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.