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Ecology learning guide

Ecology and Population Dynamics Simulator

Compare exponential and logistic population growth, carrying capacity, competition, and disturbance through an interactive ecology investigation.

Open the ecology lab →

Change growth, capacity, and ecological pressures while observing population trajectories.

Start with the model

Concept overview

Population ecology studies how population size, density, distribution, births, deaths, and movement change through time. Exponential growth is a useful limiting case when the per-capita growth rate is constant and resources do not constrain expansion. Logistic growth adds a carrying capacity, slowing net growth as population size approaches the environment's current support limit.

Neither curve is a complete description of nature. Carrying capacity can change with seasons, habitat, disturbance, and resource availability, while predation, competition, disease, migration, age structure, and chance introduce additional dynamics. The ecology lab uses simplified parameters so you can isolate these relationships, compare scenarios, and explain why models are tools for reasoning rather than promises about exact future counts.

Concept 1

Exponential growth

When net per-capita growth r is constant, the absolute number added per time increases with population size. The ideal curve is J-shaped and cannot continue indefinitely in a finite environment.

Concept 2

Logistic growth

The logistic factor 1 - N/K reduces net growth as N approaches carrying capacity K. Growth is fastest around the middle of the idealised S-shaped curve.

Concept 3

Regulation and disturbance

Density-dependent factors change with population density, while density-independent disturbances can affect populations regardless of density. Real outcomes often combine both.

Guided investigation

How does carrying capacity shape a population curve?

  1. 1Run a baseline with fixed initial population and growth rate; record the curve and final population.
  2. 2Halve carrying capacity while keeping the starting population and growth rate unchanged.
  3. 3Double carrying capacity and compare the early and late portions of the curve.
  4. 4Apply one disturbance or interaction control and explain why the result departs from the simplest logistic expectation.

Evidence to record

Record N0, r, K, disturbance settings, population at common time points, and final trend. Mark where growth is fastest and identify which conclusions depend on a fixed K.

Equations and variables

dN/dt = rN

Continuous exponential population-growth model.

  • • N: population size
  • • t: time
  • • r: net per-capita growth rate

dN/dt = rN(1 - N/K)

Logistic model with density-dependent slowing near carrying capacity.

  • • N: population size
  • • r: intrinsic growth parameter
  • • K: carrying capacity
  • • t: time

Worked example

Apply the model

A model population has N = 200, r = 0.10 per year, and K = 1000. Find the instantaneous logistic growth rate.

  1. Step 1: Calculate the limiting factor: 1 - N/K = 1 - 200/1000 = 0.8.
  2. Step 2: Substitute dN/dt = 0.10 x 200 x 0.8.

Answer: The model rate is 16 individuals per year at that instant. This continuous rate need not be a whole observed count and assumes r and K remain fixed locally.

Misconceptions to test

Common claim

“Carrying capacity is a permanent number for a species.”

Correction: It describes what a particular environment can sustain under particular conditions and can change as resources, climate, habitat, and interactions change.

Common claim

“A population at carrying capacity never changes.”

Correction: The ideal logistic model approaches an equilibrium, but real populations fluctuate because conditions and demographic events vary.

Teacher-ready worksheet

Population dynamics investigation sheet

  1. 1.Sketch and label ideal exponential and logistic curves.
  2. 2.Predict how halving K changes the result before running it.
  3. 3.Calculate one instantaneous logistic growth rate.
  4. 4.Classify two controls as density-dependent or density-independent.
  5. 5.Explain one reason a natural population might overshoot or fluctuate around K.

Print or save this page as PDF to use the investigation and worksheet offline.

Knowledge check

Check your understanding

Check exponential growth, logistic growth, capacity, and regulation.

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