The Lotka-Volterra predator-prey equations are two nonlinear differential equations that are useful in modeling the dynamics of ecological systems. The two equations are based on the assumptions that the number of prey and predators in the environment are constantly changing due to a combination of reproduction, predation, and death. In the Lotka-Volterra equations, the parameter Rprey represents the growth rate of the prey species, when predation is absent.
As explained in the Scholarpedia article on Predator-Prey Models, the parameter b represents the growth rate of prey (species x) in the absence of predation. That is, when the predator species is absent (or the prey-predator interactions have been minimized), the parameter b represents how quickly the prey population can increase. This rate of increase can be affected by factors such as resources available to the prey species, environmental conditions, and age structure.
The parameter Rprey can be more accurately thought of as the intrinsic (or maximum) growth rate of the prey population. It is the rate at which the prey can increase, in the absence of predation and other factors that can reduce the population. In the Lotka-Volterra equations, Rprey is a constant that describes the maximum rate at which the prey species can increase.
This parameter is important in determining the behavior of the predator-prey system, as it affects the stability of the equilibrium (or balance) between the predators and the prey. When Rprey is large, the equilibrium is unstable, and the system can become chaotic. On the other hand, when Rprey is small, the equilibrium is stable, and the system is less likely to become chaotic.
In summary, the parameter Rprey in the Lotka-Volterra predator-prey equations represents the maximum intrinsic growth rate of the prey species, in the absence of predation or other factors that can reduce population size. This parameter is important in determining the behavior of the predator-prey system, and understanding its value is essential for accurate predictions and successful management of the system.