Maths in biology and medicine · Ambitious · Dissertation

Predator and prey cycles: a maths EPQ idea

Why it works as an EPQ

A famous model, a famous data set (lynx and snowshoe hare fur records) and plenty of reasons to doubt the fit.

Scope and difficulty

Ambitious. Ambitious. Numerical solution, phase plane and comparison with data.

The maths

Builds on these A Level topics: Differentiation · Numerical methods.

You would learn:

• Coupled differential equations
• Phase planes and equilibria
• Model fitting

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Set up the equations and find the equilibrium.
2. Solve numerically and draw the phase plane.
3. Compare with the historical fur-trade data.
4. Judge the model and one improvement.

Pitfalls

• Euler's method with a large step creating false spirals.
• Treating fur records as population counts without comment.

Where to start reading

• Mathematical Biology (J. D. Murray)
• Search for: Lotka-Volterra lynx hare data

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in biology and medicine ideas · all 93 ideas

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