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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.
A trophic function was first introduced in the differential equations of the Kolmogorov predator–prey model. It generalizes the linear case of predator–prey interaction firstly described by Volterra and Lotka in the Lotka–Volterra equation. A trophic function represents the consumption of prey assuming a given number of predators.
Because the number of prey harvested by each predator decreases as predators become more dense, ratio-dependent predation is a way of incorporating predator intraspecific competition for food. Ratio-dependent predation may account for heterogeneity in large-scale natural systems in which predator efficiency decreases when prey is scarce. [1]
File: Computer simulation of a chaotic wake, preceded by a periodic travelling wave, in the invasion of prey by predators.gif
Huffaker was expanding upon Gause's experiments by further introducing heterogeneity. Gause's experiments had found that predator and prey populations would become extinct regardless of initial population size. However, Gause also concluded that a predator–prey community could be self-sustaining if there were refuges for the prey population.
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 ...
The predator-prey model. This model is typical for revealing the dynamics of populations. As long as the population of the prey is on the rise, the predators population also rises, since they have enough to eat. But very soon the population of the predators becomes too large so that the hunting exceeds the procreation of the prey.
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.