What is Predator-prey equations?
[[File:Milliers_fourrures_vendues_en_environ_90_ans_odum_1953_en.jpg|thumb|Numbers of [[Lepus americanus|snowshoe hare]] (yellow, background) and [[Canada lynx]] (black line, foreground) furs sold to the [[Hudson's Bay Company]]. Canada lynxes eat snowshoe hares.]] [[File:Lotka-Volterra orbits.png|thumb|Solutions of the predator-prey equations for different starting conditions]] The '''predator-prey equations''' is an [[ecological]] system. Two linked [[equation]]s model the two [[species]] which depend on each other: One is the [[prey]], which provides [[food]] for the other, the [[predator]]. Both prey and predator populations grow if conditions are right. [[Alfred J. Lotka]] found these equations in 1925.<ref>Lotka A.J. 1925. ''Elements of physical biology''. Williams and Wilkins.</ref> [[Vito Volterra]] found them, independently, in 1926. For this reason, the equations are also called '''Lotka-Volterra equations'''.<ref>Leigh E.R. 1968. The ecological role of Volterra's equations, in ''Some Mathematical Problems in Biology''. A modern discussion using Hudson's Bay Company data on lynx and hares in Canada from 1847 to 1903.</ref> The equations themselves are non-linear [[differential equation]]s. == Pre-conditions == There are a number of pre-conditions # The prey population always finds food # The size of the predator population only depends on the size of the prey population # The rate of change of a population depends on its size # There are no changes in the [[environment]] which would favor one species. [[Genetics|Genetic]] changes are not important # Predators have limitless appetite In this case the solution of the differential equations is [[Deterministic system|deterministic]] and [[Continuous function|continuous]]. This means that the generations of both the predator and prey are overlapping all the time.<ref>{{cite book|title=The Mathematical Theory of the Dynamics of Biological Populations|last1=Cooke|first1=D.|last2=Hiorns|first2=R. W.|publisher=Academic Press|year=1981|volume=II|display-a