Final answer:
The logistic function is a mathematical function used in biology to describe population growth. Yeast, sheep, and harbor seals are examples of populations that exhibit logistic growth. The logistic model helps us understand how population growth rates change as resources become limited.
Step-by-step explanation:
The logistic function is a type of mathematical function used to describe population growth. It is commonly used in biology to model the growth of populations. The logistic function represents the idea that populations tend to fluctuate around an equilibrium abundance, which is encapsulated by the general logistic (S-shaped curve) model.
For example, yeast, sheep, and harbor seals all exhibit logistic growth. Yeast populations, when grown in a test tube, show a classical S-shaped curve where growth levels off as nutrients are depleted. In wild populations like sheep and harbor seals, the population size exceeds the carrying capacity for short periods of time and then falls below it.
This fluctuation in population size continues as the population oscillates around its carrying capacity.
The logistic model is used to understand how population growth rates change as resources become limited. Initially, populations may exhibit exponential growth, but as resources become scarce, growth rate slows down and levels off to zero. The logistic model helps us understand how populations reach a stable endpoint, known as the carrying capacity.