Question

A population of blowflies experiences logistic growth with delayed density dependence. Suppose that this population has an initial size of 4,295 and follows the standard equation for delayed density dependence with a 10-week delay and an intrinsic growth rate of 0.2 per week. If these conditions remain constant and the population is tracked for a long time, what type of population dynamics should it display? (Note: The cutoff rτ value for dampened oscillations is 0.368, and the cutoff for a stable limit cycle is 1.57.)

A. A stable limit cycle
B. Logistic growth
C. Dampened oscillations
D. Exponential growth

Answer 1

The blowfly population with a growth rate of 0.2 per week and a 10-week delay exhibits a stable limit cycle due to the rτ product being 2, which exceeds the threshold for a stable limit cycle.

Step-by-step explanation:

If a population of blowflies experiences logistic growth with delayed density dependence, with an intrinsic growth rate (r) of 0.2 per week and a delay (τ) of 10 weeks, we need to assess the behavior of their population dynamics based on the product of rτ. In this case, rτ would be 2 (0.2 x 10), which notably exceeds the cutoff value for a stable limit cycle (1.57). Given this information, the population dynamics that the blowflies should display over a long time is a stable limit cycle (A). This dynamic indicates that the population size will likely fluctuate cyclically around the carrying capacity with regular and persistent oscillations.