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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 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.
Real high-dimensional data is typically sparse, and tends to have relevant low dimensional features. One task of TDA is to provide a precise characterization of this fact. For example, the trajectory of a simple predator-prey system governed by the Lotka–Volterra equations [1] forms a closed circle in state space. TDA provides tools to detect ...
The form is similar to the Lotka–Volterra equations for predation in that the equation for each species has one term for self-interaction and one term for the interaction with other species. In the equations for predation, the base population model is exponential. For the competition equations, the logistic equation is the basis.
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.
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.
Experiments on blue jays suggest they form a search image for certain prey.. Visual predators may form what is termed a search image of certain prey.. Predators need not locate their host directly: Kestrels, for instance, are able to detect the faeces and urine of their prey (which reflect ultraviolet), allowing them to identify areas where there are large numbers of voles, for example.
At low prey densities, the search time is long. Since the predator spends most of its time searching, it eats every prey item it finds. As prey density increases, the predator is able to capture the prey faster and faster. At a certain point, the rate of prey capture is so high, that the predator doesn't have to eat every prey item it encounters.