Entry requirements

150 credits including 75 credits biology, and Mathematics and Statistics, 10 credits. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

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. On completion of the 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

Content

• 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.

Instruction

Lectures, home-assignments and exercise classes.

Assessment

Home-assignments and active participation during the tutorials.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.