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Course description

Natural processes are inherently random. As a consequence, modern approaches to understand biological patterns and processes often involve stochastic models. In this course students will get acquainted with stochastic models such as Markov Chains and Brownian Motion that play a fundamental role in ecology, evolution and genetics. Building upon this foundation we will then cover maximum likelihood and Bayesian inference methods with which parameters of stochastic models can be estimated. This will also involve discussions of computational methods such as Markov Chain Monte Carlo simulations and Approximate Bayesian Computation that can be employed in the unfortunate but common situation where purely mathematical approaches are infeasible. The second part of this course will focus on applications of these methods in the context of phylogenetics. Evolutionary trees representing relationships by descent between genes or species are central to evolutionary biology but also have widespread applications in ecology, medicine and public health. Students will learn different methods of how phylogenetic trees can be estimated, including evolutionary rates and timings of events. We will then turn to what can be learned from trees, including trait evolution, patterns of macroevolution and inferences of pathogen epidemiological processes.

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