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The Lotka–Volterra predator-prey model makes a number of assumptions about the environment and biology of the predator and prey populations: [5] The prey population finds ample food at all times. The food supply of the predator population depends entirely on the size of the prey population.
The solution to these equations in the simple one-predator species, one-prey species model is a stable linked oscillation of population levels for both predator and prey. However, when time lags between respective population growths are modeled, these oscillations will tend to amplify, eventually leading to extinction of both species.
The Lotka–Volterra equations describe dynamics of the predator-prey systems. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this rate is evaluated as xy, where x is the number of prey, y is the number of predator. This is a typical example of the law of mass action.
Predators receive a reproductive payoff, e, for consuming prey, and die at rate u. Making predation pressure a function of the ratio of prey to predators contrasts with the prey-dependent Lotka–Volterra equations, where the per capita effect of predators on the prey population is simply a function of the magnitude of the prey population g(N).
The solution to this problem can be found in the application of evolutionary game theory to the prisoner's dilemma game – a game which tests the payoffs of cooperating or in defecting from cooperation. It is the most studied game in all of game theory.
For example, exploitative interactions between a predator and prey can result in the extinction of the victim (the prey, in this case), as the predator, by definition, kills the prey, and thus reduces its population. [2] Another effect of these interactions is in the coevolutionary "hot" and "cold spots" put forth by geographic mosaic theory ...
a = conversion efficiency: the fraction of prey energy assimilated by the predator and turned into new predators P = predator density V = prey density m = predator mortality c = capture rate Demographic response consists of a change in dP/dt due to a change in V and/or m. For example, if V increases, then predator growth rate (dP/dt) will increase.
A chemical mimic dupes an operator (e.g. a predator) by showing an adaptive chemical resemblance to an object of its environment and as a consequence receives selective advantage. [1] In all cases of chemical mimicry it has been found that the mimicking species is the only species to benefit from the reaction with either costs or no effect on ...