Final answer:
Prey populations in Lotka-Volterra models decrease when the predator population (P) becomes greater than the prey birth rate (r) divided by the predation rate constant (c), represented as P > r ÷ c.
Step-by-step explanation:
In the Lotka-Volterra predator-prey models, the prey populations decrease when the condition P > r ÷ c is met. This inequality implies that the population of predators (P) is greater than the prey birth rate (r) divided by the predation rate constant (c). This scenario results in a higher predation pressure on the prey, leading to a decline in the prey population. The Lotka-Volterra equations describe the dynamics of biological systems in which two species interact, one as a predator and the other as a prey.
The balance between predator and prey populations follows a cyclical pattern. As prey numbers increase, they provide more food for predators, which leads to an increase in the predator population. Eventually, this increased number of predators will capture more prey, causing the prey population to decrease over time. Subsequently, as the prey becomes scarcer, the predator population also starts to decline due to the reduced availability of food. This predator-prey relationship is a fundamental concept in ecology, illustrating how populations can regulate each other and maintain an ecological balance.