Grade: Grade 9 Subject: Science Unit: Ecology SAT: ProblemSolving+DataAnalysis ACT: Science

Population Dynamics

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Population dynamics is the study of how and why populations change in size and structure over time. Understanding population dynamics helps ecologists predict changes in ecosystems and manage wildlife and resources.

Population

A population is a group of individuals of the same species living in the same area at the same time that can interbreed. Population dynamics examines how populations change due to births, deaths, immigration, and emigration.

Key Population Characteristics

Characteristic Definition How Measured
Population size (N) Total number of individuals Census, sampling, mark-recapture
Population density Number of individuals per unit area N / area (e.g., 50 deer/km2)
Birth rate (natality) Number of births per individual per time Births / population / year
Death rate (mortality) Number of deaths per individual per time Deaths / population / year
Growth rate (r) Rate of population increase or decrease Birth rate - Death rate

Population Growth Models

Exponential Growth

When resources are unlimited, populations grow exponentially:

Nt = N0 x ert

  • Creates a J-shaped curve
  • Population doubles at regular intervals
  • Rarely sustained in nature for long periods
  • Example: bacteria in fresh nutrient broth

Logistic Growth

In reality, resources are limited. Logistic growth accounts for carrying capacity:

dN/dt = rN(K-N)/K

  • Creates an S-shaped (sigmoid) curve
  • Growth slows as population approaches carrying capacity (K)
  • Population stabilizes near K
  • More realistic model for most populations

Carrying Capacity (K)

Carrying capacity is the maximum population size that an environment can sustain indefinitely given available resources (food, water, shelter, space). When a population reaches K, birth rate equals death rate.

Limiting Factors

Factors that restrict population growth:

  • Density-dependent factors: Effects increase as population density increases (competition, disease, predation, parasites)
  • Density-independent factors: Effects are the same regardless of population size (natural disasters, weather, climate)

Population Regulation

Factor Type Examples Effect on Population
Density-dependent Competition, disease, predation Limits growth as density increases
Density-independent Floods, fires, droughts, temperature Can cause sudden population crashes

r-selected vs. K-selected Species

r-selected species (like insects, bacteria) have many offspring, little parental care, and rapid maturation. They thrive in unstable environments. K-selected species (like elephants, whales) have few offspring, extensive parental care, and slow maturation. They thrive in stable environments near carrying capacity.

SAT/ACT Connection

Science passages often present population growth curves or data tables. You may need to identify the type of growth (exponential vs. logistic), calculate growth rates, predict future population sizes, or explain why populations plateau. Understanding carrying capacity is essential.

Examples

Example 1: Calculating Population Growth Rate

Problem: A population of 500 rabbits has 150 births and 50 deaths in one year. Calculate the growth rate (r) and the population after one year.

Step 1: Calculate per capita birth rate: 150/500 = 0.30

Step 2: Calculate per capita death rate: 50/500 = 0.10

Step 3: Growth rate (r) = birth rate - death rate = 0.30 - 0.10 = 0.20

Step 4: Population change = 150 births - 50 deaths = 100 individuals gained

Step 5: New population = 500 + 100 = 600 rabbits

Answer: r = 0.20 (20% growth rate); population after one year = 600 rabbits

Example 2: Interpreting Growth Curves

Problem: A graph shows a population that grows rapidly at first, then levels off at about 1,000 individuals. What type of growth is this, and what is the carrying capacity?

Step 1: Rapid initial growth followed by leveling off describes an S-shaped curve.

Step 2: An S-shaped curve indicates logistic growth.

Step 3: The level where the population stabilizes is the carrying capacity (K).

Step 4: The population stabilizes at 1,000 individuals.

Answer: This is logistic growth with a carrying capacity (K) of approximately 1,000 individuals.

Example 3: Density-Dependent vs. Independent Factors

Problem: A forest fire kills 40% of a deer population regardless of how many deer are present. A disease outbreak kills 60% of deer, but only when the population is crowded. Classify each factor.

Step 1: Forest fire: The effect (40% killed) is the same regardless of population size.

Step 2: This makes fire a density-independent factor.

Step 3: Disease: The effect depends on population density (only affects crowded populations).

Step 4: Disease spreads more easily when individuals are close together.

Answer: Forest fire is density-independent; disease is density-dependent.

Example 4: Population Doubling Time

Problem: A population is growing exponentially with r = 0.02 per year. Approximately how long will it take to double?

Step 1: Use the Rule of 70: Doubling time = 70 / (growth rate x 100)

Step 2: Convert r to percentage: 0.02 = 2%

Step 3: Doubling time = 70 / 2 = 35 years

Answer: The population will double in approximately 35 years.

Example 5: Predicting Population Change

Problem: A population of 800 is at carrying capacity (K = 800). What happens to the population if 200 individuals are removed by hunting?

Step 1: Initial population = 800; after removal = 600

Step 2: At carrying capacity, birth rate = death rate (no growth).

Step 3: Now population is below K, so resources are more abundant.

Step 4: With more resources, birth rates increase and/or death rates decrease.

Step 5: Population will grow until it returns to K = 800.

Answer: The population will grow back toward the carrying capacity of 800, following logistic growth.

Practice

Test your understanding of population dynamics with these questions.

1. What is the carrying capacity?

A) The maximum growth rate B) The maximum population an environment can support C) The minimum viable population D) The birth rate minus death rate

2. Which growth curve is J-shaped?

A) Logistic growth B) Exponential growth C) Linear growth D) No growth

3. A population has 200 births and 150 deaths per year with a population of 1,000. What is the growth rate?

A) 0.05 B) 0.15 C) 0.20 D) 0.35

4. Which is a density-dependent limiting factor?

A) Earthquake B) Flood C) Disease outbreak D) Volcanic eruption

5. As a population approaches carrying capacity, what happens to growth rate?

A) It increases B) It stays the same C) It decreases D) It becomes negative

6. Which species would be considered r-selected?

A) Elephant B) Human C) Whale D) Mosquito

7. A population grows from 100 to 200 in 10 years with exponential growth. How long until it reaches 400?

A) 5 years B) 10 years C) 20 years D) 40 years

8. Population density is calculated by:

A) Births minus deaths B) Population divided by area C) Deaths divided by births D) Area times population

9. In logistic growth, when does the population grow fastest?

A) When N is very low B) When N = K C) When N = K/2 D) When N exceeds K

10. If a population overshoots its carrying capacity, what typically happens?

A) The carrying capacity increases B) The population crashes C) Growth continues exponentially D) Nothing changes

Click to reveal answers
  1. B) The maximum population an environment can support - Carrying capacity (K) is the maximum sustainable population given available resources.
  2. B) Exponential growth - Exponential growth produces a J-shaped curve; logistic growth produces an S-shaped curve.
  3. A) 0.05 - Growth rate = (births - deaths) / population = (200 - 150) / 1000 = 50/1000 = 0.05
  4. C) Disease outbreak - Disease spreads more easily in dense populations, making it density-dependent.
  5. C) It decreases - In logistic growth, growth rate slows as resources become limited near carrying capacity.
  6. D) Mosquito - Mosquitoes have many offspring, rapid reproduction, and little parental care - typical r-selected traits.
  7. B) 10 years - With exponential growth, doubling time is constant. If it doubled in 10 years once, it will double again in another 10 years.
  8. B) Population divided by area - Population density = N / area (e.g., individuals per square kilometer).
  9. C) When N = K/2 - In logistic growth, growth rate is maximum at half the carrying capacity.
  10. B) The population crashes - Overshooting K depletes resources, leading to increased death rates and population decline.

Check Your Understanding

1. Explain why populations cannot grow exponentially forever.

Reveal Answer

Exponential growth assumes unlimited resources, which never exists in nature. As populations grow, they consume resources (food, water, space) faster. Eventually, resources become limiting, causing increased competition, higher death rates, and/or lower birth rates. Additionally, density-dependent factors like disease and predation become more severe as populations grow. These factors slow growth and eventually bring the population to a carrying capacity. Even the fastest-reproducing organisms on Earth would run out of space and resources within relatively short timeframes if growth were truly unlimited.

2. A farmer introduces 100 rabbits to an island with abundant food and no predators. Describe and sketch what the population graph might look like over 20 years.

Reveal Answer

Initially, with abundant resources and no predators, the rabbit population would grow rapidly (nearly exponentially), showing a J-shaped curve. The population might double every few months. However, as rabbits multiply, they will eventually deplete their food supply. The growth will slow down, forming an S-shaped (logistic) curve. The population will approach and possibly overshoot carrying capacity, then fluctuate around it. If they overshoot significantly, there might be a population crash followed by recovery. The graph would show rapid initial growth, then leveling off, possibly with oscillations around the carrying capacity.

3. Why might a disease be more devastating to a crowded population than to a sparse one?

Reveal Answer

Disease is a density-dependent factor. In crowded populations: (1) Individuals have more frequent contact, increasing disease transmission; (2) Stress from crowding can weaken immune systems; (3) Resources like food may be limited, leading to malnutrition and vulnerability; (4) Waste accumulation in crowded conditions can spread pathogens; (5) Once disease starts spreading, the chain of infection is easier to maintain with many hosts nearby. In sparse populations, infected individuals are less likely to encounter susceptible hosts, breaking transmission chains. This is why epidemics are more common in dense human cities than in rural areas.

4. Compare r-selected and K-selected reproductive strategies. Which is better?

Reveal Answer

Neither strategy is "better" - they are adaptations to different environments. r-selected species (insects, bacteria, mice) produce many offspring with little parental care, mature quickly, and have short lifespans. This works well in unpredictable environments where populations frequently crash and need to recover quickly. K-selected species (elephants, whales, humans) produce few offspring with extensive parental care, mature slowly, and live long. This works well in stable environments where populations remain near carrying capacity and competition is intense. The "best" strategy depends on the environment. Many species fall somewhere between these extremes.

🚀 Next Steps

  • Review any concepts that felt challenging
  • Move on to the next lesson when ready
  • Return to practice problems periodically for review