What determines how populations grow and how large they become?
Topic 8.3 Population Ecology: explain exponential and logistic growth, carrying capacity, and the factors that regulate population size.
A focused answer to AP Biology Topic 8.3, covering exponential and logistic growth, carrying capacity, growth rate calculations, and the factors that shape population size, with a worked growth-rate calculation.
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What this topic is asking
The College Board (Topic 8.3) wants you to explain exponential and logistic population growth, carrying capacity, and the factors that regulate population size. You should use the growth-rate equations provided on the exam.
Exponential growth
Exponential growth occurs only when resources are abundant, such as a population colonizing a new, empty habitat.
Logistic growth and carrying capacity
Factors regulating population size
The per capita growth rate is the difference between the per capita birth rate and the per capita death rate; when births exceed deaths is positive and the population grows, and when deaths exceed births is negative and it shrinks. Density-dependent factors regulate a population by changing these rates as density changes, which is why logistic growth levels off: as approaches , crowding raises death rates and lowers birth rates until they balance.
The two growth equations are on the AP formula sheet, so the skill being tested is choosing the right one and interpreting the result, not memorizing them. Use the exponential equation when resources are described as unlimited or the population is far below carrying capacity, and the logistic equation when a carrying capacity is given or the population is near it.
Try this
Q1. Define carrying capacity. [1 point]
- Cue. The maximum population size that an environment can sustain over time, given its limited resources.
Q2. Explain the difference between density-dependent and density-independent limiting factors. [2 points]
- Cue. Density-dependent factors (competition, disease, predation) have a stronger effect as the population gets denser; density-independent factors (weather, disasters) affect the population regardless of its density.
Exam-style practice questions
Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
AP 2021 (style)4 marksSection II (long FRQ excerpt, graph). A population grows rapidly at first, then levels off at a stable size. (a) Identify the type of growth and explain what carrying capacity is. (b) A population of 500 has a per capita growth rate (r) of 0.04 per year. Calculate the growth rate of the population (dN/dt) at this moment, assuming exponential growth, and explain what it represents.Show worked answer →
A 4-point identify-and-calculate FRQ on population growth.
(a) Identify and explain (2 points): (1 point) logistic growth (S-shaped curve that levels off); (1 point) carrying capacity (K) is the maximum population size the environment can sustain, set by limited resources.
(b) Calculate (2 points): (1 point) using ; (1 point) this means the population is increasing by about 20 individuals per year at this moment (the number added per unit time).
Markers reward identifying logistic growth and carrying capacity and the correct calculation with interpretation.
AP 2018 (style)1 marksSection I (multiple choice). The maximum population size that a particular environment can sustain over time is called the: (A) exponential growth rate. (B) carrying capacity. (C) biotic potential. (D) population density.Show worked answer →
The correct answer is (B).
Carrying capacity (K) is the maximum population an environment can support given its resources. As a population nears K, growth slows and levels off (logistic growth). Density (D) is individuals per area, not a maximum.
Related dot points
- Topic 8.4 Effect of Density of Populations: distinguish density-dependent from density-independent factors and explain how each limits population size.
A focused answer to AP Biology Topic 8.4, covering density-dependent factors (competition, predation, disease) and density-independent factors (weather, disasters), how each regulates populations, and K-selected versus r-selected strategies, with a worked example.
- Topic 8.5 Community Ecology: explain the types of interactions between species in a community and their effects on the species involved.
A focused answer to AP Biology Topic 8.5, covering competition, predation, the niche, symbiosis (mutualism, commensalism, parasitism), keystone species and trophic relationships, with a worked interaction example.
- Topic 8.2 Energy Flow Through Ecosystems: explain how energy flows through trophic levels and why energy is lost between levels.
A focused answer to AP Biology Topic 8.2, covering trophic levels, food chains and webs, the 10 percent rule, energy pyramids, productivity, and why energy decreases up the chain, with a worked energy-transfer calculation.
- Topic 7.12 Variations in Populations: explain why genetic variation within a population is important for survival and the response to environmental change.
A focused answer to AP Biology Topic 7.12, covering the sources and importance of genetic diversity, how variation buffers populations against change, the risks of low diversity, and the role of variation in evolution, with a worked example.
- Topic 8.6 Biodiversity: explain how biodiversity contributes to ecosystem stability and resilience.
A focused answer to AP Biology Topic 8.6, covering species and genetic diversity, how diversity supports ecosystem stability and resilience, the effects of low diversity, and a worked example using a diversity comparison.
Sources & how we know this
- AP Biology Course and Exam Description — College Board (2020)