# Predicting the Impacts of Environmental Change

Introduction:

This module will provide an overview of the range of modelling techniques that can be used to model biological organisms and their interactions with each other and the environment. The module will use a combination of theory and practical examples to show the range of techniques and approaches used to model organisms, populations and their interactions. The overall aim is to help the development of professional population modellers who have basic knowledge and skills of population modelling.

Objectives:

On completion of this module participants will be able to:

• Understand the structure of basic population models and their outcomes.
• Be familiar with population modelling literature in current scientific journals including critical analysis of models and interpretation.
• Construct and analyse basic population models and understand the processes of model construction.
• Understand the language and approach to modelling biological populations including the ability to discuss modelling with fellow professionals.
• Use computational environments for numerical solution of population models (especially MatLab).
• Interpret a biological population problem into a mathematical model.

Content:

• Population dynamics modelling I – key biological processes that determine population dynamics for single populations, including competition. Individual organism behaviour determines population change, modifying individual behaviour. Population models as simple characterisation of complex processes. Logistic model analysed.
• Population dynamics modelling II – models for interactions between populations – competition, predation, infection. Lotka-Volterra models, SIR model.
• Population dynamics modelling III – structured population models – age, sex, location. Levins metapopulation model. General methods for modelling structures examined, and statistical distributions discussed.
• Spatial dynamics modelling – population dynamics expanded to allow for spatial distribution. Advantages and disadvantages of different approaches discussed and investigated. Comparisons between models for mobile and static organisms.
• Integrating the environment – nonautonomous differential equations, and how to include environmental variables within models. Examples drawn from a range of scales and applications. Methods for addressing the complexity of integrating across a range of scales presented.
• Stochastic modelling – Modelling populations including stochastic events. Designing systems of differential equations, Monte Carlo simulation and individual based models. Relationships between deterministic and stochastic models and potential application areas of each.