Final answer:
When the population of rodents on an island reaches its carrying capacity, the birth and death rates become relatively equal. Carrying capacity is the limit at which the population is sustained by the resources without environmental degradation. Selective pressures and logistic growth curves are essential in understanding population dynamics. Option a. relatively equal. is the correct answer.
Step-by-step explanation:
When a group of rodents is introduced to a remote island and the population eventually reaches the island's carrying capacity, the birth and death rates become relatively equal. Carrying capacity is the maximum number of individuals in a population that the environment can sustain indefinitely without being degraded. In the context of the rodents, carrying capacity would be reached when the number of rodents the island can support with its resources—food, shelter, etc.—is at its maximum sustainable limit. At this point, the birth and death rates stabilize to maintain this balance.
Now, during the initial phases of the rodents' colonization of the island, we would expect an exponential growth phase where the rodent population would increase rapidly due to abundant resources and fewer predators. However, as the population grows, resources such as food and hiding spaces become more limited, leading to selective pressures. These pressures would favor rodents of an optimal size that can both hide from predators and maintain their body temperature in the cold climate.
Eventually, competition for resources and other factors like predation would cause the population growth to slow down until it levels off, forming an S-shaped, or logistic growth, curve. The logistic growth model includes an acceleration phase, a deceleration phase as the population approaches carrying capacity, and finally, a plateau where the population size stabilizes. The mention correct option answer in the final answer for when the population of rodents reaches the island's carrying capacity, and the birth and death rates become relatively equal, is (a).