[{"article_type":"original","oa_version":"Published Version","type":"journal_article","department":[{"_id":"NiBa"}],"title":"Limits to selection on standing variation in an asexual population","page":"129-137","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","project":[{"_id":"bd6958e0-d553-11ed-ba76-86eba6a76c00","grant_number":"101055327","name":"Understanding the evolution of continuous genomes"}],"doi":"10.1016/j.tpb.2024.04.001","scopus_import":"1","intvolume":"       157","date_updated":"2025-09-04T13:56:11Z","publication_status":"published","status":"public","file":[{"access_level":"open_access","date_updated":"2024-05-13T08:22:21Z","file_name":"2024_TheorPopulationBiology_Barton.pdf","checksum":"78f36488d24f868d5913624e9c8d88bf","success":1,"content_type":"application/pdf","date_created":"2024-05-13T08:22:21Z","creator":"dernst","file_id":"15383","relation":"main_file","file_size":1098292}],"_id":"15358","ddc":["570"],"article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"year":"2024","day":"01","date_created":"2024-05-05T22:01:03Z","volume":157,"author":[{"last_name":"Barton","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H"},{"id":"42377A0A-F248-11E8-B48F-1D18A9856A87","first_name":"Himani","last_name":"Sachdeva","full_name":"Sachdeva, Himani"}],"quality_controlled":"1","month":"06","oa":1,"publication":"Theoretical Population Biology","corr_author":"1","abstract":[{"text":"We consider how a population of N haploid individuals responds to directional selection on standing variation, with no new variation from recombination or mutation. Individuals have trait values z1,…,zN, which are drawn from a distribution ψ; the fitness of individual i is proportional to [Formula: see text] . For illustration, we consider the Laplace and Gaussian distributions, which are parametrised only by the variance V0, and show that for large N, there is a scaling limit which depends on a single parameter NV0. When selection is weak relative to drift (NV0≪1), the variance decreases exponentially at rate 1/N, and the expected ultimate gain in log fitness (scaled by V0), is just NV0, which is the same as Robertson's (1960) prediction for a sexual population. In contrast, when selection is strong relative to drift (NV0≫1), the ultimate gain can be found by approximating the establishment of alleles by a branching process in which each allele competes independently with the population mean and the fittest allele to establish is certain to fix. Then, if the probability of survival to time t∼1/V0 of an allele with value z is P(z), with mean P¯, the winning allele is the fittest of NP¯ survivors drawn from a distribution ψP/P¯. The expected ultimate change is ∼2log(1.15NV0) for a Gaussian distribution, and ∼-12log0.36NV0-log-log0.36NV0 for a Laplace distribution. This approach also predicts the variability of the process, and its dynamics; we show that in the strong selection regime, the expected genetic variance decreases as ∼t-3 at large times. We discuss how these results may be related to selection on standing variation that is spread along a linear chromosome.","lang":"eng"}],"citation":{"ista":"Barton NH, Sachdeva H. 2024. Limits to selection on standing variation in an asexual population. Theoretical Population Biology. 157, 129–137.","ama":"Barton NH, Sachdeva H. Limits to selection on standing variation in an asexual population. <i>Theoretical Population Biology</i>. 2024;157:129-137. doi:<a href=\"https://doi.org/10.1016/j.tpb.2024.04.001\">10.1016/j.tpb.2024.04.001</a>","mla":"Barton, Nicholas H., and Himani Sachdeva. “Limits to Selection on Standing Variation in an Asexual Population.” <i>Theoretical Population Biology</i>, vol. 157, Elsevier, 2024, pp. 129–37, doi:<a href=\"https://doi.org/10.1016/j.tpb.2024.04.001\">10.1016/j.tpb.2024.04.001</a>.","chicago":"Barton, Nicholas H, and Himani Sachdeva. “Limits to Selection on Standing Variation in an Asexual Population.” <i>Theoretical Population Biology</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.tpb.2024.04.001\">https://doi.org/10.1016/j.tpb.2024.04.001</a>.","short":"N.H. Barton, H. Sachdeva, Theoretical Population Biology 157 (2024) 129–137.","apa":"Barton, N. H., &#38; Sachdeva, H. (2024). Limits to selection on standing variation in an asexual population. <i>Theoretical Population Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tpb.2024.04.001\">https://doi.org/10.1016/j.tpb.2024.04.001</a>","ieee":"N. H. Barton and H. Sachdeva, “Limits to selection on standing variation in an asexual population,” <i>Theoretical Population Biology</i>, vol. 157. Elsevier, pp. 129–137, 2024."},"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"publisher":"Elsevier","has_accepted_license":"1","pmid":1,"publication_identifier":{"eissn":["1096-0325"],"issn":["0040-5809"]},"external_id":{"pmid":["38643838"],"isi":["001237016800001"]},"acknowledgement":"We thank Emmanuel Schertzer and two reviewers for comments on this manuscript. NB thanks the European Research Council for support via the grant “HaplotypeStructure” 101055327. We would also like to give our sincere thanks to Alison Etheridge for her insight, inspiration and support over the years.","date_published":"2024-06-01T00:00:00Z","file_date_updated":"2024-05-13T08:22:21Z"},{"page":"50 - 73","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ec_funded":1,"project":[{"name":"Limits to selection in biology and in evolutionary computation","grant_number":"250152","call_identifier":"FP7","_id":"25B07788-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","type":"journal_article","department":[{"_id":"NiBa"}],"pubrep_id":"908","title":"The infinitesimal model: Definition derivation and implications","file":[{"file_name":"IST-2017-908-v1+1_1-s2.0-S0040580917300886-main_1_.pdf","checksum":"7dd02bfcfe8f244f4a6c19091aedf2c8","access_level":"open_access","date_updated":"2020-07-14T12:47:25Z","content_type":"application/pdf","date_created":"2018-12-12T10:12:45Z","file_id":"4964","creator":"system","relation":"main_file","file_size":1133924}],"_id":"626","ddc":["576"],"article_processing_charge":"No","language":[{"iso":"eng"}],"doi":"10.1016/j.tpb.2017.06.001","scopus_import":"1","intvolume":"       118","date_updated":"2025-09-11T07:29:31Z","publication_status":"published","status":"public","author":[{"full_name":"Barton, Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","last_name":"Barton","first_name":"Nicholas H"},{"full_name":"Etheridge, Alison","last_name":"Etheridge","first_name":"Alison"},{"full_name":"Véber, Amandine","first_name":"Amandine","last_name":"Véber"}],"quality_controlled":"1","month":"12","oa":1,"year":"2017","day":"01","date_created":"2018-12-11T11:47:34Z","volume":118,"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png"},"isi":1,"publisher":"Academic Press","has_accepted_license":"1","publist_id":"7169","publication_identifier":{"issn":["0040-5809"]},"file_date_updated":"2020-07-14T12:47:25Z","date_published":"2017-12-01T00:00:00Z","external_id":{"isi":["000417668700005"]},"publication":"Theoretical Population Biology","corr_author":"1","abstract":[{"text":"Our focus here is on the infinitesimal model. In this model, one or several quantitative traits are described as the sum of a genetic and a non-genetic component, the first being distributed within families as a normal random variable centred at the average of the parental genetic components, and with a variance independent of the parental traits. Thus, the variance that segregates within families is not perturbed by selection, and can be predicted from the variance components. This does not necessarily imply that the trait distribution across the whole population should be Gaussian, and indeed selection or population structure may have a substantial effect on the overall trait distribution. One of our main aims is to identify some general conditions on the allelic effects for the infinitesimal model to be accurate. We first review the long history of the infinitesimal model in quantitative genetics. Then we formulate the model at the phenotypic level in terms of individual trait values and relationships between individuals, but including different evolutionary processes: genetic drift, recombination, selection, mutation, population structure, …. We give a range of examples of its application to evolutionary questions related to stabilising selection, assortative mating, effective population size and response to selection, habitat preference and speciation. We provide a mathematical justification of the model as the limit as the number M of underlying loci tends to infinity of a model with Mendelian inheritance, mutation and environmental noise, when the genetic component of the trait is purely additive. We also show how the model generalises to include epistatic effects. We prove in particular that, within each family, the genetic components of the individual trait values in the current generation are indeed normally distributed with a variance independent of ancestral traits, up to an error of order 1∕M. Simulations suggest that in some cases the convergence may be as fast as 1∕M.","lang":"eng"}],"citation":{"ista":"Barton NH, Etheridge A, Véber A. 2017. The infinitesimal model: Definition derivation and implications. Theoretical Population Biology. 118, 50–73.","mla":"Barton, Nicholas H., et al. “The Infinitesimal Model: Definition Derivation and Implications.” <i>Theoretical Population Biology</i>, vol. 118, Academic Press, 2017, pp. 50–73, doi:<a href=\"https://doi.org/10.1016/j.tpb.2017.06.001\">10.1016/j.tpb.2017.06.001</a>.","ama":"Barton NH, Etheridge A, Véber A. The infinitesimal model: Definition derivation and implications. <i>Theoretical Population Biology</i>. 2017;118:50-73. doi:<a href=\"https://doi.org/10.1016/j.tpb.2017.06.001\">10.1016/j.tpb.2017.06.001</a>","apa":"Barton, N. H., Etheridge, A., &#38; Véber, A. (2017). The infinitesimal model: Definition derivation and implications. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1016/j.tpb.2017.06.001\">https://doi.org/10.1016/j.tpb.2017.06.001</a>","short":"N.H. Barton, A. Etheridge, A. Véber, Theoretical Population Biology 118 (2017) 50–73.","chicago":"Barton, Nicholas H, Alison Etheridge, and Amandine Véber. “The Infinitesimal Model: Definition Derivation and Implications.” <i>Theoretical Population Biology</i>. Academic Press, 2017. <a href=\"https://doi.org/10.1016/j.tpb.2017.06.001\">https://doi.org/10.1016/j.tpb.2017.06.001</a>.","ieee":"N. H. Barton, A. Etheridge, and A. Véber, “The infinitesimal model: Definition derivation and implications,” <i>Theoretical Population Biology</i>, vol. 118. Academic Press, pp. 50–73, 2017."}},{"oa_version":"Submitted Version","type":"journal_article","department":[{"_id":"NiBa"}],"pubrep_id":"972","title":"Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti","page":"45 - 60","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1016/j.tpb.2017.03.003","scopus_import":"1","intvolume":"       115","date_updated":"2025-07-10T12:01:49Z","publication_status":"published","status":"public","_id":"952","file":[{"date_created":"2019-04-17T06:39:45Z","content_type":"application/pdf","date_updated":"2020-07-14T12:48:16Z","access_level":"open_access","checksum":"9aeff86fa7de69f7a15cf4fc60d57d01","file_name":"2017_TheoreticalPopulationBio_Turelli.pdf","file_size":2073856,"relation":"main_file","file_id":"6327","creator":"dernst"}],"ddc":["576"],"language":[{"iso":"eng"}],"article_processing_charge":"No","year":"2017","day":"01","date_created":"2018-12-11T11:49:22Z","volume":115,"author":[{"full_name":"Turelli, Michael","last_name":"Turelli","first_name":"Michael"},{"orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","full_name":"Barton, Nicholas H"}],"quality_controlled":"1","month":"06","oa":1,"publication":"Theoretical Population Biology","abstract":[{"lang":"eng","text":"A novel strategy for controlling the spread of arboviral diseases such as dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness costs through lower viability or fecundity. These maternally inherited bacteria also produce a frequency-dependent advantage for infected females by inducing cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected females mated to infected males. These competing effects, a frequency-dependent advantage and frequency-independent costs, produce bistable Wolbachia frequency dynamics. Above a threshold frequency, denoted pˆ, CI drives fitness-decreasing Wolbachia transinfections through local populations; but below pˆ, infection frequencies tend to decline to zero. If pˆ is not too high, CI also drives spatial spread once infections become established over sufficiently large areas. We illustrate how simple models provide testable predictions concerning the spatial and temporal dynamics of Wolbachia introductions, focusing on rate of spatial spread, the shape of spreading waves, and the conditions for initiating spread from local introductions. First, we consider the robustness of diffusion-based predictions to incorporating two important features of wMel-Aedes aegypti biology that may be inconsistent with the diffusion approximations, namely fast local dynamics induced by complete CI (i.e., all embryos produced from incompatible crosses die) and long-tailed, non-Gaussian dispersal. With complete CI, our numerical analyses show that long-tailed dispersal changes wave-width predictions only slightly; but it can significantly reduce wave speed relative to the diffusion prediction; it also allows smaller local introductions to initiate spatial spread. Second, we use approximations for pˆ and dispersal distances to predict the outcome of 2013 releases of wMel-infected Aedes aegypti in Cairns, Australia, Third, we describe new data from Ae. aegypti populations near Cairns, Australia that demonstrate long-distance dispersal and provide an approximate lower bound on pˆ for wMel in northeastern Australia. Finally, we apply our analyses to produce operational guidelines for efficient transformation of vector populations over large areas. We demonstrate that even very slow spatial spread, on the order of 10-20 m/month (as predicted), can produce area-wide population transformation within a few years following initial releases covering about 20-30% of the target area."}],"citation":{"ista":"Turelli M, Barton NH. 2017. Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti. Theoretical Population Biology. 115, 45–60.","ama":"Turelli M, Barton NH. Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti. <i>Theoretical Population Biology</i>. 2017;115:45-60. doi:<a href=\"https://doi.org/10.1016/j.tpb.2017.03.003\">10.1016/j.tpb.2017.03.003</a>","mla":"Turelli, Michael, and Nicholas H. Barton. “Deploying Dengue-Suppressing Wolbachia: Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.” <i>Theoretical Population Biology</i>, vol. 115, Elsevier, 2017, pp. 45–60, doi:<a href=\"https://doi.org/10.1016/j.tpb.2017.03.003\">10.1016/j.tpb.2017.03.003</a>.","short":"M. Turelli, N.H. Barton, Theoretical Population Biology 115 (2017) 45–60.","chicago":"Turelli, Michael, and Nicholas H Barton. “Deploying Dengue-Suppressing Wolbachia: Robust Models Predict Slow but Effective Spatial Spread in Aedes Aegypti.” <i>Theoretical Population Biology</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.tpb.2017.03.003\">https://doi.org/10.1016/j.tpb.2017.03.003</a>.","apa":"Turelli, M., &#38; Barton, N. H. (2017). Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti. <i>Theoretical Population Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.tpb.2017.03.003\">https://doi.org/10.1016/j.tpb.2017.03.003</a>","ieee":"M. Turelli and N. H. Barton, “Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti,” <i>Theoretical Population Biology</i>, vol. 115. Elsevier, pp. 45–60, 2017."},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png"},"publisher":"Elsevier","has_accepted_license":"1","pmid":1,"publist_id":"6463","publication_identifier":{"issn":["0040-5809"]},"external_id":{"pmid":["28411063"]},"file_date_updated":"2020-07-14T12:48:16Z","date_published":"2017-06-01T00:00:00Z"},{"language":[{"iso":"eng"}],"article_processing_charge":"No","_id":"4263","status":"public","issue":"1","publication_status":"published","date_updated":"2023-06-06T09:57:49Z","intvolume":"        61","doi":"10.1006/tpbi.2001.1557","scopus_import":"1","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","page":"31 - 48","title":"Neutral evolution in spatially continuous populations","type":"journal_article","oa_version":"None","article_type":"original","acknowledgement":"This work was supported by grants from the EPSRC (GR/L10048 and an advanced fellowship for A.M.E.) and NERC (GR3/11635) and by the Darwin Trust of Edinburgh. We thank Anja Sturm for her assistance with the project and anonymous reviewers for helpful comments. This paper is dedicated to Charlotte, A.M.E.’s daughter born during the gestation of the manuscript.","external_id":{"pmid":["11895381"]},"date_published":"2002-02-01T00:00:00Z","publication_identifier":{"issn":["0040-5809"]},"publist_id":"1830","pmid":1,"publisher":"Academic Press","citation":{"ama":"Barton NH, Depaulis F, Etheridge A. Neutral evolution in spatially continuous populations. <i>Theoretical Population Biology</i>. 2002;61(1):31-48. doi:<a href=\"https://doi.org/10.1006/tpbi.2001.1557\">10.1006/tpbi.2001.1557</a>","mla":"Barton, Nicholas H., et al. “Neutral Evolution in Spatially Continuous Populations.” <i>Theoretical Population Biology</i>, vol. 61, no. 1, Academic Press, 2002, pp. 31–48, doi:<a href=\"https://doi.org/10.1006/tpbi.2001.1557\">10.1006/tpbi.2001.1557</a>.","ista":"Barton NH, Depaulis F, Etheridge A. 2002. Neutral evolution in spatially continuous populations. Theoretical Population Biology. 61(1), 31–48.","ieee":"N. H. Barton, F. Depaulis, and A. Etheridge, “Neutral evolution in spatially continuous populations,” <i>Theoretical Population Biology</i>, vol. 61, no. 1. Academic Press, pp. 31–48, 2002.","short":"N.H. Barton, F. Depaulis, A. Etheridge, Theoretical Population Biology 61 (2002) 31–48.","chicago":"Barton, Nicholas H, Frantz Depaulis, and Alison Etheridge. “Neutral Evolution in Spatially Continuous Populations.” <i>Theoretical Population Biology</i>. Academic Press, 2002. <a href=\"https://doi.org/10.1006/tpbi.2001.1557\">https://doi.org/10.1006/tpbi.2001.1557</a>.","apa":"Barton, N. H., Depaulis, F., &#38; Etheridge, A. (2002). Neutral evolution in spatially continuous populations. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1006/tpbi.2001.1557\">https://doi.org/10.1006/tpbi.2001.1557</a>"},"abstract":[{"text":"We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, σe; the effective population density, ρe; and a local scale, κ, at which local interactions become significant. The results are illustrated by simulations.","lang":"eng"}],"publication":"Theoretical Population Biology","month":"02","quality_controlled":"1","author":[{"full_name":"Barton, Nicholas H","last_name":"Barton","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240"},{"last_name":"Depaulis","first_name":"Frantz","full_name":"Depaulis, Frantz"},{"full_name":"Etheridge, Alison","first_name":"Alison","last_name":"Etheridge"}],"volume":61,"date_created":"2018-12-11T12:07:55Z","day":"01","year":"2002"},{"year":"2000","day":"01","date_created":"2018-12-11T12:07:58Z","volume":57,"author":[{"orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","last_name":"Barton","first_name":"Nicholas H","full_name":"Barton, Nicholas H"},{"last_name":"Shpak","first_name":"Max","full_name":"Shpak, Max"}],"quality_controlled":"1","month":"05","publication":"Theoretical Population Biology","abstract":[{"text":"Analysis of multilocus evolution is usually intractable for more than n ~ 10 genes, because the frequencies of very large numbers of genotypes must be followed. An exact analysis of up to n ~ 100 loci is feasible for a symmetrical model, in which a set of unlinked loci segregate for two alleles (labeled '0' and '1') with interchangeable effects on fitness. All haploid genotypes with the same number of 1 alleles can then remain equally frequent. However, such a symmetrical solution may be unstable: for example, under stabilizing selection, populations tend to fix any one genotype which approaches the optimum. Here, we show how the 2' x 2' stability matrix can be decomposed into a set of matrices, each no larger than n x n. This allows the stability of symmetrical solutions to be determined. We apply the method to stabilizing and disruptive selection in a single deme and to selection against heterozygotes in a linear cline. (C) 2000 Academic Press.","lang":"eng"}],"citation":{"ama":"Barton NH, Shpak M. The stability of symmetrical solutions to polygenic models. <i>Theoretical Population Biology</i>. 2000;57(3):249-263. doi:<a href=\"https://doi.org/10.1006/tpbi.2000.1455\">10.1006/tpbi.2000.1455</a>","mla":"Barton, Nicholas H., and Max Shpak. “The Stability of Symmetrical Solutions to Polygenic Models.” <i>Theoretical Population Biology</i>, vol. 57, no. 3, Academic Press, 2000, pp. 249–63, doi:<a href=\"https://doi.org/10.1006/tpbi.2000.1455\">10.1006/tpbi.2000.1455</a>.","ista":"Barton NH, Shpak M. 2000. The stability of symmetrical solutions to polygenic models. Theoretical Population Biology. 57(3), 249–263.","ieee":"N. H. Barton and M. Shpak, “The stability of symmetrical solutions to polygenic models,” <i>Theoretical Population Biology</i>, vol. 57, no. 3. Academic Press, pp. 249–263, 2000.","short":"N.H. Barton, M. Shpak, Theoretical Population Biology 57 (2000) 249–263.","chicago":"Barton, Nicholas H, and Max Shpak. “The Stability of Symmetrical Solutions to Polygenic Models.” <i>Theoretical Population Biology</i>. Academic Press, 2000. <a href=\"https://doi.org/10.1006/tpbi.2000.1455\">https://doi.org/10.1006/tpbi.2000.1455</a>.","apa":"Barton, N. H., &#38; Shpak, M. (2000). The stability of symmetrical solutions to polygenic models. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1006/tpbi.2000.1455\">https://doi.org/10.1006/tpbi.2000.1455</a>"},"publisher":"Academic Press","pmid":1,"publist_id":"1820","publication_identifier":{"issn":["0040-5809"]},"external_id":{"pmid":["10828217"]},"date_published":"2000-05-01T00:00:00Z","article_type":"original","oa_version":"None","type":"journal_article","title":"The stability of symmetrical solutions to polygenic models","page":"249 - 263","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","doi":"10.1006/tpbi.2000.1455","intvolume":"        57","date_updated":"2023-04-19T12:36:39Z","issue":"3","publication_status":"published","status":"public","_id":"4272","language":[{"iso":"eng"}],"article_processing_charge":"No"},{"article_processing_charge":"No","language":[{"iso":"eng"}],"_id":"3649","intvolume":"        38","scopus_import":"1","doi":"10.1016/0040-5809(90)90002-D","issue":"1","publication_status":"published","status":"public","date_updated":"2026-03-16T13:25:00Z","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1 - 57","oa_version":"None","type":"journal_article","article_type":"original","title":"Dynamics of polygenic characters under selection","publisher":"Academic Press","publication_identifier":{"issn":["0040-5809"]},"acknowledgement":"We thank R. Burger, J. A. Coyne, W. G. Hill, A. A. Hoffmann, J. H. Gillespie, M. Slatkin, T. Nagylaki and Z.-B. Zeng for helpful discussions and comments on earlier drafts. Our research is supported by grants from the National Science Foundation (BSR-8866548), the Science and Engineering Research Council, and the Institute of Theoretical Dynamics at UCD. ","date_published":"1990-01-01T00:00:00Z","publist_id":"2734","publication":"Theoretical Population Biology","citation":{"apa":"Turelli, M., &#38; Barton, N. H. (1990). Dynamics of polygenic characters under selection. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">https://doi.org/10.1016/0040-5809(90)90002-D</a>","short":"M. Turelli, N.H. Barton, Theoretical Population Biology 38 (1990) 1–57.","chicago":"Turelli, Michael, and Nicholas H Barton. “Dynamics of Polygenic Characters under Selection.” <i>Theoretical Population Biology</i>. Academic Press, 1990. <a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">https://doi.org/10.1016/0040-5809(90)90002-D</a>.","ieee":"M. Turelli and N. H. Barton, “Dynamics of polygenic characters under selection,” <i>Theoretical Population Biology</i>, vol. 38, no. 1. Academic Press, pp. 1–57, 1990.","ista":"Turelli M, Barton NH. 1990. Dynamics of polygenic characters under selection. Theoretical Population Biology. 38(1), 1–57.","mla":"Turelli, Michael, and Nicholas H. Barton. “Dynamics of Polygenic Characters under Selection.” <i>Theoretical Population Biology</i>, vol. 38, no. 1, Academic Press, 1990, pp. 1–57, doi:<a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">10.1016/0040-5809(90)90002-D</a>.","ama":"Turelli M, Barton NH. Dynamics of polygenic characters under selection. <i>Theoretical Population Biology</i>. 1990;38(1):1-57. doi:<a href=\"https://doi.org/10.1016/0040-5809(90)90002-D\">10.1016/0040-5809(90)90002-D</a>"},"abstract":[{"text":"Selection on polygenic characters is generally analyzed by statistical methods that assume a Gaussian (normal) distribution of breeding values. We present an alternative analysis based on multilocus population genetics. We use a general representation of selection, recombination, and drift to analyze an idealized polygenic system in which all genetic effects are additive (i.e., both dominance and epistasis are absent), but no assumptions are made about the distribution of breeding values or the numbers of loci or alleles. Our analysis produces three results. First, our equations reproduce the standard recursions for the mean and additive variance if breeding values are Gaussian; but they also reveal how non-Gaussian distributions of breeding values will alter these dynamics. Second, an approximation valid for weak selection shows that even if genetic variance is attributable to an effectively infinite number of loci with only additive effects, selection will generally drive the distribution of breeding values away from a Gaussian distribution by creating multilocus linkage disequilibria. Long-term dynamics of means can depart substantially from the predictions of the standard selection recursions, but the discrepancy may often be negligible for short-term selection. Third, by including mutation, we show that, for realistic parameter values, linkage disequilibrium has little effect on the amount of additive variance maintained at an equilibrium between stabilizing selection and mutation. Each of these analytical results is supported by numerical calculations.","lang":"eng"}],"month":"01","author":[{"full_name":"Turelli, Michael","first_name":"Michael","last_name":"Turelli"},{"full_name":"Barton, Nicholas H","last_name":"Barton","first_name":"Nicholas H","orcid":"0000-0002-8548-5240","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"}],"quality_controlled":"1","date_created":"2018-12-11T12:04:26Z","year":"1990","day":"01","volume":38},{"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/0040580987900165?via%3Dihub"}],"publication":"Theoretical Population Biology","citation":{"ista":"Rouhani S, Barton NH. 1987. Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. Theoretical Population Biology. 31(3), 465–492.","ama":"Rouhani S, Barton NH. Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. <i>Theoretical Population Biology</i>. 1987;31(3):465-492. doi:<a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">10.1016/0040-5809(87)90016-5</a>","mla":"Rouhani, Shahin, and Nicholas H. Barton. “Speciation and the &#38;quot;Shifting Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>, vol. 31, no. 3, Elsevier, 1987, pp. 465–92, doi:<a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">10.1016/0040-5809(87)90016-5</a>.","chicago":"Rouhani, Shahin, and Nicholas H Barton. “Speciation and the &#38;quot;Shifting Balance&#38;quot; in a Continuous Population.” <i>Theoretical Population Biology</i>. Elsevier, 1987. <a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">https://doi.org/10.1016/0040-5809(87)90016-5</a>.","short":"S. Rouhani, N.H. Barton, Theoretical Population Biology 31 (1987) 465–492.","apa":"Rouhani, S., &#38; Barton, N. H. (1987). Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population. <i>Theoretical Population Biology</i>. Elsevier. <a href=\"https://doi.org/10.1016/0040-5809(87)90016-5\">https://doi.org/10.1016/0040-5809(87)90016-5</a>","ieee":"S. Rouhani and N. H. Barton, “Speciation and the &#38;quot;shifting balance&#38;quot; in a continuous population,” <i>Theoretical Population Biology</i>, vol. 31, no. 3. Elsevier, pp. 465–492, 1987."},"abstract":[{"lang":"eng","text":"Shifts between adaptive peaks, caused by sampling drift, are involved in both speciation and adaptation via Wright's “shiftingbalance.” We use techniques from statistical mechanics to calculate the rate of such transitions for apopulation in a single panmictic deme and for apopulation which is continuously distributed over one- and two-dimensional regions. This calculation applies in the limit where transitions are rare. Our results indicate that stochastic divergence is feasible despite free gene flow, provided that neighbourhood size is low enough. In two dimensions, the rate of transition depends primarily on neighbourhood size N and only weakly on selection pressure (≈sk exp(− cN)), where k is a number determined by the local population structure, in contrast with the exponential dependence on selection pressure in one dimension (≈exp(− cN √s)) or in a single deme (≈exp(− cNs)). Our calculations agree with simulations of a single deme and a one-dimensional population."}],"publisher":"Elsevier","acknowledgement":"We thank M. Shaw, J. Felsenstein, M. Kirkpatrick, S. Via, J. S. Jones, M. Slatkin, J. Mallet, and B. Charlesworth for their helpful comments. This work was supported by grants from the SERC (GR/C/91529), the University of London Central Research Fund, and the Nufield Foundation. \r\n","date_published":"1987-06-01T00:00:00Z","publication_identifier":{"eissn":["1096-0325"],"issn":["0040-5809"]},"publist_id":"2726","date_created":"2018-12-11T12:04:28Z","day":"01","year":"1987","volume":31,"month":"06","quality_controlled":"1","author":[{"full_name":"Rouhani, Shahin","first_name":"Shahin","last_name":"Rouhani"},{"last_name":"Barton","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H"}],"intvolume":"        31","doi":"10.1016/0040-5809(87)90016-5","scopus_import":"1","status":"public","publication_status":"published","issue":"3","date_updated":"2022-02-04T12:30:10Z","article_processing_charge":"No","language":[{"iso":"eng"}],"_id":"3657","type":"journal_article","oa_version":"None","article_type":"original","title":"Speciation and the &quot;shifting balance&quot; in a continuous population","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","extern":"1","page":"465 - 492"},{"page":"407 - 437","extern":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","article_type":"original","oa_version":"None","type":"journal_article","title":"Intrachromosomal gene conversion, linkage, and the evolution of multigene families","_id":"3662","article_processing_charge":"No","language":[{"iso":"eng"}],"scopus_import":"1","doi":"10.1016/0040-5809(86)90017-1","intvolume":"        29","date_updated":"2022-02-01T15:50:10Z","issue":"3","publication_status":"published","status":"public","author":[{"full_name":"Nagylaki, Thomas","last_name":"Nagylaki","first_name":"Thomas"},{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8548-5240","first_name":"Nicholas H","last_name":"Barton","full_name":"Barton, Nicholas H"}],"quality_controlled":"1","month":"06","year":"1986","day":"01","date_created":"2018-12-11T12:04:30Z","volume":29,"publisher":"Academic Press","publist_id":"2721","publication_identifier":{"issn":["0040-5809"],"eissn":["1096-0325"]},"acknowledgement":"Supported by National Science Foundation Grant DEB81-03530","date_published":"1986-06-01T00:00:00Z","publication":"Theoretical Population Biology","abstract":[{"lang":"eng","text":"The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the “homogeneous” approximation to this “exact” model, end effects are disregarded; in the “exchangeable” approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that (i) the exchangeable and homogeneous models are both qualitatively correct, (ii) the exchangeable model is sometimes too inaccurate for quantitative conclusions, and (iii) the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions."}],"citation":{"mla":"Nagylaki, Thomas, and Nicholas H. Barton. “Intrachromosomal Gene Conversion, Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>, vol. 29, no. 3, Academic Press, 1986, pp. 407–37, doi:<a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">10.1016/0040-5809(86)90017-1</a>.","ama":"Nagylaki T, Barton NH. Intrachromosomal gene conversion, linkage, and the evolution of multigene families. <i>Theoretical Population Biology</i>. 1986;29(3):407-437. doi:<a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">10.1016/0040-5809(86)90017-1</a>","ista":"Nagylaki T, Barton NH. 1986. Intrachromosomal gene conversion, linkage, and the evolution of multigene families. Theoretical Population Biology. 29(3), 407–437.","ieee":"T. Nagylaki and N. H. Barton, “Intrachromosomal gene conversion, linkage, and the evolution of multigene families,” <i>Theoretical Population Biology</i>, vol. 29, no. 3. Academic Press, pp. 407–437, 1986.","apa":"Nagylaki, T., &#38; Barton, N. H. (1986). Intrachromosomal gene conversion, linkage, and the evolution of multigene families. <i>Theoretical Population Biology</i>. Academic Press. <a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">https://doi.org/10.1016/0040-5809(86)90017-1</a>","chicago":"Nagylaki, Thomas, and Nicholas H Barton. “Intrachromosomal Gene Conversion, Linkage, and the Evolution of Multigene Families.” <i>Theoretical Population Biology</i>. Academic Press, 1986. <a href=\"https://doi.org/10.1016/0040-5809(86)90017-1\">https://doi.org/10.1016/0040-5809(86)90017-1</a>.","short":"T. Nagylaki, N.H. Barton, Theoretical Population Biology 29 (1986) 407–437."}}]