Course Description
Review of some commonly used mathematical approaches to modeling ecological populations, including single species approaches (discrete and continuous time), age/stage structure, species interactions, spatial structure, harvesting, and management.
Athena Title
MODEL POP ECOL
Equivalent Courses
Not open to students with credit in FORS 8325-8325L or ECOL 8320-8320L
Prerequisite
ECOL(PBIO)(WILD) 8310 and permission of department
Semester Course Offered
Offered spring
Grading System
A - F (Traditional)
Course Objectives
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.
Topical Outline
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.