Final answer:
When graphing the two population growth rate models, exponential growth shows a J-shaped curve representing unlimited growth, while logistic growth exhibits an S-shaped curve that levels off at the environment's carrying capacity. The amplitude of cycling depends on the area between these curves, i.e., the delay in birth rate decrease and the initial versus final rate difference.
Step-by-step explanation:
Population Growth Models: Exponential vs Logistic Growth
When graphing the two population growth rate models, exponential and logistic growth, noticeable differences are observed.
Exponential growth, represented by a J-shaped curve, indicates unlimited population growth where the growth rate accelerates as the population increases.
In contrast, logistic growth is depicted by an S-shaped curve where the population growth rate increases initially but then decelerates and levels off at the carrying capacity of the environment.
The amplitude of cycling in these models depends on factors such as the availability of resources, predation, disease, and other environmental constraints.
Specifically, the surge in population growth is shown to be proportional to the exponential of the area between the exponential growth curve and the logistic growth curve.
This is exemplified by e(¹₁-¹₂), where the base of the trapezoid (delay in onset of birth rate decrease) and the rate difference between initial and final rates serve as the critical determinants of surge magnitude. The area increases as the delay or rate difference becomes larger, leading to a greater population surge.
Exponential growth is idealistic and often does not occur in natural populations due to limiting factors, which may be density-dependent or independent.
These factors can include competition, predation, disease, and the availability of resources. Logistic growth, being more realistic, acknowledges these limiting factors and the carrying capacity of the environment, thus demonstrating a population that will stabilize over time.