The aim of the course is to give students with a background in biology basic skills in building and analysing mathematical models of biological systems. After passing this course the student should be able to:
outline the principles behind modelling - why mathematical models?
perform the modelling cycle - (i) translate a biological question into a mathematical model, (ii) analyse the model and (iii) interpret the results
choose the appropriate modelling framework for different biological questions - quantitative vs qualitative models - deterministic vs stochastic models
analyse models formulated in terms of differential and difference equations: equilibria and their stability, basic numerical methods
understand, analyse and apply classic models in ecology and evolution: density-dependent population growth, models of species interactions and structured population models, evolutionary models of allele frequency change and invasion analysis
critically interpret scientific papers that are based on mathematical models
The modelling cycle: (i) translating a biological question into a mathematical model, (ii) mathematical analysis of the model, and (iii) interpreting the mathematical results in terms of biology
Standard models in ecology: models for the dynamics of unstructured and structured populations, models of competition and predation
Standard models in evolution: one- and two-locus models, quantitative genetics and the breeders' equation, invasion analysis, the stochastic Wright-Fisher and Moran models for allele frequency change
Stability analysis of linear and non-linear models in one and two variables, phase-plane analysis, elementary vector and matrix algebra, eigenvalues and eigenvectors, elementary probability theory.
Lectures, home-assignments and exercise classes.
Home-assignments and active participation during the tutorials.