# Modelling in Biology

5 credits

Syllabus, Master's level, 1BG383

A revised version of the syllabus is available.
Code
1BG383
Education cycle
Second cycle
Main field(s) of study and in-depth level
Biology A1N, Computational Science A1N
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 4 June 2015
Responsible department
Biology Education Centre

## Entry requirements

150 credits including 75 credits in biology, 30 credits in chemistry, and Mathematics and Statistics, 10 credits.

## 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. 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

## 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.