%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 }