My aim is to teach students with some useful and commonly used 
mathematical approaches in understanding ecological systems.  The 
kinds of techniques  explored can be split along classic lines:  
"strategic" (models not based on specific systems but useful in 
answering hypothetical questions) and "specific" (those needed 
for understanding of or making predictions about particular 
systems).  The overall motivation for the course will be first 
and foremost scientific curiosity, though some applications to 
management/conservation will also be discussed.  

Students will learn some of the necessary mathematical tools 
required to model population dynamics, along with the numerical 
skills required for their computer analysis and simulation (the 
software associated with the course is Matlab).  By the end of 
the course, each student will have a sound understanding of the 
underlying principles in modelling and their applications to 
ecological problems.  Equally importantly, they will be able to 
formulate, evaluate and analyze models relevant to their own 
systems of interest.

I.  Basic Population Ecology.  An introduction to the essential 
features of ecological populations and the general questions of 
interest, which will be tackled in the course.  Predominantly 
review material providing an overview of things to come in future 
lectures.

II. Individual-Level Considerations.  Populations are made up of 
individuals - what are the small-scale considerations that 
determine large-scale phenomena?  Discussion of life-history 
models, game theoretic approaches and dynamic models.

III. Population Regulation.  The first of these two topics will 
present a discussion of simple strategic models framed in 
continuous- and discrete-time.  Methods used to analyse them: 
stability analysis, very simple bifurcation analysis and moment 
closure techniques.  The second will deal with methods of 
exploring population regulation in real data (simple time-series 
approaches).

IV. Interacting Species.  I will give one lecture on the dynamics 
and predictions of generalised Lotka-Volterra models (2nd order 
ODEs) as applied to competition/predation/herbivory. The second 
lecture will focus on similar interactions in discrete-time and 
will perhaps include a detailed discussion of host-parasitoid 
systems (2nd order difference equations).   There will then 
follow two lectures each on host-parasite interactions: micro- 
and macro-parasitic infections.  These will systematically 
explore model construction, framework and predictions contrasted 
with findings from data.  This section may be used to introduce 
students to Monte Carlo simulations, seasonally forced models and 
wavelet spectral analysis among others.

V. Structured Populations.  Many populations are clearly 
comprised of different age or stage classes.  Are these 
important?  The first lecture will deal with matrix models as 
applied to ecology with a (brief) discussion of Peron-Frobenius 
theory and sensitivity analysis. In the second lecture, I propose 
to discuss stage-structure in insect populations, introducing 
delay differential equations as applied to host-parasitoid 
systems.

VI. Spatial Dynamics.  Given the ubiquity of spatial structure in 
ecological systems, how do we go about exploring and 
understanding its consequences?  I will start with a discussion 
of space at the level of the individual  foraging behaviour and 
its implications, mostly focused on host-parasitoids, but 
plant-herbivores would also work well here.  (This will also link 
back to some of the evolutionary issues of the first few 
lectures.)  In the two lectures that follow, I will then explore 
larger-scale metapopulation dynamics from a theoretical 
perspective (how I construct a spatial model and what does it 
tell me?), proceeded by an analysis of some spatial data.
 
VII. Applied Ecological Modelling.  How can we use models to 
determine harvesting of populations that is sustainable?  The 
first lecture will explore this in matrix-type models and the 
second will go into Maximum Sustainable Yield type approaches 
from fisheries.  The next two lectures will develop models from a 
pest management and disease control perspective.

These lectures will be augmented with practical classes, which 
may be either computer based or pen-and-paper based.  For every 2 
hours of lectures, there will be two hours of practicals to 
ensure a deep understanding of the materials.