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A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution

Christophe Coste

Methods in Ecology and Evolution

Swansea University Author: Christophe Coste

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DOI (Published version): 10.1111/2041-210x.70163

Abstract

Lifetime reproductive success (LRS) is a key metric in ecology and evolution. It measures the number of offspring produced by an individual during its lifetime. In epidemiology, it corresponds to the number of secondary cases generated by an infected individual. For structured populations, it is cru...

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Published in: Methods in Ecology and Evolution
ISSN: 2041-210X
Published: Wiley 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa70450
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last_indexed 2025-12-05T09:24:42Z
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spelling 2025-12-03T15:47:00.7559812 v2 70450 2025-09-22 A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution 8191af157a7cfb3a4249cfc270a7116a Christophe Coste Christophe Coste true false 2025-09-22 BGPS Lifetime reproductive success (LRS) is a key metric in ecology and evolution. It measures the number of offspring produced by an individual during its lifetime. In epidemiology, it corresponds to the number of secondary cases generated by an infected individual. For structured populations, it is crucial to understand how the distribution of LRS is shaped by survival, reproduction and other processes embedded in the projection model (such as dispersal or trait inheritance). Previous approaches have used diverse tools, such as Markov chains with rewards, to tackle this question, but generally consider only the total number of offspring produced, ignoring the distribution of their types (newborn states). Here, we use the framework of branching processes to derive formulas for the variance–covariance matrices and probability-generating functions (allowing us to obtain the joint distribution) of LRS structured by the type of the parent and the type of the offspring. Furthermore, this framework leads to a simple algorithm providing a numerical approximation of the distribution of total LRS that does not require explicit expression of probability-generating functions. We illustrate the power of the branching process approach, further, by studying the asymptotic behaviour of LRS, that is, the probability of producing many offspring. Finally, our general approach is applicable to any structured population model, and we provide R and Matlab code to facilitate implementation. Journal Article Methods in Ecology and Evolution 0 Wiley 2041-210X demographic stochasticity, lifetime reproductive output, lifetime reproductive success, multidimensional branching process, multi-type branching processes, net reproductive rate, probability-generating function, R0 27 11 2025 2025-11-27 10.1111/2041-210x.70163 COLLEGE NANME Biosciences Geography and Physics School COLLEGE CODE BGPS Swansea University SU Library paid the OA fee (TA Institutional Deal) This research was funded by the Natural Environment Research Council (grant no.: NE/W006731/1) and by the Norwegian Research Council (Norges Forskningsråd, grant/award numbers: 223257 and 343398). It also benefited from the support of the Chaire ‘Modélisation Mathématique et Biodiversité of Veolia–Ecole Polytechnique–MNHN–Fondation X’. 2025-12-03T15:47:00.7559812 2025-09-22T12:43:46.2925684 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Biosciences Christophe Coste 1 70450__35743__8eb4e3b7e291490da143929c219b82c3.pdf 70450.VOR.pdf 2025-12-03T15:37:53.5398929 Output 2142431 application/pdf Version of Record true © 2025 The Author(s). Methods in Ecology and Evolution published by John Wiley & Sons Ltd on behalf of British Ecological Society. This is an open access article under the terms of the Creative Commons Attribution License. true eng http://creativecommons.org/licenses/by/4.0/
title A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
spellingShingle A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
Christophe Coste
title_short A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
title_full A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
title_fullStr A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
title_full_unstemmed A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
title_sort A branching process approach to lifetime reproductive success of structured populations: Variance–covariance and distribution
author_id_str_mv 8191af157a7cfb3a4249cfc270a7116a
author_id_fullname_str_mv 8191af157a7cfb3a4249cfc270a7116a_***_Christophe Coste
author Christophe Coste
author2 Christophe Coste
format Journal article
container_title Methods in Ecology and Evolution
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publishDate 2025
institution Swansea University
issn 2041-210X
doi_str_mv 10.1111/2041-210x.70163
publisher Wiley
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Biosciences{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Biosciences
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description Lifetime reproductive success (LRS) is a key metric in ecology and evolution. It measures the number of offspring produced by an individual during its lifetime. In epidemiology, it corresponds to the number of secondary cases generated by an infected individual. For structured populations, it is crucial to understand how the distribution of LRS is shaped by survival, reproduction and other processes embedded in the projection model (such as dispersal or trait inheritance). Previous approaches have used diverse tools, such as Markov chains with rewards, to tackle this question, but generally consider only the total number of offspring produced, ignoring the distribution of their types (newborn states). Here, we use the framework of branching processes to derive formulas for the variance–covariance matrices and probability-generating functions (allowing us to obtain the joint distribution) of LRS structured by the type of the parent and the type of the offspring. Furthermore, this framework leads to a simple algorithm providing a numerical approximation of the distribution of total LRS that does not require explicit expression of probability-generating functions. We illustrate the power of the branching process approach, further, by studying the asymptotic behaviour of LRS, that is, the probability of producing many offspring. Finally, our general approach is applicable to any structured population model, and we provide R and Matlab code to facilitate implementation.
published_date 2025-11-27T05:30:55Z
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