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4.8. Mathematical Biology and Life Sciences (MBL)

This area covers the application of mathematical methods to biological systems, spanning population dynamics, epidemiology, systems biology, bioinformatics, and computational neuroscience, with emphasis on models grounded in modern experimental data.

Knowledge Area (KA)	Core Tier1	Core Tier2
4.8.1 Population Dynamics	1	1

4.8.1. MBL/Population Dynamics  (Core Tier1: 1 hr, Core Tier2: 1 hr) ↑ Back to top

Mathematical models of single and interacting populations: logistic growth, Lotka-Volterra systems, spatial ecology, and evolutionary dynamics.
Topics:
Core

• Exponential and logistic growth models; carrying capacity and the Allee effect
• Lotka-Volterra predator-prey and competition models; equilibria and stability analysis
• Age-structured models: Leslie matrices and the Euler-Lotka equation
• Reaction-diffusion models and traveling waves in spatial ecology (Fisher-KPP equation)
• Evolutionary dynamics: replicator equations, game theory, and the Price equation

Learning Outcomes:
Core:

1. Analyze the stability of equilibria in Lotka-Volterra systems using linearization and phase portraits [Familiarity]
2. Construct age-structured population models using Leslie matrices and compute long-term growth rates [Usage]
3. Apply reaction-diffusion theory to model the spatial spread of an invasive species using the Fisher-KPP equation [Assessment]