Volterra [...] investigated in considerable detail the association of two species, one of which feeds on the other: we may call them predators and prey. For this case we have the LotkaVolterra equations
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LotkaVolterra equationsLotkaVolterraGleichungen (ger.)

LotkaVolterra: Used attrib. with reference to a mathematical model of the variation with time in the populations of a predator species and a prey species, as governed by a pair of coupled differential equations (the LotkaVolterra equations). (OED 2011)
 1941

Whittaker, E.T. (1941). Vito Volterra. 18601940. Obituary Notices of Fellows of the Royal Society 3, 690729: 709.
 1946

The LotkaVolterra simultaneous equations for the population growth of two species competing for the same limited environment are also discussed in the same paper. The LotkaVolterra equations may be written […]
Crombie, A.C. (1946). Further experiments on insect competition. Proceedings of the Royal Society of London. Series B, Biological Sciences 133, 76109: 103.
 1955

[members of one generation do not survive to contribute to the census of the next generation, and the numbers observed in one generation are purely the product of events during the timeof the preceding generation. Since this advantage applies to both parasite and host, and since it can be arranged that both species have approximately the same generation time, the approach reduces to a simplified version of the LotkaVolterra model.
Utida, S. (1955). Fluctuations in the interacting populations of host and parasite in relation to the biotic potential of the host. Ecology 36, 202206: 202.]
 1959

Some of the most widely debated theoretical aspects of competition theory revolve around what have become known as the LotkaVolterra equations.
Odum, E.P. & Odum, H.T. (1959). Fundamentals of Ecolog, 2nd ed.: 232.
 1982

LotkaVolterra equations 1: A simple model for a predatorprey system; dN/dt = aN  aNP anddP/dt = bP + ßNP, where the prey population (N) has a propensity for exponential growth (aN), which is limited by predation: the effect of the predator on the prey population is measured by the functional response q.v. term aNP. The predator population (P) has an intrinsic death rate (bP) and a growth rate which depends on prey abundance, as ßNP. 2: A simple model for two competing populations (N1 and N2) based on the logistic equation: dN1/dt = r1N1 [1(N1 +a12N2)/K1] and dN2/dt = r2N2[1(N2 + a21N1)/K2], where K1 and K2 are the carrying capacities q.v. of species 1 and 2 respectively, r1 and r2 are their intrinsic growth rates, a12 is the competition coefficient measuring the effect of species 2 on species 1 and a21 measures the effect of species 1 on species 2.
Lincoln, R.J., Boxshall, G.A. & Clark, P.F. (1982). A Dictionary of Ecology, Evolution and Systematics: 143.