Population Dynamics and Sustainability

About the project

• Duration: 3-4 hours in class, 1-2 hours preparation at home

• Prerequisites: Linear algebra (matrix–vector products, eigenvalues/eigenvectors, diagonalization/eigendecomposition), basic programming (for-loops, lists/arrays, if/elif/else), basic mathematical modeling (discrete-time dynamical systems)

• Python packages: numpy, matplotlib (optional: pandas for CSV data handling, ipywidgets for interactive visualization)

• Learning objectives: Model age-structured populations as discrete dynamical systems, iterate matrix models in Python and interpret results, connect long-run behavior to dominant eigenvalues/eigenvectors and demographic profiles, build and analyze Leslie matrices (birth/survival rates) including net reproduction rate, simulate competing species with coupled matrix models and interpret competitive exclusion, use real demographic data to construct a data-driven population model, incorporate migration as an external input term and compute equilibrium via linear systems, compare computational cost of direct matrix powers versus iterative matrix–vector updates