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The Lotka–Volterra system of equations is an example of a Kolmogorov population model (not to be confused with the better known Kolmogorov equations), [2] [3] [4] which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.
He described an effect in six predator–prey models where increasing the food available to the prey caused the predator's population to destabilize. A common example is that if the food supply of a prey such as a rabbit is overabundant, its population will grow unbounded and cause the predator population (such as a lynx) to grow unsustainably ...
EcoSim is an individual-based predator-prey ecosystem simulation in which agents can evolve. It has been designed to investigate several broad ecological questions, as well as long-term evolutionary patterns and processes such as speciation and macroevolution.
Predator–prey isoclines before and after pesticide application. Pest abundance has increased. Now, to account for the difference in the population dynamics of the predator and prey that occurs with the addition of pesticides, variable q is added to represent the per capita rate at which both species are killed by the pesticide. The original ...
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.
The model assumes that predators search for prey at random, and that both predators and prey are assumed to be distributed in a non-contiguous ("clumped") fashion in the environment. [30] In the late 1980s, a credible, simple alternative to the Lotka–Volterra predator-prey model (and its common prey dependent generalizations) emerged, the ...
Smale [3] showed that Lotka–Volterra systems that meet the above conditions and have five or more species (N ≥ 5) can exhibit any asymptotic behavior, including a fixed point, a limit cycle, an n-torus, or attractors. Hirsch [4] [5] [6] proved that all of the dynamics of the attractor occur on a manifold of dimension N−1.
Predator-prey relationship between rabbits and foxes following the principle of the Red Queen hypothesis. The rabbit evolves increasing speed to escape the attack of the fox, and the fox evolves increasing speed to reach the rabbit. This evolution is constant; were one of the two to stop evolving, it would go extinct.