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The Kolmogorov model addresses a limitation of the Volterra equations by imposing self-limiting growth in prey populations, preventing unrealistic exponential growth scenarios. It also provides a predictive model for the qualitative behavior of predator-prey systems without requiring explicit functional forms for the interaction terms. [5]
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 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.
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).
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 ...
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 ...
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.
Consumer–resource interactions are the core motif of ecological food chains or food webs, [1] and are an umbrella term for a variety of more specialized types of biological species interactions including prey-predator (see predation), host-parasite (see parasitism), plant-herbivore and victim-exploiter systems.