IA idea · Differential equations & dynamics

Can the Lotka–Volterra model explain the lynx and hare cycles?

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Research question

How well does a Lotka–Volterra predator–prey model with fitted parameters reproduce the roughly ten-year cycles in the Hudson's Bay Company lynx and hare records, and what does the model get wrong?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

The fur-trade records are the most famous predator–prey data in ecology, and they do not quite behave as the textbook model predicts. Finding where and why is excellent Reflection.

The mathematics you'll need

Coupled nonlinear differential equations
Equilibrium points and their meaning
Euler's method or technology to solve the system
Phase-plane (hare vs lynx) plots
Comparing periods and amplitudes with data

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use the published pelt series (1845–1935); cite the version you use.

Hudson's Bay Company lynx and hare pelt records (1845–1935) — Annual pelt counts (thousands) used as a proxy for population; bundled with the R package astsa and reproduced in many ecology texts. Several versions of this dataset exist — cite the one you use.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain the model and each parameter.
Estimate parameters from the data (period, equilibrium levels).
Solve and compare time series and phase plots.
Investigate the famous anomaly where hares seem to “eat” lynx in some years.
Reflect on using pelts as a proxy for populations.

Pitfalls that cost marks

Treating pelt counts as population counts without comment.
Parameters chosen by eye with no reasoning.
Ignoring that the model's cycles depend on initial conditions.

Showing personal engagement

Explain the ecology in your own words.
Change one assumption (hare carrying capacity) and see if the fit improves.
Relate to a predator–prey system you have seen.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Add a logistic term for the prey and compare the phase portrait (spiral instead of closed loops).

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).