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PhD Studentship Topic

Using Mathematical models to solve problems in Aquatic Food Security

1: Control of Invasive Aquatic pathogens - Non-indigenous species (NIS) pose a major threat to global biodiversity, and incur significant economic costs. As a result it is necessary to prevent their introduction and spread. The ability to predict where, and by which pathway, an NIS is most likely to arrive, establish and subsequently spread, is invaluable in reducing the impact of NIS on our marine environment. The aim of this project is to develop this work further to in order to produce a user friendly modelling tool which managers could use to look at both biosecurity and where to focus monitoring efforts. Dynamical models of the introduction and spread of a number of key invasive species will be developed and different control mechanisms will be investigated. For example, killer shrimp are already a major problem in freshwater systems and so we need to look at control strategies against something which is already established. Sea squirts are starting to cause a problem so we need to consider how to prevent further spread as well as how to control them where they are and the Giant King Crab has not yet arrived but are a potential threat and so we need to look at how to best prevent introduction. We will use a variety of mathematical techniques to address these three different questions

2: Fish personalities - Aquaculture is the fastest growing agricultural sector with a growth rate of approximately 8% per annum over the last 30 years. However, it has been accused of having poor standards of animal welfare. This is something that has improved significantly over the years and is a major consideration for modern day fish farmers.

However it is difficult to tell when a fish is "happy" in its environment. One thing that is becoming increasingly clear is that even genetically identical fish can demonstrate different behaviours. Experimentally this means that when you put fish into a new environment some of them are "adventurous" and move around a lot and explore and others are more "timid" and stay still and/or try to hide. It is believed that these "adventurous" fish are more robust in a number of senses, ie they have higher productivity and are more resistant to infection. If we can understand these different types of fish behaviour then it may help us to adapt conditions that will encourage the more robust fish, this could benefit both fish welfare and fish production. The aims of this project are:

  • To use the available data to parameterise a mathematical model of fish movement for individual fish.
  • To look at the distribution of parameters and determine whether we can classify fish behaviour using these parameters and if so, what proportion of fish are in each category.
  • To determine if individual fish behaviour changes over time and if they remain consistent in their behaviour

3: Muscle growth in humans - Dietary protein intake plays an important role in maximizing the benefits of exercise training on skeletal muscle mass and function. The metabolic basis for changes in muscle mass is the balance between rates of muscle protein synthesis (MPS) and muscle protein breakdown (MPB). That is, the net balance (NBAL) between MPS and MPB over any given period of time determines changes in muscle mass. Exercise and dietary protein ingestion influence muscle mass primarily through changes in MPS rather than MPB.


  1. Mathematical models of the relationship between protein intake, exercise and muscle growth can be developed and parameterised using data from the literature.
  2. We can predict optimal timings of protein intake relative to exercise, optimal types of protein and how those factors interact and vary for different types of individuals using those models.

The aim of this project is to develop a mathematical model which describes how muscle grows in response to different types and doses of protein, how this interacts with exercise and ultimately how we might maximise muscle growth by altering the timing and type of protein taken and when it is taken relative to exercise.

Further Details

Contact: Prof Rachel Norman
Web page:

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Computing Science and Mathematics
Faculty of Natural Sciences
University of Stirling, Stirling FK9 4LA
Tel: +44 1786 46 7421

© University of Stirling FK9 4LA Scotland UK • Telephone +44 1786 473171 • Scottish Charity No SC011159
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