Getting started in probabilistic graphical models

Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses that are testable at the bench? This note sketches out some answers and illustrates the main ideas behind the statistical approach to biological pattern discovery.Comment: 12 pages, 1 figur

Inferring Species Trees Directly from Biallelic Genetic Markers: Bypassing Gene Trees in a Full Coalescent Analysis

The multi-species coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. Practical applications of the multi-species coalescent model are, however, limited by the need to integrate or sample over all gene trees possible for each genetic marker. Here we describe a polynomial-time algorithm that computes the likelihood of a species tree directly from the markers under a finite-sites model of mutation, effectively integrating over all possible gene trees. The method applies to independent (unlinked) biallelic markers such as well-spaced single nucleotide polymorphisms (SNPs), and we have implemented it in SNAPP, a Markov chain Monte-Carlo sampler for inferring species trees, divergence dates, and population sizes. We report results from simulation experiments and from an analysis of 1997 amplified fragment length polymorphism (AFLP) loci in 69 individuals sampled from six species of {\em Ourisia} (New Zealand native foxglove)