The Orgins and Evolution of Predator‐Prey Theory

  title={The Orgins and Evolution of Predator‐Prey Theory},
  author={Alan A. Berryman},
  • A. Berryman
  • Published 1 October 1992
  • Mathematics, Environmental Science
  • Ecology
Predator-prey theory is traced from its origins in the Malthus-Verhulst lo- gistic equation, 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… 
Prey-predator Dynamics under Herd Behavior of Prey
From the analysis of the model, it is observed that the strategy of herd behavior as self defense mechanism is stronger than the toxin producing strategy and due to herd behavior of prey the model shows ecologically meaningful dynamics near origin.
A predator-prey model with ratio-dependent functional response and Strong Allee effect on prey
A ratio-dependent predator-prey model with strong Allee effect on prey is analyzed by making a parametric analysis of stability properties of dynamics on the system in which the functional response
Predator–Prey Dynamical Behavior and Stability Analysis with Square Root Functional Response
A different predator–prey model in which the prey exhibits herd behavior so that the predator interacts with the prey along the outer corridor of the herd of the prey is considered, to study the local stability, global stability and limit cycle of the proposed model.
The Impacts of Harvesting Activities on Prey-Predator Fishery Model in the Presence of Toxin
It is found that the impact of harvesting activities is more influential on the dynamical behaviors in the fishery model than that of the toxin.
Predator density-dependent prey dispersal in a patchy environment with a refuge for the prey
A simple criterion of viability is established, namely, the existence of a positive and globally stable equilibrium, and it is shown that density dependence has beneficial effects on both species by providing larger equilibrium densities.
A Predator-Prey Model Under the Influence of Toxin and Optimal Foraging Strategy
Theoretical and numerical analysis both show that toxin-induced functional response and optimal foraging strategy have complex interactions on the dynamics of the system.
Dynamical Effects of Anti-predator Behaviour of Adult Prey in a Predator-Prey Model with Ratio-dependent Functional Response
In this paper, a three species predator-prey model has been developed. Here we divide the prey population into two subpopulations such as $(i)$ juvenile prey and $(ii)$ adult prey population along
Dynamics of predator and modular prey: effects of module consumption on stability of prey–predator system
A mathematical model, taking into account predation processes within a generation, considering post-predation survival and modularity of prey is suggested to be crucial to understand predator–prey interactions.
A review of predator–prey systems with dormancy of predators
The predator–prey system has received much attention in the field of ecology and evolution. The interaction and competition between populations in nature can be described by the predator–prey system.
Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey
In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been


The dynamics of arthropod predator-prey systems.
  • M. Hassell
  • Environmental Science
    Monographs in population biology
  • 1978
In this study of arthropod predador-prey systems Michael Hassell shows how many of the components of predation may be simply modeled in order to reveal their effects on the overall dynamics of the
Consequences of Ratio‐Dependent Predation for Steady‐State Properties of Ecosystems
The results show parallel increases in all trophic levels as a result of increased nutrient input, demonstrating that natural systems are closer to ratio dependence than to prey dependence.
Graphical Representation and Stability Conditions of Predator-Prey Interactions
The general nature of the predator-prey interaction has been depicted as a graph of predator versus prey densities from which conditions for stability of the interaction are predicted, and variations of the graph are introduced, and it is shown that an otherwise unstable interaction may be stabilized by the presence of either an inviolable prey hiding place, or extremely low predation pressure.
A Model for Tropic Interaction
The analyses suggest that realistic classes of consumer—resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable, and increases in maximum feeding rate may, under certain circumstances, result in decreases in consumer population.
The Kinetics of Functional Response
  • L. Real
  • Environmental Science
    The American Naturalist
  • 1977
Holling's Type II functional-response relationship is presented, and the formulations expressing the underlying organismal interactions which might generate such a relation arc generalized into the
Variation in Plankton Densities Among Lakes: A Case for Ratio-Dependent Predation Models
It is suggested that enrichment affects not only algal production but also Daphnia parameters, and any increase of the parameters quantifying algal productivity would lead to an increase in Daphnian biomass only.
Elements of Physical Biology.
The author has the problem of evolution always before him, and considers analytically the effect on population of a change in the behaviour of individuals in Elements of Physical Biology.
Population Dynamics: a per capita Resource Approach
  • W. Getz
  • Economics, Environmental Science
  • 1984