Population ecology: exponential growth, logistic growth and density

What the exam asks

• Section I (Multiple Choice): Expect stimulus sets with population graphs or data tables asking you to calculate $\frac{dN}{dt}$ or future population size ($N$), identify where on a curve growth is fastest, or distinguish between density-dependent and density-independent limiting factors.
• Section II (Free Response): Frequently appears in Q2 (Graphing), where you plot population data (with error bars when the data include them) and estimate $K$; Q4 (Conceptual Analysis), where you predict and justify the effect of an environmental disruption (such as a new predator, disease or drought) on $r_{\text{max}}$ or $K$; or Q6 (Analyze Data), where you describe population data and use it to evaluate a hypothesis.

Core ideas

1. Basic population change and exponential growth

A population grows when births ($B$) exceed deaths ($D$), assuming immigration and emigration are equal or negligible:

When resources (food, space, mates) are abundant and limiting factors are absent, a population grows at its maximum per capita rate of increase ($r_{\text{max}}$). This produces exponential growth:

• Graph shape: J-shaped curve when $N$ is plotted against time ($t$).
• Key dynamic: Because $r_{\text{max}}$ is constant, the population growth rate ($\frac{dN}{dt}$, the slope of the curve) increases continuously as gets larger.

2. Carrying capacity and limiting factors

No environment has infinite resources. The maximum population size that a particular environment can sustain over time is its carrying capacity ($K$).