Analysis of a stochastic tri-trophic food-chain model with harvesting
We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity...
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| Veröffentlicht in: | Journal of mathematical biology 2016-09, Vol.73 (3), p.597-625 |
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| creator | Liu, Meng Bai, Chuanzhi |
| description | We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model. |
| doi_str_mv | 10.1007/s00285-016-0970-z |
| format | Article |
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We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.</description><identifier>ISSN: 0303-6812</identifier><identifier>EISSN: 1432-1416</identifier><identifier>DOI: 10.1007/s00285-016-0970-z</identifier><identifier>PMID: 26846770</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Environment ; Food Chain ; Mathematical and Computational Biology ; Mathematics ; Mathematics and Statistics ; Models, Biological ; Stochastic Processes</subject><ispartof>Journal of mathematical biology, 2016-09, Vol.73 (3), p.597-625</ispartof><rights>Springer-Verlag Berlin Heidelberg 2016</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c405t-95540de0c792916294db30231d55d89e05ebfb717268f48760acdef9f47497983</citedby><cites>FETCH-LOGICAL-c405t-95540de0c792916294db30231d55d89e05ebfb717268f48760acdef9f47497983</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00285-016-0970-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00285-016-0970-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26846770$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu, Meng</creatorcontrib><creatorcontrib>Bai, Chuanzhi</creatorcontrib><title>Analysis of a stochastic tri-trophic food-chain model with harvesting</title><title>Journal of mathematical biology</title><addtitle>J. Math. Biol</addtitle><addtitle>J Math Biol</addtitle><description>We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.</description><subject>Applications of Mathematics</subject><subject>Environment</subject><subject>Food Chain</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Models, Biological</subject><subject>Stochastic Processes</subject><issn>0303-6812</issn><issn>1432-1416</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>BENPR</sourceid><recordid>eNqNkU1LAzEQhoMotlZ_gBdZ8OIlOpNNNptjKfUDCl70HPYj227ZbmqyVdpfb8pWEUHwNAPzzDvD-xJyiXCLAPLOA7BUUMCEgpJAd0dkiDxmFDkmx2QIMcQ0SZENyJn3SwCUQuEpGbAk5YmUMCTTcZs1W1_7yFZRFvnOFovMd3URda6mnbPrRegra0saBnUbrWxpmuij7hbRInPvJrDt_JycVFnjzcWhjsjr_fRl8khnzw9Pk_GMFhxER5UQHEoDhVRMYcIUL_MYWIylEGWqDAiTV7lEGf6reCoTyIrSVKrikiup0nhEbnrdtbNvm3Bbr2pfmKbJWmM3XmOKQkIas3-hyBQDkQT0-he6tBsXfOkphTFyFSjsqcJZ752p9NrVq8xtNYLex6H7OHSIQ-_j0Luwc3VQ3uQrU35vfPkfANYDPozauXE_Tv-p-gmK8pNF</recordid><startdate>20160901</startdate><enddate>20160901</enddate><creator>Liu, Meng</creator><creator>Bai, Chuanzhi</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</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>3V.</scope><scope>7TK</scope><scope>7TM</scope><scope>7U9</scope><scope>7X7</scope><scope>7XB</scope><scope>88A</scope><scope>88E</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>H94</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>K9.</scope><scope>L6V</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M7N</scope><scope>M7P</scope><scope>M7S</scope><scope>M7Z</scope><scope>P5Z</scope><scope>P62</scope><scope>P64</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PJZUB</scope><scope>PKEHL</scope><scope>PPXIY</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7X8</scope><scope>7QO</scope></search><sort><creationdate>20160901</creationdate><title>Analysis of a stochastic tri-trophic food-chain model with harvesting</title><author>Liu, Meng ; Bai, Chuanzhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c405t-95540de0c792916294db30231d55d89e05ebfb717268f48760acdef9f47497983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Applications of Mathematics</topic><topic>Environment</topic><topic>Food Chain</topic><topic>Mathematical and Computational Biology</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Models, Biological</topic><topic>Stochastic Processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Meng</creatorcontrib><creatorcontrib>Bai, Chuanzhi</creatorcontrib><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>Health & Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>Health & Medical Collection (Alumni Edition)</collection><collection>Medical Database</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Biochemistry Abstracts 1</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>ProQuest Central (New)</collection><collection>ProQuest One Academic (New)</collection><collection>ProQuest Health & Medical Research Collection</collection><collection>ProQuest One Academic Middle East (New)</collection><collection>ProQuest One Health & Nursing</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Applied & Life Sciences</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>MEDLINE - Academic</collection><collection>Biotechnology Research Abstracts</collection><jtitle>Journal of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Meng</au><au>Bai, Chuanzhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of a stochastic tri-trophic food-chain model with harvesting</atitle><jtitle>Journal of mathematical biology</jtitle><stitle>J. Math. Biol</stitle><addtitle>J Math Biol</addtitle><date>2016-09-01</date><risdate>2016</risdate><volume>73</volume><issue>3</issue><spage>597</spage><epage>625</epage><pages>597-625</pages><issn>0303-6812</issn><eissn>1432-1416</eissn><abstract>We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><pmid>26846770</pmid><doi>10.1007/s00285-016-0970-z</doi><tpages>29</tpages></addata></record> |
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| subjects | Applications of Mathematics Environment Food Chain Mathematical and Computational Biology Mathematics Mathematics and Statistics Models, Biological Stochastic Processes |
| title | Analysis of a stochastic tri-trophic food-chain model with harvesting |
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