A three species competition model as a decision support tool

Ecological Modelling

Volumn 211, Issue 1-2, 2008, Pages 142-152

  Fay, Temple H ^a   Greeff, Johanna C ^a  

^a TSHWANE UNIVERSITY OF TECHNOLOGY   (South Africa)

Author keywords

Cropping; Eigenvalue analysis; Inter and intraspecies competition; Localized extinction; Logistic growth; Overpopulation; Stability

Indexed keywords

DATA REDUCTION; DECISION SUPPORT SYSTEMS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; VEGETATION;

DECISION SUPPORT TOOLS; EIGENVALUE ANALYSIS; LOCALIZED EXTINCTION; LOGISTIC GROWTH;

BIODIVERSITY;

COEXISTENCE; CROPPING PRACTICE; DECISION SUPPORT SYSTEM; INTERSPECIFIC COMPETITION; INTRASPECIFIC COMPETITION; LOGISTICS; SPECIALIST; VEGETATION STRUCTURE;

AEPYCEROS MELAMPUS; TRAGELAPHUS ANGASII;

EID: 37549030563     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ecolmodel.2007.08.023     Document Type: Article

References (18)

1. Bothma-Du Preez B.L.J. Game Range Management (1996), J. L. v. Schaik, Pretoria
2. Chi C., Hsu S., and Wu L. On the assymetric May-Leonard model of three competing species. SIAM J. Appl. Math. 58 (1998) 1
3. Estes R.D. Behaviour Guide to African Mammals (1992), University of California Press, California
4. Fay T.H., and Greeff J.C. Nyala and bushbuck: a competing species model I. Math. Comput. Educ. 33 2 (1999) 17-26
5. Fay T.H., and Greeff J.C. Nyala and bushbuck: a competing species model II. Math. Comput. Educ. 33 2 (1999) 26-35
6. Fay T.H., Greeff J.C., Groeneveld H.T., and Eisenberg B.E. Testing the model for one predator and two mutualistic prey species. Ecol. Model. 196 (2006) 245-255
7. Gilpen M.E. Limit cycles in competition communities. Am. Nat. 109 (1975) 51-60
8. Holling C.S. The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Ent. Soc. Can. 45 (1965) 1-60
9. Li T.Y., and York J.A. Period times three implies chaos. Am. Math. Monthly 82 (1975) 985-992
10. Lotka A.J. Elements of Physical Biology (1956), Williams and Wilkens, Maryland (reprinted as Elements of Mathematical Biology, 1924, Dover, NY)
11. May R.M. Stability and Complexity in Model Ecosystems (1973), Princeton University Press, Princeton, NJ
12. May R.M., and Leonard W.J. Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29 (1975) 2
13. Murray J.D. Mathematical Biology (1993), Springer-Verlag, New York
14. Overton W.S. In: Hall C.A.S. (Ed). A Strategy of Model Construction. Ecosystem Modelling in Theory and in Practice vol. 5 (1984), Wiley and Sons, New York 52-53
15. Pimm S.L. The Balance of Nature? (1991), University of Chicago Press, Chicago
16. Smuts G.L. Lion (1982), Macmillan, South Africa
17. Starfield A.M., and Bleloch A.L. Building Models for Conservation and Wildlife Management (1986), Macmillan Publishing Company, Brisbane
18. Van der Hoff, Q., 2000. Stability of Three competing Species Models. M.S. thesis, University of Southern Mississippi, Hattiesburg, USA.