Under what conditions will predator and prey populations both persist indefinitely? What will be their population dynamics while they coexist? In other words, will one or both populations stabilize, or will they continue to change over time?Īs we did for the Interspecific Competition model, we will begin to answer these questions by seeking equilibrium solutions to Equations 1 and 2.Under what conditions will the predator population die off, leaving the prey population to expand unhindered?.Under what conditions (i.e., parameter values) will the predator population drive the prey to extinction?. Having created these models, we can ask several questions about the interaction they portray, such as Note that the product afV t acts as the predator’s R. In words, the predator population grows according to the attack rate, conversion efficiency, and prey population, minus losses to starvation. Taking all this into account, we can write an equation for the predator population: This will be the product of the per capita starvation rate times the predator population: qC t. We should reduce this predator population growth by some quantity to represent the starvation rate of predators who fail to consume prey. We will represent this conversion efficiency with the parameter f, so the per capita population growth of predators will be afV t C t. The growth of the predator population will depend on this number, and on the efficiency with which predators convert consumed prey into predator offspring. As in the prey model, the number of prey caught will be aC t V t. There is no simple R for the predator population because its growth rate will depend on how many prey are caught. However, there is a wrinkle in this model, because we cannot assume a constant per capita rate of population growth. To model the predator population, we also begin with an exponential model, in concept. Losses are determined by attack rate, predator population, and prey population. In words, the prey population grows according to its per capita growth rate minus losses to predators. The equation for the prey population thus becomes The number of prey killed in one time interval will be the product of these, or using the symbols given above, aC t V t. Finally, it will depend on the attack rate: the ability of a predator to find and consume prey. It will also depend on the number of prey available: the more prey, the more successful the predators. This number killed will depend on the number of predators: the more predators, the more prey they will kill. To model the prey population, we begin with a basic geometric model for the prey populationĪnd subtract the number of prey individuals killed by predators in the interval from t to t + 1. However, either or both may have an implicit carrying capacity imposed by the interaction between the two populations. In the classic Lotka-Volterra model, neither prey population nor predator population has an explicit carrying capacity. The Classical Lotka-Volterra Predator-Prey Model In this chapter, we will explore the classic Lotka-Volterra predator-prey model (Rosenzweig and MacArthur 1963), which treats each population as if it were growing exponentially.
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