Persistence of structured populations in random environments

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Theoretical population biology 2009-08, Vol.76 (1), p.19-34
Hauptverfasser: Benaïm, Michel, Schreiber, Sebastian J.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 34
container_issue 1
container_start_page 19
container_title Theoretical population biology
container_volume 76
creator Benaïm, Michel
Schreiber, Sebastian J.
description Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.
doi_str_mv 10.1016/j.tpb.2009.03.007
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_67311023</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0040580909000318</els_id><sourcerecordid>20619468</sourcerecordid><originalsourceid>FETCH-LOGICAL-c448t-7410b7d26e168b36d33000036659585ba5e86a9cbf874f7c79c243851b089b263</originalsourceid><addsrcrecordid>eNqFkM1KxDAURoMozjj6AG6kK3etN02TJuhGBv9gQBe6Dm16Cxnapiap4NvbYQbc6epuzne4HEIuKWQUqLjZZnGssxxAZcAygPKILCkokQLL-TFZAhSQcglqQc5C2AKApIydkgVVjEsp6JLcvaEPNkQcDCauTUL0k4mTxyYZ3Th1VbRuCIkdEl8NjesTHL6sd0OPQwzn5KStuoAXh7siH48P7-vndPP69LK-36SmKGRMy4JCXTa5QCpkzUTD2PwKMCG44pLXFUcpKmXqVpZFW5pSmbxgktMapKpzwVbkeu8dvfucMETd22Cw66oB3RS0KBmlkLN_wRwEVYWQM0j3oPEuBI-tHr3tK_-tKehdW73Vc1u9a6uB6bntvLk6yKe6x-Z3cYg5A7d7AOcWXxa9DsbuwjbWo4m6cfYP_Q-ELojC</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>20619468</pqid></control><display><type>article</type><title>Persistence of structured populations in random environments</title><source>MEDLINE</source><source>Access via ScienceDirect (Elsevier)</source><creator>Benaïm, Michel ; Schreiber, Sebastian J.</creator><creatorcontrib>Benaïm, Michel ; Schreiber, Sebastian J.</creatorcontrib><description>Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.</description><identifier>ISSN: 0040-5809</identifier><identifier>EISSN: 1096-0325</identifier><identifier>DOI: 10.1016/j.tpb.2009.03.007</identifier><identifier>PMID: 19358861</identifier><language>eng</language><publisher>United States: Elsevier Inc</publisher><subject>Animals ; Computer Simulation ; Conservation of Natural Resources ; Ecosystem ; Environment ; Markov Chains ; Metapopulation ; Models, Biological ; Models, Statistical ; Monte Carlo Method ; Persistence ; Plant Development ; Population Density ; Population Dynamics ; Population Growth ; Random environment ; Source-sink ; Stochastic Processes ; Structured populations</subject><ispartof>Theoretical population biology, 2009-08, Vol.76 (1), p.19-34</ispartof><rights>2009 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c448t-7410b7d26e168b36d33000036659585ba5e86a9cbf874f7c79c243851b089b263</citedby><cites>FETCH-LOGICAL-c448t-7410b7d26e168b36d33000036659585ba5e86a9cbf874f7c79c243851b089b263</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.tpb.2009.03.007$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/19358861$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Benaïm, Michel</creatorcontrib><creatorcontrib>Schreiber, Sebastian J.</creatorcontrib><title>Persistence of structured populations in random environments</title><title>Theoretical population biology</title><addtitle>Theor Popul Biol</addtitle><description>Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.</description><subject>Animals</subject><subject>Computer Simulation</subject><subject>Conservation of Natural Resources</subject><subject>Ecosystem</subject><subject>Environment</subject><subject>Markov Chains</subject><subject>Metapopulation</subject><subject>Models, Biological</subject><subject>Models, Statistical</subject><subject>Monte Carlo Method</subject><subject>Persistence</subject><subject>Plant Development</subject><subject>Population Density</subject><subject>Population Dynamics</subject><subject>Population Growth</subject><subject>Random environment</subject><subject>Source-sink</subject><subject>Stochastic Processes</subject><subject>Structured populations</subject><issn>0040-5809</issn><issn>1096-0325</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><recordid>eNqFkM1KxDAURoMozjj6AG6kK3etN02TJuhGBv9gQBe6Dm16Cxnapiap4NvbYQbc6epuzne4HEIuKWQUqLjZZnGssxxAZcAygPKILCkokQLL-TFZAhSQcglqQc5C2AKApIydkgVVjEsp6JLcvaEPNkQcDCauTUL0k4mTxyYZ3Th1VbRuCIkdEl8NjesTHL6sd0OPQwzn5KStuoAXh7siH48P7-vndPP69LK-36SmKGRMy4JCXTa5QCpkzUTD2PwKMCG44pLXFUcpKmXqVpZFW5pSmbxgktMapKpzwVbkeu8dvfucMETd22Cw66oB3RS0KBmlkLN_wRwEVYWQM0j3oPEuBI-tHr3tK_-tKehdW73Vc1u9a6uB6bntvLk6yKe6x-Z3cYg5A7d7AOcWXxa9DsbuwjbWo4m6cfYP_Q-ELojC</recordid><startdate>20090801</startdate><enddate>20090801</enddate><creator>Benaïm, Michel</creator><creator>Schreiber, Sebastian J.</creator><general>Elsevier Inc</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SN</scope><scope>C1K</scope><scope>7X8</scope></search><sort><creationdate>20090801</creationdate><title>Persistence of structured populations in random environments</title><author>Benaïm, Michel ; Schreiber, Sebastian J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c448t-7410b7d26e168b36d33000036659585ba5e86a9cbf874f7c79c243851b089b263</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Animals</topic><topic>Computer Simulation</topic><topic>Conservation of Natural Resources</topic><topic>Ecosystem</topic><topic>Environment</topic><topic>Markov Chains</topic><topic>Metapopulation</topic><topic>Models, Biological</topic><topic>Models, Statistical</topic><topic>Monte Carlo Method</topic><topic>Persistence</topic><topic>Plant Development</topic><topic>Population Density</topic><topic>Population Dynamics</topic><topic>Population Growth</topic><topic>Random environment</topic><topic>Source-sink</topic><topic>Stochastic Processes</topic><topic>Structured populations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Benaïm, Michel</creatorcontrib><creatorcontrib>Schreiber, Sebastian J.</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Ecology Abstracts</collection><collection>Environmental Sciences and Pollution Management</collection><collection>MEDLINE - Academic</collection><jtitle>Theoretical population biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Benaïm, Michel</au><au>Schreiber, Sebastian J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Persistence of structured populations in random environments</atitle><jtitle>Theoretical population biology</jtitle><addtitle>Theor Popul Biol</addtitle><date>2009-08-01</date><risdate>2009</risdate><volume>76</volume><issue>1</issue><spage>19</spage><epage>34</epage><pages>19-34</pages><issn>0040-5809</issn><eissn>1096-0325</eissn><abstract>Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.</abstract><cop>United States</cop><pub>Elsevier Inc</pub><pmid>19358861</pmid><doi>10.1016/j.tpb.2009.03.007</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0040-5809
ispartof Theoretical population biology, 2009-08, Vol.76 (1), p.19-34
issn 0040-5809
1096-0325
language eng
recordid cdi_proquest_miscellaneous_67311023
source MEDLINE; Access via ScienceDirect (Elsevier)
subjects Animals
Computer Simulation
Conservation of Natural Resources
Ecosystem
Environment
Markov Chains
Metapopulation
Models, Biological
Models, Statistical
Monte Carlo Method
Persistence
Plant Development
Population Density
Population Dynamics
Population Growth
Random environment
Source-sink
Stochastic Processes
Structured populations
title Persistence of structured populations in random environments
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T21%3A53%3A11IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Persistence%20of%20structured%20populations%20in%20random%20environments&rft.jtitle=Theoretical%20population%20biology&rft.au=Bena%C3%AFm,%20Michel&rft.date=2009-08-01&rft.volume=76&rft.issue=1&rft.spage=19&rft.epage=34&rft.pages=19-34&rft.issn=0040-5809&rft.eissn=1096-0325&rft_id=info:doi/10.1016/j.tpb.2009.03.007&rft_dat=%3Cproquest_cross%3E20619468%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=20619468&rft_id=info:pmid/19358861&rft_els_id=S0040580909000318&rfr_iscdi=true