Article

The Orgins and Evolution of Predator‐Prey Theory

First published: 01 October 1992
Cited by: 382

Abstract

Predator—prey theory is traced from its origins in the Malthus—Verhulst logistic equations, through the Lotka—Volterra equations, logistic modifications to both prey and predator equations, incorporation of the Michaelis—Menten—Holling functional response into the predator and prey equations, and the recent development of ratio—dependent functional responses and per—capita rate of change functions. Some of the problems of classical predator–prey theory, including the paradoxes of enrichment and biological control, seem to have been caused by the application of the principle of mass action to predator–prey interactions. Predator–prey models that evolved from logistic theory or that incorporate ratio—dependent functional responses do not have these problems and also seem to be more biologically plausible.

Number of times cited: 382

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  • , Stability and Hopf Bifurcation in a Modified Holling-Tanner Predator-Prey System with Multiple Delays, Abstract and Applied Analysis, 2012, (1), (2012).
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  • , A model for fire‐induced sediment yield by dry ravel in steep landscapes, Journal of Geophysical Research: Earth Surface, 116, F3, (2011).
  • , Patchiness in resource distribution mitigates habitat loss: insights from high‐shore grazers, Ecosphere, 2, 5, (1-17), (2011).
  • , The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays, Discrete Dynamics in Nature and Society, 2011, (1), (2011).
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  • , Prey consumption and functional response of a phytoseiid predator, Neoseiulus womersleyi, feeding on spider mite, Tetranychus macfarlanei, Journal of Insect Science, 11, 1, (2011).
  • , Hopf bifurcation and Turing instability in spatial homogeneous and inhomogeneous predator–prey models, Applied Mathematics and Computation, 218, 5, (1883), (2011).
  • , Codimension-Two Bifurcations of Fixed Points in a Class of Discrete Prey-Predator Systems, Discrete Dynamics in Nature and Society, 2011, (1), (2011).
  • , Positive Periodic Solutions for Neutral Delay Ratio-Dependent Predator-Prey Model with Holling-Tanner Functional Response, International Journal of Mathematics and Mathematical Sciences, 2011, (1), (2011).
  • , Comparative analysis of environmental carrying capacity of the Bohai Sea Rim area in China, Journal of Environmental Monitoring, 13, 11, (3178), (2011).
  • , Bifurcation and control of a bioeconomic model of a prey–predator system with a time delay, Nonlinear Analysis: Hybrid Systems, 5, 4, (613), (2011).
  • , Self-organised spatial patterns and chaos in a ratio-dependent predator–prey system, Theoretical Ecology, 4, 1, (37), (2011).
  • , Bacteria--phagocyte dynamics, axiomatic modelling and mass-action kinetics, Mathematical Biosciences and Engineering, 8, 2, (475), (2011).
  • , Global asymptotic stability of an almost periodic nonlinear ecological model, Communications in Nonlinear Science and Numerical Simulation, 16, 11, (4451), (2011).
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  • , Dynamics of a stochastic density dependent predator–prey system with Beddington–DeAngelis functional response, Journal of Mathematical Analysis and Applications, 381, 1, (441), (2011).
  • , Stationary Patterns of a Ratio-Dependent Predator-Prey System with Cross-Diffusion, Mathematical Modelling and Analysis, 16, 3, (461), (2011).
  • , MULTIPLE POSITIVE PERIODIC SOLUTIONS TO m-LAYER PERIODIC LOTKA–VOLTERRA NETWORK-LIKE MULTIDIRECTIONAL FOOD-CHAIN WITH HARVESTING TERMS, Analysis and Applications, 09, 01, (71), (2011).
  • , Effects of environmental fluctuation and time delay on ratio dependent hyperparasitism model, Communications in Nonlinear Science and Numerical Simulation, 16, 6, (2609), (2011).
  • , Dynamics of a Nonautonomous Leslie-Gower Type Food Chain Model with Delays, Discrete Dynamics in Nature and Society, 2011, (1), (2011).
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  • , On the existence and stability of a unique almost periodic sequence solution in discrete predator–prey models with time delays, Applied Mathematical Modelling, 35, 11, (5448), (2011).
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  • , A Bayesian Bioeconometric Model of Invasive Species Control: The Case of the Hemlock Woolly Adelgid, Environmental and Resource Economics, 50, 1, (1), (2011).
  • , Pattern Formation Controlled by External Forcing in a Spatial Harvesting Predator-Prey Model, Interdisciplinary Research and Applications in Bioinformatics, Computational Biology, and Environmental Sciences, 10.4018/978-1-60960-064-8.ch019, (214-221)
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  • , Existence of four positive periodic solutions for a ratio-dependent predator–prey system with multiple exploited (or harvesting) terms, Nonlinear Analysis: Real World Applications, 11, 3, (1560), (2010).
  • , Self-replication of spatial patterns in a ratio-dependent predator–prey model, Mathematical and Computer Modelling, 51, 1-2, (44), (2010).
  • Factory Automation (ETFA 2010) Bilbao 2010 IEEE 15th Conference on Emerging Technologies & Factory Automation (ETFA 2010) IEEE , (2010). 978-1-4244-6848-5 Biogeography-based Optimization approach based on Predator-Prey concepts applied to path planning of 3-DOF robot manipulator , (2010). 1 8 5641274 , 10.1109/ETFA.2010.5641274 http://ieeexplore.ieee.org/document/5641274/
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