Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelf...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5623783 |
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| author | Héctor A. Echavarria-Heras Cecilia Leal-Ramírez Guillermo Gómez Elia Montiel-Arzate |
| author_facet | Héctor A. Echavarria-Heras Cecilia Leal-Ramírez Guillermo Gómez Elia Montiel-Arzate |
| author_sort | Héctor A. Echavarria-Heras |
| collection | DOAJ |
| description | We examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region. |
| format | Article |
| id | doaj-art-9dba9575d2dc4481a88d47d1b60f8c23 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9dba9575d2dc4481a88d47d1b60f8c232025-02-03T05:58:23ZengWileyComplexity1099-05262021-01-01202110.1155/2021/5623783Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time DynamicsHéctor A. Echavarria-Heras0Cecilia Leal-Ramírez1Guillermo Gómez2Elia Montiel-Arzate3Departamento de EcologíaDepartamento de EcologíaFacultad de CienciasInstituto Tecnológico de MéxicoWe examine the comportment of the global trajectory of a piecewisely conceived single species population growth model. Formulation relies on what we develop as the principle of limiting factors for population growth, adapted from the law of the minimum of Liebig and the law of the tolerance of Shelford. The ensuing paradigm sets natality and mortality rates to express through extreme values of population growth determining factor. Dynamics through time occur over different growth phases. Transition points are interpreted as thresholds of viability, starvation, and intraspecific competition. In this delivery, we focus on the qualitative study of the global trajectory expressed on continuous time and on exploring the feasibility of analytical results against data on populations growing under experimental or natural conditions. All study cases sustained fittings of high reproducibility both at empirical and interpretative slants. Possible phase configurations include regimes with multiple stable equilibria, sigmoidal growth, extinction, or stationarity. Here, we also outline that the associating discrete-time piecewise model composes the logistic map applied over a particular region of the phase configuration. Preliminary exploratory analysis suggests that the logistic map’s chaos onset could surpass once the orbit enters a contiguous phase region.http://dx.doi.org/10.1155/2021/5623783 |
| spellingShingle | Héctor A. Echavarria-Heras Cecilia Leal-Ramírez Guillermo Gómez Elia Montiel-Arzate Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics Complexity |
| title | Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics |
| title_full | Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics |
| title_fullStr | Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics |
| title_full_unstemmed | Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics |
| title_short | Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics |
| title_sort | principle of limiting factors driven piecewise population growth model i qualitative exploration and study cases on continuous time dynamics |
| url | http://dx.doi.org/10.1155/2021/5623783 |
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