Exercises: Population Ecology and Density Effects

Define carrying capacity. Then describe the shape of a graph of exponential growth and of logistic growth, and state which one levels off.

Classify each limiting factor as density-dependent or density-independent:

(a) competition for food;

(b) a hurricane that destroys a coastal bird colony;

(c) a disease that spreads faster in crowded herds;

(d) a wildfire in a dry forest;

(e) predation that increases when prey are abundant.

For exponential growth, $\dfrac{dN}{dt} = r_{max}N$. A bacterial population has $N = 100$ cells and $r_{max} = 0.05$ per day. Calculate $\dfrac{dN}{dt}$ and state its units.

A population of deer introduced to an island was counted every two years.

(a) Identify the growth model and estimate the carrying capacity. (b) Estimate when the population is growing fastest, and explain why. (c) Explain why growth slows as the population approaches 1,000.

The logistic growth equation is $\dfrac{dN}{dt} = r_{max}N\left(\dfrac{K-N}{K}\right)$. A population has $r_{max} = 0.4$ per year and $K = 1{,}000$. Calculate $\dfrac{dN}{dt}$ when $N = 200$, $N = 500$, and $N = 1{,}000$. Explain what the pattern tells you about where the population grows fastest.

Flour beetles were raised at different densities in identical containers, and the average number of eggs laid per beetle was recorded.

(a) Describe the trend. (b) Identify the type of limiting factor shown, and explain how it relates to carrying capacity. (c) Predict what would happen to the growth rate of the population as density keeps increasing.

Two rodent populations were counted at the same time each year for eight years.

(a) Describe the pattern of each population. (b) Argue which population is more likely regulated by density-dependent factors and which by density-independent factors, such as rainfall. (c) Predict how a new predator that eats more prey when prey are abundant would affect each population, and justify your answer.

A sea otter population has $r_{max} = 0.3$ per year and a carrying capacity of $K = 2{,}000$. Wildlife managers want to allow a sustainable harvest. (a) Using the logistic equation $\dfrac{dN}{dt} = r_{max}N\left(\dfrac{K-N}{K}\right)$, calculate the growth rate at $N = 500$, $N = 1{,}000$, and $N = 1{,}500$. (b) Argue at which population size a harvest would be most sustainable, and explain why. (c) Explain what would happen if harvesting continued at a population near carrying capacity, and what a severe storm (density-independent event) would do to the harvest plan.