Final answer:
The duration of population cycles is determined by environmental conditions, resource availability, predation, and competition, while the magnitude of change in population sizes is influenced by these factors, as well as the initial population size and the capacity of the environment.
Step-by-step explanation:
The duration of population cycles is determined by a combination of factors, including environmental conditions, availability of resources, predation, and competition. These factors can influence birth rates, death rates, and migration patterns, which in turn affect the size of the population. For example, if resources are abundant, the population may increase rapidly, whereas if resources are scarce, the population may decline. On the other hand, the magnitude of change in population sizes is influenced by the same factors, but also by the initial population size and the capacity of the environment to support the population.