A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction

Population dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst’s logistic brake, and a functional response accounting fo...

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Main Authors: Luciano Stucchi, Juan Manuel Pastor, Javier García-Algarra, Javier Galeano
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/7961327
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author Luciano Stucchi
Juan Manuel Pastor
Javier García-Algarra
Javier Galeano
author_facet Luciano Stucchi
Juan Manuel Pastor
Javier García-Algarra
Javier Galeano
author_sort Luciano Stucchi
collection DOAJ
description Population dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst’s logistic brake, and a functional response accounting for interspecific interactions. However, intraspecific interactions are not usually included in the equations. The simplest models use linear terms to represent a simple picture of the nature; meanwhile, to represent more complex landscapes, it is necessary to include more terms with a higher order or that are analytically more complex. The problem to use a simpler or more complex model depends on many factors: mathematical, ecological, or computational. To address it, here we discuss a new model based on a previous logistic-mutualistic model. We have generalized the interspecific terms (for antagonistic and competitive relationships), and we have also included new polynomial terms to explain any intraspecific interaction. We show that, by adding simple intraspecific terms, new free-equilibrium solutions appear driving a much richer dynamics. These new solutions could represent more realistic ecological landscapes by including a new higher order term.
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spelling doaj-art-ea7b6637a4b84a7498158e492969332c2025-08-20T03:20:40ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/79613277961327A General Model of Population Dynamics Accounting for Multiple Kinds of InteractionLuciano Stucchi0Juan Manuel Pastor1Javier García-Algarra2Javier Galeano3Universidad Del Pacífico, Lima, PeruComplex Systems Group, E. T. S. I. A. A. B, Universidad Politécnica de Madrid, Madrid, SpainDepartment of Engineering, Centro Universitario U-TAD, Las Rozas, SpainComplex Systems Group, E. T. S. I. A. A. B, Universidad Politécnica de Madrid, Madrid, SpainPopulation dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst’s logistic brake, and a functional response accounting for interspecific interactions. However, intraspecific interactions are not usually included in the equations. The simplest models use linear terms to represent a simple picture of the nature; meanwhile, to represent more complex landscapes, it is necessary to include more terms with a higher order or that are analytically more complex. The problem to use a simpler or more complex model depends on many factors: mathematical, ecological, or computational. To address it, here we discuss a new model based on a previous logistic-mutualistic model. We have generalized the interspecific terms (for antagonistic and competitive relationships), and we have also included new polynomial terms to explain any intraspecific interaction. We show that, by adding simple intraspecific terms, new free-equilibrium solutions appear driving a much richer dynamics. These new solutions could represent more realistic ecological landscapes by including a new higher order term.http://dx.doi.org/10.1155/2020/7961327
spellingShingle Luciano Stucchi
Juan Manuel Pastor
Javier García-Algarra
Javier Galeano
A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
Complexity
title A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
title_full A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
title_fullStr A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
title_full_unstemmed A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
title_short A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction
title_sort general model of population dynamics accounting for multiple kinds of interaction
url http://dx.doi.org/10.1155/2020/7961327
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