Module manager: Prof. Mauro Mobilia
Email: M.Mobilia@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
None
| MATH1005 | Core Mathematics |
| MATH1700 | Probability and Statistics |
| MATH2400 | Mathematical Modelling |
MATH3567/5567M Evolutionary Modelling/Advanced Evolutionary Modelling
This module is not approved as an Elective
Darwin’s natural selection theory is a cornerstone of modern science. Recently, mathematical and computational modelling has led to significant advances in our understanding of evolutionary puzzles, such as what determines biodiversity or the origin of cooperative behaviour. This module introduces the fundamental ideas underpinning evolutionary processes across the life sciences using a range of mathematical tools.
Students of this module will be exposed to fundamental ideas of evolutionary modelling, and to the mathematical tools needed to pursue their study. These will be illustrated by numerous examples motivated by exciting developments in mathematical biology.
On the completion of the module, students will be familiar with a range of mathematical tools, ideas and paradigmatic models allowing them to understand an important class of evolutionary phenomena, based notably on concepts of evolutionary game theory, Mendelian and population genetics. Concretely, at the end of this module, students will be able to: 1. Understand and analyse evolutionary models formulate as maps or ordinary differential equations (one or two variables, stability and qualitative analysis); 2. Understand and use key concepts of game theory and evolutionary game theory (Nash equilibrium, evolutionary stability, paradigmatic games); 3. Demonstrate familiarity with the key concepts of fitness, selection, fixation, fluctuations in evolutionary processes; 4. Analyse the evolutionary dynamics of interacting populations in terms of replicator equations and Markov chains; 5. Understand and use the key concepts of Mendelian and population genetics; 6. Demonstrate familiarity with birth-and-death processes, the Moran and Wright-Fisher models, and understand their main properties; 7. Demonstrate familiarity with the Fokker-Planck equation and use diffusion processes for first-passage problems; 8. Use diffusion processes in the context of population genetics.
1. Introduction to evolutionary modelling and Darwin's theory. 2. Evolutionary modelling with difference equations (linear and nonlinear maps, examples and applications) 3. Evolutionary modelling with ordinary differential equations (predator-prey, Lotka-Volterra, exclusion principle) 4. Evolutionary modelling with Markov chains: Discrete and continuous time, birth-and-death processes, master equation, extinction, fixation. 5. Introduction to Mendelian genetics: Key concepts, Hardy-Weinberg principle, fitness and selection. 6. Classical game theory, evolutionary game theory, replicator dynamics, fitness-dependent Moran model, evolutionarily stability. 7. Diffusion processes with applications to population genetics: Fokker-Planck equation, Wright-Fisher and Moran models. Additional topics building the above may be covered as time allows. These may include stochastic simulation algorithm to efficiently model the role of chance fluctuations on evolutionary processes, with implications on species diversity (biodiversity), and cooperative behaviour. Further details of possible topics will be delivered closer to the time that the module runs.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lectures | 33 | 1 | 33 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
Errors, omissions, failed links etc should be notified to the Catalogue Team