Notes
Describing and modeling populations
- Density $\displaystyle = \frac{\text{individuals}}{\text{area}}$. Distribution can be clumped, uniform, or random.
- Exponential growth (J curve) happens without limits. Logistic growth (S curve) levels off at carrying capacity (K).
- Growth rate (%) $\displaystyle = \frac{\text{births} - \text{deaths}}{\text{population}} \times 100$. Rule of 70: doubling time $\displaystyle = \frac{70}{\text{growth rate (\%)}}$.
Limits and strategies
- Density-dependent factors (competition, disease, predation) get stronger in crowded populations; density-independent factors (fire, storms, drought) do not.
- r-strategists have many offspring with little care; K-strategists have few offspring with much care and are more extinction-prone.
Human population
- Growth came mainly from falling death rates. Natural growth rate (%) $\displaystyle = \frac{\text{CBR} - \text{CDR}}{10}$. Replacement fertility is about 2.1.
- Demographic transition: stage 1 (high birth and death), stage 2 (death falls, rapid growth), stage 3 (birth falls), stage 4 (low both).
- Wide-base age diagrams signal rapid growth; population momentum keeps young populations growing.
Topics in this unit
Each topic has its own short notes and practice.
Practice
Constant doubling with unlimited resources is exponential growth.
$70 \div 1.75 = 40$ years.
A wildfire kills organisms regardless of how dense the population is.
Mice have many offspring with little care; elephants have few with long care.
$\displaystyle \frac{11 - 13}{10} = -0.2\%$.
Falling death with high birth is stage 2, a period of rapid growth.
Free response
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Free-response question
Country X has a population of 40 million, a crude birth rate of 32 per 1,000, and a crude death rate of 12 per 1,000. Assume no migration.
(a) Calculate the natural growth rate of Country X as a percent.
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$\displaystyle \frac{32 - 12}{10} = 2.0\%$ per year.
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(b) Use the rule of 70 to find the doubling time, and the population after one doubling.
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$70 \div 2 = 35$ years. The population would be about $2 \times 40 = 80$ million.
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(c) Identify the likely demographic transition stage and give one policy that could slow growth.
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Stage 2, because the birth rate is high and the death rate is lower. Education for girls and women, access to family planning, or reducing infant mortality are measures that tend to lower fertility.
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