Optimal harvesting in a two-species model under critical depensation: The case of optimal harvesting in semi-arid grazing systems
Ecological systems in general often exhibit the mechanism of critical depensation, i.e. the system may collapse due to decreasing population densities caused by, for example, an increasing predation pressure on the prey that causes both populations to collapse to extinction. In this study a semi-ari...
Saved in:
| Published in: | Ecological modelling Vol. 179; no. 2; pp. 153 - 161 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
25.11.2004
Elsevier |
| Subjects: | |
| ISSN: | 0304-3800, 1872-7026 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Ecological systems in general often exhibit the mechanism of critical depensation, i.e. the system may collapse due to decreasing population densities caused by, for example, an increasing predation pressure on the prey that causes both populations to collapse to extinction. In this study a semi-arid predator–prey grazing system is taken as an example and optimal, model based, harvesting rates for the herbivore population are presented that allow survival of both herbivores and grasses during long dry periods without precipitation. Recovery to a maximum sustainable yield is achieved in the next rain season under the assumption of model validity. Optimal control theory is utilized in this example as the principal method of solution. Both analytical and numerical issues of the solution method and obtained solutions are discussed. Survival of the system is possible if the pastoralist is willing to decrease his population considerably once the dry period has set in. The social willingness, necessary to implement these management strategies, can be interpreted in terms of a discount rate in the current value Hamiltonian associated with the dynamical grazing system. The example is worked out in more detail and dynamical solutions for two discount rates are presented. |
|---|---|
| AbstractList | Ecological systems in general often exhibit the mechanism of critical depensation, i.e. the system may collapse due to decreasing population densities caused by, for example, an increasing predation pressure on the prey that causes both populations to collapse to extinction. In this study a semi-arid predator- prey grazing system is taken as an example and optimal, model based, harvesting rates for the herbivore population are presented that allow survival of both herbivores and grasses during long dry periods without precipitation. Recovery to a maximum sustainable yield is achieved in the next rain season under the assumption of model validity. Optimal control theory is utilized in this example as the principal method of solution. Both analytical and numerical issues of the solution method and obtained solutions are discussed. Survival of the system is possible if the pastoralist is willing to decrease his population considerably once the dry period has set in. The social willingness, necessary to implement these management strategies, can be interpreted in terms of a discount rate in the current value Hamiltonian associated with the dynamical grazing system. The example is worked out in more detail and dynamical solutions for two discount rates are presented. |
| Author | van Langevelde, F. Stigter, J.D. |
| Author_xml | – sequence: 1 givenname: J.D. surname: Stigter fullname: Stigter, J.D. email: hans.stigter@wur.nl organization: Systems and Control Group, Wageningen University and Research Center, Bornsesteeg 59, 6708 PD Wageningen, The Netherlands – sequence: 2 givenname: F. surname: van Langevelde fullname: van Langevelde, F. organization: Resource Ecology Group, Wageningen University and Research Center, Bornsesteeg 69, 6708 PD Wageningen, The Netherlands |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16127115$$DView record in Pascal Francis |
| BookMark | eNptUcFu1TAQtKoi9bXwDfgCt4S1nThJb1VFAalSL-VsOfbm1U-JHeykT-XGn9fhVZw4rbSamd2ZuSTnPngk5CODkgGTXw4lmjBOweJYcoCqBFkCiDOyY23Diwa4PCc7EFAVogW4IJcpHQCA8ZbvyJ-HeXGTHumTjs-YFuf31Hmq6XIMRZrROEz0rzhdvcVITXSLM5lgcUaf9OKCv6aPT0iNTkjDQMN_FRNOrtDRWbqP-ve2TC9pwSm9J-8GPSb88DavyM-7r4-334v7h28_bm_uCxRcLEXVtX1r61pa3lUNk1ANg66ENdZWveHaSs2hNRUMnIumY4axvsnbQXDGGdTiilyfdI96jz4_gF55HY1LKminRtdHHV_UcY3Kj9uY1z4pIQTvWCZ_PpHnGH6t2ZWaXDI4jtpjWJNiLdSyqbsM_PQG1CmnNETttwtzzJFkdSYZbxjbvrk54TBbfnYYVcpRe4PWRTSLssEpBmprWB3Uv4bV1rACqXLD4hUD06LP |
| CODEN | ECMODT |
| ContentType | Journal Article Conference Proceeding |
| Copyright | 2004 Elsevier B.V. 2004 INIST-CNRS Wageningen University & Research |
| Copyright_xml | – notice: 2004 Elsevier B.V. – notice: 2004 INIST-CNRS – notice: Wageningen University & Research |
| DBID | IQODW 7SN C1K QVL |
| DOI | 10.1016/j.ecolmodel.2004.06.003 |
| DatabaseName | Pascal-Francis Ecology Abstracts Environmental Sciences and Pollution Management NARCIS:Publications |
| DatabaseTitle | Ecology Abstracts Environmental Sciences and Pollution Management |
| DatabaseTitleList | Ecology Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Ecology Environmental Sciences |
| EISSN | 1872-7026 |
| EndPage | 161 |
| ExternalDocumentID | oai_library_wur_nl_wurpubs_333291 16127115 S0304380004002534 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29G 4.4 457 4G. 53G 5GY 5VS 7-5 71M 8P~ 9JM AABNK AABVA AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALCJ AALRI AAOAW AAQFI AAQXK AATLK AAXUO ABEFU ABFNM ABFYP ABGRD ABLST ABMAC ABTAH ABXDB ABYKQ ACDAQ ACGFS ACIUM ACRLP ADBBV ADEZE ADMUD ADQTV AEBSH AEKER AENEX AEQOU AFFNX AFKWA AFTJW AFXIZ AGHFR AGUBO AGYEJ AHEUO AHHHB AI. AIEXJ AIKHN AITUG AJBFU AJOXV AKIFW ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BKOJK BLECG BLXMC CBWCG CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HLV HMC HVGLF HZ~ IHE J1W KCYFY KOM LW9 LY9 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SAB SCC SDF SDG SDP SEN SES SEW SPCBC SSA SSJ SSZ T5K VH1 WH7 WUQ Y6R ZY4 ~02 ~G- AAHBH AATTM AAXKI ABJNI ABWVN ACRPL ADNMO AEGFY AEIPS AFJKZ AKRWK ANKPU BNPGV IQODW SSH 7SN AAYWO ACLOT ACVFH ADCNI AEUPX AFPUW AIIUN AKBMS AKYEP C1K EFKBS ~HD 02 08R 0R 1 8P AAPBV ABPTK ADALY AFRUD G- HZ K M QVL UNR X |
| ID | FETCH-LOGICAL-e323t-498b8d556d29471604ffa43dcdd4bc2ad6a208c40f223791c11b7ad6f32121053 |
| ISICitedReferencesCount | 12 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000224143200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0304-3800 |
| IngestDate | Tue Jan 05 18:17:46 EST 2021 Mon Oct 06 17:34:36 EDT 2025 Wed Apr 02 07:23:13 EDT 2025 Fri Feb 23 02:30:24 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Management of ecosystems Semi-arid grazing systems Optimal control Semi arid zone Ecosystem Models Climatic zone |
| Language | English |
| License | CC BY 4.0 |
| LinkModel | OpenURL |
| MeetingName | Control of Distributed Systems and Environmental Applications |
| MergedId | FETCHMERGED-LOGICAL-e323t-498b8d556d29471604ffa43dcdd4bc2ad6a208c40f223791c11b7ad6f32121053 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 18056759 |
| PQPubID | 23462 |
| PageCount | 9 |
| ParticipantIDs | wageningen_narcis_oai_library_wur_nl_wurpubs_333291 proquest_miscellaneous_18056759 pascalfrancis_primary_16127115 elsevier_sciencedirect_doi_10_1016_j_ecolmodel_2004_06_003 |
| ProviderPackageCode | QVL |
| PublicationCentury | 2000 |
| PublicationDate | 2004-11-25 |
| PublicationDateYYYYMMDD | 2004-11-25 |
| PublicationDate_xml | – month: 11 year: 2004 text: 2004-11-25 day: 25 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Ecological modelling |
| PublicationYear | 2004 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Kirk, D.E., 1970. Optimal Control Theory: An Introduction. Prentice-Hall. Van de Koppel, Rietkerk (BIB24) 2000; 90 Chaudhuri (BIB5) 1986; 32 Meyers, Barrowman, Hutchings, Rosenberg (BIB16) 1995; 269 Sinclair, Fryxell (BIB22) 1985; 63 Walker, Ludwig, Holling, Peterman (BIB26) 1981; 69 Wilen, Brown (BIB27) 1986; 13 Mesterton-Gibbons (BIB15) 1996; 92 Graetz, R.D., 1991. Desertification: a tale of two feedbacks. In: Mooney, H.A., Medina, E., Schindler, D.W., Schulzer, E.D., Walker, B.H. (Eds.), Ecosystem Experiments. Wiley, Chichester, pp. 59–87. Mesterton-Gibbons (BIB14) 1988; 3 Bryson, A.E., 1999. Dynamic Optimization. Addison Wesley. Armsworth, Roughgarden (BIB3) 2001; 16 Rietkerk, Van de Koppel (BIB19) 1997; 78 Mesterton-Gibbons (BIB13) 1987; 2 Stephens, Sutherland (BIB23) 1999; 14 Bryson Jr., A.E., Ho, Y., 1975. Applied Optimal Control: Optimization, Estimation, and Control. Wiley. Chaudhuri (BIB6) 1988; 41 Lande, Engen, Saether (BIB12) 1994; 372 Shea (BIB21) 1998; 13 Clark, C.W., 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Pure & Applied Mathematics. Wiley Interscience. Van de Koppel, Rietkerk, Weissing (BIB25) 1997; 12 Khan, Ampong-Nyarko, Chiliswa, Hassanali, Kimani, Lwande, Overholt, Picketta, Smart, Woodcock (BIB10) 1997; 388 Alvarez (BIB2) 1998; 152 Ragozin, Brown (BIB17) 1985; 12 Rietkerk, Bosch, Van de Koppel (BIB18) 1997; 80 Schlesinger, Reynolds, Cunningham, Huenneke, Jarrell, Virginia, Whitford (BIB20) 1990; 247 Kelly, Walker (BIB9) 1976; 64 |
| References_xml | – volume: 388 start-page: 631 year: 1997 end-page: 632 ident: BIB10 article-title: Intercropping increases parasitism of pests publication-title: Nature – volume: 78 start-page: 69 year: 1997 end-page: 76 ident: BIB19 article-title: Alternate stable states and threshold effects in semi-arid grazing systems publication-title: Oikos – volume: 13 start-page: 225 year: 1986 end-page: 234 ident: BIB27 article-title: Optimal recovery paths for perturbations of trophic level bioeconomic systems publication-title: J. Environ. Econ. Manage. – reference: Bryson, A.E., 1999. Dynamic Optimization. Addison Wesley. – volume: 12 start-page: 352 year: 1997 end-page: 356 ident: BIB25 article-title: Catastrophic vegetation shifts and soil degradation in terrestrial grazing systems publication-title: Trends Ecol. Evol. – volume: 14 start-page: 401 year: 1999 end-page: 405 ident: BIB23 article-title: Consequences of the allee effect for behaviour, ecology and conservation publication-title: Trends Ecol. – volume: 247 start-page: 1043 year: 1990 end-page: 1048 ident: BIB20 article-title: Biological feedbacks in global desertification publication-title: Science – volume: 41 start-page: 17 year: 1988 end-page: 25 ident: BIB6 article-title: Dynamic optimization of combined harvesting of a two-species fishery publication-title: Ecol. Modell. – volume: 90 start-page: 253 year: 2000 end-page: 260 ident: BIB24 article-title: Herbivore regulation and irreversible vegetation change in semi-arid grazing systems publication-title: Oikos – volume: 92 start-page: 235 year: 1996 end-page: 244 ident: BIB15 article-title: A technique for finding optimal two-species harvesting policies publication-title: Ecol. Modell. – volume: 269 start-page: 1106 year: 1995 end-page: 1108 ident: BIB16 article-title: Population dynamics of exploited fish stocks at lower population levels publication-title: Science – volume: 80 start-page: 241 year: 1997 end-page: 252 ident: BIB18 article-title: Site-specific properties and irreversable vegetation changes in semi-arid grazing systems publication-title: Oikos – volume: 152 start-page: 63 year: 1998 end-page: 85 ident: BIB2 article-title: Optimal harvesting under stochastic fluctuations and critical depensation publication-title: Math. Biosci. – volume: 69 start-page: 473 year: 1981 end-page: 498 ident: BIB26 article-title: Stability of semi-arid savannah grazing systems publication-title: J. Ecol. – volume: 2 start-page: 109 year: 1987 end-page: 134 ident: BIB13 article-title: On the optimal policy for combined harvesting of independent species publication-title: Nat. Resour. Modell. – volume: 12 start-page: 155 year: 1985 end-page: 168 ident: BIB17 article-title: Harvest policies and nonmarket valuation in a predator–prey system publication-title: J. Environ. Econ. Manage. – reference: Bryson Jr., A.E., Ho, Y., 1975. Applied Optimal Control: Optimization, Estimation, and Control. Wiley. – volume: 63 start-page: 987 year: 1985 end-page: 994 ident: BIB22 article-title: The Sahel of Africa: ecology and disaster publication-title: Can. J. Zool. – volume: 16 start-page: 229 year: 2001 end-page: 234 ident: BIB3 article-title: An invitation to ecological economics publication-title: Trends Ecol. Evol. – reference: Kirk, D.E., 1970. Optimal Control Theory: An Introduction. Prentice-Hall. – volume: 3 start-page: 63 year: 1988 end-page: 90 ident: BIB14 article-title: On the optimal policy for combined harvesting of predator and prey publication-title: Nat. Resour. Modell. – volume: 372 start-page: 88 year: 1994 end-page: 90 ident: BIB12 article-title: Optimal harvesting, economic discounting and extinction risk in fluctuating populations publication-title: Nature – volume: 32 start-page: 267 year: 1986 end-page: 279 ident: BIB5 article-title: A bioeconomic model of harvesting a multispecies fishery publication-title: Ecol. Modell. – reference: Graetz, R.D., 1991. Desertification: a tale of two feedbacks. In: Mooney, H.A., Medina, E., Schindler, D.W., Schulzer, E.D., Walker, B.H. (Eds.), Ecosystem Experiments. Wiley, Chichester, pp. 59–87. – reference: Clark, C.W., 1976. Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Pure & Applied Mathematics. Wiley Interscience. – volume: 64 start-page: 553 year: 1976 end-page: 576 ident: BIB9 article-title: The effects of different forms of land use on the ecology of a semi-arid region in south-eastern rhodesia publication-title: J. Ecol. – volume: 13 start-page: 371 year: 1998 end-page: 375 ident: BIB21 article-title: Management of population in conservation, harvesting and control publication-title: Trends Ecol. Evol. |
| SSID | ssj0001282 |
| Score | 1.8052635 |
| Snippet | Ecological systems in general often exhibit the mechanism of critical depensation, i.e. the system may collapse due to decreasing population densities caused... |
| SourceID | wageningen proquest pascalfrancis elsevier |
| SourceType | Open Access Repository Aggregation Database Index Database Publisher |
| StartPage | 153 |
| SubjectTerms | Animal, plant and microbial ecology Biological and medical sciences conservation ecology fishery Fundamental and applied biological sciences. Psychology General aspects. Techniques Management of ecosystems Methods and techniques (sampling, tagging, trapping, modelling...) Optimal control policies populations Semi-arid grazing systems |
| Title | Optimal harvesting in a two-species model under critical depensation: The case of optimal harvesting in semi-arid grazing systems |
| URI | https://dx.doi.org/10.1016/j.ecolmodel.2004.06.003 https://www.proquest.com/docview/18056759 http://www.narcis.nl/publication/RecordID/oai:library.wur.nl:wurpubs%2F333291 |
| Volume | 179 |
| WOSCitedRecordID | wos000224143200002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-7026 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001282 issn: 0304-3800 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Nb9MwGLaqDaRJHGBsonwMH7hVmZLYTZzdKihjEyqTKKg3y43jqVOXVEm7jiN_gN_M648kLauEOHBJKkd1mj5P3g_7_UDoXSS11tBLYEpFHlUp9VjKhAf8kFNKJWgkZppNxKMRm0ySq07nV50LczeP85zd3yeL_wo1jAHYOnX2H-BuJoUB-AygwxFgh-ND4Hfqn2HaSDTT6GZeX3bU-AJi4lbnQIrSFNmwWS2it1wXns68BOfZftE0yS17ad0OwXTMrZp4EE2xVNjNgGLnnFV2O_PAG5e961LXsb52laMbQ_7r-OJ8bIMxLk_b6OPvg1Hv82B0rjuEfhi2Acj18gTVeXo2ldmumTkFvyHWiN6LYb6_JYNtRxlHtnBDoga2lrBTzoGt3P5A7tsliJtTcNnn5g8ynr-pzOqTVtXV2_t_aMAmLhGmD-NA1yzYD0nEwJnfH1wMJ5eNbgdt7val7DNsRQzuvPmWkfNkISqAS9meKVtOzcEani83CXUbBs74KTpqUz_xVUOqZ6iT5YfosWXUj0N0PGwTI8UcO81QPUc_HalwSwA8y7HAG6TC5mdjQypckwpvkOoMA6WwphQuFC52zthQCjtKYUepI_Tt43D8_pPn2nt4GQnJ0qMJmzLZ70cyTMBEinyqlKBEplLSaRoKGYnQZyn1FQiMOAnSIJjGMKpIqKve9ckx2suLPHuBMFUiS2I_VpJRqmLKgiihUtEgBn8hk1EXndUgcGdZWouRA4F4Heh4wxsEdXdWyk3IJ-miky3Y-MLWgeE1W7robY0jB-Gsd9xEnhWrigcM_Iu4n3QRaeHlue4SVnFd2N0t1fL1quT5XJ_gpak4ISRMgpd_u_ErdNC-cq_R3rJcZW_Qo_RuOavKE8fd39Uix5c |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=Ecological+modelling&rft.atitle=Optimal+harvesting+in+a+two-species+model+under+critical+depensation%3A+The+case+of+optimal+harvesting+in+semi-arid+grazing+systems&rft.au=STIGTER%2C+J.+D&rft.au=VAN+LANGEVELDE%2C+F&rft.date=2004-11-25&rft.pub=Elsevier&rft.issn=0304-3800&rft.volume=179&rft.issue=2&rft.spage=153&rft.epage=161&rft_id=info:doi/10.1016%2Fj.ecolmodel.2004.06.003&rft.externalDBID=n%2Fa&rft.externalDocID=16127115 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3800&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3800&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3800&client=summon |