Applied mathematics and modelling · Maths EE idea · Solid

Predicting a population with Leslie matrices

A research question to start from

How does a Leslie matrix model predict the long-term growth rate and age structure of a population?

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Why it works as a maths EE

Linear algebra with a biological meaning: the dominant eigenvalue gives the answer.

Mathematics you would need

Matrix multiplication
Eigenvalues and eigenvectors
Long-term behaviour of matrix powers

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Build a Leslie matrix for a simple species with made-up but plausible rates.
Find the dominant eigenvalue and eigenvector.
Show convergence of the age structure and discuss assumptions.

Scope and difficulty

Solid. Solid.

Pitfalls

Invented data presented as real.
Eigenvalues from software without interpretation.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Leslie matrix dominant eigenvalue stable age distribution. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

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