8.3 Population Ecology

Population ecology studies how and why the size and composition of populations change over time—focusing on members of the same species interacting with each other and their environment (birth rate, death rate, N). You learn it because those dynamics (dN/dt = B − D; exponential dN/dt = r_max N) explain real-world patterns: population booms, crashes, effects of limited resources (carrying capacity), density-dependent vs. density-independent factors, and different life-history strategies (r- vs. K-selection, fecundity, survivorship curves). On the AP exam this is LO 8.3.A territory: expect questions that ask you to describe growth dynamics, interpret graphs, do simple calculations, and apply concepts to experiments or conservation scenarios (Unit 8: Ecology, 10–15% of MC). For a focused review, see the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK), the unit overview (https://library.fiveable.me/ap-biology/unit-8), and 1,000+ practice questions (https://library.fiveable.me/practice/ap-biology).

In real life, population growth starts with births and deaths: dN/dt = B − D, and per-capita growth gives dN/dt = r_max N for ideal, unlimited conditions (exponential growth). But nature isn’t unlimited—resources, disease, and interactions cause density-dependent factors that slow growth as N approaches carrying capacity (K), producing logistic growth (S-shaped curve). Density-independent factors (storms, fires) can cause sudden drops regardless of N. Life-history strategies matter: r-selected species have high fecundity and fast growth; K-selected species have lower fecundity and higher survivorship. Stochastic events and migration also change population size and allele frequencies. For AP exam answers, name the equations, note birth/death and density-dependent vs. independent factors, and relate patterns to r/K strategies (CED EK 8.3.A.1–2). For a quick refresher, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and practice problems (https://library.fiveable.me/practice/ap-biology).

Birth rate = how many individuals are born into a population per unit time; death rate = how many die per unit time. On the AP/CED level you should think about these as either absolute counts (B and D in dN/dt = B − D) or as per-capita rates (b and d, so dN/dt = (b − d)N). If births > deaths (b − d > 0) the population grows; if deaths > births it shrinks. Unconstrained reproduction with a positive per-capita growth rate gives exponential growth (dN/dt = r_max N). Density-dependent factors (competition, disease) usually raise death rate or lower birth rate as N increases; density-independent factors (weather) affect them regardless of N. For AP practice and worked examples on LO 8.3.A, see the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and try problems at (https://library.fiveable.me/practice/ap-biology).

dN/dt = r_max N just says: the bigger the population (N), the faster it grows, and the speed of growth is proportional to N. dN/dt is the change in population per time; r_max is the intrinsic (per-capita) maximum growth rate—how fast each individual, on average, adds to population when resources aren’t limiting. So if N = 100 and r_max = 0.1 per year, dN/dt = 10 individuals/year. Mathematically it gives exponential growth: N(t) = N0 e^(r_max t). Key assumptions: unlimited resources, no density-dependent factors (no carrying capacity K), constant birth/death rates. On the AP exam you should link this to birth/death rates, r-selection vs K-selection, and when exponential vs logistic models apply (see Topic 8.3 in the CED). For a quick review, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and practice problems (https://library.fiveable.me/practice/ap-biology).

They grow exponentially because each individual reproduces at a constant per-capita rate (r_max) when resources and space aren’t limiting. Mathematically dN/dt = r_max N: the change in population (dN/dt) is proportional to current size (N), so as N gets bigger, the absolute number of births grows faster—producing that J-shaped curve. This assumes birth and death rates are constant (high birth, low death), no density-dependent factors (competition, disease, limited food), and no density-independent shocks. In real populations those constraints eventually slow growth (moving toward carrying capacity K), but "no constraints" = intrinsic rate of increase dominates so exponential growth occurs. For the AP exam, this is EK 8.3.A.2 and ties to LO 8.3.A—review the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and the Unit 8 overview (https://library.fiveable.me/ap-biology/unit-8) for practice and examples; more practice problems are at (https://library.fiveable.me/practice/ap-biology).

Short answer: r_max isn’t just “the growth rate”—it’s the maximum intrinsic (per capita) rate of increase a population can achieve under ideal, unlimited conditions. In the exponential model dN/dt = r_max N, r_max is the per-individual contribution to population growth (birth rate minus death rate, per time). A few quick clarifications you should remember for AP Bio: - It’s an intrinsic or “per capita” rate (so units like individuals per individual per year). - r_max is the theoretical maximum—real populations often have lower realized r because of limits (resources, predation, disease). - r_max can be positive (growth), zero (stable), or negative (decline). - It’s central to r/K life-history ideas: high r_max → r-selected traits (fast reproduction), low r_max near carrying capacity K → K-selected traits. For practice applying this to dN/dt and exam problems, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and AP practice problems (https://library.fiveable.me/practice/ap-biology).

Population size changes because of births minus deaths (dN/dt = B − D). On a per-capita basis growth depends on r (intrinsic rate); without limits dN/dt = r_max N (exponential). But actual speed is shaped by: - Demography: birth rate, death rate, age structure, fecundity, and survivorship curves. - Density-dependent factors: competition for resources, disease, predation and waste buildup—these slow growth as N approaches carrying capacity (K). - Density-independent factors: weather, fires, floods—these change B and D regardless of N. - Life-history strategy: r-selected species reproduce fast; K-selected species have slower growth but higher survival. - Random effects: demographic and environmental stochasticity, migration/immigration. For AP exam framing, use CED terms (birth rate, death rate, per-capita growth rate, carrying capacity) and practice applying dN/dt equations. For a clear review, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and try practice problems (https://library.fiveable.me/practice/ap-biology).

Organisms in a population interact with each other and their environment through processes that change population size and structure. Key factors are birth rate (B), death rate (D), and population size (N)—dN/dt = B − D. Without limits a population can grow exponentially (dN/dt = r_max N), but resources, disease, predation and space (density-dependent factors) or storms and temperature (density-independent factors) slow growth and set a carrying capacity (K). Interactions include competition for resources, mate choice, social behaviors that affect survival, and life-history strategies (r-selected: high fecundity, low survivorship vs. K-selected: fewer offspring, higher survivorship). Demographic stochasticity and adaptations for obtaining energy/matter also shape dynamics. For AP exam, be ready to describe/quantify growth using the equations above and explain density effects (LO 8.3.A, EK 8.3.A.1–2). Review the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and practice problems (https://library.fiveable.me/practice/ap-biology).

If the birth rate equals the death rate, net population growth is zero. Using the CED equation dN/dt = B − D, if B = D then dN/dt = 0, so population size (N) stays constant over time. In per-capita terms, r = b − d = 0 (intrinsic rate of increase is zero), so you won’t get exponential growth or decline. For example, if a population has 50 births and 50 deaths per year, dN/dt = 0 and N stays the same that year. Note: that’s an ideal, average result—real populations can still fluctuate because of demographic stochasticity, immigration/emigration, or changing density-dependent/independent factors. For AP review, this ties directly to LO 8.3.A and the population growth equations in the CED. For more practice and examples, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and the AP practice problems (https://library.fiveable.me/practice/ap-biology).

"dN/dt" is just math shorthand that means "the instantaneous rate of change of the population size N with respect to time t." Saying "population change over time" is vague—it could mean total change over a year, or average change, or the rate at one moment. dN/dt tells you how fast N is changing right now, which you need for models and calculations in population ecology. - In the CED equations dN/dt = B − D and dN/dt = r_max N, dN/dt links births, deaths, and population size to an instantaneous growth rate (and to the intrinsic/per capita growth rate r_max). - Using dN/dt lets you plug into differential equations, predict future population size, and distinguish density-dependent vs. density-independent effects on growth. Practice using these equations for AP-style problems—see the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and try more practice questions (https://library.fiveable.me/practice/ap-biology).

Adaptations for getting energy change birth and death rates, so they directly alter population growth (LO 8.3.A). If a trait (like efficient foraging, photosynthetic pigments, or a new digestive enzyme) raises per-capita energy intake, individuals usually have higher fecundity and/or survival—increasing B and lowering D, so dN/dt and r_max go up. With plentiful resources that boosts r_max → potential for exponential growth (dN/dt = r_maxN). But as resources limit growth, energy-related adaptations interact with density-dependent factors and carrying capacity (K), shifting populations toward K-selection (fewer, competitive offspring) or r-selection (many, fast-reproducing offspring). Density-independent events (storms, temperature) can still cause mortality regardless of adaptations. For AP review, connect adaptations to birth/death rates, r_max vs logistic growth, and life-history strategies (see the Topic 8.3 study guide for examples: https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK). For extra practice, try problems at https://library.fiveable.me/practice/ap-biology.

In exponential growth, the absolute growth rate of a population (dN/dt) is directly proportional to population size: dN/dt = r_max * N. That means if r_max (the intrinsic, per-capita max growth rate) is constant, larger populations add more individuals per unit time than smaller ones because you multiply by a bigger N. Important distinction: the per-capita growth rate (r_max) stays constant during exponential growth, while the total (absolute) growth increases as N increases. On AP questions you might be asked to use this equation, interpret graphs (steepness increases with N), or compare birth/death effects on r (EK 8.3.A.2i). For more review and practice with population ecology concepts and AP-style problems, see the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK), the Unit 8 overview (https://library.fiveable.me/ap-biology/unit-8), and Fiveable practice problems (https://library.fiveable.me/practice/ap-biology).

Think of reproduction without limits as “every individual adds the same fraction of new individuals per time.” If each organism has a constant per-capita birth minus death rate (r_max), then the population change equals r_max times N: dN/dt = r_max N. That equation means the bigger the population, the more new individuals are produced each time step, so growth speeds up—you get a J-shaped curve (exponential growth). Key conditions: unlimited resources, no density-dependent checks, and the intrinsic rate of increase (r_max) stays constant. On the AP CED this is EK 8.3.A.2 and LO 8.3.A: birth rate, death rate, and N set dynamics. In real populations exponential growth is short-lived because carrying capacity and density-dependent factors kick in (see Topic 8.4). For more examples and practice problems tied to this idea, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK), the full Unit 8 overview (https://library.fiveable.me/ap-biology/unit-8), and extra practice (https://library.fiveable.me/practice/ap-biology).

The B − D equation just says change in population size per time = births minus deaths: dN/dt = B − D. B and D can be total numbers (e.g., 30 births, 10 deaths per year) or written as per-capita rates times population size. If b = per-capita birth rate and d = per-capita death rate, then B = bN and D = dN, so dN/dt = (b − d)N. That (b − d) is the population’s per-capita growth rate r. Example: if b = 0.4/year, d = 0.1/year and N = 200, then dN/dt = (0.4 − 0.1)·200 = 0.3·200 = 60 individuals/year. If r is at its maximum (r_max) and growth is unconstrained, you use dN/dt = r_max N (exponential growth). This is exactly the kind of math AP Bio expects you to do (LO 8.3.A). For a quick topic review see the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and try practice problems (https://library.fiveable.me/practice/ap-biology).

Exponential growth shows up whenever reproduction happens without strong limits. Real examples: bacteria or yeast in rich lab culture (E. coli can double ~20 min under ideal conditions), early phases of viral outbreaks in a susceptible population, invasive species after introduction (e.g., zebra mussels or kudzu spreading rapidly), phytoplankton/algae blooms after nutrient inputs, and agricultural pest outbreaks when predators or controls are absent. In each case dN/dt ≈ r_max·N, so growth rate scales with N (EK 8.3.A.2). Remember on the AP exam you may need to link these examples to r-selection, high fecundity, and how density-dependent factors later slow growth toward K (logistic). For quick review on population ecology and practice problems, check the Topic 8.3 study guide (https://library.fiveable.me/ap-biology/unit-8/population-ecology/study-guide/JiYkhCa7zQ0XPgs6OpbK) and the Unit 8 overview (https://library.fiveable.me/ap-biology/unit-8). For extra practice, see Fiveable’s problem set collection (https://library.fiveable.me/practice/ap-biology).