📚Study Guide: Populations
Unit 3: Populations
Population ecology examines how and why populations change over time and space. This unit is heavily mathematical, requiring students to understand and apply exponential and logistic growth models, calculate doubling times, and interpret age-structure diagrams and survivorship curves. Exponential growth (dN/dt = rN) occurs when resources are unlimited, producing a J-shaped curve characteristic of invasive species or populations recovering from disturbance. Logistic growth (dN/dt = rN[(K-N)/K]) incorporates carrying capacity (K), producing an S-shaped curve as density-dependent limiting factors slow growth. The AP exam frequently presents population data and asks students to identify which model applies, calculate r or K, and explain limiting factors. Density-dependent factors (competition, disease, predation) intensify as population density increases, whereas density-independent factors (natural disasters, climate extremes) affect populations regardless of density. Life history strategies distinguish r-selected species (many offspring, little parental care, early maturity) from K-selected species (few offspring, high parental care, late maturity). Human population growth is a special focus; students must analyze demographic transition models, interpret age-structure pyramids, and evaluate the factors that have allowed human populations to grow exponentially while most other species follow logistic patterns.
Key Concepts
- Population Growth Models: Exponential: dN/dt = rN, J-shaped curve. Logistic: dN/dt = rN[(K-N)/K], S-shaped curve. Carrying capacity (K) is the maximum population size sustainable by available resources.
- Density-Dependent Factors: Competition for food/space, predation, disease, parasitism, accumulation of wastes. Effects increase as density increases.
- Density-Independent Factors: Natural disasters (earthquakes, fires, floods), extreme weather, climate change. Affect population size regardless of density.
- Life History Strategies: r-selected: high growth rate, many offspring, little parental investment, early reproduction, small body size (e.g., insects, weeds). K-selected: low growth rate, few offspring, high parental investment, late reproduction, large body size (e.g., elephants, whales, humans).
- Survivorship Curves: Type I: low mortality early, high in old age (humans, elephants). Type II: constant mortality (songbirds, rodents). Type III: high mortality early, low later (trees, marine invertebrates).
- Human Population Dynamics: Demographic transition model links economic development to declining birth and death rates. Age-structure pyramids show past fertility and predict future growth. Total fertility rate (TFR) and replacement-level fertility (~2.1 in developed countries) determine population momentum.
Vocabulary
- Biotic Potential: The maximum reproductive capacity of a population under optimal environmental conditions.
- Carrying Capacity (K): The maximum population size of a species that the environment can sustain indefinitely.
- Replacement-Level Fertility: The total fertility rate at which a population exactly replaces itself from one generation to the next, approximately 2.1 children per woman in developed countries.
- Demographic Momentum: The tendency for population growth to continue beyond the point where replacement-level fertility is reached due to a large proportion of young people entering reproductive age.
- Total Fertility Rate (TFR): The average number of children a woman will have during her childbearing years (ages 15-49).
- Cohort: A group of individuals of the same age born during the same time period, tracked through survivorship studies.
Essential Formulas
- Exponential Growth: dN/dt = rN
- Logistic Growth: dN/dt = rN[(K-N)/K]
- Doubling Time (rule of 70): T = 70 / r (where r is % growth rate)
- Population Growth Rate: r = b - d + i - e (births - deaths + immigration - emigration)
Common Mistakes
- Confusing r and K: r is the intrinsic growth rate (max per capita growth). K is carrying capacity (environmental limit). They are independent parameters.
- Thinking Humans Have No Carrying Capacity: Humans temporarily exceed K through technology and resource importation, but this creates environmental degradation that may lower K in the future (overshoot and collapse).
- Confusing Birth Rate and Total Fertility Rate: Birth rate is births per 1,000 individuals per year. TFR is average children per woman over her lifetime.
- Assuming Logistic Growth Always Reaches K Smoothly: Real populations often overshoot K and then crash due to time lags in density-dependent responses.
AP Exam Strategies
- Identify the Growth Model from a Graph: J-shaped = exponential; S-shaped = logistic. Label K on logistic curves.
- Calculate Doubling Time: Use the rule of 70: T = 70 / r. Remember r must be expressed as a percentage (e.g., 2% -> T = 35 years).
- Interpret Age-Structure Pyramids: Broad base = rapid growth (high TFR). Uniform = stable. Narrow base = declining.
- Connect Human Development to Fertility: Explain that increased education (especially for women), urbanization, and economic development reduce TFR through the demographic transition.
Real-World Applications
- Invasive Species Management: Understanding exponential growth helps predict and control outbreaks of invasive species like zebra mussels or kudzu.
- Fisheries Quotas: Maximum sustainable yield (MSY) is harvested at K/2; setting quotas requires understanding logistic growth and avoiding overfishing.
- Family Planning Programs: Countries like Bangladesh and Iran reduced TFR dramatically through education, access to contraception, and economic incentives, demonstrating demographic transition in action.