Invasive Species Population Lab
A new invader like the zebra mussel can grow explosively at first. Compare unlimited (exponential) growth with growth limited by the ecosystem's carrying capacity, and see what predators or other losses do.
Controls
r = 1.0 means the population doubles each generation when nothing limits it; r = 2.0 triples it.
Share of the population removed each generation.
Model: exponential Nₘ₊₁ = Nₘ(1 + r − p). Logistic Nₘ₊₁ = Nₘ + rNₘ(1 − Nₘ/K) − pNₘ. These are teaching models, not measured mussel data.
Unlimited, gen 10
individuals
Limited, gen 10
individuals
Limited, gen 20
Doubling time (unlimited)
generations
Try this
- Turn the log scale on. Why does exponential growth look like a straight line?
- Set predation near the growth rate. What happens to the unlimited curve?
- Raise r toward 2.0 and watch the limited curve overshoot K and bounce around it.
What to notice
- Early on both curves match; the limit only matters as the population approaches K.
- The limited population levels off near K × (1 − p/r).
- Predation lowers the plateau and can stop growth entirely if p ≥ r.
Connect to the lab
- Extends the Zebra Mussels lab: the lab's ×3 per generation is r = 2.0. Set r = 2.0 and a start of 100 to reproduce its table.
- See the teacher key for sample answers.