[{"_id":"626","license":"https://creativecommons.org/licenses/by/4.0/","scopus_import":1,"author":[{"full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","last_name":"Barton","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Etheridge","first_name":"Alison","full_name":"Etheridge, Alison"},{"last_name":"Véber","first_name":"Amandine","full_name":"Véber, Amandine"}],"publication_status":"published","department":[{"_id":"NiBa"}],"date_created":"2018-12-11T11:47:34Z","title":"The infinitesimal model: Definition derivation and implications","pubrep_id":"908","intvolume":"       118","page":"50 - 73","ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:47:25Z","publisher":"Academic Press","date_updated":"2021-01-12T08:06:50Z","year":"2017","citation":{"ista":"Barton NH, Etheridge A, Véber A. 2017. The infinitesimal model: Definition derivation and implications. Theoretical Population Biology. 118, 50–73.","short":"N.H. Barton, A. Etheridge, A. Véber, Theoretical Population Biology 118 (2017) 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>.","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.","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>"},"doi":"10.1016/j.tpb.2017.06.001","day":"01","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"}],"volume":118,"ddc":["576"],"publication":"Theoretical Population Biology","has_accepted_license":"1","oa_version":"Published Version","project":[{"grant_number":"250152","name":"Limits to selection in biology and in evolutionary computation","_id":"25B07788-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"month":"12","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2017-12-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["00405809"]},"oa":1,"publist_id":"7169","file":[{"creator":"system","file_id":"4964","relation":"main_file","access_level":"open_access","file_name":"IST-2017-908-v1+1_1-s2.0-S0040580917300886-main_1_.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:47:25Z","file_size":1133924,"checksum":"7dd02bfcfe8f244f4a6c19091aedf2c8","date_created":"2018-12-12T10:12:45Z"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"has_accepted_license":"1","publication":"Theoretical Population Biology","oa_version":"Submitted Version","month":"06","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png"},"type":"journal_article","date_published":"2017-06-01T00:00:00Z","publication_identifier":{"issn":["00405809"]},"publist_id":"6463","oa":1,"file":[{"creator":"dernst","file_id":"6327","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_name":"2017_TheoreticalPopulationBio_Turelli.pdf","date_updated":"2020-07-14T12:48:16Z","file_size":2073856,"checksum":"9aeff86fa7de69f7a15cf4fc60d57d01","date_created":"2019-04-17T06:39:45Z"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","scopus_import":"1","pmid":1,"_id":"952","author":[{"last_name":"Turelli","first_name":"Michael","full_name":"Turelli, Michael"},{"id":"4880FE40-F248-11E8-B48F-1D18A9856A87","first_name":"Nicholas H","last_name":"Barton","orcid":"0000-0002-8548-5240","full_name":"Barton, Nicholas H"}],"department":[{"_id":"NiBa"}],"date_created":"2018-12-11T11:49:22Z","article_processing_charge":"No","publication_status":"published","intvolume":"       115","pubrep_id":"972","title":"Deploying dengue-suppressing Wolbachia: Robust models predict slow but effective spatial spread in Aedes aegypti","quality_controlled":"1","page":"45 - 60","file_date_updated":"2020-07-14T12:48:16Z","publisher":"Elsevier","citation":{"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>","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.","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>.","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.","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."},"year":"2017","date_updated":"2023-09-22T10:02:21Z","external_id":{"pmid":["28411063"]},"day":"01","doi":"10.1016/j.tpb.2017.03.003","abstract":[{"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.","lang":"eng"}],"volume":115,"ddc":["576"]}]