minor corrections to ms, thanks matt!

manuscript/biblio.bib

@@ -1,6 +1,50 @@
 % Generated by Paperpile. Check out https://paperpile.com for more information.
 % BibTeX export options can be customized via Settings -> BibTeX.
 
+@ARTICLE{Leroy2021-gy,
+ title = "Island songbirds as windows into evolution in small populations",
+ author = "Leroy, Thibault and Rousselle, Marjolaine and Tilak, Marie-Ka and
+ Caizergues, Aude E and Scornavacca, C{\'e}line and Recuerda,
+ Mar{\'\i}a and Fuchs, J{\'e}r{\^o}me and Illera, Juan Carlos and
+ De Swardt, Dawie H and Blanco, Guillermo and Th{\'e}baud,
+ Christophe and Mil{\'a}, Borja and Nabholz, Benoit",
+ abstract = "Due to their limited ranges and inherent isolation, island
+ species have long been recognized as crucial systems for tackling
+ a range of evolutionary questions, including in the early study
+ of speciation.1,2 Such species have been less studied in the
+ understanding of the evolutionary forces driving DNA sequence
+ evolution. Island species usually have lower census population
+ sizes (N) than continental species and, supposedly, lower
+ effective population sizes (Ne). Given that both the rates of
+ change caused by genetic drift and by selection are dependent
+ upon Ne, island species are theoretically expected to exhibit (1)
+ lower genetic diversity, (2) less effective natural selection
+ against slightly deleterious mutations,3,4 and (3) a lower rate
+ of adaptive evolution.5-8 Here, we have used a large set of newly
+ sequenced and published whole-genome sequences of Passerida
+ species (14 insular and 11 continental) to test these
+ predictions. We confirm that island species exhibit lower census
+ size and Ne, supporting the hypothesis that the smaller area
+ available on islands constrains the upper bound of Ne. In the
+ insular species, we find lower nucleotide diversity in coding
+ regions, higher ratios of non-synonymous to synonymous
+ polymorphisms, and lower adaptive substitution rates. Our results
+ provide robust evidence that the lower Ne experienced by island
+ species has affected both the ability of natural selection to
+ efficiently remove weakly deleterious mutations and also the
+ adaptive potential of island species, therefore providing
+ considerable empirical support for the nearly neutral theory. We
+ discuss the implications for both evolutionary and conservation
+ biology.",
+ journal = "Curr. Biol.",
+ month = jan,
+ year = 2021,
+ keywords = "adaptive substitutions; background selection; census population
+ sizes; insularity; molecular evolution; neutral theory; purifying
+ selection;phh\_qlink2",
+ language = "en"
+}
+
 @ARTICLE{Roux2016-lm,
  title = "Shedding Light on the Grey Zone of Speciation along a Continuum
  of Genomic Divergence",
@@ -1622,6 +1666,39 @@ @MISC{noauthor_2020-ey
  keywords = "phh\_qlink2"
 }
 
+@ARTICLE{Galtier2020-fb,
+ title = "How Much Does Ne Vary Among Species?",
+ author = "Galtier, Nicolas and Rousselle, Marjolaine",
+ abstract = "Genetic drift is an important evolutionary force of strength
+ inversely proportional to N e , the effective population size.
+ The impact of drift on genome diversity and evolution is known to
+ vary among species, but quantifying this effect is a difficult
+ task. Here we assess the magnitude of variation in drift power
+ among species of animals via its effect on the mutation load -
+ which implies also inferring the distribution of fitness effects
+ of deleterious mutations (DFE). To this aim, we analyze the
+ non-synonymous (amino-acid changing) and synonymous (amino-acid
+ conservative) allele frequency spectra in a large sample of
+ metazoan species, with a focus on the primates vs. fruit flies
+ contrast. We show that a Gamma model of the DFE is not suitable
+ due to strong differences in estimated shape parameters among
+ taxa, while adding a class of lethal mutations essentially solves
+ the problem. Using the Gamma + lethal model and assuming that the
+ mean deleterious effects of non-synonymous mutations is shared
+ among species, we estimate that the power of drift varies by a
+ factor of at least 500 between large-N e and small-N e species of
+ animals, i.e., an order of magnitude more than the among-species
+ variation in genetic diversity. Our results are relevant to
+ Lewontin's paradox while further questioning the meaning of the N
+ e parameter in population genomics.",
+ journal = "Genetics",
+ month = aug,
+ year = 2020,
+ keywords = "distribution of fitness effects; genetic drift; mutation load;
+ population size; site frequency spectrum;phh\_qlink2",
+ language = "en"
+}
+
 @MANUAL{Pateiro-Lopez2019-fp,
  title = "alphahull: Generalization of the Convex Hull of a Sample of
  Points in th e Plane",

manuscript/manuscript.tex

@@ -85,9 +85,23 @@
 \maketitle
 
 
-\begin{abstract} 
+% Neutral theory predicts that genetic diversity increases with population size,
+% yet observed levels of diversity across species vary only two orders of
+% magnitude while population sizes likely vary over several. The causes of this
+% discrepancy, known as Lewontin's Paradox of Variation, remain unknown. Here I
+% revisit Lewontin's Paradox by quantifying the relationship between pairwise
+% diversity and approximate census size for 172 metazoan species. Using
+% phylogenetic comparative methods, I show this relationship is significant
+% accounting for phylogeny, but has high phylogenetic signal and some lineages
+% experience shifts in diversity deep in the past. I find a negative relationship
+% between recombination map length and census size, suggesting abundant species
+% have less recombination and could experience greater reductions in diversity
+% due to linked selection. However, I show that even using strong selection
+% parameter estimates, models of linked selection are unlikely to explain the
+% observed relationship between diversity and census sizes across species.
 
- Under neutral theory, the level of polymorphism in an equilibrium population
+\begin{abstract} 
+ Under neutral theory, genetic diversity in an equilibrium population
  is expected to increase with population size. However, observed levels of
  diversity across metazoans vary only two orders of magnitude, while census
  population sizes ($N_c$) are expected to vary over several. This unexpectedly
@@ -167,7 +181,8 @@ \subsection*{Possible Explanations of Lewontin's Paradox}
 quantification of the evolutionary processes that prevent diversity from
 scaling with census sizes across species. This would necessarily connect to the
 broader literature on the empirical relationship between diversity and
-population size \parencite{Frankham1996-yb,Nei1984-zi,Soule1976-he}, and the
+population size
+\parencite{Frankham1996-yb,Nei1984-zi,Soule1976-he,Leroy2021-gy}, and the
 ecological and life history correlates of genetic diversity
 \parencite{Nevo1978-wh,Powell1975-lg,Nevo1984-hp}. Three categories of
 processes stand out as potentially capable of decoupling census sizes from
@@ -259,11 +274,6 @@ \subsection*{Recent Approaches Towards Solving Lewontin's Paradox}
 propose a mechanism by which these traits act to constrain diversity within a
 few orders of magnitude. 
 
-% Furthermore, Coop's re-analysis finds no evidence
-% of a remaining correlation between recombination and diversity among the
-% highest recombination windows, as would be expected if these $\pi_0$ estimates
-% were still impacted by linked selection. 
-
 Here, I revisit Lewontin's Paradox by integrating a variety of data sets and
 assessing the predicted reductions in diversity under different selection
 models. Prior surveys of genetic diversity either lacked census population size
@@ -288,7 +298,7 @@ \subsection*{Recent Approaches Towards Solving Lewontin's Paradox}
 and investigating how these traits evolve along the phylogeny.
 
 Finally, I explore whether the predicted reductions of diversity under
-background selection and recurrent hitchhiking are sufficiently strong enough
+background selection and recurrent hitchhiking are sufficiently strong 
 to resolve Lewontin's Paradox. These predicted reductions in diversity across
 species are generously estimated using selection strength parameters from
 \emph{Drosophila melanogaster}, a species known to be strongly affected by
@@ -375,9 +385,9 @@ \subsection*{Quantifying Lewontin's Paradox}
 predominantly from either synonymous or non-coding DNA (see Methods:
 \Newnameref{sec:methods-diversity}). Overall, an ordinary least squares (OLS)
 relationship on a log-log scale fits the data well (Figure \ref{fig:figure-1}).
-The OLS slope estimate is significant and implies an increase in diversity of
-0.09 differences per basepair for every order of magnitude census size grows
-(95\% confidence interval $[0.08, 0.12]$; see also the OLS fit per-phyla,
+The OLS slope estimate is significant and implies a 0.09 percent increase in
+differences per basepair for every order of magnitude census size grows (95\%
+confidence interval $[0.08, 0.12]$; see also the OLS fit per-phyla,
 Supplementary Figure \ref{suppfig:figure-1-ave}). 
 
 Notably, this relationship has few outliers and is relatively homoscedastic.
@@ -464,7 +474,7 @@ \subsection*{Phylogenetic Non-Independence and the Population Size Diversity Rel
 the synthetic chronogram. As with the non-phylogenetic regression, this
 relationship was positive and significant (95\% credible interval $0.04,
 0.11$), though somewhat attenuated compared to the OLS estimates (Figure
-\ref{fig:figure-1}B). Since the population size estimates are based on range
+\ref{fig:figure-2}B). Since the population size estimates are based on range
 and body mass, they are essentially a composite trait; fitting phylogenetic
 mixed-effects models separately on body mass and range indicates these have
 significant negative and positive effects, respectively (Supplementary Figure
@@ -514,9 +524,9 @@ \subsection*{Phylogenetic Non-Independence and the Population Size Diversity Rel
 population size, node-height tests indicate a significant increase in the rate
 of evolution towards the present (robust regression p-values 0.028 and 0.00070
 respectively; Figure \ref{fig:figure-2}C). Considering the constituents of the
-population size estimate, range and body mass, separately, range but not body
-mass shows a significant increase (p-value $1.9 \times 10^{-7}$) in rate
-towards the present. 
+population size estimate, range and body mass, separately, the rate of
+evolution of range but not body mass shows a significant increase (p-value $1.9
+\times 10^{-7}$) towards the present. 
 
 Interestingly, the diversity node-height test reveals two rate shifts at deeper
 splits (Figure \ref{fig:figure-2}C, top left) around 570 Mya. These nodes
@@ -565,14 +575,14 @@ \subsection*{Assessing the Impact of Linked Selection on Diversity Across Taxa}
 functional density across the genome to fit linked selection models that
 incorporate both hitchhiking and background selection
 \parencite{Elyashiv2016-vt,Corbett-Detig2015-gt}. The second difficulty is
-understanding how $R$ varies across taxa, since we lack estimates of critical
-model parameters for most species. Still, I can address a key question: if
-diversity levels were determined by census sizes ($\pi_0 = 4N_c \mu$), are the
-combined effects of background selection and recurrent hitchhiking sufficient
-to reduce diversity to observed levels? Furthermore, does the relationship
-between census size and predicted diversity under linked selection across
-species, $\pi_{BGS+HH} = R \pi_0$, match the observed relationship in Figure
-\ref{fig:figure-1}? 
+understanding of how $R$ varies across taxa, since we lack estimates of
+critical model parameters for most species. Still, I can address a key
+question: if diversity levels were determined by census sizes ($\pi_0 = 4N_c
+\mu$), are the combined effects of background selection and recurrent
+hitchhiking sufficient to reduce diversity to observed levels? Furthermore,
+does the relationship between census size and predicted diversity under linked
+selection across species, $\pi_{BGS+HH} = R \pi_0$, match the observed
+relationship in Figure \ref{fig:figure-1}? 
 
 Since we lack estimates of key linked selection parameters across species, I
 generously parameterize the hitchhiking and BGS models using estimates from
@@ -602,11 +612,11 @@ \subsection*{Assessing the Impact of Linked Selection on Diversity Across Taxa}
 they occur across the genome (c.f. $J_{2,2}$ in equation 15 of
 \cite{Coop2012-cd}). 
 
-Parameterizing the model this way, I then set the key parameters that
-determine the impact of recurrent hitchhiking and background selection
-($\gamma$, $J$, and $U$) to high values estimated from \emph{Drosophila
-melanogaster} by \textcite{Elyashiv2016-vt}. My estimate of
-$\gamma_\text{Dmel}$ based Elyashiv et al. implies $\nu_\text{BP,Dmel} \approx
+Parameterizing the model this way, I then set the key parameters that determine
+the impact of recurrent hitchhiking and background selection ($\gamma$, $J$,
+and $U$) to high values estimated from \emph{Drosophila melanogaster} by
+\textcite{Elyashiv2016-vt}. My estimate of $\gamma_\text{Dmel}$ based Elyashiv
+et al. implies a rate of sweeps per basepair of $\nu_\text{BP,Dmel} \approx
 2.34 \times 10^{-11}$, which is close to other estimates from \emph{D.
 melanogaster} (see Supplementary Figure \ref{suppfig:linked-sel-params}A). The
 rate of deleterious mutations per diploid genome, per generation is
@@ -913,13 +923,13 @@ \subsection*{Measures of Effective Population Size, Timescales, and Lewontin's P
 implied by diversity, $\widetilde{N}_e$, diverge from census population sizes.
 However, there are a variety other effective population size estimates
 calculable from different data and summary statistics
-\parencite{Wang2016-mi,Caballero1994-ao,Caballero2020-wm}. These include
-estimators based on the observed decay in linkage disequilibrium or temporal
-estimators that use the variance in allele frequency change. These alternate
-estimators capture summaries of the effective population size on shorter
-timescales than coalescent-based estimators \parencite{Wang2005-wy}, and thus
-could be used to tease out processes that impact the $N_e$-$N_c$ relationship
-in the more recent past. 
+\parencite{Wang2016-mi,Caballero1994-ao,Caballero2020-wm,Galtier2020-fb}. These
+include estimators based on the observed decay in linkage disequilibrium or
+temporal estimators that use the variance in allele frequency change. These
+alternate estimators capture summaries of the effective population size on
+shorter timescales than coalescent-based estimators \parencite{Wang2005-wy},
+and thus could be used to tease out processes that impact the $N_e$-$N_c$
+relationship in the more recent past. 
 
 Temporal $N_e$ estimators already play an important role in understanding
 another summary of the $N_e$-$N_c$ relationship: the ratio
@@ -1163,9 +1173,9 @@ \section*{Acknowledgments}
 supporting me during this work, and Graham Coop for inspiration and helpful
 feedback during socially distanced nature walks at Yolo Basin. I thank Jessica
 Stapley for kindly providing the recombination map length data, and Yaniv
-Brandvain, Amy Collins, Doc Edge, Tyler Kent, Chuck Langley, Sally Otto, Jeff
-Ross-Ibarra, Aaron Stern, Anastasia Teterina, Michael Turelli, and my
-Kern-Ralph labmates for helpful discussions. Sarah Friedman, Katherine Corn,
+Brandvain, Amy Collins, Doc Edge, Tyler Kent, Chuck Langley, Matt Osmond, Sally
+Otto, Jeff Ross-Ibarra, Aaron Stern, Anastasia Teterina, Michael Turelli, and
+my Kern-Ralph labmates for helpful discussions. Sarah Friedman, Katherine Corn,
 and Josef Uyeda provided very useful advice about phylogenetic comparative
 methods; yet I take full responsibility for any shortcomings of my analysis. I
 would like to also thank UO librarian Dean Walton for helping me track down