Estimating the genome-wide contribution of selection to temporal allele frequency change

Vince Buffaloa,b,1 and Graham Coopb

aPopulation Biology Graduate Group, University of California, Davis, CA 95616; and bCenter for Population Biology, Department of Evolution and Ecology, University of California, Davis, CA 95616

Edited by Montgomery Slatkin, University of California, Berkeley, CA, and approved July 13, 2020 (received for review October 31, 2019)

Rapid phenotypic adaptation is often observed in natural popula- a polygenic trait (such as fitness) is distributed across numerous tions and selection experiments. However, detecting the genome- loci. This can lead to subtle allele frequency shifts on standing wide impact of this selection is difficult since adaptation often variation that are difficult to distinguish from background lev- proceeds from standing variation and selection on polygenic els of genetic drift and sampling variance. Increasingly, genomic traits, both of which may leave faint genomic signals indistin- experimental evolution studies with multiple time points, and guishable from a noisy background of genetic drift. One promis- in some cases multiple replicate populations, are being used ing signal comes from the genome-wide covariance between to detect large-effect selected loci (30, 31) and differentiate allele frequency changes observable from temporal genomic data modes of selection (32–34). In addition, these temporal–genomic (e.g., evolve-and-resequence studies). These temporal covariances studies have begun in wild populations, some with the goal of reflect how heritable fitness variation in the population leads finding variants that exhibit frequency changes consistent with changes in allele frequencies at one time point to be predic- fluctuating selection (35, 36). In a previous paper, we pro- tive of the changes at later time points, as alleles are indirectly posed that one useful signal for understanding the genome-wide selected due to remaining associations with selected alleles. Since impact of polygenic linked selection detectable from temporal genetic drift does not lead to temporal covariance, we can use genomic data is the temporal autocovariance (i.e., covariance these covariances to estimate what fraction of the variation in between two time points) of allele frequency changes (37). These allele frequency change through time is driven by linked selec- covariances are created when the loci that underly heritable tion. Here, we reanalyze three selection experiments to quantify fitness variation perturb the frequencies of linked alleles; in the effects of linked selection over short timescales using covari- contrast, when genetic drift acts alone in a closed population, ance among time points and across replicates. We estimate that these covariances are expected to be zero for neutral alleles. at least 17 to 37% of allele frequency change is driven by selec- Mathematically, temporal covariances are useful because it is tion in these experiments. Against this background of positive natural to decompose the total variance in allele frequency genome-wide temporal covariances, we also identify signals of change across a time interval into the variances and covari- negative temporal covariance corresponding to reversals in the ances in allele frequency change between generations. Further- direction of selection for a reasonable proportion of loci over more, biologically, these covariances reflect the extent to which the time course of a selection experiment. Overall, we find that allele frequency changes in one generation predict changes in in the three studies we analyzed, linked selection has a large another due to shared selection pressures and associations with impact on short-term allele frequency dynamics that is readily selected loci. distinguishable from genetic drift.

Significance linked selection | experimental evolution | adaptation

A long-standing problem in evolutionary biology is to under- long-standing problem in evolutionary genetics is quan- stand the processes that shape the genetic composition of Atifying the roles of genetic drift and selection in shaping populations. In a population without migration, two pro- genome-wide allele frequency changes. Selection can affect allele cesses that change allele frequencies are selection, which frequencies, both directly and indirectly, with the indirect effect increases beneficial alleles and removes deleterious ones, and coming from the action of selection on correlated loci elsewhere genetic drift, which randomly changes frequencies as some in genome [e.g., linked selection (1–4); ref. 5 has a review]. Previ- parents contribute more or fewer alleles to the next gener- ous work has mostly focused on teasing apart the impacts of drift ation. Previous efforts to disentangle these processes have and selection on genome-wide diversity using population sam- used genomic samples from a single time point and models ples from a single contemporary time point, often by modeling of how selection affects neighboring sites (linked selection). the correlation between regional recombination rate, gene den- Here, we use genomic data taken through time to quantify sity, and diversity created in the presence of linked selection (6, contributions of selection and drift to genome-wide frequency 7). This approach has shown that linked selection has a major changes. We show that selection acts over short timescales role in shaping patterns of genome-wide diversity across the in three evolve-and-resequence studies and has a sizable genomes of a range of sexual species (8–16) and has allowed us genome-wide impact. to quantify the relative influence of positive selection (hitchhik- ing) and negative selection (background selection) (8, 9, 16–19). Author contributions: V.B. and G.C. designed research; V.B. performed research; V.B. con- However, we lack an understanding of both how linked selection tributed new reagents/analytic tools; V.B. analyzed data; and V.B. and G.C. wrote the acts over short time intervals and its full impact on genome-wide paper.y allele frequency changes. The authors declare no competing interest.y There are numerous examples of rapid phenotypic adapta- This article is a PNAS Direct Submission.y tion (20–23) and rapid, selection-driven genomic evolution in Published under the PNAS license.y asexual populations (24–26). Yet, the polygenic nature of fit- 1 To whom correspondence may be addressed. Email: [email protected] ness makes detecting the impact of selection on genome-wide This article contains supporting information online at https://www.pnas.org/lookup/suppl/ variation over short timescales in sexual populations remark- doi:10.1073/pnas.1919039117/-/DCSupplemental.y ably difficult (27–29). This is because the effect of selection on First published August 12, 2020.

20672–20680 | PNAS | August 25, 2020 | vol. 117 | no. 34 www.pnas.org/cgi/doi/10.1073/pnas.1919039117 Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 ufl n Coop and Buffalo selection, in linked matrix by covariance temporal explained 95 the change the with frequency replicates, allele across in averaged variance total ( color the same of the with matrix covariance temporal the oaineCov(∆p covariance 1. Fig. genome- the estimated we populations, wide replicate 10 time seven and the Using points evolve- generations. 10 an every sequenced gener- (33), and 60 ations, for al. a evolved to et environment, exposed laboratory Barghi populations high-temperature replicate of 10 with dataset study the and-resequence analyzed first We Results experimental allele in genome-wide timescales shaping short in very evolution. role over changes powerful frequency a linked allele has that between demonstrate selection we correlation change Overall, con- pressures. the frequency by selection caused as vergent allele populations replicate well in between changes as variance frequency selection, of would by lower fraction approaches a caused estimate the other We of drift. that genetic bound manner from differentiate a able changes be in not frequency genome allele acting the genome-wide selection from across signal perturb linked a far significantly with find yet consistent repeatedly to are We covariance, as changes drift. temporal frequency is genetic of or allele it selection genome-wide contribut- by however, of driven loci response; much adaptive how selected clear the uncover to to ing started selection sequencing have These experiments gener- (39). an experiment of and selection (tens 38) (33, artificial timescales studies short evolve-and-resequence two over across ations) acting selection linked of B A ee epoieeprclaaye oqatf h impact the quantify to analyses empirical provide we Here, 6 eprlcvrac,aeae cosal1 elct ouain,truhtm rmteBrh ta.(3 td.Ec iedpcstetemporal the depicts line Each study. (33) al. et Barghi the from time through populations, replicate 10 all across averaged covariance, Temporal (A) × 6 eprlcvrac matrix covariance temporal s , ∆p t rmsm eeec generation reference some from ) Right % sbigicue ntecluainof calculation the in included being is lc otta I h te ie r the are lines other The CI. bootstrap block Q o aho h 10 the of each for Right .Terne rudec on r 95% are point each around ranges The ). s oaltrtime later a to t hc aisaogthe along varies which , G(t etwehrlreotirrgosdietegnm-iesignal genome-wide To the regions. drive outlier regions few outlier a large by whether affected test strongly be could estimate pattern S23). general Fig. this tempo- Appendix, but (SI noisier, The holds are (37). replicate new per weakens) a covariances selection for reaches ral population directional variance a and genetic as occur optimum additive could associated (which decays the fitness disequi- and linkage linked (LD) ultimately affects librium until selection trajectories directional intervals frequency time when The distant variants’ expected more as periods. at look 1A), and we time (Fig. as positive zero are short toward intervals decay time very then adjacent all over between changes covariances contain genome-wide perturbing not frequency selection do allele linked CIs with bootstraps temporal consistent block sta- zero), replicate are (95% that 10 significant covariances temporal can tistically the find fitness we across closed matrices, for a covariances Averaging variation in changes (37). heritable frequency only population allele as between when covariance zero acting, be create and is to expected noise drift are sampling covariances only sections These to Appendix, S1.4). (SI and due heterozygosity S1.2 for created entries biases the normalized for matrices these point time later generation reference tempo- denoted tial the intervals, 10-generation represents (in matrices change these covariance of ral row Each replicates. G(t ). ic u oaine r vrgsoe oi h covariance the loci, over averages are covariances our Since ,a tvre hog time through varies it as ), G(t o ahidvda elct,wt oosidctn htsbe of subset what indicating colors with replicate, individual each for ) Cov(∆ oe on nteproportion the on bound lower A (B) CIs. bootstrap block PNAS x t xs ahln orsod oarwo h rageof triangle the of row a to corresponds line each axis; teclm ftemti) ecorrected We matrix). the of column (the 10 10 | 1020304050600 p uut2,2020 25, August s ∆ , s t 20 ln the along terwo h arx n some and matrix) the of row (the 10 p 30 t ) ewe h leefrequency allele the between 40 x xs h lc iei the is line black The axis. | 50 o.117 vol. ∆ 60 10 p | t fsm ini- some of ) o 34 no. | 20673 G(t )

EVOLUTION we see in the Barghi et al. (33) data, we calculate the covari- negative covariances between dissimilar seasonal changes (e.g., ances in 100-kb windows along the genome (we refer to these spring–fall and fall–spring in two adjacent years). However, we as windowed covariances throughout) and take the median win- find no such signal over years, and in reproducing their original dowed covariance (and trimmed-mean windowed covariance) analysis, we find that their number of statistically significant sea- as a measure of the genome-wide covariance robust to large- sonal polymorphisms is not enriched compared with an empirical effect loci. These robust estimates (SI Appendix, Table S1 and null distribution created by permuting seasonal labels (we discuss Fig. S24) confirm the patterns we see using the mean covariance, this in more depth in SI Appendix, section S6). establishing that genomic temporal covariances are nonzero The replicate design of Barghi et al. (33) allows us to quantify due to the impact of selection acting across many genomic another covariance: the covariance in allele frequency change regions. between replicate populations experiencing convergent selec- While the presence of positive temporal covariances is con- tion pressures. These between-replicate covariances are created sistent with selection affecting allele frequencies over time, in the same way as temporal covariances: alleles linked to a this measure is not easily interpretable. We can calculate particular fitness background are expected to have allele fre- a more intuitive measure from the temporal covariances to quency changes in the same direction if the selection pressures quantify the impact of selection on allele frequency change: are similar. Intuitively, where temporal covariances reflect that the ratio of total covariance in allele frequency change to alleles associated with heritable fitness backgrounds are pre- the total variance in allele frequency change. We denote the dictive of frequency changes between generations, replicate change in allele frequency as ∆pt = pt+1 − pt , where pt is covariances reflect that heritable fitness backgrounds common to the allele frequency in generation t. Since the total variation each replicate predict (under the same selection pressures) fre- in allele frequency change can be partitioned into variance quency changes between replicates; we note that there is not a Pt−1 and covariance components, Var(pt − p0) = i=0 Var(∆pi ) + direct one-to-one correspondence between temporal and repli- Pt−1 Pt−1 cate covariances since the latter are driven by a shared selection Cov(∆pi , ∆pj ) (we correct for biases due to i=0 j 6=i pressure and the stochastic genetic backgrounds across replicate sequencing depth), and the covariances are zero when drift acts populations. We measure this through a statistic similar to a alone, this is a lower bound on how much of the variance in allele correlation, which we call the convergent correlation: the ratio frequency change is caused by linked selection (37). We call this of average between-replicate covariance across all pairs to the measure G(t), defined as average SD across all pairs of replicates: Pt−1 Pt−1 Cov(∆pi , ∆pj ) i=0 j 6=i EA6=B (Cov(∆ps,A, ∆pt,B )) G(t) = . [1] cor(∆ps , ∆pt ) = , [2] Var(pt − p0) p  EA6=B Var(∆ps,A)Var(∆pt,B ) This estimates the impact of selection on allele frequency change between the initial generation 0 and some later generation t, where A and B here are two replicate labels, and for the Barghi

which can be varied to see how this quantity grows through time. et al. (33) data, we use ∆10 pt . When the sum of the covariances is positive, this measure can We have calculated the convergent correlation for all rows of intuitively be understood as a lower bound on relative fraction the replicate covariance matrices. Like temporal covariances, we of allele frequency change normally thought of as “drift” that visualize these through time (Fig. 2 A, Left), with each line rep- is actually due to selection. Additionally, G(t) can be under- resenting the convergent correlation from a particular reference stood as a short-timescale estimate of the reduction in neutral generation s as it varies with t (shown on the x axis). In other diversity due to linked selection (or equivalently, the reduction words, each of the colored lines corresponds to the like-colored in neutral effective population size needed to account linked row of the convergence correlation matrix (Fig. 2 A, Right). We selection) (SI Appendix, section S7). Since the Barghi et al. (33) find that these convergent correlation coefficients are relatively experiment is sequenced every 10 generations, the numerator weak and decay very quickly from an initial value of about 0.1 uses the covariances estimated between 10-generation blocks of (95% block bootstrap CIs [0.094, 0.11]) to around 0.01 (95% CIs allele frequency change; thus, the strong, unobservable covari- [0.0087, 0.015]) within 20 generations. This suggests that while ances between adjacent generations do not contribute to the a substantial fraction of the initial response is shared over the numerator of G(t). Had these covariances been measurable on replicates, this is followed by a rapid decay, a result consistent shorter timescales, their cumulative effect would likely have been with the primary finding of the original Barghi et al. (33) study: higher yet (SI Appendix, sections S2 and S8.4 have more details). that alternative loci contribute to longer-term adaptation across Additionally, selection inflates the variance in allele frequency the different replicates. change per generation; however, this effect cannot be easily dis- A benefit of between-replicate covariances is that unlike tinguished from drift. For both these reasons, our measure G(t) temporal covariances, these can be calculated with only two is quite conservative (we demonstrate this through simulations sequenced time points and a replicated study design. This in SI Appendix, section S8.4). Still, we find a remarkably strong allowed us to assess the impact of linked selection in driving signal. Greater than 20% of total, genome-wide allele frequency convergent patterns of allele frequency change across repli- change over 60 generations is the result of selection (Fig. 1B). cate populations in two other studies. First, we reanalyzed the This proportion of variance attributable to selection builds over selection experiment of Kelly and Hughes (38), which evolved time in Fig. 1B as the effects of linked selection are compounded three replicate wild populations of Drosophila simulans for over the generations unlike genetic drift. Our G(t) starts to 14 generations adapting to a novel laboratory environment. plateau to a constant level as the covariances from earlier gen- Since each replicate was exposed to the same selection pres- erations have decayed and so, no longer contribute as strongly sure and shared LD common to the original natural founding (Fig. 1). population, we expected each of the three replicate popula- Additionally, we looked for a signal of temporal autocovari- tions to have positive convergence correlations. We find that ance in Bergland et al. (35), a study that collected Drosophila all three convergent correlation coefficients between replicate melanogaster through spring–fall season pairs across 3 years. If pairs are significant (Fig. 2B) and average to 0.36 (95% CI there was a strong pattern of genome-wide fluctuating selection, [0.31, 0.40]). Additionally, we can calculate the proportion of the we might expect a pattern of positive covariances between simi- total variance in allele frequency change from convergent selec- lar seasonal changes (e.g., spring–fall in two adjacent years) and tion pressure, analogous to our G(t), where the numerator is the

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EVOLUTION observed covariance between replicates (Materials and Methods and SI Appendix, section S4 have more details). We estimate at least 32% (95% CI [21%, 48%]) of the variance in allele fre- quency change is driven by the effects of selection, of which 14% (95% CI [3%, 33%]) is estimated to be unique to a selection line, and 17% (95% CI [9%, 23%]) is the effect of shared selection k = 2 between the two Longshanks selection lines. A We observed that in the longest study we analyzed (33), some genome-wide temporal covariances become negative at future time points (the first two rows in Fig. 1 A, Left). This shows that alleles that were on average going up initially are later going down in frequency (i.e., that the average direc- tion of selection experienced by alleles has flipped). This might reflect either a change in the environment or the genetic back- ground, due to epistatic relationships among alleles altered by frequency changes (which can occur during an optima shift; ref. 43) or recombination breaking up selective alleles. Such reversals in selection dynamics could be occurring at other time points, but the signal of a change in the direction of selec- tion at particular loci may be washed out when we calculate our genome-wide average temporal covariances. To address this limitation, we calculated the distribution of the temporal covariances over 100-kb windowed covariances (Fig. 3 shows B k = 4 these distributions pooling across all replicates, and SI Appendix, Fig. S26 shows individuals replicates). The covariance estimate of each genomic window will be noisy, due to sampling and genetic drift, and the neutral distribution of the covariance is complicated due to LD, which can occur over long physical dis- tances in evolve-and-resequence and selection studies (44, 45). To address this, we have developed a permutation-based pro- cedure that constructs an empirical neutral null distribution by randomly flipping the sign of the allele frequency changes in each genomic window (i.e., a single random sign flip is applied to all loci in a window). This destroys the systematic covariances created by linked selection and creates a sampling distribu- tion of the covariances spuriously created by neutral genetic drift while preserving the complex dependencies between adja- cent loci created by LD. This empirical neutral null distribution C is conservative in the sense that the variances of the covari- ances are wider than expected under drift alone, as selection upper tail not only creates covariance between time intervals but also, inflates the magnitude of allele frequency change within a time interval. We see (Fig. 3 A and B) that there is an empirical excess of windows with positive covariances between close time points compared with the null distribution (a heavier right tail) lower tail and that this then shifts to an excess of windows with nega- tive covariances between more distant time points (a heavier left tail). We quantified the degree to which the left and right tails are inflated compared with the null distribution as a function of time and see excesses in both tails in Fig. 3C. This finding is also robust to sign-permuting allele frequency changes on a chromo- Fig. 3. (A and B) The distribution of temporal covariances calculated in some level, the longest extent that gametic LD can extend (SI 100-kb genomic windows from the Barghi et al. (33) study plotted alongside Appendix an empirical neutral null distribution created by recalculating the windowed , Fig. S29). We see a striking pattern that the windowed covariances on 1,000 sign permutations of allele frequency changes within covariances not only decay toward zero but in fact, become neg- tiles. The number of histogram bins is 88, chosen by cross-validation (SI ative through time, consistent with many regions in the genome Appendix, Fig. S25). In A, windowed covariances Cov(∆pt , ∆pt+k) are sep- having had a reversed fitness effect at later time points. arated by k = 2 × 10 generations, and in A, the covariances are separated Finally, we used forward-in-time simulations to explore the by k = 4 × 10 generations; each k is an off diagonal from the variance conditions under which temporal and convergent correlations diagonal of the temporal covariance matrix (cartoon of upper triangle of arise. We show a subset of our results for a model of stabi- covariance matrix in A and B, where the first diagonal is the variance, and lizing selection on a phenotype where directional selection is the dark gray indicates which off diagonal of the covariance matrix is plot- induced by a sudden shift in the optimum phenotype of varying ted in the histograms). (C) The lower and upper tail probabilities of the magnitudes (Fig. 4A). We find that positive temporal covari- observed windowed covariances, at 20 and 80% quintiles of the empir- B ical neutral null distribution, for varying time between allele frequency ances are produced by such selection (Fig. 4 ) and that these changes (i.e., which off diagonal k). The CIs are 95% block bootstrap CIs, positive temporal covariances can compound together to gener- and the light gray dashed line indicates the 20% tail probability expected ate a large proportion of allele frequency change being due to under the neutral null. Similar figures for different values of k are in SI selection [i.e., large G(t)] over the relatively short time peri- Appendix, Fig. S27. ods similar to our analyzed selection datasets span (Fig. 4C).

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EVOLUTION to selection or create spurious covariances when selection is experiments, selection pressures may have been stronger or more not acting. However, these spurious covariances do not share sustained than in natural populations (51, 52). Conversely, these a directional signal, whereas the covariances created by linked laboratory populations were maintained at relatively small cen- selection do; consequently, averaging across the entire genome, sus sizes (Table 1), which will amplify the role of genetic drift, the temporal signal exceeds sampling noise. and increase the frequency of rare deleterious alleles in selection Our analyses reveal that a sizable proportion of allele fre- lines due to founder effects. The advantage of laboratory experi- quency change in these experimental evolution populations is ments is that they are closed populations; in natural populations, due to the (likely indirect) action of selection. Capitalizing on temporal covariance could also arise from the systematic migra- replicated designs, we characterized the extent to which con- tion of alleles from differentiated populations. Adapting these vergent selection pressures lead to parallel changes in allele methods to natural populations will require either populations frequencies across replicate populations and found that a sub- that are reasonably closed to migration or the effect of migration stantial proportion of the response is shared across short to be accounted for possibly either by knowledge of allele fre- timescales. These likely represent substantial underestimates quencies in source populations or the identification of migrant of the contribution of linked selection because the studies we individuals. have reanalyzed do not sequence the population each gen- While it challenging to apply temporal methods to natural eration, preventing us from including the effects of stronger populations, there is a lot of promise for these approaches (35, correlations between adjacent generations. Furthermore, our 36). Efforts to quantify the impact of linked selection have found estimation methods are intentionally conservative: for example, that obligately sexual organisms have up to an 89% reduction they exclude the contribution of selection that does not persist in genome-wide diversity over long time periods (16, 18, 53–55) across generations and selection that reverses sign; thus, they Thus, linked selection makes a sizable contribution to long-term can be seen as a lower bound of the effects of selection, which allele frequency change in some species, and there is reason we have confirmed through forward-in-time simulations. Finally, to be hopeful that we could detect this from temporal data, through simulation results, we show that for a given level of which would help to resolve the timescales that linked selection additive genetic variance, the strengths of temporal and repli- acts over in the wild. In our reanalysis of the Barghi et al. (32) cate covariances depend on the mode of selection, the details study, we find evidence of complex linked selection dynamics, of the populations or selection experiment, and the level of with selection pressures flipping over time due to environmental LD, yet the level of temporal covariance is relatively invari- change, the breakup of epistatic combinations, or advantageous ant to the number of loci underlying fitness, as long as fitness haplotypes. Such patterns would be completely obscured in sam- is sufficiently polygenic. ples from only contemporary populations. Thus, we can hope to These estimates of the contribution of selection could be have a much richer picture of the impact of selection as tempo- refined by using patterns of LD and recombination, which would ral sequencing becomes more common, allowing us to observe allow us to more fully parameterize a linked selection model of the effects of ecological dynamics in genomic data (52). temporal allele frequency change (37). The basic prediction is Furthermore, understanding the dynamics of linked selection that regions of higher LD and lower recombination should have over short timescales will help to unite phenotypic studies of greater temporal autocovariance than regions with lower LD and rapid adaptation with a detectable genomic signature to address higher recombination. However, one limitation of these pooled long-standing questions concerning linked selection, evolution- sequence datasets is that none of the studies we reanalyzed esti- ary quantitative genetics, and the overall impact selection has on mated LD data for the evolved populations. While there are genetic variation. LD data for a natural population of D. simulans (49, 50), we did not find a relationship between temporal covariance and Materials and Methods LD. We believe that this is driven by the idiosyncratic nature of Datasets Analyzed. We used available genomic data data from four stud- LD in evolve-and-resequence populations, which often extends ies: pooled population resequencing data from Barghi et al. (33), Kelly and over large genomic distances (38, 44). Future studies complete Hughes (38), and Bergland et al. (35) and individual-level sequencing data from Castro et al. (39). In all cases, we used the variants kept after the with LD data and recombination maps would allow one to filtering criteria of the original studies. disentangle the influence of closely linked sites from more distant sites in causing temporal autocovariance and allow the fitting of Variance and Covariance Estimates. To remove systematic covariances in more parametric models to estimate population parameters such allele frequency change caused by tracking the reference or minor as the additive genetic variance for fitness directly from tempo- allele, we randomly choose an allele to track frequency for each locus. ral genomic data alone (37). Future work could refine our G(t) Then, we calculate the variance–covariance matrix of allele frequency estimates by including selection’s impact on the variance in allele changes using a Python software package we have written, available at frequency terms (e.g., equation 26 of ref. 37) and possibly quan- http://github.com/vsbuffalo/cvtk. This simultaneously calculates temporal tifying the covariances missed when sequencing is not done each variances and covariances and replicate covariances and uses the sampling depth and number of diploid individuals to correct for bias in the variance generation; both would lead to less conservative estimates that estimates and a bias that occurs in covariance estimates between adjacent could show a large impact of selection. time points due to shared sampling noise (SI Appendix, sections S1.2–S1.4 Our primary focus here has been on evolution in laboratory have mathematical details of these estimators). We assess that our bias populations. It is unclear whether we should expect a similar correction procedure is working adequately through a series of diagnos- impact of selection in natural populations. In some of these tic plots that ensure that the procedure removes the relationship between

Table 1. Summary of the main selection studies we analyzed Study Species Selection Replicates Population size* Generations Time points

Kelly and Hughes (38) D. simulans Laboratory adaptation 3 ∼1,100 14 2 Barghi et al. (33) D. simulans Laboratory adaptation 10 ∼1,000 60 7 Castro et al. (39) Mus musculus Tibiae length 2 32 17 2 Mus musculus Control 1 28 17 2

*Approximate census population size during experiment.

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(to (to 1353380 1650042 Grant NSF supported Grant and was G.C.), Fellowship (to research Research R01-GM108779 This Graduate whose manuscript. reviewer NSF anonymous the by an improved and greatly Langley, Sella discus- Guy Chuck comments helpful for thank Kern, Yair we Sivan Andy Additionally, and Friedman, sions. Ralph, Peter Sarah and Osmond, Matt Calfee, Turelli, Rolian, Erin Michael Campbell Begun, Petrov, Dave Frank Dmitri and Bergland, Kelly, Alan Schl John Barton, Christian Hughes, Nick Kimberly Barghi, Neda Chan, including analyzed, have from downloaded ACKNOWLEDGMENTS. were data 65) and (39, mpg.de/fml/ag-chan/Longshanks/. al. , et Castro https://datadryad.org/stash/dataset/doi:10.5061/dryad.v883p from and 6) l aaaefo rvossuisadaalbe agie l 3,62) (33, al. et from Barghi available; downloaded and studies were previous from data are GitHub, data on All available (61). are reproduce to analyses notebooks and these code reanalysis (57–60); notebooks Jupyter and Availability. Data frequency covariances, population temporal the neutral correlations. calculated convergence the and we trajectories, Using simulations, to these ). S7 response from directional Fig. expected data expected as Appendix , the converged (SI showed it trait that selection a the saw (as (con- we and shifted mean, burn-in, direction trait optima during same the one the tracking only in By or were control). (diverging), generations shifts four directions optima first different These the verging), with control. 5, a generation on as 1 serving or an 0.5, underwent diploids, 0.1, then of 1,000 population shift and Each optima bottleneck). 500, no 50, representing between latter varied the exper- different sizes optimum selection two population in the into bottlenecks (these of to split iments effect was converged the capture population it to the populations that burn-in, replicate the found After we expected. burn-in, as the a through have in mean to Mb selected 50 randomly a was were region of simulated one-quarter Our (about covariances. length temporal the calculate mutation to 10 trait of the mutation purposes setting neutral illustrative by for architecture 10 to are polygenic rate they a and simulated We population, reflect- only. natural as taken specific be not any should ing simulations these that means size population invariance 10N tion for GSS under hereafter) burn-in of ulation detail. in others and routines el n uhs(8 3 aawr onoddfrom downloaded were data 63) (38, Hughes https://gsajournals.figshare.com/articles/Supplemental and Kelly dryad.rr137kn, .P nofto ichkn fet frcretbnfiilaioai substitu- acid amino beneficial recurrent of corre- spatial effects Genomewide Hitchhiking Petrov, Andolfatto, A. P. D. 9. Davis, C. J. Sella, G. the Macpherson, in selection M. natural J. Pervasive Andolfatto, 8. P. Przeworski, M. Petrov, A. D. Sella, G. 7. esmltddrcinlslcino ri yfis vligec pop- each evolving first by trait a on selection directional simulated We in nthe in tions reveals polymorphism in neutral adaptation and extensive divergence nonsynonymous between spondence Drosophila h az genome. maize the in divergence and (2007). 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PLoS eto S8 section Appendix, SI Drosophila. −8 etakteatoso h rgnlsuiswe studies original the of authors the thank We hc rae eta uain htw used we that mutations neutral created which , | uut2,2020 25, August 68 (2016). 16084 2, oepoehwapcso eei architec- genetic of aspects how explore To https://datadryad.org/resource/doi:10.5061/ 1045(2009). e1000495 5, Drosophila Genetics 1efc ie ytakn h trait the tracking By size. effect ±0.01 LSBiol. PLoS eeain ihtesaiiigselec- stabilizing the with generations genome. 0329 (2007). 2083–2099 177, https://github.com/vsbuffalo/cvtk/ hoooe,adtatalleles trait and chromosome), 30(2007). e310 5, | o.117 vol. ecie hs simulation these describes eoeRes. Genome http://ftp.tuebingen. Material | o 34 no. 1755–1762 17, for | Kelly 20679 G(t )

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