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The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
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 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.
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 ...
If predators learn while foraging, but do not reject prey before they accept one, the functional response becomes a function of the density of all prey types. This describes predators that feed on multiple prey and dynamically switch from one prey type to another. This behaviour can lead to either a type II or a type III functional response.
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.
Anti-predator adaptations are mechanisms developed through evolution that assist prey organisms in their constant struggle against predators. Throughout the animal kingdom, adaptations have evolved for every stage of this struggle, namely by avoiding detection, warding off attack, fighting back, or escaping when caught.