The Advantage of Arriving First: Characteristic Times in Finite Size Populations of Error-Prone Replicators
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{"title"=>"The advantage of arriving first: Characteristic times in finite size populations of error-prone replicators", "type"=>"journal", "authors"=>[{"first_name"=>"Arturo", "last_name"=>"Marín", "scopus_author_id"=>"36131889700"}, {"first_name"=>"Héctor", "last_name"=>"Tejero", "scopus_author_id"=>"35111765200"}, {"first_name"=>"Juan Carlos", "last_name"=>"Nuño", "scopus_author_id"=>"7005114440"}, {"first_name"=>"Francisco", "last_name"=>"Montero", "scopus_author_id"=>"55199205200"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"372292928", "scopus"=>"2-s2.0-84893441502", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"24376656", "sgr"=>"84893441502", "issn"=>"19326203", "doi"=>"10.1371/journal.pone.0083142"}, "id"=>"098b6114-c505-3d20-a2fc-76c8f1960823", "abstract"=>"We study the evolution of a finite size population formed by mutationally isolated lineages of error-prone replicators in a two-peak fitness landscape. Computer simulations are performed to gain a stochastic description of the system dynamics. More specifically, for different population sizes, we compute the probability of each lineage being selected in terms of their mutation rates and the amplification factors of the fittest phenotypes. We interpret the results as the compromise between the characteristic time a lineage takes to reach its fittest phenotype by crossing the neutral valley and the selective value of the sequences that form the lineages. A main conclusion is drawn: for finite population sizes, the survival probability of the lineage that arrives first to the fittest phenotype rises significantly.", "link"=>"http://www.mendeley.com/research/advantage-arriving-first-characteristic-times-finite-size-populations-errorprone-replicators", "reader_count"=>11, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>2, "Researcher"=>3, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>1, "Student > Postgraduate"=>1, "Student > Master"=>1, "Professor"=>1}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>2, "Researcher"=>3, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>1, "Student > Postgraduate"=>1, "Student > Master"=>1, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>1, "Engineering"=>1, "Biochemistry, Genetics and Molecular Biology"=>1, "Agricultural and Biological Sciences"=>4, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>2, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>4}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>1}}, "reader_count_by_country"=>{"Brazil"=>1, "Israel"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1326396"], "description"=>"<p>In all cases, the rest of the population is formed by . Each graph considers a different value of the amplification factors of the fittest phenotypes . Concretely: (A) ; (B) ; (C) and (D) . The rest of the amplification factors are: and and the mutation rates of and are and , respectively. As in the previous figure, for each experimental setup runs were performed for and runs for larger populations sizes.</p>", "links"=>[], "tags"=>["fixation", "lineage", "percentages"], "article_id"=>884955, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g008", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentage_of_fixation_of_lineage_in_terms_of_the_population_size_in_the_competition_against_for_different_initial_percentages_of_blue_lines_green_lines_red_lines_cyan_lines_and_violet_lines_/884955", "title"=>"Percentage of fixation of lineage in terms of the population size in the competition against for different initial percentages of : (blue lines), (green lines), (red lines), (cyan lines) and (violet lines).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326374"], "description"=>"<p>The mutation rates are (A) and (B) . Note that the trajectories of both models are quite similar to the trajectories corresponding to the reduced model shifted to the left i.e. to lower values of time.</p>", "links"=>[], "tags"=>["molar", "fractions", "phenotypes", "h-model", "divided", "hamming", "classes", "subindex", "curves", "reduced", "r-model"], "article_id"=>884943, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g002", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_evolution_of_the_molar_fractions_of_each_of_the_three_phenotypes_and_for_the_h_model_divided_into_Hamming_classes_denoted_by_the_subindex_and_curves_in_blue_and_the_reduced_r_model_subindex_and_red_curves_/884943", "title"=>"Time evolution of the molar fractions of each of the three phenotypes (, and ) for the h-model divided into Hamming classes (denoted by the subindex and curves in blue) and the reduced r-model (subindex and red curves).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326375"], "description"=>"<p>The mutation rate varies in the interval in constant steps of . The amplification factors are , and . Note that both curves are qualitatively similar to that corresponding to the reduced model shifted to lower values of the characteristic time.</p>", "links"=>[], "tags"=>["molar", "phenotype", "genotype", "formed", "mutation", "h-model", "r-model"], "article_id"=>884944, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Characteristic_time_of_the_molar_fraction_of_the_phenotype_whose_genotype_is_formed_by_all_1_as_a_function_of_the_mutation_rate_for_both_the_h_model_blue_and_the_r_model_red_/884944", "title"=>"Characteristic time of the molar fraction of the phenotype whose genotype is formed by all 1 as a function of the mutation rate for both the h-model (blue) and the r-model (red).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326398"], "description"=>"a<p>Lowest values of .</p><p>Mean and standard deviation of for the phenotype for different values of the mutation rate, population size and amplification factor . In all simulations, the whole population is initially formed by sequences with an amplification factor . As before, the amplification factor of the error tail is . For each experimental setup 200 runs were performed.</p>", "links"=>[], "tags"=>["deviation", "stochastic"], "article_id"=>884957, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.t001", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Mean_and_standard_deviation_of_the_characteristic_time_obtained_in_the_stochastic_simulations_/884957", "title"=>"Mean and standard deviation of the characteristic time obtained in the stochastic simulations.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326373"], "description"=>"<p>Initially, the whole population is formed by sequences , i.e. . It is assumed that the amplification factors of all the sequences that belong to the Hamming classes are equal and are given by . The amplification factors of the master copies that form the Hamming classes and are and , respectively. The mutation rate is .</p>", "links"=>[], "tags"=>["molar", "hamming", "classes"], "article_id"=>884942, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g001", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Time_evolution_of_the_molar_fraction_of_each_of_the_eleven_Hamming_classes_to_that_form_the_sequence_space_when_/884942", "title"=>"Time evolution of the molar fraction of each of the eleven Hamming classes ( to ) that form the sequence space when .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326397"], "description"=>"<p>Percentage of fixation of each of the five lineages with different mutation rates in terms of the population size () and the amplification factor of the fittest phenotype (). As before, and in all the lineages. For each experimental setup 1000 runs were performed for , and 200 runs for .</p>", "links"=>[], "tags"=>["fixation", "lineage", "stochastic"], "article_id"=>884956, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.t002", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentage_of_fixation_of_each_lineage_during_the_stochastic_competition_of_five_lineages_/884956", "title"=>"Percentage of fixation of each lineage during the stochastic competition of five lineages.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326387"], "description"=>"<p>The mutation rates of the two lineages and are and , respectively. As before, the amplification factors of each phenotype in both lineages are: , and . The whole population is initially formed by genotypes , shared equally in both lineages. Figure (A) depicts the time evolution of each of the three phenotypes that form each lineage. Solid curves correspond to phenotypes of , whereas dashed lines are for phenotypes of . In figure (B) the three phenotypes are aggregated to yield the molar fraction of each lineage, (solid blue line) and (dashed green line). In (C) the time evolution of the average fitness of the population () is shown. The three phases that appear in the temporal evolution of the phenotypes and molar fractions of the lineages are separated by vertical black lines (see main text for more details).</p>", "links"=>[], "tags"=>["deterministic", "numerical", "corresponding", "ode"], "article_id"=>884951, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g006", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Lineage_competition_in_the_deterministic_limit_obtained_by_numerical_integration_of_the_corresponding_ODE_system_/884951", "title"=>"Lineage competition in the deterministic limit obtained by numerical integration of the corresponding ODE system.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326388"], "description"=>"<p>In all cases, the values of the other amplification factors are and and the mutation rate of is . As before, the initial population is divided equally into genotypes of both lineages. The values of used are: 0.1 (blue lines), 0.075 (green lines), 0.05 (red lines) and 0.025 (cyan lines). The population sizes simulated are: , , , , and . For low populations sizes runs were carried out for each experimental setup, whereas for two hundred runs were enough to have negligible statistical errors.</p>", "links"=>[], "tags"=>["fixation", "lineage", "mutation", "sequences", "amplification"], "article_id"=>884952, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g007", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentage_of_fixation_of_lineage_as_a_function_of_the_population_size_in_the_competition_against_the_other_lineage_for_different_values_of_the_mutation_rate_of_the_sequences_that_form_and_for_different_values_of_the_amplification_factor_A_B_C_and_D_/884952", "title"=>"Percentage of fixation of lineage as a function of the population size in the competition against the other lineage for different values of the mutation rate of the sequences that form and for different values of the amplification factor : (A) ; (B) ; (C) and (D) .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326383"], "description"=>"<p> of the initial population is formed by genotypes of lineage and the rest of genotypes . The amplification factors are: for and , and for . The mutation rate of the sequences of , , ranges from to . Concretely, the -values used are: and . The population sizes that correspond to each curve are: (blue line), (green) and (red). The right vertical axis represents the deterministic molar fraction. The violet curve represents the equilibrium molar fraction obtained by numerical integration of the ODE system for values of at constant steps of . Note that in the deterministic limit of infinite population an abrupt transition occurs at a mutation rate of . As it can be seen, this transition occurs gradually for finite size populations.</p>", "links"=>[], "tags"=>["fixation", "lineage", "formed", "error-prone", "self-replicative", "sequences", "null", "mutation", "sizes"], "article_id"=>884947, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g005", "stats"=>{"downloads"=>0, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentage_of_fixation_of_lineage_formed_by_error_prone_self_replicative_sequences_against_lineage_formed_by_a_sequence_with_a_null_mutation_rate_i_e_for_different_population_sizes_/884947", "title"=>"Percentage of fixation of lineage formed by error-prone self-replicative sequences against lineage formed by a sequence with a null mutation rate (i.e. ) for different population sizes .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}
  • {"files"=>["https://ndownloader.figshare.com/files/1326381"], "description"=>"<p>In the main figure the amplification factor of the fittest phenotype is: 5 (blue curve), 10, (green), 20 (red) and 30 (cyan). In the inset, takes the values: (blue curve), (green curve) and (red curve). In all cases, and . The points in the curves of the main picture correspond to the values mutation rate (from left to right), . These values are applied later in stochastic simulations. As expected, increasing the value of the highest peak in the sequence landscape, , reduces the characteristic time. Furthermore, as depicted in the inset, as approaches the curves tend to become monotonous and move up several order of magnitude.</p>", "links"=>[], "tags"=>["reduced", "r-model", "mutation", "rates", "steps"], "article_id"=>884946, "categories"=>["Biological Sciences", "Ecology"], "users"=>["Arturo Marín", "Héctor Tejero", "Juan Carlos Nuño", "Francisco Montero"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0083142.g004", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Values_of_the_characteristic_time_for_the_reduced_r_model_for_mutation_rates_in_the_range_at_constant_steps_/884946", "title"=>"Values of the characteristic time for the reduced r-model for mutation rates in the range at constant steps .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-12-23 03:09:43"}

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