524 Announcement

Theoretical Population Genetics

ECOL, ANTH, GENE: 524 and 424

Where and When:

Course is usually taught every other year. The next time it will be offered is in Spring 1999, T: 9:30-11:45am

Level and Credits:

400/500; Units 3

Instructor:

Dr. Rick Michod, EEB (621-7517, 410 BSW Building)

Books and Materials:

(i) Michod, R. E. 1999. Darwinian Dynamics, Evolutionary Transitions in Fitness and Individuality. Princeton Univ. Press (ii) Class packet at copy center

Objectives of Course:

The course concerns the development of mathematical models of population genetics and the evolutionary deductions derived from these models. Special attention is given to mutation, population structure, covariance approaches to natural selection, the evolution of interactions (cooperation), and the emmergence of new levels of complexity. The field of population genetics is one of the most mathematically developed fields in biology. The basic principles of population genetics were developed early this century, not as empirical generalizations from nature, but as deductions from mathematical models. As is the case with any field of inquiry, it is illuminating to understand the methodology used in obtaining results. For theoretical science, this means understanding the mathematical techniques employed in analyzing models. Thus, you will be exposed to a sampling of mathematical techniques including difference equations, statistics, probability theory, branching processes, diffusion processes, linear stability analysis and matrix algebra. I hope you will come to appreciate both the beauty of model construction and analysis as well as its utility in evolutionary analysis.

Topics

	History and origins of theoretical population genetics
	Role of theoretical models in science
	Mutation and selection balance, mutation load
	Probability of fixation of a mutation using branching processes
	Genetic drift
	Natural selection as a covariance involving fitness and traits
	Frequency dependent fitness
	Population structure and inbreeding
	Wright's hierarchical model, F-statistics
	Group selection in a structured population
	Joint action of evolutionary forces using diffusion equations
	Two locus modifier theory.
	Evolution of interactions especially cooperation (kin selection, reciprocation and group selection)
	Introductory game theory and ESS
	Transitions in the level of fitness during the emergence of higher levels of complexity
	Additional topics depending on student interest

Prerequisites:

It depends. Undergraduate courses in genetics, ecology and evolution are especially useful. Students with a strong math background will probably do fine without these. Undergraduate courses in quantitative methods such as statistics, calculus, linear algebra, advanced calculus, and probability theory are useful but not required. Most motivated students do fine. If you have any questions, please stop by and see me.

Grading:

Class participation, exams and problems; graduate students may be required to make an oral presentation