Evolutionary Quantitative Genetics Workshop

       
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Lecture 2-4: Brownian motion in populations and on trees

Joe Felsenstein

In which it is shown how Brownian Motion, a physical process discovered by a botanical anatomist who had connections to Charles Darwin, can be used to (rather roughly) approximate changes of gene frequencies by genetic drift. And how that leads to an approximation of changes of quantitative characters. How one can get from theoretical population genetics a rough approximation of how much additive genetic variance will be maintained in a population when it undergoes neutral mutation and genetic drift.

How simple forms of optimum selection, where the fitness surface is shaped like a Gaussian (normal) distribution, lead to simple rules for change of the character(s).

What if the optima themselves move through time? Can we model that as being just like change of quantitative characters? Why that is questionable. A simple computer simulation suggests that in the short term the change of characters will be affected strongly by genetic covariances. But not nearly as much in the long term. The result is that “selective covariance” (Tedin, 1926; Stebbins, 1950; Armbruster, 1996) must be considered in addition to genetic covariances.

Lecture projection

PDF of projection: Brownian motion in populations and on trees