What is Population Growth?
Population dynamics studies how the size of a population changes over time due to births, deaths, immigration, and emigration. Ecologists use growth models like exponential and logistic growth to predict how populations respond to resources and limiting factors.
Population growth is the change in the number of individuals in a population over time; under unlimited resources it follows exponential growth, N = N0·e^(rt), where r is the intrinsic growth rate.
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Step-by-step worked examples
A bacterial population starts at 200 cells and grows at r = 0.2/year (continuous rate). Find the population after 5 years.
N0 = 200, r = 0.2/year, t = 5 years N = N0 × e^(rt) = 200 × e^(0.2×5) = 200 × e^1 e^1 ≈ 2.718 N ≈ 200 × 2.718 ≈ 544 individuals
A deer population of 50 grows at r = 0.1/year. Estimate the population after 10 years.
N0 = 50, r = 0.1/year, t = 10 years N = 50 × e^(0.1×10) = 50 × e^1 N ≈ 50 × 2.718 ≈ 136 individuals
A town of 1000 people has a birth rate of 0.03/year and death rate of 0.01/year (no migration). Find the population after 20 years.
r = birth rate − death rate = 0.03 − 0.01 = 0.02/year N0 = 1000, t = 20 years N = 1000 × e^(0.02×20) = 1000 × e^0.4 e^0.4 ≈ 1.492 N ≈ 1492 people
Flashcards
Quick quiz
Q1.A population grows exponentially with N0 = 100 and r = 0.1/year. What is N after 10 years (e^1 ≈ 2.72)?
Q2.What best describes carrying capacity?
Q3.Which factor DECREASES population size?
Q4.Logistic growth differs from exponential growth because it...
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Common mistakes
Population growth is always exponential. — Correct: Exponential growth only occurs with unlimited resources; real populations follow logistic growth and level off near K.
Immigration and emigration don't affect population size. — Correct: Population change = (births + immigrants) − (deaths + emigrants).
Carrying capacity is a fixed, unchangeable number. — Correct: K depends on resources and can change with environmental conditions (drought, disease, food supply).
A higher growth rate r always means a larger final population regardless of time. — Correct: The final population also depends heavily on time t and starting population N0, since growth is exponential in t.
FAQ
What is the formula for population growth?
For exponential growth: N = N0·e^(rt), where N0 is the initial population, r is the growth rate, and t is time.
What is population growth in biology?
It's the change in the number of individuals in a population over time, driven by births, deaths, immigration, and emigration.
How do you calculate population growth rate?
r equals the birth rate minus the death rate (adjusted for migration); plug it into N = N0·e^(rt) to project future size.
What are examples of population growth?
Bacterial cultures doubling in a nutrient-rich dish, deer populations rebounding after a mild winter, and human population growth in a city are all examples.