Biological control does not imply paradox

Mathematical Biosciences

Volumn 208, Issue 1, 2007, Pages 26-32

  Deng, Bo ^a   Jessie, Shannon ^b   Ledder, Glenn ^a   Rand, Alex ^c   Srodulski, Sarah ^d  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

^c NEW MEXICO INSTITUTE OF MINING AND TECHNOLOGY   (United States)

^d GEORGETOWN COLLEGE   (United States)

Author keywords

Biological control; Holling Type II functional form; Intraspecific interference predator prey model; Ratio dependent predation

Indexed keywords

BIOACTIVITY; BIODIVERSITY; CONTROL THEORY; ECOLOGY; MATHEMATICAL MODELS;

HOLLING TYPE II FUNCTIONAL FORM; INTRASPECIFIC INTERFERENCE PREDATOR-PREY MODELS; RATIO-DEPENDENT PREDATION;

PATHOLOGY;

BIOLOGICAL CONTROL; MODELING; PREDATOR-PREY INTERACTION; THEORY;

ARTICLE; ECOSYSTEM; GROWTH RATE; PREDATION; PREDATOR PREY INTERACTION; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; ECOSYSTEM; MODELS, BIOLOGICAL; PEST CONTROL, BIOLOGICAL; POPULATION DYNAMICS; PREDATORY BEHAVIOR;

EID: 34249292595     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.03.002     Document Type: Article

References (25)

1. Abrams P.A. The fallacies of ratio-dependent predation. Ecology 75 (1994) 1842
2. Akcakaya H.R., Arditi R., and Ginzburg L.R. Ratio-dependent predation: an abstraction that works. Ecology 76 (1995) 995
3. Abrams P.A., and Ginzburg L.R. The nature of predation: prey dependent, ratio dependent or neither?. Trends Ecol. Evol. 15 (2000) 337
4. Arditi R., and Berryman A.A. The biological control paradox. Trends Ecol. Evol. 6 (1991) 32
5. Arditi R., Ginzburg L.R., and Akcakaya H.R. Variation in plankton densities among lakes: a case for ratio-dependent models. Am. Nat. 139 (1991) 1287
6. Astrom M. The paradox of biological control revisited: per capita non-linearities. Oikos 78 (1997) 618
7. Bazykin A.D. In: Khibnik A.I., and Krauskopf B. (Eds). Nonlinear dynamics of interacting populations (1998), World Scientific Press, Singapore
8. Berezovskaya F., Karev G., and Arditi R. Parametric analysis of the ratio-dependent predator-prey model. Journal of Mathematical Biology 43 (2001) 221
9. Cosner C., DeAngelis D.L., Ault J.S., and Olson D.B. Effects of spatial grouping on the functional response of predators. Theor. Pop. Biol. 56 (1999) 65
10. Deng B. Food chain chaos due to junction-fold point. Chaos 11 (2001) 514
11. Hairston N.G., Frederick S.E., and Lawrence B. Community structure, population control, and competition. Am. Nat. 94 (1960) 421
12. Hassell M.P., and May R.M. Stability in insect host parasite models. J. Anim. Ecol. 42 (1973) 693
13. Hassell M.P., and Rogers D.J. Insect parasite responses in the development of population models. J. Anim. Ecol. 41 (1972) 661
14. Holling C.S. Some characteristics of simple types of predation and parasitism. Can. Entomol. 91 (1959) 385
15. Hsu S.-B., Hwang T.-W., and Kuang Y. A ratio-dependent food chain model and its applications to biological control. Math. Biosci. 181 (2003) 55
16. Jost C., Arino O., and Arditi R. About deterministic extinction in ratio-dependent predator-prey models. Bull. Math. Biol. 61 (1999) 19
17. Lotka A.J. Elements of physical biology (1925), Williams and Wilkins, Baltimore, MD
18. Luck R.F. Evaluation of natural enemies for biological control: a behavior approach. Trends Ecol. Evol. 5 (1990) 196
19. McAllister C.D., and LeBrasseur R.J. Stability of enriched aquatic ecosystems. Science 175 (1971) 562
20. Rogers D.J., and Hassell M.P. General models for insect parasite and predator searching behavior interference. J. Anim. Ecol. 43 (1974) 239
21. Rosenzweig M.L. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171 (1971) 385
22. Royama T. A comparative study of models for predation and parasitism. Res. Popul. Ecol. Kyoto Univ. Suppl. 1 (1971) 1
23. Skalski G.T., and Gilliam J.F. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology 82 (2001) 3083
24. Verhulst P.F. Notice sur la loi que la population suit dans son accroissement. Corr. Math. Phys. 10 (1838) 113
25. Volterra V. Fluctuations in the abundance of species, considered mathematically. Nature 118 (1926) 558