The prey population is thus decreased by the term ENP.

The Lotka-Volterra model assumes that an encounter leads to the death of a prey individual. This product, therefore, includes the numerical response to an increase in the prey population, and a linear functional response. The population growth term for the predator is: (xp)(E)(N)(P). In essence this is the assimilation efficiency of the predator. The increase in the predator population is the encounter term (10.3) times a constant xp, which measures the efficiency by which the food (prey) is turned into new predator individuals. The coefficient E is a functional-response term based on the rate of predation per individual predator per unit time. Equation 10.3 assumes that the number of prey taken varies linearly with prey abundance. The chance of an encounter between the predator and prey is the product:Į is a number less than one, which measures the searching (and capturing) efficiency of the predator. Without prey, the predator population (P) dies off based on the instantaneous density-independent mortality rate, mp, and the population declines according to Equation 10.2: Where Kn is a carrying capacity for the prey population.

If the prey population grows according to the logistic, the prey equation is: Where rn is the prey intrinsic growth rate and N is the prey population size. In the version of the Lotka-Volterra model in which the prey population grows exponentially in the absence of predators, the prey growth rate is: Predation is random there is no refuge for the prey and there is no carrying capacity for the predator independent of that set by the prey population. Most of the eight points raised in Section 10.1 are ignored in the Lotka-Volterra model. That is, both prey and predator individuals move at random.ĥ The predator has a density-independent, constant mortality rate. Encounter rate is a random function of population density. The relatively simple Lotka-Volterra model was based on the following assumptions:ġ In the absence of predators, the prey population grows either exponentially or logistically.Ģ The population growth of the predator is limited only by the availability of the prey.ģ Both predator and prey reproduce continuously, have no age structure, and all individuals are identical.Ĥ The predation rate is proportional to the rate of encounter between predators and prey. The growth rate of the predator is then decreased by a mortality factor, which can be either density-independent or density-dependent. The growth of the predator population is a function of the overall predation rate, and is similar to the negative part of the prey equation. The predator equation also consists of two parts. In the prey equation, the rate of growth is decreased by the overall predation rate, which is a function of both the numerical and functional responses of the predator. The second factor, which increases the overall predation rate, is the rate of consumption of prey per individual predator, the functional response. The numerical response of the predator is a function of an increased rate of reproduction, an increase in immigration, or both. These losses are due to the overall predation rate, which itself consists of two parts. Subtracted from this are losses due to predation. The prey population grows according to a simple exponential or logistic model. The Lotka-Volterra model, like most predator-prey models, consists of two parts. As Hudson and Bj0rnstad (2003) put it, 'the fundamental theory of predator-prey interactions encapsulated in the worthy Lotka-Volterra model predicts cycles in prey and predator abundance.' Although the Lotka-Volterra model has been critiqued on many grounds (May 1975a, 1976c), it is still well respected, and forms the basis for models still in use today. The first well-known models of predator-prey interactions can be traced to Lotka (1925) and Volterra (1926).

Predator population vs prey population