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<!DOCTYPE html> <html > <head> <meta charset="utf-8"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <meta content="width=device-width, initial-scale=1" name="viewport"> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs"> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="2qpriWjSkQnQYVP0zjI4YJq55nxapMhJLXxzqcC9lZZntJl0CElTB8zqSRpuc6B8mUxAAVSOAfWR9H_N-YqRZg" /> <meta name="citation_title" content="Dynamic Mutation–Selection Balance as an Evolutionary Attractor" /> <meta name="citation_publication_date" content="2012" /> <meta name="citation_journal_title" content="Genetics" /> <meta name="citation_author" content="Sidhartha Goyal" /> <meta name="citation_author" content="Daniel J Balick" /> <meta name="citation_author" content="Elizabeth R Jerison" /> <meta name="citation_author" content="Richard A Neher" /> <meta name="citation_author" content="Boris I Shraiman" /> <meta name="citation_author" content="Michael M Desai" /> <meta name="citation_volume" content="191" /> <meta name="citation_issue" content="4" /> <meta name="citation_firstpage" content="1309-1319" /> <meta name="citation_issn" content="1943-2631" /> <meta name="twitter:card" content="summary" /> <meta name="twitter:url" content="https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor" /> <meta name="twitter:title" content="Dynamic Mutation–Selection Balance as an Evolutionary Attractor" /> <meta name="twitter:description" content="The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by" /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor" /> <meta property="og:title" content="Dynamic Mutation–Selection Balance as an Evolutionary Attractor" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by" /> <meta property="article:author" content="https://independent.academia.edu/BorisShraiman" /> <meta name="description" content="The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by" /> <title>(PDF) Dynamic Mutation–Selection Balance as an Evolutionary Attractor</title> <link rel="canonical" href="https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = 'b092bf3a3df71cf13feee7c143e83a57eb6b94fb'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1739829272000); window.Aedu.timeDifference = new Date().getTime() - 1739829272000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller’s ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation–selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that ma...","author":[{"@context":"https://schema.org","@type":"Person","name":"Boris Shraiman","url":"https://independent.academia.edu/BorisShraiman"}],"contributor":[],"dateCreated":"2023-03-05","datePublished":"2012-01-01","headline":"Dynamic Mutation–Selection Balance as an Evolutionary Attractor","image":"https://attachments.academia-assets.com/99473552/thumbnails/1.jpg","inLanguage":"en","keywords":["Genetics","Algorithms","Population Genetics","Biology","Medicine","Population","Computer Simulation","Mutation","Population Density","Asexual Reproduction","Negative Selection Algorithm","Genetic Fitness","Mutation Accumulation","Mutation Rate"],"publication":"Genetics","publisher":{"@context":"https://schema.org","@type":"Organization","name":"Oxford University Press (OUP)"},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":null}],"thumbnailUrl":"https://attachments.academia-assets.com/99473552/thumbnails/1.jpg","url":"https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor"}</script><style type="text/css">@media(max-width: 567px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 #22223340;--primary-brand: #0645b1;--error-dark: #b60000;--success-dark: #05b01c;--inactive-fill: #ebebee;--hover: #0c3b8d;--pressed: #082f75;--button-primary-fill-inactive: #ebebee;--button-primary-fill: #0645b1;--button-primary-text: #ffffff;--button-primary-fill-hover: #0c3b8d;--button-primary-fill-press: #082f75;--button-primary-icon: #ffffff;--button-primary-fill-inverse: #ffffff;--button-primary-text-inverse: #082f75;--button-primary-icon-inverse: #0645b1;--button-primary-fill-inverse-hover: #cddaef;--button-primary-stroke-inverse-pressed: 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{"work":{"id":98003501,"created_at":"2023-03-05T23:13:38.588-08:00","from_world_paper_id":228982713,"updated_at":"2024-11-08T01:04:04.479-08:00","_data":{"abstract":"The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller’s ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation–selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that ma...","publisher":"Oxford University Press (OUP)","publication_date":"2012,,","publication_name":"Genetics"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Dynamic Mutation–Selection Balance as an Evolutionary Attractor","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [49581400]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":99473552,"attachmentType":"pdf"}"><img alt="First page of “Dynamic Mutation–Selection Balance as an Evolutionary Attractor”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/99473552/mini_magick20230306-1-btfe4g.png?1678087008" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Dynamic Mutation–Selection Balance as an Evolutionary Attractor</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="49581400" href="https://independent.academia.edu/BorisShraiman"><img alt="Profile image of Boris Shraiman" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Boris Shraiman</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2012, Genetics</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">18 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 98003501; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">The vast majority of mutations are deleterious and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller’s ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller’s ratchet can lead to a rapid degradation of population fitness. Evidently, the long-term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Hence any stable evolutionary state of a population in a static environment must involve a dynamic mutation–selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that such a state can exist for any population size N and mutation rate U and calculate the fraction of beneficial mutations, ε, that ma...</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":99473552,"attachmentType":"pdf","workUrl":"https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":99473552,"attachmentType":"pdf","workUrl":"https://www.academia.edu/98003501/Dynamic_Mutation_Selection_Balance_as_an_Evolutionary_Attractor"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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We find that the accumulation of deleterious mutations, due to the operation of Muller's ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller's ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller's ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (s d ) are higher than the beneficial effects (s a ). When s a Ͼ s d , the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Adaptive Evolution of Asexual Populations Under Muller's Ratchet","attachmentId":47156025,"attachmentType":"pdf","work_url":"https://www.academia.edu/26891594/Adaptive_Evolution_of_Asexual_Populations_Under_Mullers_Ratchet","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/26891594/Adaptive_Evolution_of_Asexual_Populations_Under_Mullers_Ratchet"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="94012927" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/94012927/The_Evolution_of_Mutation_Rate_in_Finite_Asexual_Populations">The Evolution of Mutation Rate in Finite Asexual Populations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="251526311" href="https://independent.academia.edu/JeanBaptisteAndr%C3%A92">Jean-Baptiste André</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Genetics, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">In this article, we model analytically the evolution of mutation rate in asexual organisms. Three selective forces are present. First, everything else being equal, individuals with higher mutation rate have a larger fitness, thanks to the energy and time saved by not replicating DNA accurately. Second, as a flip side, the genome of these individuals is replicated with errors that may negatively affect fitness. Third, and conversely, replication errors have a potential benefit if beneficial mutations are to be generated. Our model describes the fate of modifiers of mutation rate under the three forces and allows us to predict the long-term evolutionary trajectory of mutation rate. We obtain three major results. First, in asexuals, the needs for both adaptation and genome preservation are not evolutionary forces that can stabilize mutation rate at an intermediate optimum. When adaptation has a significant role, it primarily destabilizes mutation rate and yields the emergence of strong...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Evolution of Mutation Rate in Finite Asexual Populations","attachmentId":96590681,"attachmentType":"pdf","work_url":"https://www.academia.edu/94012927/The_Evolution_of_Mutation_Rate_in_Finite_Asexual_Populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/94012927/The_Evolution_of_Mutation_Rate_in_Finite_Asexual_Populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="81309359" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/81309359/Fluctuations_of_Fitness_Distributions_and_the_Rate_of_Muller_s_Ratchet">Fluctuations of Fitness Distributions and the Rate of Muller’s Ratchet</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="49581400" href="https://independent.academia.edu/BorisShraiman">Boris Shraiman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Genetics, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">The accumulation of deleterious mutations is driven by rare fluctuations that lead to the loss of all mutation free individuals, a process known as Muller’s ratchet. Even though Muller’s ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution, which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fluctuations of Fitness Distributions and the Rate of Muller’s Ratchet","attachmentId":87398266,"attachmentType":"pdf","work_url":"https://www.academia.edu/81309359/Fluctuations_of_Fitness_Distributions_and_the_Rate_of_Muller_s_Ratchet","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/81309359/Fluctuations_of_Fitness_Distributions_and_the_Rate_of_Muller_s_Ratchet"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="74728995" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74728995/Distribution_of_fixed_beneficial_mutations_and_the_rate_of_adaptation_in_asexual_populations">Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="194511207" href="https://independent.academia.edu/IgorRouzine">Igor Rouzine</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the National Academy of Sciences, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic bac...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations","attachmentId":82774193,"attachmentType":"pdf","work_url":"https://www.academia.edu/74728995/Distribution_of_fixed_beneficial_mutations_and_the_rate_of_adaptation_in_asexual_populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74728995/Distribution_of_fixed_beneficial_mutations_and_the_rate_of_adaptation_in_asexual_populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="74156533" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/74156533/Beneficial_mutations_and_the_dynamics_of_adaptation_in_asexual_populations">Beneficial mutations and the dynamics of adaptation in asexual populations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="50566687" href="https://independent.academia.edu/PGerrish">Philip Gerrish</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Philosophical Transactions of the Royal Society B: Biological Sciences, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">We discuss the dynamics of adaptive evolution in asexual (clonal) populations. The classical ‘periodic selection’ model of clonal evolution assumed that beneficial mutations are very rare and therefore substitute unfettered into populations as occasional, isolated events. Newer models allow for the possibility that beneficial mutations are sufficiently common to coexist and compete for fixation within populations. Experimental evolution studies in microbes provide empirical support for stochastic models in which both selection and mutation are strong effects and clones compete for fixation; however, the relative importance of competition among clones bearing mutations of different selective effects versus competition among clones bearing multiple mutations remains unresolved. We provide some new theoretical results, moreover, suggesting that population dynamics consistent with the periodic selection model can arise even in a deterministic model that can accommodate a very high benef...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Beneficial mutations and the dynamics of adaptation in asexual populations","attachmentId":83655782,"attachmentType":"pdf","work_url":"https://www.academia.edu/74156533/Beneficial_mutations_and_the_dynamics_of_adaptation_in_asexual_populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/74156533/Beneficial_mutations_and_the_dynamics_of_adaptation_in_asexual_populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="17478895" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17478895/Diminishing_Returns_from_Mutation_Supply_Rate_in_Asexual_Populations">Diminishing Returns from Mutation Supply Rate in Asexual Populations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37236119" href="https://independent.academia.edu/BlanchardJeffrey">Jeffrey Blanchard</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Science, 1999</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Diminishing Returns from Mutation Supply Rate in Asexual Populations","attachmentId":39533030,"attachmentType":"pdf","work_url":"https://www.academia.edu/17478895/Diminishing_Returns_from_Mutation_Supply_Rate_in_Asexual_Populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17478895/Diminishing_Returns_from_Mutation_Supply_Rate_in_Asexual_Populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="112157684" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/112157684/Hidden_role_of_mutations_in_the_evolutionary_process">Hidden role of mutations in the evolutionary process</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32647109" href="https://unicamp.academia.edu/LouisKlaczko">Louis B . Klaczko</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical review, 2021</p><p class="ds-related-work--abstract ds2-5-body-sm">Mutations not only alter allele frequencies in a genetic pool but may also determine the fate of an evolutionary process. Here we study which allele fixes in a one-step, one-way model including the wild type and two adaptive mutations. We study the effect of the four basic evolutionary mechanisms-genetic drift, natural selection, mutation, and gene flow-on mutant fixation and its kinetics. Determining which allele is more likely to fix is not simply a question of comparing fitnesses and mutation rates. For instance, if the allele of interest is less fit than the other, then not only must it have a greater mutation rate, but also its mutation rate must exceed a specific threshold for it to prevail. We find exact expressions for such conditions. Our conclusions are based on the mathematical description of two extreme but important regimes, as well as on simulations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Hidden role of mutations in the evolutionary process","attachmentId":109474437,"attachmentType":"pdf","work_url":"https://www.academia.edu/112157684/Hidden_role_of_mutations_in_the_evolutionary_process","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/112157684/Hidden_role_of_mutations_in_the_evolutionary_process"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="11109957" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/11109957/The_dynamical_way_to_mutation_selection_balance_of_an_infinite_population_evolving_on_a_truncated_fitness_landscape">The dynamical way to mutation-selection balance of an infinite population evolving on a truncated fitness landscape</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26841840" href="https://usp-br.academia.edu/LeonardoMaia">Leonardo Maia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Biology, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">This paper presents the exact analytical solution, valid for all generations and initial conditions, for the frequency distribution of haploids with infinite-sites genome carrying a given number of mutations in a population evolving deterministically on a truncated fitness landscape. This landscape is a generalization of the single sharp peak one, widely used in quasispecies theory, although here there are no reverse mutations.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The dynamical way to mutation-selection balance of an infinite population evolving on a truncated fitness landscape","attachmentId":46894255,"attachmentType":"pdf","work_url":"https://www.academia.edu/11109957/The_dynamical_way_to_mutation_selection_balance_of_an_infinite_population_evolving_on_a_truncated_fitness_landscape","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/11109957/The_dynamical_way_to_mutation_selection_balance_of_an_infinite_population_evolving_on_a_truncated_fitness_landscape"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="17939417" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/17939417/From_Bad_to_Good_Fitness_Reversals_and_the_Ascent_of_Deleterious_Mutations">From Bad to Good: Fitness Reversals and the Ascent of Deleterious Mutations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38273700" href="https://independent.academia.edu/MatthewCowperthwaite">Matthew Cowperthwaite</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="37853997" href="https://independent.academia.edu/LaurenMeyers1">Lauren Meyers</a></div><p class="ds-related-work--metadata ds2-5-body-xs">PLoS Computational Biology, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10 À5 of all mutations). Citation: Cowperthwaite MC, Bull JJ, Meyers LA (2006) From bad to good: Fitness reversals and the ascent of deleterious mutations. PLoS Comput Biol 2(10): e141.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"From Bad to Good: Fitness Reversals and the Ascent of Deleterious Mutations","attachmentId":39789373,"attachmentType":"pdf","work_url":"https://www.academia.edu/17939417/From_Bad_to_Good_Fitness_Reversals_and_the_Ascent_of_Deleterious_Mutations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/17939417/From_Bad_to_Good_Fitness_Reversals_and_the_Ascent_of_Deleterious_Mutations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="31625249" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/31625249/The_Fixation_Probability_of_Rare_Mutators_in_Finite_Asexual_Populations">The Fixation Probability of Rare Mutators in Finite Asexual Populations</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32605520" href="https://independent.academia.edu/DavidKessler3">David S Kessler</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Genetics, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Fixation Probability of Rare Mutators in Finite Asexual Populations","attachmentId":51950472,"attachmentType":"pdf","work_url":"https://www.academia.edu/31625249/The_Fixation_Probability_of_Rare_Mutators_in_Finite_Asexual_Populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/31625249/The_Fixation_Probability_of_Rare_Mutators_in_Finite_Asexual_Populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":99473552,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":99473552,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_99473552" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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ds2-5-body-xs">Proceedings of the National …, 1983</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Modifiers of mutation rate: Evolutionary optimum with complete selfing","attachmentId":5691440,"attachmentType":"pdf","work_url":"https://www.academia.edu/933563/Modifiers_of_mutation_rate_Evolutionary_optimum_with_complete_selfing","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/933563/Modifiers_of_mutation_rate_Evolutionary_optimum_with_complete_selfing"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://www.academia.edu/75394259/Shortcut_Predictions_for_Fitness_Properties_at_the_Mutation_Selection_Drift_Balance_and_for_Its_Buildup_After_Size_Reduction_Under_Different_Management_Strategies">Shortcut Predictions for Fitness Properties at the Mutation-Selection-Drift Balance and for Its Buildup After Size Reduction Under Different Management Strategies</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="58022129" href="https://independent.academia.edu/AGarciaDorado">A. Garcia-Dorado</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Genetics, 2006</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Shortcut Predictions for Fitness Properties at the Mutation-Selection-Drift Balance and for Its Buildup After Size Reduction Under Different Management Strategies","attachmentId":83180242,"attachmentType":"pdf","work_url":"https://www.academia.edu/75394259/Shortcut_Predictions_for_Fitness_Properties_at_the_Mutation_Selection_Drift_Balance_and_for_Its_Buildup_After_Size_Reduction_Under_Different_Management_Strategies","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/75394259/Shortcut_Predictions_for_Fitness_Properties_at_the_Mutation_Selection_Drift_Balance_and_for_Its_Buildup_After_Size_Reduction_Under_Different_Management_Strategies"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="13440514" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/13440514/Mutational_Meltdowns_in_Sexual_Populations">Mutational Meltdowns in Sexual Populations</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32663232" href="https://univie.academia.edu/ReinhardB%C3%BCrger">Reinhard Bürger</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Evolution, 1995</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Mutational Meltdowns in Sexual Populations","attachmentId":45340415,"attachmentType":"pdf","work_url":"https://www.academia.edu/13440514/Mutational_Meltdowns_in_Sexual_Populations","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/13440514/Mutational_Meltdowns_in_Sexual_Populations"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="9" data-entity-id="2738697" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/2738697/Mutation_accumulation_in_growing_asexual_lineages">Mutation accumulation in growing asexual lineages</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="411724" href="https://mtsu.academia.edu/RStephenSteveHoward">R. Stephen (Steve) Howard</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2003</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Mutation accumulation in growing asexual lineages","attachmentId":30714356,"attachmentType":"pdf","work_url":"https://www.academia.edu/2738697/Mutation_accumulation_in_growing_asexual_lineages","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/2738697/Mutation_accumulation_in_growing_asexual_lineages"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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ds2-5-body-link" href="https://www.academia.edu/71166034/Joint_Prediction_of_the_Effective_Population_Size_and_the_Rate_of_Fixation_of_Deleterious_Mutations">Joint Prediction of the Effective Population Size and the Rate of Fixation of Deleterious Mutations</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="125798852" href="https://uniovi.academia.edu/EnriqueSantiago">Enrique Santiago</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Genetics, 2016</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Joint Prediction of the Effective Population Size and the Rate of Fixation of Deleterious 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Colato</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of The Royal Society Interface, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Genomic mutation rates that neutralize adaptive evolution and natural selection","attachmentId":41256577,"attachmentType":"pdf","work_url":"https://www.academia.edu/20032176/Genomic_mutation_rates_that_neutralize_adaptive_evolution_and_natural_selection","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/20032176/Genomic_mutation_rates_that_neutralize_adaptive_evolution_and_natural_selection"><span 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