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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| 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. |
| format | Article |
| id | doaj-art-ea7b6637a4b84a7498158e492969332c |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| 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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