In this paper a question of " how much overconsumption a renewable resource can tolerate" is addressed using a mathematical model, where individuals in a parametrically heterogeneous population not only compete for the common resource but can also contribute to its restoration. Through bifurcation analysis a threshold of system resistance to over-consumers (individuals that take more than they restore) was identified, as well as a series of transitional regimes that the population goes through before it exhausts the common resource and thus goes extinct itself, a phenomenon known as " the tragedy of the commons" It was also observed that (1) for some parameter domains a population can survive or go extinct depending on its initial conditions, (2) under the same set of initial conditions, a heterogeneous population survives longer than a homogeneous population and (3) when the natural decay rate of the common resource is high enough, the population can endure the presence of more aggressive over-consumers without going extinct. Â\copyright 2012.
Resource overconsumption; Tipping points; Tragedy of the commons; Transitional regimes
issn
00255564
correspondence_address1
Berezovskaya, F.; Department of Mathematics, Howard University, Washington, DC 20895, United States; email: fsberezo@hotmail.com
affiliation
Mathematical, Computational Modeling Sciences Center, Arizona State University, P.O. Box 871904, Tempe, AZ 85287, United States; Department of Mathematics, Howard University, Washington, DC 20895, United States; School of Human Evolution and Social Changes, Arizona State University, Tempe, AZ 85287, United States; School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, United States
%0 Journal Article
%1 Kareva2012114
%A Kareva, I.
%A Berezovskaya, F.
%A Castillo-Chavez, C.
%D 2012
%J Mathematical Biosciences
%K (mathematics); (organic); Bifurcation Common Competition Decay Dynamics Early Ecosystem; Heterogeneous Humans; Initial Mathematical Models, Natural Population Renewable Resource Restoration, System Theoretical; Tipping Tragedy Transitional adaptation; analysis; article; bifurcation; commons; competition; conditions; consumer; decay; dynamics; early management; mathematical model; models, numerical of overconsumption; partitioning; point; population populations; regimes, renewable resistance; resource resource, resource; resources; survival, system; the warning warning;
%N 2
%P 114-123
%R http://dx.doi.org/10.1016/j.mbs.2012.06.001
%T Transitional regimes as early warning signals in resource dependent competition models
%U http://dx.doi.org/10.1016/j.mbs.2012.06.001
%V 240
%X In this paper a question of " how much overconsumption a renewable resource can tolerate" is addressed using a mathematical model, where individuals in a parametrically heterogeneous population not only compete for the common resource but can also contribute to its restoration. Through bifurcation analysis a threshold of system resistance to over-consumers (individuals that take more than they restore) was identified, as well as a series of transitional regimes that the population goes through before it exhausts the common resource and thus goes extinct itself, a phenomenon known as " the tragedy of the commons" It was also observed that (1) for some parameter domains a population can survive or go extinct depending on its initial conditions, (2) under the same set of initial conditions, a heterogeneous population survives longer than a homogeneous population and (3) when the natural decay rate of the common resource is high enough, the population can endure the presence of more aggressive over-consumers without going extinct. Â\copyright 2012.
@article{Kareva2012114,
abstract = {In this paper a question of " how much overconsumption a renewable resource can tolerate" is addressed using a mathematical model, where individuals in a parametrically heterogeneous population not only compete for the common resource but can also contribute to its restoration. Through bifurcation analysis a threshold of system resistance to over-consumers (individuals that take more than they restore) was identified, as well as a series of transitional regimes that the population goes through before it exhausts the common resource and thus goes extinct itself, a phenomenon known as " the tragedy of the commons" It was also observed that (1) for some parameter domains a population can survive or go extinct depending on its initial conditions, (2) under the same set of initial conditions, a heterogeneous population survives longer than a homogeneous population and (3) when the natural decay rate of the common resource is high enough, the population can endure the presence of more aggressive over-consumers without going extinct. {\^A}{\copyright} 2012.},
added-at = {2017-11-10T22:48:29.000+0100},
affiliation = {Mathematical, Computational Modeling Sciences Center, Arizona State University, P.O. Box 871904, Tempe, AZ 85287, United States; Department of Mathematics, Howard University, Washington, DC 20895, United States; School of Human Evolution and Social Changes, Arizona State University, Tempe, AZ 85287, United States; School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, United States},
author = {Kareva, I. and Berezovskaya, F. and Castillo-Chavez, C.},
author_keywords = {Resource overconsumption; Tipping points; Tragedy of the commons; Transitional regimes},
biburl = {https://www.bibsonomy.org/bibtex/20b9b35093330c6953c0070c21ae58e8c/ccchavez},
coden = {MABIA},
correspondence_address1 = {Berezovskaya, F.; Department of Mathematics, Howard University, Washington, DC 20895, United States; email: fsberezo@hotmail.com},
date-added = {2017-11-10 21:45:26 +0000},
date-modified = {2017-11-10 21:45:26 +0000},
document_type = {Article},
doi = {http://dx.doi.org/10.1016/j.mbs.2012.06.001},
interhash = {aa8e3c3f96ed1c95a6c899bc3ef651fa},
intrahash = {0b9b35093330c6953c0070c21ae58e8c},
issn = {00255564},
journal = {Mathematical Biosciences},
keywords = {(mathematics); (organic); Bifurcation Common Competition Decay Dynamics Early Ecosystem; Heterogeneous Humans; Initial Mathematical Models, Natural Population Renewable Resource Restoration, System Theoretical; Tipping Tragedy Transitional adaptation; analysis; article; bifurcation; commons; competition; conditions; consumer; decay; dynamics; early management; mathematical model; models, numerical of overconsumption; partitioning; point; population populations; regimes, renewable resistance; resource resource, resource; resources; survival, system; the warning warning;},
language = {English},
number = 2,
pages = {114-123},
pubmed_id = {22735716},
timestamp = {2017-11-10T22:48:29.000+0100},
title = {Transitional regimes as early warning signals in resource dependent competition models},
url = {http://dx.doi.org/10.1016/j.mbs.2012.06.001},
volume = 240,
year = 2012
}