Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory
Multivariate count distributions are crucial for the inference of ecological processes underpinning biodiversity. In particular, neutral theory provides useful null distributions allowing the evaluation of adaptation or natural selection. In this paper, we build a broader family of multivariate distributions: the Polya-splitting distributions. We show that they emerge naturally as stationary distributions of a multivariate birth–death process. This family of distributions is a consistent extension of non-zero sum neutral models based on a master equation approach. It allows considering both total abundance of the community and relative abundances of species. We emphasize that this family is large enough to encompass various dependence structures among species. We also introduce the strong closure under addition property that can be useful to generate nested multi-level dependence structures. Although all Pólya splitting distributions do not share this property, we provide numerous example verifying it. They include the previously known example with independent species, and also new ones with alternative dependence structures. Overall, we advocate that Polya-splitting distribution should become a part of the classic toolbox for the analysis of multivariate count data in ecology, providing alternative approaches to joint species distribution framework. Comparatively, our approach allows to model dependencies between species at the observation level, while the classical JSDM's model dependencies at the latent process strata.
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Subjects: | U10 - Informatique, mathématiques et statistiques, F40 - Écologie végétale, modèle mathématique, méthode statistique, modélisation environnementale, biodiversité, dynamique des populations, distribution géographique, http://aims.fao.org/aos/agrovoc/c_24199, http://aims.fao.org/aos/agrovoc/c_7377, http://aims.fao.org/aos/agrovoc/c_9000056, http://aims.fao.org/aos/agrovoc/c_33949, http://aims.fao.org/aos/agrovoc/c_6111, http://aims.fao.org/aos/agrovoc/c_5083, |
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dig-cirad-fr-6084192024-04-11T08:09:41Z http://agritrop.cirad.fr/608419/ http://agritrop.cirad.fr/608419/ Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory. Peyhardi Jean, Laroche Fabien, Mortier Frédéric. 2024. Journal of Theoretical Biology, 582:111755, 12 p.https://doi.org/10.1016/j.jtbi.2024.111755 <https://doi.org/10.1016/j.jtbi.2024.111755> Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory Peyhardi, Jean Laroche, Fabien Mortier, Frédéric eng 2024 Journal of Theoretical Biology U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 Multivariate count distributions are crucial for the inference of ecological processes underpinning biodiversity. In particular, neutral theory provides useful null distributions allowing the evaluation of adaptation or natural selection. In this paper, we build a broader family of multivariate distributions: the Polya-splitting distributions. We show that they emerge naturally as stationary distributions of a multivariate birth–death process. This family of distributions is a consistent extension of non-zero sum neutral models based on a master equation approach. It allows considering both total abundance of the community and relative abundances of species. We emphasize that this family is large enough to encompass various dependence structures among species. We also introduce the strong closure under addition property that can be useful to generate nested multi-level dependence structures. Although all Pólya splitting distributions do not share this property, we provide numerous example verifying it. They include the previously known example with independent species, and also new ones with alternative dependence structures. Overall, we advocate that Polya-splitting distribution should become a part of the classic toolbox for the analysis of multivariate count data in ecology, providing alternative approaches to joint species distribution framework. Comparatively, our approach allows to model dependencies between species at the observation level, while the classical JSDM's model dependencies at the latent process strata. article info:eu-repo/semantics/article Journal Article info:eu-repo/semantics/publishedVersion http://agritrop.cirad.fr/608419/1/peyhardi24.pdf text cc_by info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.1016/j.jtbi.2024.111755 10.1016/j.jtbi.2024.111755 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jtbi.2024.111755 info:eu-repo/semantics/altIdentifier/purl/https://doi.org/10.1016/j.jtbi.2024.111755 info:eu-repo/grantAgreement///ANR-18-CE02-0025//(FRA) Nouvelles avancées dans la modélisation de la biodiversité et des services écosystémiques : améliorations statistiques et pertinences écologiques des modèles de distribution multi-espèces/GAMBAS info:eu-repo/grantAgreement///ANR-19-CE32-0002//(FRA) Approches neutres par blocs pour prédire l'effet de la gestion forestière sur la biodiversité au sein des dendromicrohabitats/BloBiForM |
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U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 |
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U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 Peyhardi, Jean Laroche, Fabien Mortier, Frédéric Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
description |
Multivariate count distributions are crucial for the inference of ecological processes underpinning biodiversity. In particular, neutral theory provides useful null distributions allowing the evaluation of adaptation or natural selection. In this paper, we build a broader family of multivariate distributions: the Polya-splitting distributions. We show that they emerge naturally as stationary distributions of a multivariate birth–death process. This family of distributions is a consistent extension of non-zero sum neutral models based on a master equation approach. It allows considering both total abundance of the community and relative abundances of species. We emphasize that this family is large enough to encompass various dependence structures among species. We also introduce the strong closure under addition property that can be useful to generate nested multi-level dependence structures. Although all Pólya splitting distributions do not share this property, we provide numerous example verifying it. They include the previously known example with independent species, and also new ones with alternative dependence structures. Overall, we advocate that Polya-splitting distribution should become a part of the classic toolbox for the analysis of multivariate count data in ecology, providing alternative approaches to joint species distribution framework. Comparatively, our approach allows to model dependencies between species at the observation level, while the classical JSDM's model dependencies at the latent process strata. |
format |
article |
topic_facet |
U10 - Informatique, mathématiques et statistiques F40 - Écologie végétale modèle mathématique méthode statistique modélisation environnementale biodiversité dynamique des populations distribution géographique http://aims.fao.org/aos/agrovoc/c_24199 http://aims.fao.org/aos/agrovoc/c_7377 http://aims.fao.org/aos/agrovoc/c_9000056 http://aims.fao.org/aos/agrovoc/c_33949 http://aims.fao.org/aos/agrovoc/c_6111 http://aims.fao.org/aos/agrovoc/c_5083 |
author |
Peyhardi, Jean Laroche, Fabien Mortier, Frédéric |
author_facet |
Peyhardi, Jean Laroche, Fabien Mortier, Frédéric |
author_sort |
Peyhardi, Jean |
title |
Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
title_short |
Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
title_full |
Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
title_fullStr |
Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
title_full_unstemmed |
Pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
title_sort |
pólya-splitting distributions as stationary solutions of multivariate birth-death processes under extended neutral theory |
url |
http://agritrop.cirad.fr/608419/ http://agritrop.cirad.fr/608419/1/peyhardi24.pdf |
work_keys_str_mv |
AT peyhardijean polyasplittingdistributionsasstationarysolutionsofmultivariatebirthdeathprocessesunderextendedneutraltheory AT larochefabien polyasplittingdistributionsasstationarysolutionsofmultivariatebirthdeathprocessesunderextendedneutraltheory AT mortierfrederic polyasplittingdistributionsasstationarysolutionsofmultivariatebirthdeathprocessesunderextendedneutraltheory |
_version_ |
1798165173320548352 |