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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.
The model was particularly inspired by the work of Italian physicist Vito Volterra, who had developed his predator-prey equations based on observations of fish populations in the Adriatic Sea during World War I. Volterra's work showed that during the war, when fishing was reduced due to military activities, the proportion of predator fish ...
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.
When all prey species are at equal densities, the predator will indiscriminately select between prey species. However, if the density of one of the prey species decreases, then the predator will start selecting the other, more common prey species with a higher frequency because if it can increase the efficiency which with it captures the more ...
Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism. Evolutionary game models have been created for pairwise and multi-species coevolutionary systems. [58] The general dynamic differs between competitive systems and mutualistic systems.
Invulnerable prey: even with a single prey species, if there is a degree of temporal or spatial refuge (the prey can hide from the predator), destabilisation may not happen. Unpalatable prey: if prey do not fulfil the nutritional preferences of the predator to as great an extent at higher densities, as with some algae and grazers, there may be ...
In order to study predation and population oscillations, Huffaker used mite species, one being the predator and the other being the prey. [4] He set up a controlled experiment using oranges, which the prey fed on, as the spatially structured habitat in which the predator and prey would interact. [5]
This model can be generalized to any number of species competing against each other. One can think of the populations and growth rates as vectors, α 's as a matrix.Then the equation for any species i becomes = (=) or, if the carrying capacity is pulled into the interaction matrix (this doesn't actually change the equations, only how the interaction matrix is defined), = (=) where N is the ...