Final answer:
Predator populations in the Lotka-Volterra model decrease when the availability of prey is insufficient to support the predator population, mathematically expressed as N ÷ ac < m. This leads to cyclical fluctuations in the populations of both predators and prey.
Step-by-step explanation:
In the Lotka-Volterra predator-prey models, the predator populations decrease when the number of prey (N) is not sufficient to sustain the predator population. Mathematically, this can be represented as the condition when N divided by the product of the prey's capture efficiency by predators (a) and the conversion rate of prey into predator offspring (c) is less than predator mortality rate (m). Hence, predator populations decrease when N ÷ ac < m, which supports the observed cyclic fluctuations of predator and prey populations as described in various biological studies.
Predators are highly dependent on the availability of prey for their survival. When prey are abundant, predator numbers can increase. However, as the predator population grows, it will capture more prey, leading to a decrease in the prey population. Ultimately, a scarcity of prey causes the predator population to decline as well. This dynamic balance is typical of predator-prey interactions, which can result in a cyclical pattern of population fluctuations for both species.