estimates from D. melanogaster. Namely, the effects of background selection can be shown for a few different values of Udel, e.g., between 0.3-3 (this range seems plausible based on many estimates). They can be shown both accounting and not accounting for the relationship between map length and census size. Similarly, the effect of sweeps can be shown for several values of corresponding parameters, and perhaps even for different models for how the number of beneficial substitutions varies with census size (see Gillespie's work to that effect). I believe that such illustrations will be fairly intuitive and less restrictive.

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  5. Evaluation Summary:

    The manuscript revisits an enduring and central question in population genetics known as Lewontin's paradox: that in contrast to the prediction of the field's null model, which suggests that levels of neutral genetic diversity should be proportional to the census population size, in reality, census population sizes span several orders of magnitude more than the approximately three orders of magnitude spanned by levels of genetic diversity. The manuscript provides a nice review of previous work as well as thought-provoking novel analyses. There are also several issues that make it difficult to interpret the new results.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 and Reviewer #4 agreed to share their names with the authors.)

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