27.3: Ancestral Recombination Graphs

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In Figure 28.24 a, the two chromosomes at the top represent the homologous chromosomes of a parent. The red chromosome represents the genetic information from the mother and the blue chromosome represents the genetic information from the father (of the grandparent generation). Without crossing-over (recombination), the parent will either pass on the red or the blue genetic information to the offspring. In reality, recombination happens during meiosis so that a parent will pass on some genetic information from both grandparents, effectively passing on a better representation of the parent genetic information.
At each generation, a recombination event can occur at any loci. The evolutionary history of recombination can be tracked through a sequential graph of trees, such that the ith tree in the graph represents recombination at the ith locus.

Fill in this section based on: www.eecs.berkeley.edu/yss/Pub/SH-JCBO5.pdf and the course notes from 2012. More on this topic could be added in the future

The Sequentially Markov Coalescent

The Sequentially Markov Coalescent Model addresses the role of recombination in tree construction. With recombination involved, a sequence may have two parents, which complicates construction. The Sequentially Markov Coalescent Model tells us that move sequentially from left to right is a simpler and much more efficient approach to analyzing the tree; the approach essentially breaks the tree into local trees and overlays them to describe recombination events. More can be read in the following paper:

Elaborate upon intricacies of the model itself: http://www.ncbi.nlm.nih.gov/pubmed/21270390