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...

Full description

Saved in:
Bibliographic Details
Published in:Ecological modelling Vol. 179; no. 2; pp. 153 - 161
Main Authors: Stigter, J.D., van Langevelde, F.
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