The Arrival of the Frequent: How Bias in Genotype-Phenotype Maps Can Steer Populations to Local Optima
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{"title"=>"The arrival of the frequent: How bias in genotype-phenotype maps can steer populations to local optima", "type"=>"journal", "authors"=>[{"first_name"=>"Steffen", "last_name"=>"Schaper", "scopus_author_id"=>"55128015200"}, {"first_name"=>"Ard A.", "last_name"=>"Louis", "scopus_author_id"=>"7004751956"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"arxiv"=>"arXiv:1402.1410v1", "issn"=>"19326203", "pui"=>"372535264", "doi"=>"10.1371/journal.pone.0086635", "sgr"=>"84895529107", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"24505262", "scopus"=>"2-s2.0-84895529107"}, "id"=>"a0caebd5-23c7-3d1f-af50-66eddea8dc69", "abstract"=>"Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The total number of genotypes [Formula: see text] is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies [Formula: see text], with [Formula: see text] the number of genotypes mapping onto phenotype [Formula: see text], is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype [Formula: see text] scales to first order as [Formula: see text], although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time [Formula: see text] of a phenotype [Formula: see text] similarly scales to first order as [Formula: see text] for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger [Formula: see text] is therefore be much more likely to arise than variation with a small [Formula: see text]. We show, using the RNA model, that frequent phenotypes (with larger [Formula: see text]) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never 'arrive' on the timescales of evolutionary change, then they can't fix. We call this highly non-ergodic effect the 'arrival of the frequent'.", "link"=>"http://www.mendeley.com/research/arrival-frequent-bias-genotypephenotype-maps-steer-populations-local-optima", "reader_count"=>33, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>2, "Researcher"=>7, "Student > Ph. D. Student"=>9, "Student > Postgraduate"=>2, "Student > Master"=>5, "Student > Bachelor"=>6, "Professor"=>2}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>2, "Researcher"=>7, "Student > Ph. D. Student"=>9, "Student > Postgraduate"=>2, "Student > Master"=>5, "Student > Bachelor"=>6, "Professor"=>2}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Engineering"=>1, "Biochemistry, Genetics and Molecular Biology"=>4, "Mathematics"=>1, "Agricultural and Biological Sciences"=>12, "Medicine and Dentistry"=>3, "Neuroscience"=>1, "Physics and Astronomy"=>8, "Chemistry"=>1, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>1}, "Chemistry"=>{"Chemistry"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>8}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>12}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>4}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"Netherlands"=>1, "United States"=>2, "Slovakia"=>1}, "group_count"=>1}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1377637"], "description"=>"<p><i>A</i>) RNA neutral component for phenotype with genotypes (drawn in blue). Lines depict single mutations to itself, or to two alternative phenotypes (grey) and (red). The genotypes were ordered using the Fruchterman-Reingold algorithm <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635-Fruchterman1\" target=\"_blank\">[30]</a>. <i>B</i>) Illustration of the fitness landscape.</p>", "links"=>[], "tags"=>["biophysics", "Computational biology", "Evolutionary modeling", "population genetics", "Evolutionary biology", "mutation", "Evolutionary developmental biology", "Evolutionary ecology", "evolutionary theory", "Theoretical biology", "Nucleic acids", "rna", "RNA structure", "spaces", "evolutionary"], "article_id"=>927318, "categories"=>["Physics", "Biological Sciences"], "users"=>["Steffen Schaper", "Ard A. Louis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086635.g003", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Interconnections_of_neutral_spaces_in_RNA_influence_evolutionary_trajectories_/927318", "title"=>"Interconnections of neutral spaces in RNA influence evolutionary trajectories.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:39:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377634"], "description"=>"<p><i>A</i>) An example genotype space: Each point corresponds to a unique genotype; shape and color of the marker indicate the phenotype. Genotypes joined by edges can be interconverted by single mutations. Edges for neutral mutations share the color of the (conserved) phenotype, non-neutral mutations are shown as black dashed lines. The shading of the genotypes illustrates the number of individuals carrying the respective genotype in a hypothetical population. The mutations away from the genotypes occupied by the population determine the accessible phenotypes. <i>B</i>) Our meanfield approximation averages over the internal structure of neutral spaces. So neutral spaces are represented by the markers of their phenotypes only, with the size representing the neutral space size (ie. number of genotypes in the space). The uniform shading of the blue neutral space implies that in the meanfield approximation, the population is assumed to continually explore the neighbourhood of its entire neutral space. Mutational outcomes are thus determined from the local frequencies of phenotypes around the neutral space, as measured by the coefficients. This mean field approximation allows us to derive analytic forms that can be compared to simulations of the full GP map.</p>", "links"=>[], "tags"=>["biophysics", "Computational biology", "Evolutionary modeling", "population genetics", "Evolutionary biology", "mutation", "Evolutionary developmental biology", "Evolutionary ecology", "evolutionary theory", "Theoretical biology", "Nucleic acids", "rna", "RNA structure"], "article_id"=>927315, "categories"=>["Physics", "Biological Sciences"], "users"=>["Steffen Schaper", "Ard A. Louis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086635.g001", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_mean_field_approximation_/927315", "title"=>"Illustration of the mean field approximation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:39:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377635"], "description"=>"<p><i>A</i>) Median discovery times for the random GP map averaged over 100 simulations with and varying mutation rates. Note that the y-axis is scaled with . In the the polymorphic limit (), <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635.e113\" target=\"_blank\">Eq. (4)</a> (dashed line) describes discovery times well for . Phenotypes with larger are part of the standing variation typically found in the first generation (yellow dash-dotted line). In the monomorphic limit (), <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635.e168\" target=\"_blank\">Eq. (7)</a> (dotted line) quantitatively describes for , whereas <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635.e113\" target=\"_blank\">Eq. (4)</a> tracks the simulation data with just one fit parameter multiplying for the intermediate regime with (solid line). For the curves follow <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635.e113\" target=\"_blank\">Eq. (4)</a>, for reasons described in the text. <i>Inset</i>: For the random GP map the local phenotype frequency correlates very well with the global frequency . <i>B</i>) Local frequency ranked for the phenotypes that link with single point mutations from the genotypes that map to this RNA structure; an example sequence from is shown in the figure. <i>Inset</i>: The local connections are roughly proportional to the global frequency , but there is significant scatter due to the internal correlations of the RNA neutral spaces. Organge points depict the phenotypes for which . Light blue points depict the phenotypes that are discovered in our simulations, and the dark blue points depict the accessible phenotypes that are not found ( itself is shown in green). <i>C</i>) Simulations of (blue dots) versus for the RNA phenotype shown in B), compared to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086635#pone.0086635.e113\" target=\"_blank\">Eq. (4)</a> (solid line) with a factor multiplying . Here , and the simulations were run for generations. Also shown are the purely polymorphic (dashed) and monomorphic (dotted) predictions. Dark blue dots above (dot-dashed line) depict some of the accessible phenotypes that are not found (as can be seen in see the inset of B). We estimate that about generations would be needed to find the phenotypes with the smallest .</p>", "links"=>[], "tags"=>["biophysics", "Computational biology", "Evolutionary modeling", "population genetics", "Evolutionary biology", "mutation", "Evolutionary developmental biology", "Evolutionary ecology", "evolutionary theory", "Theoretical biology", "Nucleic acids", "rna", "RNA structure", "meanfield"], "article_id"=>927316, "categories"=>["Physics", "Biological Sciences"], "users"=>["Steffen Schaper", "Ard A. Louis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086635.g002", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Test_of_the_meanfield_model_/927316", "title"=>"Test of the meanfield model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:39:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377640", "https://ndownloader.figshare.com/files/1377641", "https://ndownloader.figshare.com/files/1377642", "https://ndownloader.figshare.com/files/1377643", "https://ndownloader.figshare.com/files/1377644", "https://ndownloader.figshare.com/files/1377645", "https://ndownloader.figshare.com/files/1377646"], "description"=>"<div><p>Genotype-phenotype (GP) maps specify how the random mutations that change genotypes generate variation by altering phenotypes, which, in turn, can trigger selection. Many GP maps share the following general properties: 1) The total number of genotypes is much larger than the number of selectable phenotypes; 2) Neutral exploration changes the variation that is accessible to the population; 3) The distribution of phenotype frequencies , with the number of genotypes mapping onto phenotype , is highly biased: the majority of genotypes map to only a small minority of the phenotypes. Here we explore how these properties affect the evolutionary dynamics of haploid Wright-Fisher models that are coupled to a random GP map or to a more complex RNA sequence to secondary structure map. For both maps the probability of a mutation leading to a phenotype scales to first order as , although for the RNA map there are further correlations as well. By using mean-field theory, supported by computer simulations, we show that the discovery time of a phenotype similarly scales to first order as for a wide range of population sizes and mutation rates in both the monomorphic and polymorphic regimes. These differences in the rate at which variation arises can vary over many orders of magnitude. Phenotypic variation with a larger is therefore be much more likely to arise than variation with a small . We show, using the RNA model, that frequent phenotypes (with larger ) can fix in a population even when alternative, but less frequent, phenotypes with much higher fitness are potentially accessible. In other words, if the fittest never ‘arrive’ on the timescales of evolutionary change, then they can't fix. We call this highly non-ergodic effect the ‘arrival of the frequent’.</p></div>", "links"=>[], "tags"=>["biophysics", "Computational biology", "Evolutionary modeling", "population genetics", "Evolutionary biology", "mutation", "Evolutionary developmental biology", "Evolutionary ecology", "evolutionary theory", "Theoretical biology", "Nucleic acids", "rna", "RNA structure", "genotype-phenotype", "maps", "populations"], "article_id"=>927321, "categories"=>["Physics", "Biological Sciences"], "users"=>["Steffen Schaper", "Ard A. Louis"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0086635.s001", "https://dx.doi.org/10.1371/journal.pone.0086635.s002", "https://dx.doi.org/10.1371/journal.pone.0086635.s003", "https://dx.doi.org/10.1371/journal.pone.0086635.s004", "https://dx.doi.org/10.1371/journal.pone.0086635.s005", "https://dx.doi.org/10.1371/journal.pone.0086635.s006", "https://dx.doi.org/10.1371/journal.pone.0086635.s007"], "stats"=>{"downloads"=>7, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_Arrival_of_the_Frequent_How_Bias_in_Genotype_Phenotype_Maps_Can_Steer_Populations_to_Local_Optima_/927321", "title"=>"The Arrival of the Frequent: How Bias in Genotype-Phenotype Maps Can Steer Populations to Local Optima", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-02-05 03:39:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377638"], "description"=>"<p>Probability that phenotype is discovered (dotted lines) or is fixed (dashed lines) as a function of mutation rate for different relative selection coefficients for . The probability that is discovered is independent of relative fitness (within statistical simulation errors). Phenotype is much more likely to fix than phenotype , even when the latter is much more fit, due to an “arrival of the frequent” phenomenon.</p>", "links"=>[], "tags"=>["biophysics", "Computational biology", "Evolutionary modeling", "population genetics", "Evolutionary biology", "mutation", "Evolutionary developmental biology", "Evolutionary ecology", "evolutionary theory", "Theoretical biology", "Nucleic acids", "rna", "RNA structure"], "article_id"=>927319, "categories"=>["Physics", "Biological Sciences"], "users"=>["Steffen Schaper", "Ard A. Louis"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086635.g004", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_arrival_of_the_frequent_/927319", "title"=>"The arrival of the frequent.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:39:53"}

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