Final answer:
Intrinsic growth rate and time delay in delayed density dependence models determine the magnitude of population cycling as they affect the speed and timing of population responses to changes in density, leading to potential overshoots and undercuts of carrying capacity.
Step-by-step explanation:
In models of delayed density dependence, intrinsic growth rate and the amount of time delay determine the magnitude of population cycling because these factors directly influence how quickly a population can respond to changes in density. A high intrinsic growth rate implies a population can increase rapidly when conditions are favorable but may also suffer dramatic declines when conditions become unfavorable. Time delay is the period between the change in density and the population's response to this change. When the delay is long, it can result in overshooting the carrying capacity or decaying to levels lower than the carrying capacity. These overshoots and decays cause the population size to fluctuate significantly, hence leading to pronounced cycles.
Population dynamics involve both density-dependent factors, which change in effect according to population density, and density-independent factors. Delayed density-dependent factors can lead to complex population cycling as seen in species like the lynx and hare, where the dynamics of one species influence the other.