Population Growth Model Explorer

View Population Growth Model Explorer Fullscreen

About This MicroSim

This interactive visualization compares exponential and logistic population growth models side by side. Students adjust four key parameters — intrinsic growth rate (\(r_{max}\)), carrying capacity (\(K\)), initial population size (\(N_0\)), and number of generations — and immediately see how each parameter affects the growth curves. The exponential model (\(dN/dt = rN\)) shows unlimited growth, while the logistic model (\(dN/dt = rN(K-N)/K\)) demonstrates density-dependent growth that levels off at the carrying capacity. An overshoot mode adds a time lag that produces oscillations around \(K\).

How to Use

Select a view — click "Both Models", "Exponential", or "Logistic" to focus on one or both curves.
Adjust parameters using the sliders on the right:
r — intrinsic rate of increase (0.01 to 2.0)
K — carrying capacity (100 to 10,000)
N₀ — starting population (1 to 1,000)
Generations — time range (10 to 200)
Enable Overshoot to add a 3-generation time lag, causing the logistic population to oscillate around \(K\).
Click "Data Table" to see numerical values at each time step.
Hover over the chart to see exact population values at any generation.

Lesson Plan

Grade Level

9-12 (college placement Biology)

Duration

10-15 minutes

Prerequisites

Understanding of population as a group of interbreeding organisms
Familiarity with birth rate, death rate, and growth rate concepts
Basic understanding of exponential functions

Activities

Exploration (5 min): Start with both models visible. Set r=0.5, K=1000, N₀=10. Notice where the two curves diverge. At what population size does the logistic curve start to slow down? What fraction of K is this? (Answer: approximately K/2, the inflection point where dN/dt is maximized.)
Guided Practice (5 min): Switch to logistic only. Increase r from 0.1 to 1.5 — how does r affect how quickly the population reaches K? Now enable Overshoot — what happens when r is high (>1.0)? Why do real populations sometimes overshoot K?
Assessment (5 min): A population of rabbits has r=0.3, K=500, and starts with 20 individuals. Predict: How many generations until the population reaches 250 (half of K)? Set the parameters and check. Then answer: If K drops to 200 due to habitat loss, what happens to the population trajectory?

Assessment

Can students explain why the exponential model is unrealistic for long-term population growth?
Can students identify the inflection point of the logistic curve and explain its biological significance?
Can students predict how changing r, K, or N₀ will affect the growth curve shape?
Can students explain why time lags cause population oscillations around K?