Population Growth and Demographic Dynamics

Population Size ( $N$ ): Total number of individuals in a given area at a given time. Larger populations are generally safer from decline.
Density: Number of individuals per unit area (e.g., $12 \text{ panthers/km}^2$ ). High density increases competition, disease transmission, and food depletion.
Distribution: Spacing of individuals compared to one another. * Random: (e.g., trees). * Uniform: (e.g., territorial animals). * Clumped: (e.g., herd/group animals).
Sex Ratio: Ratio of males to females. A ratio closer to $50:50$ is ideal for breeding. Bottleneck effects can skew this ratio, limiting growth.
Density-Dependent Factors: Factors that influence growth based on population size (e.g., food, habitat competition, water, light, disease).
Density-Independent Factors: Factors affecting growth regardless of size (e.g., natural disasters like floods, hurricanes, and fires).

Population Size Formula: $\text{Population Size} = (\text{Immigrations} + \text{Births}) - (\text{Emigrations} + \text{Deaths})$ . * Example: Elk population ( $52 \text{ elk}$ ) with $19 \text{ births}$ , $6 \text{ deaths}$ , $5 \text{ immigrants}$ , and $0 \text{ emigrants}$ . * $(19 + 5) - (6 + 0) = +18 \text{ elk}$ . * $52 + 18 = 70 \text{ elk}$ .
Biotic Potential (Exponential Growth): Maximum potential growth rate without limiting resources; represented as a J-shaped curve.
Environmental Resistance (Logistic Growth): Initial rapid growth followed by limiting factors (competition, food, predators) slowing growth until it plateaus at the carrying capacity ( $K$ ).
Limiting Resources Illustration: In Paramecium aurelia and Paramecium caudatum studies, doubling the food supply increased the carrying capacity by approximately $2\times$ .

Age Cohorts: * $0-14$ : Prereproductive. * $15-44$ : Reproductive age. * $45+$ : Post-reproductive.
Growth Trends by Shape: * Rapid Growth (Extreme Pyramid): Large prereproductive cohort (e.g., Guatemala, Nigeria, Saudi Arabia, India with $360 \text{ million}$ youth). * Slow/Stable Growth (Less Extreme Pyramid/House Shape): Roughly equal prereproductive and reproductive cohorts (e.g., United States with $62 \text{ million}$ youth, Australia, Canada). * Stable but Declining (Narrow Base): Larger reproductive cohort than prereproductive cohort (e.g., Germany with $11.5 \text{ million}$ youth, Bulgaria, Italy, Japan).

Total Fertility Rate (TFR): Average number of children a woman bears in her lifetime. Higher TFR leads to higher population growth rates.
Replacement Level Fertility: The TFR required to offset deaths and stabilize population size ( $\approx 2.1$ in developed countries).
Infant Mortality Rate (IMR): Number of deaths of children under $1 \text{ year}$ per $1,000$ people. Higher IMR is common in less developed countries due to lack of health care, clean water, and food.
Factors Affecting TFR Decrease: * Affluence/Development: Wealthier nations have lower TFR. * Education for Women: More eduction leads to fewer unplanned pregnancies and later age of first pregnancy. * Government Policy: Such as China's former 1-child (now 2-child) policy or tax incentives for smaller families.

Malthusian Theory: Proposed by Thomas Malthus, suggesting human population growth outpaces food production growth, leading to a "Malthusian catastrophe" at carrying capacity.
Technological Advancement: Humans can alter carrying capacity through innovation, such as the synthetic fixation of Nitrogen in $1918$ for fertilizer, which exponentially increased food supply.
Global Population Growth Rate ( $r$ ): Calculated as $\frac{[CBR - CDR]}{10}$ . Divide by $10$ because CBR (Crude Birth Rate) and CDR (Crude Death Rate) are per $1,000$ .
Rule of 70 (Doubling Time): $\text{Doubling Time (years)} = \frac{70}{r}$ . * Example: If $r = 1.2\%$ , the population doubles in $58.3 \text{ years}$ .
Standard of Living Indicators: Gross Domestic Product (GDP) and Life Expectancy. High GDP and life expectancy typically correlate with low population growth.

Stage 1 (Pre-industrial): High IMR and death rates due to lack of medical care; high TFR for farm labor; stable or low growth.
Stage 2 (Industrializing/Developing): Access to clean water and medicine causes IMR and CDR to decline; TFR remains high due to societal lag; results in rapid population growth (e.g., many developing nations).
Stage 3 (Developed/Industrialized): Modernized economy increases income and education for women; TFR declines toward replacement level ( $2.1$ ); growth slows.
Stage 4 (Post-industrial): Highly affluent; TFR drops below replacement level; CBR falls below CDR, leading to population decline.

FRQ Practice 3.5: Calculate the percent change in the population size of a $14 \text{ wolf pack}$ that experiences $5 \text{ deaths}$ , $3 \text{ births}$ , and $4 \text{ new wolves}$ released into the pack from a nearby wildlife sanctuary.
FRQ Practice 3.6: [Referencing age structure diagrams for India, US, China, and Germany] Identify the country with the slowest population growth rate and explain your answer.
FRQ Practice 3.7: [Referencing worldwide TFR trends from 1950 to 2015] Identify and discuss TWO of the causes for the trend in worldwide TFR.
FRQ Practice 3.8: Describe one human activity related to a rapidly growing human population that is having an impact on biodiversity. Propose a solution a government could take to slow population growth.
FRQ Practice 3.9: Identify the stage of the demographic transition graph in which population grows the fastest and explain why this is the case. Besides population growth rate, describe one economic or societal indicator of a country in this phase.