1. Core Concepts of Population Ecology★★☆☆☆⏱ 3 min

Population ecology is the subfield of ecology that studies how species populations change in size, age structure, and composition over time, and how they interact with environmental limiting factors. For AP Biology, a population is defined as a group of interbreeding individuals of the same species that occupy the same geographic range at the same time.

Population ecology makes up ~2-3% of total AP Biology exam score, and is often combined with other ecology concepts in multi-part FRQs. Standard notation used across all AP problems follows this convention: $N$ = total population size, $b$ = per capita birth rate, $d$ = per capita death rate, $r$ = intrinsic per capita growth rate, $K$ = carrying capacity.

2. Measuring Population Size and Density★★★☆☆⏱ 4 min

Population density is defined as the number of individuals of a species per unit area (terrestrial organisms) or volume (aquatic organisms), the foundational parameter for any population study. Measurement techniques differ based on whether the organism is sessile (non-moving) or mobile.

For mobile organisms, the most common estimation method is the mark-recapture method (Lincoln Index), which follows these steps: 1) capture an initial sample of individuals, 2) mark them with a harmless permanent mark, 3) release them back into the population and allow time for random mixing, 4) capture a second random sample. The total population size $N$ is estimated with the formula:

Where: $M$ = number of marked individuals released, $C$ = total number of individuals captured in the second sample, $R$ = number of marked individuals recaptured in the second sample. This method relies on four key assumptions commonly tested on the AP exam:

• No births, deaths, or migration occur between the two sampling periods

• Marks do not change an individual's chance of being recaptured

• Marks are not lost between sampling events

• Marked individuals mix randomly with the unmarked population

3. Population Growth Models★★★☆☆⏱ 4 min

The core question of population ecology is how population size changes over time, described by two widely used models tested repeatedly on the AP exam. First, the intrinsic per capita growth rate $r$ is calculated as $r=b-d$, where $b$ is average per capita birth rate and $d$ is average per capita death rate.

When resources are unlimited (no competition, no predation, enough space and food for all individuals), the population grows exponentially: the per capita growth rate stays constant, so the total number of new individuals added increases as the population gets larger. The continuous-time exponential growth model used on the AP exam is:

Exponential growth produces a characteristic J-shaped curve, and only occurs in very specific natural scenarios like colonization of a new empty habitat or recovery after a mass extinction event.

In all natural ecosystems, resources are finite, so growth cannot continue exponentially forever. As population size increases, competition for resources increases, birth rates drop and death rates rise, so growth slows until the population stabilizes at carrying capacity ($K$), the maximum number of individuals the environment can support indefinitely. This pattern is called logistic growth, which produces an S-shaped (sigmoidal) curve, with the formula:

The $\frac{K-N}{K}$ term adjusts growth for resource limitation: when $N$ is very small, the term is nearly 1, so growth is almost exponential; when $N=K$, the term equals 0, so growth stops entirely.

4. Limiting Factors and Population Regulation★★★★☆⏱ 3 min

All population growth is limited by factors that restrict maximum population size. A key AP exam distinction categorizes these factors by how their effect relates to population density.

Two additional core concepts tested on the AP exam are survivorship curves and age structure:

• Survivorship curves: Plot the proportion of individuals alive at each age, with three common types: Type I (low early mortality, high late mortality, typical of K-selected species like large mammals), Type II (constant mortality across all ages, typical of many birds), Type III (very high early mortality, low late mortality, typical of r-selected species like insects or fish).

• Age structure diagrams: Show the proportion of the population in each age group, used to predict future population growth. A broad base means many young reproductive individuals, so rapid future growth, while a narrow base predicts slow or negative growth.