Exchange studies

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.

Reading list

Applies from: week 02, 2016

  • Otto, Sarah P.; Day, Troy A biologist's guide to mathematical modeling in ecology and evolution

    Princeton, N.J.: Princeton University Press, cop. 2007

    Find in the library