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# Syllabus for Modelling in Biology

Modellering i biologi

## Syllabus

• 5 credits
• Course code: 1BG383
• Education cycle: Second cycle
• Main field(s) of study and in-depth level: Biology A1N, Computational Science A1N
• Grading system: Fail (U), 3, 4, 5
• Established: 2009-03-12
• Established by: The Faculty Board of Science and Technology
• Revised: 2015-06-04
• Revised by: The Faculty Board of Science and Technology
• Applies from: week 01, 2016
• Entry requirements: 150 credits including 75 credits in biology, 30 credits in chemistry, and Mathematics and Statistics, 10 credits.
• Responsible department: Biology Education Centre

## 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.