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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Autor*in:	Héctor A. Echavarria-Heras [verfasserIn] Cecilia Leal-Ramírez [verfasserIn] Guillermo Gómez [verfasserIn] Elia Montiel-Arzate [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Übergeordnetes Werk:	In: Complexity - Hindawi-Wiley, 2017, (2021)
Übergeordnetes Werk:	year:2021

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1155/2021/5623783

Katalog-ID:	DOAJ063295407

Internformat


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allfields	10.1155/2021/5623783 doi (DE-627)DOAJ063295407 (DE-599)DOAJ9dba9575d2dc4481a88d47d1b60f8c23 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Héctor A. Echavarria-Heras verfasserin aut Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Electronic computers. Computer science Cecilia Leal-Ramírez verfasserin aut Guillermo Gómez verfasserin aut Elia Montiel-Arzate verfasserin aut In Complexity Hindawi-Wiley, 2017 (2021) (DE-627)312897278 (DE-600)2004607-8 10990526 nnns year:2021 https://doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 kostenfrei http://dx.doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/toc/1099-0526 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2021
spelling	10.1155/2021/5623783 doi (DE-627)DOAJ063295407 (DE-599)DOAJ9dba9575d2dc4481a88d47d1b60f8c23 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Héctor A. Echavarria-Heras verfasserin aut Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Electronic computers. Computer science Cecilia Leal-Ramírez verfasserin aut Guillermo Gómez verfasserin aut Elia Montiel-Arzate verfasserin aut In Complexity Hindawi-Wiley, 2017 (2021) (DE-627)312897278 (DE-600)2004607-8 10990526 nnns year:2021 https://doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 kostenfrei http://dx.doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/toc/1099-0526 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2021
allfields_unstemmed	10.1155/2021/5623783 doi (DE-627)DOAJ063295407 (DE-599)DOAJ9dba9575d2dc4481a88d47d1b60f8c23 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Héctor A. Echavarria-Heras verfasserin aut Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Electronic computers. Computer science Cecilia Leal-Ramírez verfasserin aut Guillermo Gómez verfasserin aut Elia Montiel-Arzate verfasserin aut In Complexity Hindawi-Wiley, 2017 (2021) (DE-627)312897278 (DE-600)2004607-8 10990526 nnns year:2021 https://doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 kostenfrei http://dx.doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/toc/1099-0526 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2021
allfieldsGer	10.1155/2021/5623783 doi (DE-627)DOAJ063295407 (DE-599)DOAJ9dba9575d2dc4481a88d47d1b60f8c23 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Héctor A. Echavarria-Heras verfasserin aut Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Electronic computers. Computer science Cecilia Leal-Ramírez verfasserin aut Guillermo Gómez verfasserin aut Elia Montiel-Arzate verfasserin aut In Complexity Hindawi-Wiley, 2017 (2021) (DE-627)312897278 (DE-600)2004607-8 10990526 nnns year:2021 https://doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 kostenfrei http://dx.doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/toc/1099-0526 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2021
allfieldsSound	10.1155/2021/5623783 doi (DE-627)DOAJ063295407 (DE-599)DOAJ9dba9575d2dc4481a88d47d1b60f8c23 DE-627 ger DE-627 rakwb eng QA75.5-76.95 Héctor A. Echavarria-Heras verfasserin aut Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. Electronic computers. Computer science Cecilia Leal-Ramírez verfasserin aut Guillermo Gómez verfasserin aut Elia Montiel-Arzate verfasserin aut In Complexity Hindawi-Wiley, 2017 (2021) (DE-627)312897278 (DE-600)2004607-8 10990526 nnns year:2021 https://doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 kostenfrei http://dx.doi.org/10.1155/2021/5623783 kostenfrei https://doaj.org/toc/1099-0526 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_151 GBV_ILN_161 GBV_ILN_165 GBV_ILN_170 GBV_ILN_171 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2014 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2021
language	English
source	In Complexity (2021) year:2021
sourceStr	In Complexity (2021) year:2021
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Electronic computers. Computer science
isfreeaccess_bool	true
container_title	Complexity
authorswithroles_txt_mv	Héctor A. Echavarria-Heras @@aut@@ Cecilia Leal-Ramírez @@aut@@ Guillermo Gómez @@aut@@ Elia Montiel-Arzate @@aut@@
publishDateDaySort_date	2021-01-01T00:00:00Z
hierarchy_top_id	312897278
id	DOAJ063295407
language_de	englisch
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callnumber-first	Q - Science
author	Héctor A. Echavarria-Heras
spellingShingle	Héctor A. Echavarria-Heras misc QA75.5-76.95 misc Electronic computers. Computer science Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
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topic_title	QA75.5-76.95 Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
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title	Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
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title_full	Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
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author_browse	Héctor A. Echavarria-Heras Cecilia Leal-Ramírez Guillermo Gómez Elia Montiel-Arzate
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title_sort	principle of limiting factors-driven piecewise population growth model i: qualitative exploration and study cases on continuous-time dynamics
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title_auth	Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Principle of Limiting Factors-Driven Piecewise Population Growth Model I: Qualitative Exploration and Study Cases on Continuous-Time Dynamics
url	https://doi.org/10.1155/2021/5623783 https://doaj.org/article/9dba9575d2dc4481a88d47d1b60f8c23 http://dx.doi.org/10.1155/2021/5623783 https://doaj.org/toc/1099-0526
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