•To provide a theoretical basis for the understanding of population ecology

•To explore the classical models of population dynamics

•To learn basic techniques of qualitative analysis of mathematical models

(LO1) The ability to relate the predictions of the mathematical models to experimental results obtained in the field.

(LO2) The ability to  recognise the limitations of mathematical modelling in understanding the mechanics of complex biological systems.

(LO3) The ability to use analytical and graphical methods to investigate population growth and the stability of equilibrium states for continuous-time and discrete-time models of ecological systems.

(S1) Problem solving skills

(S2) Numeracy

Single species systems:
•Fundamental balance equations.
•Malthus''s model. Intraspecific competition.
•Continuous time logistic model.

Discrete time models:
•Hassell model and logistic map.
•Relationship between continuous and discrete time models.
•Equilibria, stability, cycles and a mention of period doubling and chaos in the discrete time models. Explicit time delays, stability triangle.
•Age structure, use of Leslie matrices for linear problems.

Multi-species systems:
•Coupled balance equations leading to m-species discrete and continuous time models.
•Linear stability analysis, community matrix for both continuous and discrete time.
•Lotka-Volterra-Gause models for interspecific competition.
•Gause''s competitive exclusion principle.
•Lotka-Volterra and other predator-prey models, including a discussion of f unctional and numerical responses.
•Nicholson-Bayley host-parasitoid model as a predator-prey system in discrete time.
•Kermack-McKendrick models of infectious diseases.

Methods of analysis:
•Linear stability analysis and phase plane analysis.
•Poincare-Andronov-Hopf theorem.
•Lyapunov stability theory.
•Poincare-Bendixson theory.