Estimating fitness effects of mutations in the presence of genetic linkage

Estimating fitness effects of mutations in the presence of genetic linkage | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Estimating fitness effects of mutations in the presence of genetic linkage S.V. Lagunov , View ORCID Profile I.M. Rouzine doi: https://doi.org/10.1101/2025.11.26.690712 S.V. Lagunov 1 Sechenov Institute of Evolutionary Physiology and Biochemistry Russian Academy of Sciences , St Petersburg, Russia Find this author on Google Scholar Find this author on PubMed Search for this author on this site I.M. Rouzine 1 Sechenov Institute of Evolutionary Physiology and Biochemistry Russian Academy of Sciences , St Petersburg, Russia Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for I.M. Rouzine For correspondence: igor.rouzine{at}iephb.ru Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF ABSTRACT Probabilistic prognosis of the evolution of population requires the knowledge of the fitness effects of mutations at different genomic sites. However, the signature of natural selection is eclipsed by strong noise in data, because the common ancestors of different sites render their evolution inter-dependent. Together with mutation and recombination, genetic linkage also makes evolution stochastic and requires averaging over many independent populations. Here we develop a method designed to work in the presence of strong linkage effects. For testing, we apply it to simulated genomic sequences generated by a Monte Carlo algorithm with known selection coefficients. Results demonstrate the good accuracy of the estimates of relative selection coefficients, if more than ten independent populations are used for averaging. Infrequent recombination partly compensates linkage effects and improves the accuracy. The method is then used to estimate the selection coefficients of 10,000 genomic sites of E. coli . These findings enable the inference of adaptive landscape under the conditions of strong multi-site linkage. AUTHOR SUMMARY Probabilistic prognosis of evolution of an organism requires the knowledge of fitness effects of mutations at different genomic sites. However, genetic linkage between different sites due to their common phylogenetic history obscures the effects of natural selection. Here we develop a linkage-resistant method to infer fitness effects and test its accuracy on mock sequences generated by an evolutionary algorithm with known fitness effects. Results demonstrate fair accuracy when averaging is performed over ten or more independently-evolving populations. After application of this program to genomic data for E. coli , relative selection coefficients for thousands of genomic sites are obtained. INTRODUCTION Evolutionary dynamics of a population of DNA sequences is controlled by the interplay of various evolutionary factors, including random mutation, natural selection, genetic drift, and recombination. Of central interest is adaptation to a new environment, which occurs due to emergence of rare mutations that increase the fitness of the organism (average progeny number). Deleterious mutations emerge during adaptation as well. The advantage of each favorable or deleterious mutation is measured by the relative change it causes in fitness. Thus, the knowledge of fitness effects for different mutations is essential for predicting the evolutionary trajectory. Measuring fitness effects of mutations directly is possible only in some cases, for example, in viruses and bacteria, but even then it requires rather elaborate experiments [ 1 - 5 ]. Therefore, a great effort has been invested in their estimation from genomic data using simplifying models. The average fitness effect of a beneficial mutation in HIV genome was estimated using genetic samples from infected patients and an one-site model [ 6 ]. Selection coefficients in the hemagglutinin gene of influenza A H3N2 were estimated by fitting the predictions of one-site and two-site models to the time-series sequence data on the hemagglutinin gene of influenza virus A H3N2 [ 7 ]. Another group [ 8 ] proposed a method of estimating selection coefficients of deleterious mutations based on an assumption about the form of fitness effect distribution among loci. In SARS-CoV-2, fitness effects of mutations were computed as the natural logarithm of the ratio of their actual to expected counts, with a correction for the codon founder effect [ 9 ]. One-locus Wright-Fisher model was used to estimate selection coefficients from genomic data for Sindbis virus [ 10 ]. A major complication in predicting the evolutionary trajectory and estimating the fitness effects of mutations is that the evolution of different sites is coupled due to their common phylogeny. Because different sites share ancestors, genetic linkage effects between them arise, including clonal interference and the genetic background effect [ 11 ]. Linkage limits the use of one-site and two-site models for the inference of observable properties, and a more complex framework taking into account a large number of genomic sites must be used [ 12 , 13 ]. The multi-site linkage modifies all evolutionary observables, from the evolution rate and fitness distribution[ 12 , 14 ] to phylogenetic properties [ 15 - 17 ]. Recombination compensates linkage effects, but only partly [ 15 , 18 - 20 ]. The multi–site models have been successfully applied to predict evolutionary parameters of several pathogenic viruses, including HIV [ 21 ] and influenza [ 22 - 26 ]. Of great practical importance is the ability to predict virus evolution, in the probabilistic sense, with the goal of optimizing vaccines and antiviral drugs [ 27 ], with the caveat that vaccines can expedite the rate of virus evolution [ 28 ]. Based on multi-site models, methods of predicting the fitness of whole virus strains from their position on the phylogenetic trees [ 29 ] and from the immune memory of extinct strains [ 24 , 30 ] have been developed. In addition to whole strains, the evolution of specific genomic sites represents biomedical interest as well, which brings us back to estimating their selection coefficients. A recent modeling work [ 31 ] demonstrated that, when many genomic sites adapt slowly, alleles are distributed among genomes and sites to maximize disorder at any one time. The average evolutionary dynamics of separate sites was mapped onto an one-site model, where time is effectively slowed down by a factor, the same for all sites [ 32 , 33 ]. These findings allowed to develop a method estimating the relative fitness effects of mutations from the evolutionary dynamics, without neglecting linkage effects [ 33 ]. In the present work, we test the accuracy of this method [ 32 , 33 ] on simulated sequences with known fitness effects of mutations. Then, the method is applied to the genomic data on Escherichia coli . RESULTS Linkage-proof method to estimate the fitness effect of mutation We determined the relative influence of individual mutations on fitness (selection coefficient) by using a time series of allelic frequencies at many sites and averaging them across independently-evolving populations. Genomic samples were collected at multiple time points from several independent populations. All genomes were aligned, and the consensus of the entire dataset was found. At each polymorphic site and each time point, the frequency of minority allele was calculated. The relative value of the selection coefficient was estimated for each site, using a procedure described in Methods . Computer model of population The accuracy of the method was tested on artificial sequences generated by a Monte Carlo algorithm of Wright–Fisher type. An individual genome was represented by a binary sequence showing an allele at each locus, one of the two possible. In each generation, the population was replaced with a new one, taking into account the effects of mutation, natural selection, random genetic drift, genetic linkage, and occasional recombination. Fitness of a genome (average progeny number) was calculated from the sum of beneficial alleles weighted with their fitness effects set in the program. See Methods for the details. Testing the accuracy of the method Before applying the method to real biological data, a series of computational experiments was conducted on simulated binary sequence data to test the accuracy. We applied the algorithm to sequences obtained from simulations, where all parameters are set in advance including the value of selection coefficient, denoted s i , at each genomic site i . Using the method described above, for each time point t m , we estimated the relative value of selection coefficient for each site in the form β ( t m ) s i , where β ( t ) is a function of time ( Methods ). To verify the accuracy of the predicted values of selection coefficients, they were compared with the known values of selection coefficients. Results demonstrate fairly good linear correlation between the inferred and the actual values ( Figure 1 ). Download figure Open in new tab Figure 1. Selection coefficients plotted against their estimates. X-axis: values of s set in the simulation. Y-axis: their estimates in relative units, βs . Red line: linear fit with slope β = 2.5 and correlation r 2 = 0.46. (For L = 100, r 2 = 0.93.) Simulation parameters: initial mutation frequency f 0 = 0.5, mutation rate µL = 0.07, uniform distribution of selection coefficients with average s = 0.1, population size N = 1000, the number of simulation runs run = 50, genome length L = 400, no recombination. To determine under which parameter values the highest accuracy was achieved, Pearson correlation coefficient was calculated between the estimated values of β ( t m ) s i and the values of s i set in the simulation. Pearson coefficient was averaged over time points and, because it always negative, multiplied by −1. The results demonstrate that the correlation between the estimated and the actual values decreases with the length of genome due to increasing linkage effects and increases with the number of independent runs and the probability of recombination ( Figure 2 ). This correlation depends weakly on population size, sample size, and mutation rate ( Figure S2 ). Download figure Open in new tab Figure 2. Correlations between the estimated and the actual values of selection coefficient. Numbers at columns are different values of genome length. Rows correspond to different numbers of random simulation runs, parameter r is the probability of recombination, and M denotes the number of crossovers. The numbers in cells show Pearson’s correlation coefficient between the actual values of selection coefficients and their estimates, multiplied by −1. Simulation parameters, except for those shown, are the same as in Figure 1 . Sensitivity to population size, sample size, and mutation rate is shown in Fig. S2 in Supplement. Application to genomic data of E. Coli After validating the method on simulated data, it was applied to data from a real biological population. The sequences were downloaded from a database created in a long-term evolution experiment on E. coli [ 34 ]. Data analysis was performed for early generations to avoid two issues: the influence of variants with increased mutation probabilities and the population segregation due to differential food use that emerged in several populations over time [ 34 ]. The algorithm identified approximately 10,000 evolving sites. The values of relative selection coefficients for some sites are presented in Tables 1 and 2 . The distribution of selection coefficients ( Figure 3 ) has a non-monotonous form slightly resembling a distribution previously observed for poliovirus [ 3 ]. The full table for all sites is provided in Supplement online, file coeff_s_ecoli . csv . View this table: View inline View popup Download powerpoint Table 1. The values of β ( t m ) S i for three chosen generations of E. Coli sorted by site number. Only some genomic sites are shown. The full table for all sites is provided in Supplement online in file coeff_s_ecoli . csv . View this table: View inline View popup Download powerpoint Table 2. Results from Table 1 sorted by the values of β ( t m ) S i Download figure Open in new tab Figure 3. Histograms of the distribution of values. Values to the right of the orange line correspond to positive selection coefficient s , and those to the left correspond to negative values. The four panels correspond to three different time points (generations 1000, 1500, and 2000) and the average over time. DISCUSSION The present work offers a software package implementing an algorithm for estimating relative selection coefficients from genomic data despite the presence of strong linkage effects caused by common phylogeny. A test on simulated data demonstrates good accuracy, if ten or more populations are used for averaging. Then the method is used to estimate selection coefficients for 10,000 evolving sites of E. Coli. The method relies on averaging over multiple independently-evolving populations. This is not a limitation of this specific method of measurement, but a fundamental limitation arising from the stochastic effects of genetic linkage due to the common phylogeny of different sites. Examples of systems where such data can be obtained include various microbiological experiments in multiple serial passages. Another example is the evolution of different metastases in a patient. When addressing human evolution, it is advisable to compare DNA samples of diverged populations from different geographic locations that evolved under similar conditions. It has been known for a long time that the evolution of a population is strongly affected by the fact that the fates of alleles at different loci are linked unless separated by recombination [ 11 ]. Effects of genetic linkage include clonal interference [ 11 , 35 ], background selection, genetic hitchhiking [ 36 ], enhanced accumulation of deleterious mutations (Muller’s ratchet) [ 12 , 37 ], and the increase of genetic drift at one locus due to selection at another [ 38 ]. Genetic linkage also decreases the speed of adaptation due to clonal interference [ 12 , 39 ]. For this reason, one-locus models usually do not apply in real populations, and multi-locus models based on traveling wave methods must be used [ 13 , 40 ]. Importantly, genetic linkage makes evolutionary dynamics at different sites stochastic and interdependent, which is a serious obstacle to the inference of fitness landscape from genetic data [ 41 ]. To fill this gap, a method based on the approximation of quasi-equilibrium was recently proposed [ 32 , 33 ]. The cited work demonstrated that the entropy of the distribution of alleles across genomes and sites is maximal conditioned on the value of average population fitness. This approximation, formulated for multi-site adaptation [ 12 ], was tested by Monte Carlo simulation [ 31 - 33 ]. The present work is the first application of this method to real genomic data. After successfully applying to data on E. Coli , we also made an attempt to apply this method to data on SARS-CoV-2 and HIV. We found out, however, that the method works only for the systems with a unique best-fit sequence. The method requires averaging allelic frequencies over an ensemble of independently-evolving populations with the same or similar parameters, including the same best-fit sequence. These viruses do not meet this criterion. Indeed, the best-fit sequence for HIV varies between individuals due to the variation of HLA allele subtypes. Coronaviruses, influenza virus and hepatitis C virus are in the state of perpetual antigenic escape from the collective immune memory of population (“Red Queen effect”). In this case, the best-fit sequence does not exist at all. Estimating selection coefficients for such situations will require development of a different approach. The question of generalization of this approach to the system with multiple best-fit sequences remain opens. Other groups developed a number of methods to estimate selection coefficients neglecting linkage effects. In one work, selection coefficient was estimated from a hidden Markov chain assuming a single-locus model[ 42 ]. Another team [ 43 ] developed a method for measuring the selection coefficient considering a single locus with two alleles and using data on time series. In their model, backward Kolmogorov equation is used to describe transition probabilities. Another group [ 7 ] presented a method for detecting selection signature from population history, by maximizing a likelihood function derived from a two-locus evolutionary model. A likelihood estimation method was used to jointly estimate the selection coefficient and the allele age based on time series data [ 44 ]. All these methods neglected linkage effects. Note that the proportion of beneficial mutations predicted is higher than previously estimated for E. coli [ 45 , 46 ]. The proportion of beneficial alleles is not a universal property of the organism. It varies broadly depending on the state of a population (i.e., time of evolution) and external conditions. Hence the probable reason for discrepancy is that the cited authors propagate E. Coli . under different conditions than in [ 34 ] whose data we used here. The proportion of deleterious alleles decreases in the process of evolution. If an organism is well– evolved, their deleterious alleles are very rare. Also, the previous method of estimating s is based on a 1-locus model. Conclusions Using a method developed to withstand linkage effects, we estimate the relative values of selection coefficient for several thousand sites of the evolving E. Coli . genome. These results demonstrate the feasibility of the measurements of selection coefficients from genomic data in populations evolving under directional selection in the presence of strong linkage effects. METHODS Generating sequences for method testing Evolution of a haploid asexual population of N binary sequences is simulated by a Monte Carlo code. In an individual genome, each locus (site, nucleotide position, amino acid position) numbered i = 1, 2, …, L is occupied by one of two alleles, either the wild-type allele, denoted K i = 0, or the mutant allele, K i = 1.We use a discrete generation scheme in the absence of generation overlap (Wright-Fisher model). The evolutionary factors included in the model are random mutation with rate µL per genome, constant directional selection, random genetic drift due to random sampling of progeny and recombination with rate r . Selection includes an epistatic network with a set strength and topology. The logarithm of the average progeny number of an individual genome, W , depends on sequence [ K i ] as given by where T ij = 0 or 1 is the binary matrix that shows interacting pairs. Here the selection coefficients s i denotes the individual fitness costs of two deleterious mutations that are partially compensated by each other. In our simulation example in Fig 2 , we consider a haploid population with the initial frequency of deleterious alleles, f 0 = 0.5, mutation rate, µL = 0.07, uniformly distibuted selection coefficient with average s = 0.1, population size N = 1000 individuals. We have assumed a uniform distribution of selection coefficients in our simulation test. Other distributions are also used in simulation studies as well [ 47 ]. Frequency of deleterious alleles vary broadly depending on a locus and how well a population is adapted to environment. If it is well adapted, their frequencies are very low. For sites in the middle of adaption, which was the focus of our study, it is very high. In the cited experiment we fit, the authors use poorly adapted E Coli to have a large number of adapting sites. Hence, we used the case of poorly adapted populations for testing. Monte-Carlo simulation code is written in MATLAB™ and deposited at https://github.com/Rictograf/s_measurement/tree/main/monte-carlo%20simulation . Estimating selection coefficients from genomic data Data curation for aligned sequences We downloaded genomic sequences of E . Coli . obtained in long-term experiments [ 34 ] from a public database https://www.ncbi.nlm.nih.gov/bioproject/?term=PRJNA380528 . If sequences contained deletions or unspecified nucleotides (‘−’ or ‘N’), the data were cleaned of them, as follows. Sequences, in which the number of such occurrences exceeded a certain threshold, were removed. Then sites where the number of deletions and unspecified nucleotides exceeded the SeqGapsThreshold threshold were removed. Thus, insertions are not considered by our algorithm, because during alignment they form a column of ‘−’ values at the site where they arise. Next, any remaining ‘−’ or ‘N’ values are considered minor variants and assigned a value of 1. If the frequency of a variant at a site is below threshold SiteMonomorphThreshold , the site is considered monomorphic at that point in time and removed. The result is an L × N table, where L is the total site number, and N is the number of genomes considered. To binarize the data, the majority variant averaged over all populations and time points for each site is replaced by 0, and all other (minor) variants at that site are replaced by 1. Thresholds are SeqGapsThreshold = 0.05, SiteGapsThreshold = 0.06, SiteMonomorphThreshold = 0.06. The sequencing data was mapped to consensus NC_007779 ( https://www.ncbi.nlm.nih.gov/nuccore/NC_007779.1/ ) using the Geneious Prime ( https://www.geneious.com/ ) program. Use tool Map to Reference(s). That program was also used to find allele frequencies f i . Estimating selection coefficient To estimate selection coefficients, we employ the method developed in [ 32 , 33 ]. This method is based on the assumption [ 31 ] that the entropy of genomic configurations (distribution of alleles over genomes and sites) is maximal given the fitness, at any one time. Intuitive reason for this assumption tested on simulated sequences by Monte Carlo simulation in [ 31 , 33 ], is that a slow speed evolution allows the system to reach statistical quasi-equilibrium at any time. The frequency of anti-consensus variants denoted f i ( t m ) is calculated for each site i and time point t m = t 1, t 2, …. Next, the relative values of the selection coefficient for each site at each time point are found, as follows. Genomic sites i are ordered by the value of f i averaged over the genome sample and time. The value of β ( t m ) s i is calculated, for each time t m , as [ 32 , 33 ] Derivation Consider a site with selection coefficient − s ( Eq. 1 ) in a long genome with total log-fitness W. The models of population genetics (see Discussion) demonstrate that the distribution density of fitness W across individual genomes is a narrow solitary wave moving at a slow speed; in the context of our work, we can consider W fixed. We classify all individual genomes in the population according to the allele at the site: 0 and 1. According to Eq. (1) , the contribution of the site to the logarithm of genome fitness depends on the allele: W site = 0 and W site = − s , for alleles 0 and 1, respectively. In the course of evolution, random drift and mutation tend to maximize disorder. On the other hand, the effect of Darwinian selection is to maximize fitness. The standard measure of disorder is configuration entropy S defined as the logarithm of the number of possible configurations. The balance between entropy and fitness is satisfied when entropy is maximal under the restriction that fitness value W is fixed (i.e. changes slowly). The maximum value of S depends on W, as given by S = S ( W ). The fitness of the part of genome that does not include the pair is the difference W − W site . Hence, entropy of each allele’s subset of sequences is S ( W − W site ). Since the genome is long, we can safely assume that W site is much smaller than W , so that the corresponding change in entropy is small, S ( W − W site ) ≈ S ( W ) − βW site , where β ≡ dS / dW . The frequency of each haplotype is proportional to the corresponding configuration number, exp [ S ( W − W pair )], and we arrive at Eq. (2) with C = 0. Finally, coefficient C is introduced to account for the difference between the best fit sequence and the consensus sequence in experiment. Application of the method In Eq. 2 , the initial value of normalization factor C is set to 0 ( Figure 4 , bottom). Then, C is determined as the ordinate of the intersection point of all curves obtained for different time points t m . To find this point, each curve is approximated by a fourth-degree polynomial ( Figure 4 ). Thus, we obtain the estimate of the selection coefficients of all sites multiplied by the common coefficient β ( t m ), which depends on time. Download figure Open in new tab Figure 4. Ranked curves from Eq. 2 with and without C for three time points for simulated sequences. Algorithm visualization. f 0 = 0.5 is the initial mutation rate, mutation rate µL = 0.07, average selection coefficient s = 0.1, N = 1000 individuals in the population, r = 0 is the recombination probability, run = 50 is the number of simulation runs, L = 400 is the genome length. Time points are shown Testing accuracy Above procedure is illustrated, for a representative parameter set, in Figure 1 using simulated sequences produce by Monte Carlo simulation (see Methods above). To test its accuracy, the estimated values of selection coefficients are plotted against their values set in simulation that generated genomic sequences ( Figure 3 ). Funding The study was funded by Russian Science Foundation, grant 24-24-00529 to I.M.R. Conflict of interests Authors declare no conflict of interest. Ethical statement No ethical statement is required. Software The codes are available at https://github.com/Rictograf/s_measurement Supplement Figure S1 . Correlations between the estimated and the actual values of selection coefficient in the absence of recombination. Supplemental table https://github.com/Rictograf/s_measurement/blob/main/coeff_s_ecoli.csv Supplemental information Download figure Open in new tab Figure S1. Correlations between the estimated and the actual values of selection coefficient at r = 0. Other parameters are the same as in Figure 2 . Download figure Open in new tab Figure S2. Correlations between the estimated and the actual values of selection coefficient. The version of Figure 2 with other variable parameters. Fixed parameters: initial mutation frequency f 0 = 0.5, average selection coefficient s = 0.1, recombination probability r = 0, the number of simulation runs run = 10, genome length L = 100. Acknowledgements This work originated in long discussions with Igor Likhachev. We thank A.A. Makashov for technical help and discussion. We are grateful to A. I. Pikhulya, D. A. Gorshkova, E. A. Vigovskaya, and E. I. Stroganova for technical help. Funder Information Declared Russian Science Foundation, https://ror.org/03y2gwe85 , 24-24-00529 Footnotes The sensitivity test for the sample size and population size is added. The analytic derivation of the method (obtained previously) is added. Clarified: The method relies on averaging over multiple independently-evolving populations. This is not a limitation of this specific method of measurement, but a fundamental limitation arising from the stochastic effects of genetic linkage due to the common phylogeny of sites. Clarified: The proportion of beneficial alleles is not a universal property of the organism. It varies broadly depending on time of evolution and external conditions. If an organism is well evolved, their deleterious alleles are very rare. 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