## Summary

Throughout the human genome, there are large-scale fluctuations in genetic variety attributable to the oblique results of choice. This “linked choice sign” displays the influence of choice in response to the bodily placement of purposeful areas and recombination charges alongside chromosomes. Earlier work has proven that purifying choice performing in opposition to the regular inflow of latest deleterious mutations at purposeful parts of the genome shapes patterns of genomic variation. To this point, statistical efforts to estimate purifying choice parameters from linked choice fashions have relied on basic Background Choice principle, which is barely relevant when new mutations are so deleterious that they can’t repair within the inhabitants. Right here, we develop a statistical technique primarily based on a quantitative genetics view of linked choice, that fashions how polygenic additive health variance distributed alongside the genome will increase the speed of stochastic allele frequency change. By collectively predicting the equilibrium health variance and substitution price as a result of each sturdy and weakly deleterious mutations, we estimate the distribution of health results (DFE) and mutation price throughout three geographically distinct human samples. Whereas our mannequin can accommodate weaker choice, we discover proof of sturdy choice working equally throughout all human samples. Though our quantitative genetic mannequin of linked choice suits higher than earlier fashions, substitution charges of probably the most constrained websites disagree with noticed divergence ranges. We discover {that a} mannequin incorporating selective interference higher predicts noticed divergence in conserved areas, however total our outcomes recommend uncertainty stays concerning the processes producing health variation in people.

## Writer abstract

Throughout the human genome, there are large-scale fluctuations in genetic variety attributable to the oblique results of choice. This “linked choice sign” displays the influence of choice in response to the bodily placement of purposeful areas and recombination charges alongside chromosomes. Earlier work has proven that purifying choice performing in opposition to the regular inflow of latest deleterious mutations at purposeful parts of the genome shapes patterns of genomic variation. To this point, statistical efforts to estimate purifying choice parameters from linked choice fashions have relied on basic Background Choice principle, which is barely relevant when new mutations are so deleterious that they can’t repair within the inhabitants. Right here, we develop a statistical technique primarily based on a quantitative genetics view of linked choice, that fashions how polygenic additive health variance distributed alongside the genome will increase the speed of stochastic allele frequency change. By collectively predicting the equilibrium health variance and substitution price as a result of each sturdy and weakly deleterious mutations, we estimate the distribution of health results (DFE) and mutation price throughout three geographically distinct human samples. Whereas our mannequin can accommodate weaker choice, we discover proof of sturdy choice working equally throughout all human samples. Though our quantitative genetic mannequin of linked choice suits higher than earlier fashions, substitution charges of probably the most constrained websites disagree with noticed divergence ranges. We discover {that a} mannequin incorporating selective interference higher predicts noticed divergence in conserved areas, however total our outcomes recommend uncertainty stays concerning the processes producing health variation in people.

**Quotation: **Buffalo V, Kern AD (2024) A quantitative genetic mannequin of background choice in people. PLoS Genet 20(3):

e1011144.

https://doi.org/10.1371/journal.pgen.1011144

**Editor: **Bret Payseur,

College of Wisconsin–Madison, UNITED STATES

**Acquired: **September 17, 2023; **Accepted: **January 19, 2024; **Printed: ** March 20, 2024

**Copyright: ** © 2024 Buffalo, Kern. That is an open entry article distributed beneath the phrases of the Creative Commons Attribution License, which allows unrestricted use, distribution, and replica in any medium, offered the unique writer and supply are credited.

**Information Availability: **All code from bgspy and our Jupyter Lab (Kluyver et al. n.d.) notebooks for evaluation can be found on GitHub (https://github.com/vsbuffalo/bprime). The principle mannequin suits can be found as Python Pickle objects on Information Dryad repository (https://doi.org/10.5061/dryad.qnk98sfnv).

**Funding: **This analysis was supported by Nationwide Institute of Well being awards R35GM148253 and R01HG010774 to ADK. The funders had no position in examine design, information assortment and evaluation, resolution to publish, or preparation of the manuscript.

**Competing pursuits: ** The authors have declared that no competing pursuits exist.

## Introduction

The continuous inflow of latest mutations into populations is the last word supply of all variations, however the overwhelming majority of mutations both don’t have an effect on health or are deleterious. Pure choice works to remove these deleterious mutations from the inhabitants, thus we anticipate them to look at low frequencies inside populations [1], and be much less more likely to repair between lineages. Conserved genomic areas replicate the product of a whole lot of hundreds of thousands of years of evolutionary optimization; thus the overwhelming majority of segregating variation in these areas can have deleterious health results. Consequently, a very good predictor of whether or not a brand new mutation will scale back health is that if it happens in a area of the genome that has been conserved over phylogenetic timescales [2, 3]. Furthermore, segregating uncommon variation in these areas is answerable for a major proportion of the genetic contribution to phenotypic variation and illness in people [4–7].

Choice on each helpful and deleterious variants perturbs the allele frequencies of neighboring linked websites, a phenomenon generally known as linked choice [8–12]. Since deleterious variation is clustered in purposeful parts of the genome, we anticipate linked choice to cut back ranges of variety round evolutionarily constrained segments (e.g. coding sequences, splice websites, regulatory components, and so forth.). The genomic association of those conserved areas coupled with heterogeneous recombination charges create a large-scale spatial sign of linked collection of genetic variety alongside chromosomes. Since genome-wide recombination maps and purposeful annotations can be found for a lot of species, there was constant effort to suit fashions of linked choice to patterns of variety. This basic method offers estimates of inhabitants genetic parameters such because the energy of choice and the deleterious mutation price [13, 14], and doubtlessly distinguishes the roles of constructive and damaging choice and estimate the speed of helpful mutations [15, 16]. In people, earlier work has proven that damaging choice performs the dominant position in shaping megabase-scale patterns of variety, with constructive choice having an almost negligible influence [16].

Prior work to mannequin the discount in linked variety as a result of deleterious mutations has largely relied on the basic Background Choice (BGS) mannequin [8, 11, 13, 17]. Whereas the BGS mannequin has been profitable in becoming many patterns of variety, a few of its simplifying assumptions might distort inferences concerning the selective course of. First, since fixation possibilities finally rely on the product of the deleterious choice coefficient (*s*) and inhabitants dimension (*N*), the efficacy of choice is dependent upon previous inhabitants sizes. Sadly, accommodating such demography into analytic fashions of purifying choice stays an open, troublesome drawback [18, 19] although simulation-based inference could also be a route ahead [20]. Second because the BGS mannequin builds off basic fashions of mutation-selection stability [21, 22], it assumes that new mutations are sufficiently deleterious that they’re invariably pushed to loss. Below this assumption, the impact of choice is well-approximated by merely rescaling the impartial coalescent by a discount issue generally known as [23]. Nevertheless, this easy rescaling method isn’t acceptable throughout elements of parameter house which might be related to pure populations [24, 25]. Particularly, the BGS mannequin can not accommodate the potential of weakly deleterious mutations (these with health results 2*Ns* ≤ 1) reaching fixation, which ends up in incorrect predictions of variety ranges because the energy of choice diminishes. Lastly, the basic BGS mannequin assumes that the selective dynamics at one website should not impacted by choice at different positions, i.e. no selective or “Hill–Robertson” interference [24, 26, 27].

On this work, we use one other class of linked choice fashions that derive from quantitative genetics to handle limitations of the basic BGS mannequin [28–31]. These fashions think about how polygenic health variance unfold alongside the genome will increase the variance of stochastic allele frequency change, as alleles change into randomly linked to health backgrounds over time and their frequency trajectories are perturbed by choice at different websites. Whereas these fashions can theoretically accommodate additive health variance from any supply so long as its price of change isn’t too fast, we focus particularly on a deleterious-mutations-only mannequin of health variance from [29]. This mannequin is an identical to BGS when choice in opposition to deleterious mutations is robust, but it surely additionally appropriately predicts the discount in variety when choice is weak by collectively predicting the deleterious substitution price. We lengthen the Santiago and Caballero (hereafter the SC16) mannequin of the damaging choice course of in order that it may be match utilizing a composite chance method to patterns of genome-wide variety, in response to the spatial distribution of genomic options that would harbor deleterious health variation. Utilizing ahead simulations, we present this mannequin results in extra correct estimates of the distribution of health results (DFE) beneath weak choice. We apply our composite-likelihood technique to human inhabitants genomic information and supply new parameter estimates of the genome-wide influence of purifying choice in people. We present that our new technique is best capable of predict the patterns of variety alongside human chromosomes than earlier fashions. Nevertheless, our mannequin results in predictions of the deleterious substitution price that disagree with noticed ranges of divergence. We focus on the potential causes and implications of such discrepancies and what it’d imply for future efforts to suit linked choice fashions to genomic patterns of variation.

## Concept

Our work extends quantitative genetic fashions of linked choice ([28–31]; see additionally the Appendix of [8]), which approximate the discount in genetic variety as a result of linked choice by way of polygenic additive health variance (*V*_{A}). These fashions are approximations to pretty sophisticated choice dynamics; in actuality, background choice can’t be absolutely summarized by merely rescaling efficient inhabitants dimension throughout all of parameter house [25, 32, 33]. Consequently, we use in depth, real looking ahead simulations (within the subsequent part) to show the validity of those fashions within the area of parameter house that the human genome occupies.

Right here we evaluate the related principle earlier than introducing our genome-wide extension. These linked choice fashions stem from Robertson [31], which in essence describes how polygenic additive health variation will increase the tempo of stochastic allele frequency change, thus lowering efficient inhabitants dimension. On the particular person stage Robertson thought-about, choice generates an autocorrelation in fecundity as offspring from massive households are likely to beget many descendants themselves (and likewise with small households) when health is heritable. This identical across-generation autocorrelation happens on the genomic stage as a result of linkage [28, 34], because the perturbations to a impartial allele’s trajectory from its explicit health background are likely to happen in the identical course throughout generations till the background recombines off. Quantitative genetic fashions similar to Santiago and Caballero’s [28] quantify the whole influence of the autocorrelation generated by choice by way of what we consider as a *fitness-effective* inhabitants dimension *N*_{f} (to distinguish it from the *drift*-effective inhabitants dimension, which is the scale of the perfect inhabitants when there isn’t any health variation).

The important thing perception is that in the long term, the regular presence of additive genetic health variance (*V*_{A} > 0) contributes an additional supply of variance in offspring quantity past the variance anticipated beneath pure drift [35]. Nevertheless, as a result of heritable health variation generates across-generation autocorrelation, the cumulative impact of this health variance on the variance in allele frequency change is inflated by an element of *Q*^{2}. Intuitively, the product *V*_{A}*Q*^{2} represents the anticipated whole variance in reproductive success a impartial mutation experiences over its lifetime in a system with weak choice at linked websites.

Following Robertson and Santiago and Caballero [30, 31], we outline the fitness-effective inhabitants dimension *N*_{f} by together with the whole extra variance created by heritable health into Wright’s equation [35] for efficient inhabitants dimension,

(1)

(c.f. [30, 31]; see S1 Text Part 1 for a proof). The good thing about modeling linked choice with Robertson’s forward-time mannequin is that the inflation issue beneath weak choice is invariant with respect to the actual health background (i.e. excessive or low health backgrounds are exchangeable on this mannequin) the impartial allele turns into stochastically related to. Against this, modeling variety ranges beneath linked choice backwards in time requires monitoring the actual related health backgrounds, as coalescence charges skilled by a lineage should not invariant with respect to their health background, i.e. excessive and low health backgrounds should not exchangeable.

Eq (1) is basic, since completely different modes of choice and linkage could be accommodated by completely different expressions for *V*_{A} and the inflation issue *Q*^{2} [28, 30]. When health variation has a multiplicative polygenic foundation, as is commonly assumed for genome-wide choice processes, the fitness-effective inhabitants dimension skilled by an arbitrary impartial website beneath the affect of all *S* linked areas is,

(2)

the place the issue of one-half comes from ignoring the short-lived associations with the homologous chromosome, which have a weak impact on the focal allele (see S1 Text Part 1.3). In our genome-wide mannequin, we think about the summation in Eq (2) over non-overlapping contiguous, putatively conserved segments *i* ∈ {1, 2, …, *S*} (e.g. exons, splice websites, and so forth.) every present process choice such that phase *i* contributes additive health variance *V*_{A,i} to the whole additive genetic health variance. The influence this phase’s health variance *V*_{A,i} has on the fitness-effective inhabitants dimension is mediated by the autocorrelation time period *Q*_{i}, which is a decaying operate of the recombination price between the phase and focal impartial allele. Particularly, the autocorrelation operate for a impartial allele related to phase *i* is *C*(*t*) = [(1 − *r*_{i})(1 − *κ*_{i})]^{t}, the place *r*_{i} is the recombination fraction to the phase and *κ*_{i} is the speed that the related health variance decays as a result of selective dynamics. Then, the cumulative autocorrelation over the lifespan of the allele is,

(3)

(see S1 Text Equation 20). This basic equation can accommodate fashions of polygenic choice so long as the equilibrium additive health variation *V*_{A,i} could be specified and the change in variance as a result of choice could be approximated as a geometrical decay, i.e. Δ*V*_{A,i} = −*κV*_{A,i} [28, 36–38]. That is normally an inexpensive assumption since within-generation choice removes a fraction of phenotypic variation from the inhabitants, and a few fraction of that’s additive genetic variation [36, 37, 39].

The remaining required expressions are for the equilibrium additive health variance *V*_{A} and the decay price in related health 1 − *κ*. Health variance might come up from helpful or deleterious alleles, however given prior work has discovered choice in opposition to new deleterious mutations in conserved areas performs a dominant position in shaping genome-wide patterns of variety and divergence [14, 16], we focus particularly on purifying choice. We think about a mutation-selection course of that creates health variation as deleterious mutations enter a inhabitants at price *μ* per basepair per technology in a conserved area of *L* basepairs, such that the region-wide per technology diploid mutation price is *U* = 2*μL*. Every mutation imposes a selective price of *s* in heterozygotes and a pair of*s* in homozygotes, and health results are multiplicative throughout websites.

Below this choice mannequin, the additive genic health variance created by a brand new mutation (at frequency ) is . For the whole inhabitants of two*N* chromosomes, the mutational variance enter every technology in phase *i* is *V*_{M,i} ≈ *U*_{i}*s*^{2} the place *U*_{i} = 2*μL*_{i} is the diploid mutation price per technology inside the phase. Below the mutation-selection stability assumed by basic BGS principle, an *L*_{i}-basepair phase has equilibrium additive genetic variance (see S1 Text Equation 40) and thus . Substituting and in Eq (2) and simplifying, now we have

(4)

which is an identical to the genome-wide mannequin of background choice utilized in earlier research [14–16]. Thus, the basic background choice mannequin is a particular case of the extra basic principle of Santiago and Caballero [29], which they’d proven beforehand [28].

Nevertheless, when new mutations are solely weakly deleterious, they will drift up in frequency earlier than their eventual loss or fixation. At this level, the variety of deleterious mutations per haplotype is now not well-approximated by the deterministic mutation-selection-balance principle, and their dynamics are strongly influenced by stochastic perturbations as a result of each drift and linked choice. On this weak choice regime, basic BGS principle now not precisely predicts ranges of linked variety [11, 24, 25, 40]. Furthermore, choice in opposition to weakly deleterious mutations alters the topology of genealogies, such that they’re now not well-approximated by a rescaled impartial coalescent as assumed beneath the basic BGS mannequin [41–43]. To additional complicate issues, the distribution of the variety of deleterious mutations (and its corresponding health distribution) is now not a stationary Poisson distribution, as an alternative changing into a touring wave [33, 44, 45] in the direction of elevated numbers of deleterious alleles per chromosome and decreased imply inhabitants health. In asexual populations, every click on of “Muller’s ratchet”, which is the stochastic lack of the least-loaded class [46, 47], on common results in one deleterious substitution [43]. Sadly, figuring out the speed of deleterious substitutions is one other troublesome drawback [40, 43, 45, 48, 49] associated to Hill–Robertson interference [27, 50].

Quantitative genetic fashions of linked choice approximate an equilibrium *V*_{A} beneath each sturdy and weakly deleterious mutations by concurrently modeling the speed of fixation of deleterious alleles within the area, *R* (for readability, we think about only a single phase and omit the index *i*). Santiago and Caballero [29] recommend that equilibrium health variance is decrease than predicted by as soon as weakly deleterious mutations start to have an considerable price of fixation *R* > 0 per technology within the area. The substitution price *R* decreases health variance since every substitution removes a segregating website and thus its contribution to health variance. Thus the steady-state additive genetic variance of health beneath mutation and damaging choice is,

(5)

the place the situation *V*_{A} ≥ 0 is met when the chance of fixation is lower than or equal to the impartial fixation chance of , as is true for all deleterious mutations. This equation describes the equilibrium additive genetic health variance because the stability of the flux of latest variation in to the inhabitants from deleterious mutations, and the removing of variation as a result of their substitution (and the decline in imply inhabitants health). When *R* = 0, choice is so sturdy deleterious alleles can not repair, and the equilibrium health variation is due solely to younger uncommon mutations earlier than their extinction . Santiago and Caballero derive Eq (5) by Fisher’s Elementary Theorem of Pure Choice, however we discover an alternate proof ([43]; see S1 Text Part 1.9). We additionally discover that the steady-state additive genic variance in Eq (5) outcomes from diffusion fashions with a flux of mutations into discrete websites ([51]).

Whereas utilizing Eq (5) in Eq (1) results in a prediction for the fitness-effective inhabitants dimension *N*_{f}, closed-form expressions for the deleterious substitution price *R* have typically been exhausting to seek out [29, 43, 45, 48]. A key perception of Santiago and Caballero [29] is that the deleterious substitution price with linked choice could be approximate through the use of the chance of fixation *p*_{F}(*N*_{f}, *s*) [52, 53] utilizing the rescaled fitness-effective inhabitants dimension, i.e. *R* = *NUp*_{F}(*N*_{f}, *s*). Given this equation for the substitution price and Eq (2) for *N*_{f} beneath linked choice, now we have a system of two non-linear equations that may be solved numerically for *N*_{f} and *R* for every phase (once more, omitting the phase index *i* for readability),

(6) (7)

We denote the options to those equations, which signify equilibria beneath mutation-selection-drift course of, as and . These equilibria additionally suggest an equilibrium stage of additive health variation within the phase, that are used to calculate the discount issue at every other genomic place *x* (see Methods Part Calculating the discount maps). In our inference technique, described in Strategies Part Composite chance and optimization), we lengthen these equations to deal with a distribution of choice coefficients, and a number of characteristic lessons. Throughout inference, we additionally think about an alternate “native rescaling” mannequin that units the *N* within the fitness-effective inhabitants dimension equation to *B*(*x*)*N* and re-solves these equations. This different mannequin approximates the influence of different segments on every focal phase’s choice dynamics through the use of the native efficient inhabitants dimension implied by the estimated B map. We be aware that options to those equations don’t precisely mannequin the substitution price beneath all areas of parameter house [25, 49, 54]; within the subsequent part we present by in depth simulations that this approximation works fairly effectively beneath human parameters.

## Outcomes

We offer two foremost lessons of outcomes. First, we present simulation outcomes which show the accuracy of the SC16 mannequin over the BGS approximation throughout the parameter house, in addition to validations of the composite chance technique we use to suit the SC16 mannequin. Second, we offer suits of our technique to human genome information, the place we present comparability of fashions match utilizing completely different annotations, the estimated DFEs, and predictions of the deleterious substitution price.

### Simulation validation of principle and strategies

On condition that modeling the interaction of mutation, drift, and linked choice beneath each weak and powerful choice has confirmed to be a troublesome drawback, we first sought to confirm the SC16 principle and our genome-wide extension with three ranges of simulations: ahead simulations of purifying choice in a area, chromosome-scale ahead simulations of purifying choice, and simulations of a “artificial genome” (i.e. by combining independently simulated chromosomes) to check our composite-likelihood technique primarily based on this principle.

#### Simulations of a phase beneath purifying choice.

Our first set of ahead simulations was to make sure that the SC16 mannequin adequately captures selective dynamics in a single 100 Mbp basepair area beneath choice, throughout quite a lot of mutation charges and choice coefficients (see Methods Ahead simulations). We discover a shut correspondence between the noticed and predicted reductions in efficient inhabitants dimension over all choice and mutation parameters together with weak choice (Fig 1A), in distinction to basic BGS principle. Moreover, to research whether or not this accuracy was attributable to the mannequin appropriately predicting the equilibrium health variance and substitution price, we additionally measured these all through the simulation. Once more, we discover diploid SC16 principle precisely predicts each the deleterious substitution price (Fig 1B) and the genic health variance (Fig 1C).

Fig 1. Santiago and Caballero (2016) principle fashions the weak choice regime higher than basic BGS principle.

(A) The anticipated discount issue beneath basic B principle (darkish grey line) and the diploid SC16 mannequin (coloured traces comparable to mutation price) in comparison with common discount throughout 10,000 simulation replicates (factors). The inset determine is zoomed out to point out extent of disagreement beneath basic BGS. (B) The anticipated deleterious substitution price beneath the SC16 mannequin, scaled by mutation price (coloured traces) in comparison with the substitution price estimated from simulation (factors). When 2*Ns* > 1, the substitution price is close to zero. (C) The genic variance from simulations (factors) in opposition to the expected variance beneath the SC16 mannequin (coloured traces). As substitutions start to happen, the genic variance is decreased from the extent anticipated beneath sturdy BGS (dashed line). (D, backside) The imply squared error (MSE) between whole-chromosome simulations and predicted basic B (dots), new B’ (strong), and domestically rescaled B’ (dashed) for various mutation charges (colours). Regionally rescaled B’ (yellow traces) are omitted for readability within the prime and backside rows, since they’re an identical to B’; Native rescaling solely impacts B’ within the 2*Ns* ≈ = 1 area. The dashed horizontal line is the approximate theoretic minimal MSE. (D, prime) The build-up of damaging linkage disequilibria round 2*Ns* = 1 in whole-chromosome simulations proven within the backside panel. (E) The common B map from 100 chromosome 10 simulation replicates (grey) in opposition to completely different predictions, for parameters that correspond to 2*Ns* < 1, 2*Ns* = 1, and a pair of*Ns* > 1. The chromosome exhibits the density of conserved websites and recombination map utilized in simulations.

Furthermore, these simulations present instinct concerning the underlying choice course of. When mutations are strongly deleterious, there isn’t any probability they will repair, and the substitution price is zero (Fig 1B for two*Ns* > 1). On this sturdy choice regime, the additive genic health variation carefully matches the theoretic deterministic equilibrium of *V*_{A} = *Us* (dashed grey line, Fig 1C) Nevertheless, round 2*N*_{e}*s* ≈ 1, the substitutions start to happen as *p*_{F} strikes away from zero. When this happens, every fixation eliminates variation, and the equilibrium variation diverges from the deterministic mutation-selection equilibrium (Fig 1C).

#### Chromosome-wide simulations and fashions of damaging choice.

Given the accuracy of the SC16 mannequin in predicting the discount issue *B* and the deleterious substitution price for a single phase beneath basic mutation-selection processes, we subsequent prolonged their mannequin in order that it might be match to patterns of windowed genome-wide variety by a composite chance method. Our software program technique bgspy numerically solves Eq (6) to compute the equilibrium additive genic health variance () and the deleterious substitution price () throughout grids of mutation charges and choice coefficients. That is achieved for every pre-specified phase within the genome (doubtlessly tens of hundreds of thousands of small areas, which rely on the actual annotation of putatively conserved areas used) which may be beneath purifying choice (e.g. coding sequences or UTRs). We name the set of theoretic predicted reductions throughout these grids the B’ maps (to tell apart them from McVicker’s B maps [14]; these can be utilized to seek out the equilibrium discount issue *B*(*x*) for any genomic place *x*.

We validated our predicted B’ discount maps with real looking chromosome-scale ahead simulations of purifying choice utilizing putatively conserved areas and recombination maps for the human genome. We discover that our B’ maps and the basic BGS principle B maps carefully match simulations when choice is robust (prime row of Fig 1E), other than slight discrepancies in low recombination areas (Fig 1E). Second, we discover our principle is vastly extra correct than the basic BGS when choice may be very weak (2*N*_{e}*s* ≪ 1; backside row of Fig 1E). In essence, these findings signify the information that basic BGS principle (which as proven in (4) is a particular case of the SC16 mannequin) is correct when choice is comparatively sturdy and Eq (6) are correct as *s* → 0. Throughout all mutation and choice parameters simulated, the relative error of the basic B maps is 14.6% whereas the relative error within the new B’ maps is 5%. Almost all of this error is within the almost impartial area (2*N*_{e}*s* ≈ 1 area); for sturdy and weak choice, the imply squared error between simulations and B’ maps is near the theoretic decrease sure of the imply squared error, set by the coalescence variance for a ten kb area [55].

We hypothesized this error within the almost impartial area could also be as a result of selective interference between segments that isn’t taken into consideration after we numerically resolve Eq (6) independently for every phase. Particularly, after we numerically resolve these equations, we use a hard and fast drift-effective inhabitants dimension, *N* = 1, 000, comparable to the variety of diploids within the simulations. Nevertheless, in actuality, choice all through the genome would lead a phase at place *x* to expertise a domestically decreased efficient inhabitants dimension of roughly *B*(*x*)*N*, which is a consequence of selective interference [26, 27, 50]. To check this, we applied a “domestically rescaled” model of the B’ maps, which makes use of *B*(*x*)*N* because the inhabitants dimension when numerically fixing these equations. We use this method as a result of (1) iteratively fixing Eq (6) for the whole genome in an inference framework is computationally infeasible, and (2) evaluating the preliminary suits and native rescaling suits permits us to watch how incorporating the native fitness-effective inhabitants dimension impacts parameter estimates, if in any respect. We discover the domestically rescaled B’ maps scale back the relative error from 5% to 0.4% and imply squared error (Fig 1D, dashed coloured traces), however doesn’t solely remove the error within the 2*Ns* ≈ 1 area (the place the linkage disequilibrium construct up is the best, Fig 1D, prime row).

#### Validation of composite-likelihood technique utilizing ahead Simulations.

Our composite-likelihood technique estimates the distribution of choice coefficients for every characteristic kind, the mutation price, and the variety within the absence of linked choice (*π*_{0}) by becoming the theoretic discount map to windowed genome-wide variety (see Methods Composite chance and optimization). We validated that our technique can precisely estimate the selective parameters by simulation a “artificial genome” of the primary 5 human chromosomes (see Methods Ahead simulations). We be aware three findings from these simulations.

First, each our implementation of basic BGS principle and our B’ technique precisely infer the common choice coefficient beneath sturdy choice (Fig 2, center row). Nevertheless, when choice was weak, the basic BGS mannequin erroneously estimated sturdy choice and a really low mutation price. Against this, our B’ technique estimated choice coefficients far more precisely. A minor discrepancy happens round 2*Ns* = 1, probably as a result of sensitivity of mutations on this area to selective interference (these outcomes don’t use native rescaling). To ease computational prices, we solely simulated fastened choice coefficients and 5 chromosomes, and we solely assessed the accuracy of common choice coefficients slightly than the complete estimated DFE.

Fig 2. Comparability of parameter estimates utilizing basic BGS principle (inexperienced traces) with our new B’ technique (blue traces) throughout each full and sparse monitor sorts (darkish versus gentle hue), and completely different mutation charges (columns).

Each basic BGS and B’ strategies appropriately estimate sturdy choice coefficients when annotation tracks are sparse, however solely B’ can precisely estimate choice coefficients when choice is weak or full annotation tracks are used (first row). Mutation price estimates (second row) are extra precisely estimated by the B’ technique than basic BGS throughout choice parameters, however total present slight biases. Moreover, *R*^{2} between predictions and observations will increase with choice depth (third row). General, basic BGS strategies break down as anticipated when full-coverage tracks are used, because it can not accommodate weak choice and neutrality in putatively conserved areas. See Methods for particulars on sparse versus full tracks.

Second, we discover slight biases in mutation price estimates from each our B’ and the basic BGS strategies (Fig 2, backside row). Nevertheless, mutation price estimates primarily based on our B’ technique are extra correct than basic BGS principle throughout a variety of choice coefficients. General, this bias in estimated mutation charges means that benchmarking genome-wide damaging choice fashions primarily based on their settlement with pedigree-based price estimates might not be acceptable. When BGS isn’t occurring, both as a result of weak choice or a low price of deleterious mutations (Fig 2, proper column), all estimates deteriorate. That is comprehensible, as the general sign from linked choice weakens relative to drift-based noise. We should always be aware, although, that that is an unlikely area of parameter house and this subject could be readily recognized from the low *R*^{2} values. Lastly, we discover in extra exams that our estimates are sturdy to demographic expansions however inaccurate when mutations have recessive results, since our mannequin assumes additive results (see S1 Text Part 5.3). We didn’t check the affect of inhabitants bottlenecks, since parameter estimates of out-of-Africa bottlenecked populations (CHB and CEU) didn’t differ a lot from YRI estimates (see beneath).

Third, we discover the coefficient of dedication, *R*^{2}, between predicted and simulated megabase-scale variety serves as a measure of the energy of the linked choice sign in genome-wide information. *R*^{2} will increase with the depth of choice in opposition to new deleterious mutations and mutation price (Fig 2, prime row). Below simply drift or weak purifying choice, the variance in variety is pushed by unstructured coalescence noise alongside the genome and the expected discount map, *B*(*x*), and doesn’t match the information effectively. Below very sturdy choice (*s* = 0.05), *R*^{2} is decreased; that is probably as a result of very sturdy choice having much less localized results and impacting total genome-wide variety [30, 31].

### Software to human genomic information

#### Annotation mannequin comparability.

Our composite chance technique takes tracks of annotated options (an “annotation mannequin”) which might be *a priori* anticipated to have the same distribution of health results, and estimates the general mutation price and distribution of health results for every characteristic kind. These annotation fashions specify the putatively conserved “segments” utilized in Eqs (2) and (4). We think about two lessons of annotation fashions: (1) CADD-based fashions, which think about the highest *x*% most pathogenic basepairs in response to the CADD rating, and (2) and extra interpretable, feature-based fashions that features protein coding areas, introns and UTRs, and PhastCons areas. We embody PhastCons areas as a result of they embody highly-conserved, non-coding areas recognized to harbor necessary features [2, 56–58], that might be missed by gene characteristic solely annotation. These two lessons of annotation fashions have a trade-off between fine-scaled specificity to which basepairs are more likely to be beneath damaging choice, and interpretability of the DFE estimates for every characteristic. Lastly, for every annotation mannequin, we match a “sparse” monitor model (conserved areas solely) and a “full monitor” model (which incorporates one other characteristic class referred to as “different” that features the remainder of the genome).

Our technique estimates a distribution of health results (DFE) for every characteristic class. Whereas CADD-based fashions solely have a single conserved characteristic class (e.g. CADD 6%), feature-based fashions can have a number of characteristic lessons beneath various ranges of selective constrain. Nevertheless, overlapping options (e.g. a basepair that’s annotated as each PhastCons and coding sequence) have to be assigned to at least one class or the opposite. Since this task impacts DFE estimates, we match each of the 2 different fashions. First, a *PhastCons Precedence* mannequin, the place genic options that overlap PhastCons areas are labeled as PhastCons, and all remaining coding basepairs are labeled as CDS. Second, a *Function Precedence* mannequin, the place all coding basepairs are assigned to CDS, and the PhastCons class catches the remaining highly-conserved non-genic areas.

In whole, we match 4 annotation fashions (CADD 6%, CADD 8%, PhastCons Precedence, and Function Precedence) to high-coverage 1000 Genome information for 3 reference samples: Yoruba (YRI), Han Chinese language (CHB), and European (CEU). We assess and evaluate our fashions in response to how effectively they predict patterns of variety on entire chromosomes left-out in the course of the mannequin becoming course of (e.g. leave-one-chromosome-out, LOCO). We use the metric , which is the proportion of the noticed variance in genomic variety on the megabase scale predicted by our mannequin on held out information. We experimented with a couple of smaller spatial scales (e.g. 100 kbp), however our outcomes had been according to earlier outcomes suggesting the human linked choice sign as a result of purifying choice suits greatest on the megabase scale [16]. Intuitively, the poorer mannequin suits at smaller spatial scales could be understood on account of fewer mutations and marginal coalescent genealogies being averaged over, rising these sources of noise relative to the linked choice sign.

General, we discover the PhastCons Precedence and CADD 6% fashions match equally effectively (Fig 2A), according to latest work utilizing basic BGS principle [16]. Nevertheless, we discover that our fashions predict out-of-sample variety ranges barely higher than earlier strategies. For these two fashions, we discover that our B’ technique predicts and of the out-of-sample variance in Yoruba pairwise variety on the megabase-scale, respectively. Against this, the best-fitting CADD 6% mannequin from Murphy et al. [16] defined 60% of variety in left-out 2 Mbp home windows throughout YRI samples. We be aware that this distinction might be defined by different variations in information processing, optimization, and so forth. For lineages impacted by the out-of-Africa bottleneck, the goodness-of-fit was decrease throughout all fashions (e.g. 61.0% and 58.8% for CEU and CHB respectively within the PhastCons Precedence mannequin).

Since our technique is constructed upon principle that fixes the weak choice drawback of basic BGS principle, it ought to in precept match equally effectively when an annotation mannequin consists of areas which might be beneath no or little selective constraint and thus (almost) neutrally evolving. Consequently, our B’ technique ought to match equally effectively when utilized to “sparse” and “full” monitor fashions, since our technique in precept can accommodate weak choice and neutrality. Certainly, we discover that each in-sample *R*^{2} and out-of-sample values are almost an identical throughout full and sparse-track fashions (Fig 2A and 2B, spherical factors), which demonstrates that our technique is ready to take care of weak choice and that there’s little extra predictive energy to realize from together with websites thought-about “different” as annotations.

Against this, full annotation fashions match poorly beneath basic BGS principle, and result in unreasonable parameter estimates. Moreover, when sparse annotation fashions comprise genomic options which might be probably beneath weak constraint (similar to introns and UTRs), fashions match worse beneath basic BGS principle than our B’ technique (Fig 2A). Nevertheless, among the many CADD annotation fashions, the goodness-of-fit is sort of an identical between B’ and basic BGS strategies. This conduct is what we’d anticipate on condition that the CADD fashions comprise solely probably the most pathogenic websites, that are *a priori* very probably beneath the sturdy choice area beneath which B’ and basic BGS principle agree. Lastly, we be aware that the expected basic B and B’ maps are almost an identical beneath the CADD 6% mannequin (*R*^{2} = 99.99%, see S1 Text Part 5.6 for a comparability). This displays the truth that the highest 6% most pathogenic CADD websites are beneath sturdy choice, and each fashions are an identical on this area.

General, our estimates recommend our mannequin explains as much as 67% of out-sample variance in variety of the megabase scale, although our technique assumes fixed demography and homogeneous mutation charges alongside the genome. A worthwhile query is: how a lot variation *might* we anticipate to suit at this scale? On condition that choice alters genealogies in methods past simply lowering imply pairwise coalescence time and populations have non-constant demography, a precise analytic reply is intractable. Nevertheless, we will get an approximate thought if we assume that the residual variance is set solely by the anticipated impartial coalescence noise across the anticipated coalescence time 2*B*(*b*)*N*. This may be be discovered analytically, plugging-in our predictions for *B*(*b*). This enables us to calculate to ballpark the theoretic variance that’s able to being defined, assuming this coalescent noise course of alone (see S1 Text Part 3.6). We be aware that choice is anticipated to *lower* the variance in coalescence instances past a rescaled efficient inhabitants dimension implies, thus our can be an underestimate beneath fashions with choice.

We discover that our out-sample for the Yoruba samples () is barely above the theoretic . This implies our mannequin is within the neighborhood of becoming all of the sign doable, beneath the coalescence-only noise assumption. Against this, for bottlenecked out-of-Africa samples, we discover a bigger discrepancy between and noticed out-sample . The theoretic for each samples, in comparison with the noticed for CEU and for CHB beneath the PhastCons Precedence mannequin. On condition that bottlenecks would act to extend the residual variance in coalescence instances past the extent implied by the efficient inhabitants dimension, this hole would probably shrink beneath extra real looking fashions or simulation-based approximations for . General, this means that purifying choice fashions match the overwhelming majority coalescence time variation on the megabase-scale that’s able to being defined (i.e. that isn’t coalescent noise).

#### Estimated distribution of health results.

Our composite chance technique has three units of parameters: the anticipated variety within the absence of linked choice variety *π*_{0}, the mutation price *μ*, and the matrix of distribution of health results **W** throughout the choice grid for every of the *Ok* characteristic sorts. On condition that the connection between *π* and the energy choice is U-shaped (i.e., see Fig 1A), we questioned whether or not our new B’ mannequin accommodating weak choice would match the linked choice sign beneath a special mixture of weak and powerful choice parameters than noticed beforehand. Nevertheless, throughout all of our annotation fashions, new deleterious mutations in conserved characteristic lessons (e.g. CADD tracks and PhastCons areas) had been constantly estimated to have strongly deleterious results (Fig 3A), according to earlier work [14, 16]. The DFE estimates for CADD and PhastCons areas constantly locations ≥ 75% of mass on the most important choice coefficient we used, *s* = 10^{−2}. The CADD 6% DFE estimates suggest a median choice coefficient of for CEU, for CHB, and for YRI. Equally, the PhastCons Precedence mannequin implies common choice coefficient estimates of , , and for CEU, CHB, and YRI respectively for PhastCons areas. Our DFE estimates for CDS beneath the Function Precedence mannequin are weaker than these for non-coding PhastCons areas; this displays the truth that round 30% of mutations to coding sequences lead to a synonymous change [59] and are thus probably successfully impartial. Our outcomes are qualitatively according to the U-shaped DFEs discovered for amino acids by Poisson Random Discipline technique [60], however differ from different estimates primarily based on the depletion of uncommon variants in purposeful areas [61]. Given the massive variations in pattern dimension between the current examine and that of [61] in addition to the variations in methodology, it’s maybe unsurprising that our outcomes are in nearer alignment with SFS approaches. Nevertheless, we be aware that our BGS parameterization of Eq (2), excludes a task for weak constructive choice; this type of mannequin misspecification might bias our DFE estimates and our outcomes ought to be interpreted in gentle of this.

Fig 3. The distribution of health results of latest mutations estimates for YRI reference samples.

(A) The DFEs utilizing sparse (left column) and full-coverage (proper column) tracks, throughout completely different annotation fashions (row). Colour signifies the characteristic kind. (B) The DFE of the full-coverage Function Precedence mannequin evaluating the estimates throughout reference inhabitants samples. Though this mannequin match the information much less effectively than options, its outcomes are extra interpretable.

Following earlier work, our technique used a grid of choice coefficients as much as *s* = 10^{−2}. Nevertheless, we additionally experimented with a powerful choice grid that features *s* = 10^{−1}. We discover that fashions match with the sturdy choice grid have predictive accuracy, as measured with , that had been about one share level larger. That is suggestive of stronger choice than has beforehand been estimated utilizing constrained grids (see S1 Text Desk 2). For this sturdy choice grid, we estimate common choice coefficients for the CADD 6% mannequin of for CEU, 0.032 for CHB, and 0.044 for YRI. Thus, the predefined choice coefficient grid impacts final estimates of the DFE and common choice coefficient.

Nevertheless, we discover indications of mannequin non-identifiability throughout the sturdy choice grid runs. First, estimates of the DFE with the sturdy grid are bimodal (S1 Fig). For instance, beneath the CADD 6% sturdy choice grid mannequin, new mutations are estimated to have a range coefficients of *s* = 10^{−1} with 43% probability, *s* = 10^{−2} with 7.8% probability, and *s* = 10^{−3} with 41% probability within the YRI samples. We suggest that one mechanism for this non-identifiability is that very deleterious mutations result in bigger whole-genome reductions in variety, that are troublesome to tell apart from a smaller drift efficient inhabitants dimension (i.e. the *π*_{0} parameter). One technique to check this speculation is to look to see if there’s a systematic constructive relationship throughout fashions between common choice coefficient and *π*_{0}, which is consists of the drift-effective inhabitants dimension *N*_{e}. We discover that is the case for all of our CADD 6% fashions. Throughout all reference samples, common choice was about 7.1 instances bigger utilizing the sturdy choice grid, and *π*_{0} was 5.6% larger (see S2 Fig). There was no comparable constant change in mutation price estimates amongst reference samples. Within the CADD 6% mannequin, genome-wide common discount issue was ≈6.1% decrease within the default versus constrained grid. General, this means that the linked choice sign alone can not differentiate very sturdy choice from a barely smaller drift-effective inhabitants dimension.

On condition that it’s debated how strongly demography impacts the deleterious mutation load [62–66], we had been curious how constant our DFE estimates are throughout samples from completely different reference populations. General, we discover DFE estimates are comparatively secure throughout samples from completely different reference populations and annotation fashions (S1 Text Part 6). Solely in our Function Precedence mannequin (Fig 3B, prime row) will we see a barely completely different DFE estimate for coding sequences between YRI and CEU/CHB samples, however this might be as a result of poorer match this mannequin has to information.

Though the Function Precedence mannequin suits the information much less effectively than different fashions, its DFE estimates are extra interpretable. We discover that our B’ technique estimates a bimodal DFE for coding sequences for the Function Precedence mannequin, with a big mass positioned on 10^{−3} ≤ *s* ≤ 10^{−2} and one other on the impartial class *s* = 10^{−8}. That is anticipated, on condition that the synonymous and non-synonymous websites that represent coding sequences are beneath vastly completely different ranges of constraint and are lumped collectively in our annotation class. Furthermore, options anticipated to be solely weakly constrained similar to introns and UTRs have the majority of DFE mass on the impartial class, with a small however vital quantity of mass (≈ 3%) positioned on *s* = 10^{−2}. As anticipated, the DFE for PhastCons areas (which on this mannequin correspond to highly-conserved non-coding components) suggests it’s beneath sturdy selective constraint; nevertheless, we be aware that block jackknife-based uncertainty estimates recommend the mannequin is unsure whether or not there’s some mass on the impartial class. Lastly, we spotlight one end result from our PhastCons Precedence annotation mannequin (Fig 4A backside row): the DFE estimate for coding sequences excluding PhastCons areas is estimated as impartial. This too is anticipated; the choice sign in coding areas is absorbed by the PhastCons characteristic, leaving solely conditionally impartial websites.

Fig 4. The *R*^{2} estimates for sparse (A) and full (B) fashions, for all samples (colours) match on the megabase-scale.

Spherical factors are our B’ technique and diamonds are the basic BGS (we exclude basic BGS within the full monitor subfigure, since these all match very poorly). Lighter colour spherical factors are the out-sample estimates for our B’ technique, and arrows present the decline in goodness-of-fit as a result of in-sample overfitting (out-sample weren’t calculated for traditional B values as a result of computational prices). The horizontal dashed traces are the anticipated when the residual variance is given by the theoretic variance in coalescence instances as a result of drift alone.

#### Estimates of the deleterious mutation price are delicate to mannequin alternative.

Prior work on genome-wide inference utilizing the basic BGS mannequin match the patterns of variety effectively, however led to unusually excessive estimates of the mutation price [14]. This led to the speculation that these fashions might be absorbing the sign of constructive choice [67], although different work has discovered a restricted position for hitchhiking at amino acid substitutions [16, 68, 69]. Whereas our simulation outcomes recommend estimates of the mutation price from linked choice fashions are biased, we nonetheless verify for tough settlement with pedigree-based estimates [70, 71]. We discover throughout all populations, our mutation price estimates from CADD-based fashions are roughly according to pedigree-based estimates (Fig 5A), according to latest work [16]. Our full-track CADD 6% mannequin estimates the mutation price as for YRI, 1.64 × 10^{−8} for CEU, and 1.60 × 10^{−8} for CHB reference samples (S1 Text Part 3.6). As anticipated, the sparse-track CADD mannequin mutation price estimates are almost an identical between the B’ and basic BGS strategies (Fig 5A prime row).

Fig 5. Mutation price estimates throughout the sparse (prime row) and full-coverage tracks (backside row) fashions, for the brand new B’ (circles) and basic BGS (diamonds) strategies.

Estimates of the mutation price are constant between basic BGS and B’ strategies for sparse tracks CADD fashions (overlapping diamonds and circles, prime row). General, mutation price estimates are delicate to the underlying annotation mannequin.

Nevertheless, mutation price estimates for feature-based annotation fashions don’t agree with pedigree-based estimates. First, mutation price estimates beneath from basic BGS principle are an order of magnitude beneath the anticipated vary (Fig 5A prime row). We observe comparable conduct after we use the basic BGS mannequin to suit full-coverage annotation fashions (Fig 5A backside row). This conduct is according to basic BGS principle being unable to suit the DFE to options beneath weak constraint (e.g. introns, UTRs, and the “different” characteristic), and thus should compensate by estimating too low a mutation price.

Second, we seen that throughout all populations and sparse and full tracks, the CADD 6% mannequin constantly led to barely larger mutation charges than the CADD 8% mannequin (Fig 5A backside row; S1 Text Part 3.6). This identical sample was noticed in Murphy et al. [16] (Appendix 1, Fig 16). This conduct suggests a non-identifiability subject between larger per-basepair mutation charges and annotation tracks that comprise extra conserved sequence. That is anticipated from principle, since each basic BGS and SC16 fashions solely rely on mutation price by the compound parameter *μL*, the place *L* is the size of the conserved phase. Although our technique is far more sturdy to the inclusion of non-conserved areas like introns, we nonetheless observe this non-identifiability subject.

Lastly, we be aware that mutation price estimates from the Function Precedence mannequin are themselves too excessive (), harking back to the excessive mutation price estimates discovered beneath McVicker et al.’s mannequin. Whereas each our and Murphy et al.’s CADD and PhastCons-based fashions alleviate this subject, it’s value contemplating why this might happen. We are able to doubtlessly achieve some perception from evaluating the estimated mutation charges from our Function and PhastCons Precedence annotation fashions, which every comprise the very same variety of characteristic basepairs, however whose composition varies primarily based on the precedence of overlapping options. That considered one of these fashions is our best-fitting mannequin and the opposite our worst signifies that mannequin suits are delicate to characteristic lessons which themselves have heterogeneous DFEs. CADD-based fashions match higher partly as a result of their fine-scale decision of selective results throughout the genome. Whereas ideally we’d match a CADD mannequin with completely different options comparable to the completely different percentiles of pathogenicity, these options are on the basepair scale and thus too memory-intensive for our technique to at present accommodate.

#### Regardless of shut match, residual purifying choice sign stays.

Evaluating predicted in opposition to noticed variety alongside chromosomes, we discover a shut correspondence according to the excessive (Fig 6A). As soon as scaled by the genome-wide common, predicted and noticed variety ranges throughout the genome differ little throughout samples from reference populations. On condition that the CEU and CHB samples are from bottlenecked out-of-Africa populations and their mutation price and DFE estimates are comparable, that is an empirical demonstration that our mannequin is pretty sturdy to violations of the fixed inhabitants dimension assumption of the speculation (see S1 Text Part 5.7 for a comparability of the expected B’ maps throughout completely different populations).

Fig 6.

(A) Noticed and predicted variety of the B’ mannequin match with the CADD 6% full-track annotation. As soon as scaled by common variety, predicted variety for populations (coloured traces) differs little throughout populations, and carefully matches noticed variety inside every inhabitants (gentle grey traces). Moreover, we present summaries of CADD density and recombination price alongside the chromosome beneath. (B) Predicted*B* and noticed *π* for every window. The purple dashed line signifies the noticed 2 commonplace deviation ellipsoid, which has almost the identical width because the anticipated by , indicating the residual variance is near theoretic expectations. The yellow factors are binned means, and the yellow line is the lowess curve by predicted and noticed values. (C) CADD 6% residuals (YRI proven) plotted in opposition to the common LoF choice coefficient throughout genes in megabase home windows (estimated by [72]).

Nevertheless, we be aware a couple of massive (tens of megabases) areas with systematically poorer match (S1 Text Part 5.6). In Fig 6A we see one such area on the brief arm of chromosome 2, from 30 Mbp to 60 Mbp. Curiously, predicted variety carefully follows the peaks and troughs of this area, nevertheless, predicted variety is decrease than noticed. We be aware {that a} small area inside this stretch had been discovered by a genome-wide scan for associative overdominance [73]. We additional examine this by inspecting whether or not observations are systematically completely different from predictions. We affirm a discovering of Murphy et al. [16] that areas predicted to expertise little discount in variety as a result of background choice (i.e. *B* ≈ 1) have larger variety than predicted (Fig 6B, orange line). Murphy et al. [16] instructed that this might replicate historical introgression between archaic people and ancestors of up to date people. Regardless of the prediction error on this area, the variance round noticed and predicted variety ranges falls very near what we’d anticipate beneath the theoretic coalescent-noise-only expectation ().

As DFE heterogeneity inside a category of websites could also be poorly match by our mannequin, we regarded for unaccounted choice in our mannequin residuals. First, we inspected whether or not there was a relationship between the fraction of CADD 2% and 6% basepairs and the residual throughout megabase home windows (S3 Fig), discovering a damaging vital relationship in each circumstances. CADD 2% was used on this case to seek for a residual sign from highly-constrained areas. Furthermore, our mannequin over-predicted variety in home windows containing extra CADD 2% basepairs than CADD 6%, according to heterogeneity in website pathogenicity being poorly match by our mannequin. Nevertheless, the whole residual variance defined is *R*^{2} = 0.3% and *R*^{2} = 0.9% for the CADD 2% and 6% tracks respectively, suggesting solely a modest quantity of choice sign stays inside the CADD annotations. There was no relationship between residuals and recombination price (S4 Fig); we be aware predicted *B* values per megabase window are strongly correlated with CADD 6% and recombination price as anticipated by principle (S5 and S6 Figs).

Since our technique doesn’t embody the doable results of linked constructive choice, we’d anticipate home windows containing exhausting or smooth sweeps would have systematically decrease variety ranges than predicted. Utilizing the areas of soppy and exhausting sweeps detected utilizing a machine studying method [74, 75], we examined whether or not the residuals of the CADD 6% mannequin containing sweeps had been systematically completely different than these not containing sweeps. We discover no vital distinction between the magnitude of residuals of home windows containing sweeps versus these that don’t (S7 Fig; Kolmogorov–Smirnov p-value = 0.71). The identical was true if we checked out exhausting or smooth sweeps individually as a category.

We additional examined for remaining choice sign in our CADD 6% mannequin residuals through the use of gene-specific estimates of the health price of loss-of-function (LoF) mutations from Agarwal et al. [72]. These estimates are primarily based on an Approximate Bayesian Computation method that estimates the posterior distribution over LoF health prices from the noticed dearth of LoF mutations per gene, and thus is an impartial method to evaluate the energy of purifying choice. We averaged the estimated LoF health prices throughout genes for every of our megabase home windows, and plotted our residuals in opposition to these common LoF health prices. Opposite to the weak CADD residual sign described above, we discover proof of a reasonably sturdy relationship between our residuals and common LoF health price (Fig 6C; *R*^{2} = 2.1%, p-value 1.27 × 10^{−10}). In different phrases, roughly 2% of the variance in these residuals is defined by the common health prices of LoF mutations within the window. Consequently, our mannequin over-predicts variety by about or extra in home windows harboring the highest 1.7% most LoF-intolerant genes.

#### Predicted substitution charges point out potential mannequin misspecification.

Since our B’ technique additionally predicts deleterious substitution charges () for every characteristic class, it permits for an additional verify of mannequin sufficiency by evaluating the expected substitution charges to noticed ranges of divergence. We estimated sequence divergence on the human lineage utilizing a a number of alignment of 5 primates for every characteristic in our feature-based fashions (Strategies Part Substitution price prediction and divergence estimates). We in contrast these to the expected substitution charges per characteristic, averaging over all segments within the genome. Since our simulations present that mutation price estimates could be biased, we predicted substitution charges beneath a hard and fast mutation price of *μ* = 1.5 × 10^{−8}. Fixing the mutation price additionally permits us to extra simply evaluate the predictions throughout our feature-based fashions. Sadly, a cautious comparability between our predictions and noticed divergence charges is hindered by appreciable uncertainty in technology instances, heterogeneity within the purposeful constraint throughout genes, and the human-chimpanzee divergence time. We assume a technology time of 28 years [76], and calculate the sequence divergence implied by our predicted substitution charges over a variety of divergence instances, from 6 Mya to 12 Mya [77–80].

We discover that predicted substitution charges are qualitatively according to the noticed divergence alongside the human lineage for all options besides the PhastCons areas (Fig 7). As anticipated, the expected substitution charges in options beneath decreased selective constraint (introns and UTRs, and the “different” characteristic) are very near the mutation price. All through, we report our substitution charges as a % relative to the whole mutation price, *μ* (right here fastened to 1.5×10^{−8}). In our Function Precedence mannequin, coding sequences are predicted to have a substitution price of 41.20% of the mutation price, introns and UTRs 94.71%, PhastCons areas 0%, and the “different” characteristic 99.98%. For comparability, the substitution charges alongside the human lineage (as a proportion to the substitution price in putatively impartial areas) are 74.15% in UTRs, 92.44% in introns, 50.96% in coding sequences, and 49.56% in PhastCons areas. The massive discrepancy between predicted and noticed PhastCons substitution charges is pushed by our DFE estimates suggesting that the majority of mass is on choice coefficients larger than 10^{−3}, which don’t have any probability of fixation in a inhabitants of *N*_{e} ≈ 10, 000. We be aware that our DFE estimates are qualitatively just like these inferred utilizing the basic BGS mannequin, so the disagreement between noticed divergence and predicted substitution charges might point out a possible mannequin misspecification drawback.

Fig 7. The divergence implied from predicted substitution charges beneath the B’ mannequin versus noticed divergence alongside the human lineage.

Black factors are the PhyloFit divergence price estimates per characteristic (on x-axis). Line ranges are the implied divergences throughout a variety of human-chimpanzee divergence instances of 6–12 Mya (utilizing a technology time of 28 years). We present the expected divergences for our Function (turquoise) and PhastCons precedence (inexperienced) annotation fashions. Moreover, we present the expected PhastCons area divergences when native rescaling is utilized (blue; we omit different domestically rescaled predictions since these to not differ considerably).

#### Doable sign of selective interference.

Given the prediction error for substitution charges in highly-conserved areas and that simulation signifies that *B*(*x*) is extra precisely predicted after we use native rescaling, we modified our composite-likelihood technique in order that it may be run a second time, on B’ maps domestically rescaled by the expected from the preliminary match. Intuitively, that is primarily based on the notion that if a impartial allele experiences a fitness-effective inhabitants dimension of *B*(*x*)*N*, so too ought to a particular allele, and this ought to be thought-about in how the SC16 equations are solved. That is an approximation to selective interference, since interference acts to lowers the efficient inhabitants dimension in different areas [26, 27, 50].

There are 5 necessary however tentative outcomes to attract from this evaluation. First, estimated mutation charges are on the whole larger. Below the CADD 6% mannequin, they’re throughout populations; for the PhastCons Precedence mannequin, they attain the higher restrict of our optimization boundary of *μ* = 8 × 10^{−8} (S1 Text Part 5.1). Second, all of our leave-one-chromosome-out are about one share level larger than the unrescaled mannequin. Third, the DFE estimates for each CADD 6% and PhastCons areas within the PhastCons Precedence mannequin is now U-shaped (S8 Fig), with 70–77% of mass being positioned on a weakly deleterious class, *s* = 10^{−}5. Curiously, that is the to begin with of our fashions the place such an considerable mass has been positioned on a midpoint in our choice coefficient grid; in all different circumstances, non-strongly deleterious estimates had been impartial (*s* = 10^{−8}). Fourth, predicted pairwise variety is sort of an identical to our unique, non-rescaled match (see S9 Fig). Lastly, since native rescaling will increase the DFE mass over *s* < 10^{−3}, mutations in PhastCons areas now have the potential of fixation. We discover that native rescaling the PhastCons Precedence, leads the expected substitution charges in PhastCons areas to be a lot nearer to noticed ranges (blue line, Fig 6).

Lastly, we be aware an necessary caveat about this evaluation. Since native rescaling is completed utilizing the primary spherical of most chance estimates, there’s some risk of statistical “double dipping”, for the reason that *B*(*x*) at this place consists of the contribution of the focal phase that’s being rescaled, and it has already been included within the preliminary match that lead produced the expected *B*(*x*) map. Ideally, one would exclude this phase’s contribution to *B*(*x*); nevertheless, that is computationally unfeasible. Nevertheless, two observations point out our findings listed below are comparatively sturdy regardless of this limitation. First, the outcomes don’t change primarily based on whether or not the *B*(*x*) is averaged on the 1 kbp stage or on the megabase scale; for the latter, a single phase makes little contribution to the common. Second, we investigated the extent to which native rescaling modified the B’ maps throughout choice parameters. We discover minor variations between the domestically rescaled and commonplace B’ maps for fastened choice coefficients (i.e. earlier than mannequin becoming) within the nearly-neutral area (0.2 ≤ 2*N*_{e}*s* ≤ 2). Moreover, the domestically rescaled and commonplace maps are an identical beneath sturdy choice (2*N*_{e}*s* = 20) as anticipated (S10 Fig). Furthermore, the correlations between the usual and domestically rescaled B’ maps throughout the genome are excessive (100% for two*N*_{e}*s* = 20, 96.5% for two*N*_{e}*s* = 2, and 60.21% for two*N*_{e}*s* = 0.2). The general realized impact of native rescaling is to only alter how deep the “U” is within the relationship between the discount issue *B* and the choice coefficient (S11 Fig).

General, this means that fashions of the sign of linked choice are worryingly delicate to the theoretic B’ values within the 2*Ns* ≤ 1 area. The truth that predicted variety differs little between commonplace and domestically rescaled B’ strategies signifies there might not be sufficient data in pairwise variety alone to distinguish when interference is going on or the causes of health variance alongside the genome. Furthermore, native rescaling seems to solely barely alter the B’ maps, but considerably modifies the DFE estimates. This brings the deleterious substitution price in settlement with observations (since that is predicted with a hard and fast *μ* = 1.5 × 10^{−8}; nevertheless, the utmost chance estimate of mutation is implausibly excessive. This implies both the native rescaling approximation to interference isn’t appropriate (although our chromosome-wide simulations present domestically rescaled B’ maps are near the reductions noticed from simulations), or that the deleterious mutations-only mannequin doesn’t adequately describe the processes producing health variance.

## Dialogue

New mutations at functionally necessary areas of the genome are a significant supply of health variation in pure populations, because the overwhelming majority of such mutations are deleterious. Purifying choice, working to take away these deleterious variants, perturbs genealogies at linked websites, creating large-scale patterns in genomic variety. Whereas this has been acknowledged for many years [8, 17], the provision of genomic information permits for strategies to estimate the diploma to which purifying choice shapes genomic variation and at what scale.

Accordingly, there have been various latest efforts to suit parametric fashions of linked choice to polymorphism and divergence information in Drosophila [15] and people [14, 16]. These efforts have yielded affordable estimates of the energy of choice on new mutations in addition to offered mutation price estimates that largely agree with pedigree-based estimates. Nevertheless, earlier strategies have relied on the canonical background choice mannequin, which assumes that mutations are sufficiently deleterious such that they can’t repair. Consequently, statistical strategies utilizing the BGS mannequin ought to solely be anticipated to suit effectively when some areas are *a priori* beneath sturdy selective constraint. In actuality, the connection between impartial variety ranges and the energy of choice from purifying choice in linked areas is U-shaped, which suggests there might be extra uncertainty than beforehand appreciated within the distribution of weak and strongly deleterious mutations.

On this work, we developed and match a special class of linked choice fashions primarily based on the equilibrium health variance [28, 29]. Basically, we mannequin the discount in variety as a operate of how additive health variance is distributed alongside the recombination map of the genome [28]. We match a particular mannequin for this health variance that supposes all variation is the results of choice in opposition to new additive deleterious mutations [29]. Not like basic background choice principle [8, 11, 13, 17], the SC16 mannequin explains equilibrium health variance throughout all choice coefficients by collectively predicting one other central amount in evolutionary genomics: the substitution price of deleterious alleles.

Our technique has not less than 4 enhancements over earlier whole-genome linked choice strategies primarily based on the BGS mannequin. First, our mannequin results in higher suits to information than these primarily based on basic BGS, as measured by predicted out-of-sample variety. Second, in contrast to BGS-based strategies, our mannequin is able to becoming weak choice. When areas beneath weak or little selective constraint are included in strategies utilizing basic BGS, parameter estimates can change into severely biased. Against this, now we have demonstrated through simulation that our technique can estimate the energy of choice even for weakly constrained options (e.g. introns and UTRs), in addition to remaining unannotated areas of the genome. Third, becoming our mannequin produces a simultaneous prediction of substitution charges, which could be in comparison with noticed divergence charges. Lastly, the impact of selective interference could be approximated by domestically rescaling the B’ maps, which our ahead simulations present scale back prediction error of genome-wide variety ranges.

Although our mannequin is ready to match weak choice, our preliminary estimates of mutation price and DFEs had been according to prior work [16]. This, at first look, suggests additional affirmation that sturdy purifying choice is the dominant mode of linked choice within the genome. Nevertheless, we discover that predicted substitution charges for highly-conserved PhastCons options disagree with noticed charges of divergence alongside the human lineage. This disparity between noticed divergence and predicted substitution charges is probably going a consequence of our DFE estimate for PhastCons areas containing little mass over weakly deleterious and impartial choice coefficients that might have some risk of fixation—a attribute of DFE estimates from different work too [16].

Our simulation outcomes reveal one other doable supply of disagreement: within the weak choice area of two*N*_{e}*s* ≈ 1 there’s an considerable stage of disagreement between principle and simulation. We hypothesize that this might be as a result of as 2*N*_{e}*s* approaches 1, a phase beneath selective constraint experiences a neighborhood fitness-effective inhabitants dimension of *B*(*x*)*N*, and never simply *N*. This native fitness-effective inhabitants dimension is induced by choice at different segments that isn’t being taken into consideration by basic BGS principle or our commonplace SC16 mannequin. Once we experimented by becoming our mannequin after which utilizing the expected discount map to domestically rescale *N*_{e} to the fitness-effective inhabitants dimension , we discovered the disagreement between predicted and noticed substitution charges disappears. That is anticipated since domestically rescaled DFE estimates have an considerable mass on weakly deleterious choice coefficients, opposite to the usual suits.

This sample is according to a state of affairs the place the identical choice processes that scale back variety over lengthy stretches alongside the chromosome additionally lower the efficacy of purifying choice. This concept has been proposed earlier than in an extension to the McDonald–Kreitman check that accounts for a way background choice can bias estimates of the proportion of adaptive substitutions [81]. Whereas our simulation outcomes point out native rescaling reduces error within the weak choice area, it’s value noting some caveats about this method. First, native rescaling is barely an approximation to selective interference; as our simulations present, this approximation reduces error within the predicted discount *B*(*x*), however this will not absolutely account for a way damaging linkage disequilibrium builds up and reduces health variance. A advantage of the SC16 method is that the equations could be solved with a domestically rescaled efficient inhabitants that approximates this course of. Second, there’s the potential of circularity, since a preliminary match have to be made to estimate *B*(*x*), which is then used to re-solve the SC16 equations with a neighborhood fitness-effective inhabitants dimension.

Regardless of these caveats, the native rescaling method suggests selective interference might alter inferences concerning the DFE and produce predicted substitution charges into settlement with noticed divergence charges. Nevertheless, these outcomes additionally show that parameter estimates are extraordinarily delicate to how correct the theoretic B’ maps are on this area. Furthermore, we discover that predicted variety differs little throughout DFE and mutation price estimates, suggesting there could also be restricted data in pairwise variety to distinguish between fashions, thus inclusion of allele or haplotype frequency data is perhaps informative sooner or later. Nonetheless, our mutation and DFE estimates are comparatively secure throughout reference populations, suggesting these estimates should not too noisy, although they might be biased as a result of mannequin misspecification. Whereas native rescaling brings substitution charges into settlement, it additionally re-introduces the same drawback discovered by Murphy et al. [14]: the estimated mutation price is simply too excessive. Whereas our mutation price consists of level mutations in addition to all different types of deleterious variation (e.g. insertions/deletions, copy quantity variants, and so forth.), our estimations recommend exceedingly excessive charges of deleterious variation per technology.

Examination of the native residuals of our predicted variety ranges demonstrated no systematic impact of beforehand recognized exhausting and smooth selective sweeps [75]. This end result echoes what has been noticed in earlier efforts to have a look at genome-wide patterns of linked choice [16, 69], and means that the size of perturbation as a result of choice sweeps is extra restricted (e.g. on the kilobase scale, [82]) than the size at which we’re modeling variation. Taken collectively this means that selective sweeps should not probably answerable for shaping nearly all of variance in large-scale patterns of chromosomal variation in people.

On condition that our mannequin is basically parameterized by ranges of health variance alongside the genome, the excessive estimates of mutation price might recommend that purifying choice isn’t the one supply of health variance producing the genome-wide linked choice sign in people. Choice on polygenic traits might be one other supply of health variance, for the reason that underlying principle suggests ranges of pairwise variety are decided by whole additive health variance (i.e. Eq (2)). Alternatively, purifying choice might be the principle supply of health variance, however the complexity of selective interference could also be poorly approximated by the native rescaling method. One other risk is that our assumption all through of additive results might result in biases given the overwhelming majority of deleterious mutations are partially recessive. Moreover, our method has ignored the potential of again mutations at websites at which there had been a previous deleterious substitution, which can also bias the expected discount in variety. Future theoretic work testing the robustness to those types of mannequin misspecification, maybe with real looking ahead simulations of a number of modes of linked choice (e.g. [83]) are wanted to completely disentangle these processes. Moreover, our DFE estimates are achieved utilizing a discretized logarithmic-spaced grid following earlier work [15, 16]; future work might discover steady and parametric types for the DFE. As we discover proof of sturdy choice in opposition to loss-of-function in our mannequin residuals, it is usually doable that the majority of health variance *is* as a result of purifying choice, however our mannequin is unable to account for sturdy heterogeneity within the DFE per annotation class.

Shifting ahead it stays a central aim to grasp how the sources of health variation form the placing patterns of variety alongside the human genome. Our work embeds this query within the quantitative genetic framework that’s extra correct and versatile than continuing fashions, however there’s a lot work but to do to include necessary inhabitants genetic options similar to dominance results and selective interference. General, the advanced interaction of mutation, choice, drift, and interference might confound our understanding of choice within the human genome for a while.

## Strategies

### Calculating the discount maps

Our technique makes use of the pre-computed equilibria for every phase *g* (specified by the actual annotation mannequin) to calculate the discount map *B*(*x*;*m*_{i}, *s*_{j}) at positions *x* throughout the parameter grids described above. Since we assume multiplicative health, the discount is the product of every phase’s contribution accounting for the recombination is,

(13)

the place *r*_{x,g} is the recombination fraction between the focal website and phase *g*. Right here, *Q*^{2}(*m*_{i}, *s*_{j}, *r*_{x,g}) is given by Eq (3) squared. A separate discount map is calculated for all options *G* inside a particular characteristic kind. We calculate B’ calculate for log_{10}-spaced grids over 10^{−1} ≤ *s* ≤ 10^{−8} and 10^{−11} ≤ *m* ≤ 10^{−7}, in 10kb increments throughout the genome.

### Composite chance and optimization

Following earlier approaches [14–16], we use a composite chance method to suit our damaging choice mannequin. Per-basepair allele rely information (described beneath) is summarized into the variety of identical and completely different pairwise variations per window. All of our major fashions had been match with megabase home windows, since earlier work has discovered the strongest choice sign at this scale (we affirm this with one CADD 6% match on the 100 kbp scale).

Our binomial chance fashions the variety of completely different pairwise comparisons noticed per window given the whole variety of pairwise comparisons. The binomial chance for window *b* is , the place bars point out averages over some bin width. The free parameters *Ψ* = {*π*_{0}, *μ*, **W**} are the anticipated variety within the absence of choice (*π*_{0}), the mutation price (*μ*), and the distribution of health results for the discretized choice grid and *Ok* options (**W**). The discount at place *x* is then,

(14)

See S1 Text Sections 2.5 and three.11 for extra particulars.

Our technique makes use of two methods to enhance optimization over the mutation and DFE parameters. First, we discover our pre-computed *B*(*x*;*μ*, **W**) discount maps (described within the earlier part) are exponential over columns of *μ***W**, which permits for optimization over this clean operate slightly than the grid. Second, we use softmax to transform constrained optimization over the DFE columns (which should sum to at least one) to unconstrained. We examined a number of completely different optimization routines, discovering that BOBYQA outperformed options [85, 86]. We inspected and confirmed convergence with diagnostic plots discovering secure optima throughout 10,000 random begins (see S1 Text Part 3.10). We assessed mannequin match utilizing out-sample predictive error, calculated by leaving out an entire chromosome throughout becoming and predicting its variety. To calculate uncertainty, we used a block jackknife method in 10 Mbp home windows (S1 Text Part 3.13). All mannequin suits, analyses, and produced information can be found on Dryad [87].

### Human inhabitants genomic information

Our analyses was performed on the Yoruba (YRI), European (CEU), and Han Chinese language (CHB) reference pattern people from the high-coverage 1000 Human Genomes information aligned to GRCh38/hg38 [88]. Since nucleotide variety is a ratio estimator, it may be biased when subtly completely different filtering standards are utilized to variant and invariant websites. To stop this, we performed our analyses on Genomic VCF (gVCF) information that comprise genotype requires each variant and invariant websites [89]. Then, we apply the identical genotype filtering standards to all referred to as websites (S1 Text Part 3.2). We additionally utilized sequence accessibility masks that containing solely non-repeat, non-centromeric sequence that handed the 1000 Genomes strict filter ([90]; S1 Part 3.3). Since our principle solely considers the oblique results of linked choice on a website, we moreover masked websites which might be probably beneath direct selective constraint (see S1 Text Part 3.4). Lastly, for each basepair passing these filtering and masking standards, we counted the variety of reference and different allele counts (excluding all multiallelic, indel, and CNV variants).

For all of our foremost analyses, we used the recombination map from Halldorsson et al. [91] estimated from a trio-based design to keep away from circularity that would happen through the use of LD-based maps. We use Ensembl gene annotation [92], a particular CADD Rating dataset with McVicker B scores eliminated (to keep away from circularity; [93, 94]), and PhastCons areas [2]. We didn’t account for mutation price heterogeneity alongside the genome, since this is able to require utilizing divergence-based estimates of native mutation charges that might introduce circularity after we predict divergence charges beneath our mannequin.

### Ahead simulations

We performed ahead simulations of damaging choice on entire human chromosomes to validate our technique at two levels. First, we simulated damaging choice on chromosome 10 utilizing a practical recombination map and putatively conserved options to substantiate that our basic B and new B’ maps matched the common simulation discount map throughout mutation and choice parameters. Second, we evaluated our composite chance technique by simulating damaging choice on the primary 5 human chromosomes, throughout grids of fastened mutation and choice parameters. We then mixed these into an artificial genome, and overlaid mutations on the ARG. Then, we ran our chance strategies on the ensuing allele rely information to evaluate mannequin accuracy. We ran extra artificial genome simulations like these to guage the influence of two mannequin violations: recessivity of deleterious mutations and increasing populations. For the latter, after 9.3 generations, we grew the inhabitants by issue of 1.004 every technology to imitate the human growth out-of-Africa [95]. We didn’t simulate inhabitants bottlenecks since our analyses confirmed little distinction between bottlenecked out-of-Africa samples (CEU and CHB) and YRI samples. Extra particulars about these and the phase simulations proven in Fig 1A–1C could be discovered S1 Text Part 4.

### Substitution price prediction and divergence estimates

Substitution charges had been predicted by resolving Eq (6) for the given estimated product between mutation price and DFE weight, *w*_{i,j} = *μW*_{i,j}. We estimated the divergence alongside the human department utilizing PhyloFit [96] run on a subset of the UCSC 17-way Multiz alignments [97] consisting of people and 4 different primates (*Pongo abelii*, *Pan troglodytes*, *Pan paniscus*, *Gorilla gorilla*). PhyloFit was run utilizing the HKY85 substitution mannequin per-feature; estimates from alternate substitution fashions yielded equal outcomes. Additional particulars about this course of could be be discovered within the GitHub repository (https://github.com/vsbuffalo/bprime).

## Supporting data

### S2 Fig. The utmost chance estimates of *π*_{0} and common choice coefficient implied by the estimated DFE for the CADD 6% fashions.

Diamonds point out estimates beneath the sturdy choice grid (as much as *s* = 10^{−1}) and circles point out estimates beneath the default grid (as much as *s* = 10^{−2}).

https://doi.org/10.1371/journal.pgen.1011144.s003

(TIF)

### S9 Fig. Chromosome 2 predictions on the YRI samples, with domestically rescaled mannequin suits.

The noticed information is the darkish grey line, and the traditional MLE for the PhastCons Precedence mannequin is the blue line. The domestically rescaled predictions are the inexperienced line. The dashed purple line are the prediction utilizing the usual B’ map (with out native rescaling) and the utmost chance estimates from the domestically rescaled suits. The massive discrepancy on this exhibits that estimates are extremely depending on the B’ map.

https://doi.org/10.1371/journal.pgen.1011144.s010

(TIF)

### S10 Fig. The usual (darkish grey) and domestically rescaled (blue) B’ maps for various *μ* = 1.6 × 10^{−8} and three completely different choice coefficients.

For *s* = 10^{−5} (2*N*_{e}*s* = 0.2), domestically rescaling alters the expected discount in order that it’s primarily insignificant (*B* ≈ 1). For mid-strength choice *s* = 10^{−4} (2*N*_{e}*s* = 2), there’s solely a really slight distinction between commonplace and domestically rescaled B’ maps. Lastly, for sturdy choice *s* = 10^{−3} (2*N*_{e}*s* = 20), native rescaling doesn’t change the B’ maps, as anticipated.

https://doi.org/10.1371/journal.pgen.1011144.s011

(TIF)

### S11 Fig. Genome-wide common *B*(*x*) values throughout choice coefficients for *μ* = 1.58 × 10^{−8}, for each the usual (blue) and domestically rescaled B’ (orange) maps.

This means that domestically rescaling the B’ maps solely in follow modifications how deep the “U” is.

https://doi.org/10.1371/journal.pgen.1011144.s012

(TIF)

## Acknowledgments

We wish to thank Doc Edge, Ben Good, Taylor Kessinger, Graham McVicker, Priya Moorjani, David Murphy, Rasmus Nielsen, Man Sella, Joshua Schraiber, and Peter Sudmant for useful discussions, and Martin Kircher for offering modified CADD tracks. We thank Brian Charlesworth, Graham Coop, Matt Hahn, Nate Pope, Enrique Santiago for feedback on the manuscript.

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