Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

The dynamics of a specific consumer-resource model for <i>Daphnia magna</i> is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the mo...

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Autores principales:	Luis M. Abia, Óscar Angulo, Juan Carlos López-Marcos, Miguel Ángel López-Marcos
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	size-structured population numerical methods characteristics method growth laws asymptotic behaviour <i>Daphnia magna</i> Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8e683866ba8b4bbaa52b975403b89958
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spelling	oai:doaj.org-article:8e683866ba8b4bbaa52b975403b899582021-11-11T18:17:40ZComputational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource10.3390/math92127462227-7390https://doaj.org/article/8e683866ba8b4bbaa52b975403b899582021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2746https://doaj.org/toc/2227-7390The dynamics of a specific consumer-resource model for <i>Daphnia magna</i> is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.Luis M. AbiaÓscar AnguloJuan Carlos López-MarcosMiguel Ángel López-MarcosMDPI AGarticlesize-structured populationnumerical methodscharacteristics methodgrowth lawsasymptotic behaviour<i>Daphnia magna</i>MathematicsQA1-939ENMathematics, Vol 9, Iss 2746, p 2746 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	size-structured population numerical methods characteristics method growth laws asymptotic behaviour <i>Daphnia magna</i> Mathematics QA1-939
spellingShingle	size-structured population numerical methods characteristics method growth laws asymptotic behaviour <i>Daphnia magna</i> Mathematics QA1-939 Luis M. Abia Óscar Angulo Juan Carlos López-Marcos Miguel Ángel López-Marcos Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
description	The dynamics of a specific consumer-resource model for <i>Daphnia magna</i> is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.
format	article
author	Luis M. Abia Óscar Angulo Juan Carlos López-Marcos Miguel Ángel López-Marcos
author_facet	Luis M. Abia Óscar Angulo Juan Carlos López-Marcos Miguel Ángel López-Marcos
author_sort	Luis M. Abia
title	Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
title_short	Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
title_full	Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
title_fullStr	Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
title_full_unstemmed	Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource
title_sort	computational study on the dynamics of a consumer-resource model: the influence of the growth law in the resource
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/8e683866ba8b4bbaa52b975403b89958
work_keys_str_mv	AT luismabia computationalstudyonthedynamicsofaconsumerresourcemodeltheinfluenceofthegrowthlawintheresource AT oscarangulo computationalstudyonthedynamicsofaconsumerresourcemodeltheinfluenceofthegrowthlawintheresource AT juancarloslopezmarcos computationalstudyonthedynamicsofaconsumerresourcemodeltheinfluenceofthegrowthlawintheresource AT miguelangellopezmarcos computationalstudyonthedynamicsofaconsumerresourcemodeltheinfluenceofthegrowthlawintheresource
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Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

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