Many marine fish species can grow in body mass more than seven orders of magnitude over their lifetime. As fish grow, their target prey and their growth, mortality and reproduction rates change drastically with body mass. This means that body mass is a crucial variable in any mathematical model. Size-spectrum models put body mass foremost by doing a bookkeeping of biomass as it flows from prey to predator, and from parent to offspring. This is a different paradigm from the classical species-based predator-prey model.

This talk will give an overview of size-spectrum models and the insights they have given us into marine community dynamics. Size-spectrum models are based on a generalisation of the McKendrick-von Foerster equation to a nonlinear, partial integro-differential equation. I will show some theoretical results about the equilibrium size structure and stability, as well as applications in fisheries management and fisheries-induced evolution. Size-spectrum models are particularly suited to investigating the effects of different distributions of fishing mortality over body mass and species, which is a key question for ecosystem-based fisheries management.

About Maths Colloquium

The Mathematics Colloquium is directed at students and academics working in the fields of pure and applied mathematics, and statistics. 

We aim to present expository lectures that appeal to our wide audience.

Information for speakers

Information for speakers

Maths colloquia are usually held on Mondays, from 2pm to 3pm, in various locations at St Lucia.

Presentations are 50 minutes, plus five minutes for questions and discussion.

Available facilities include:

  • computer 
  • data projector
  • chalkboard or whiteboard

To avoid technical difficulties on the day, please contact us in advance of your presentation to discuss your requirements.