An introduction to reconstructing ancestral genomes
  Recent advances in high-throughput genomics technologies have resulted in the sequencing of large numbers of (near) complete genomes. These genome sequences are being mined for important functional elements, such as genes. They are also being compared and contrasted in order to identify other functional sequences, such as those involved in the regulation of genes. In cases where DNA sequences from different organisms can be determined to have originated from a common ancestor, it is natural to try to infer the an- cestral sequences. The reconstruction of ancestral genomes can lead to insights about genome evolution, and the origins and diversity of function. There are a number of interesting foundational questions associated with reconstructing ancestral genomes: Which statistical models for evolution should be used for making inferences about ancestral sequences? How should extant genomes be compared in order to facilitate ancestral reconstruction? Which portions of ancestral genomes can be reconstructed reliably, and what are the limits of ancestral reconstruction? We discuss recent progress on some of these questions, offer some of our own opinions, and highlight interesting mathematics, statistics, and computer science problems. 
Lior Pachter