ACG : How does it work?
Briefly, ACG works by simultaneously trying to estimate many parameters of an evolutionary model. The model contains many features, including how the nucleotide sequences have changed over time, what the population size is, and what the shape of the (recombinant) genealogy is. Some parts of the model are simply numbers - for instance, the transition-to-transversion ratio. Other parts of the model are more complex. For instance, the recombinant genealogy is composed of branches, recombination breakpoints, and coalescent nodes. Instead of trying to find the single most likely combination of parameters, ACG uses a stochastic, Markov chain Monte Carlo method to estimate the distribution of likely values. This takes some time, and it doesn't always work perfectly, but the final result is more informative than a single most likely set of values.
Don't other programs already do this?
ACG is closely related to (and inspired by) other "genealogy samplers" such as BEAST and LAMARC, and it shares many features of these powerful tools. One drawback of BEAST is that it simply can't handle recombination, thus it should only be used on nonrecombining sequences, such as mitochondria and nonrecombining viruses (this fact hasn't stopped people from trying to use it on recombinant data, but it's a dangerous game to play). LAMARC can be used on recombinant data, but LAMARC is fairly slow (ACG is about 100X faster) and doesn't emit some useful information, such as position-specific TMRCA estimates or the locations of recombination breakpoints.
Sounds cool, how do I learn more?
ACG brings together ideas from a number of research areas. Mary Kuhner's excellent review of genealogy samplers is a great place to start.
Coalescent theory forms the basis for much of the calculations. John Wakeley's Introduction to Coalescent Theory is a great introduction.
If you want to learn more about ARGs, Griffith and Marjoram's paper provides an informative (but technical) overview.
Soon enough, you'll be able to check out the paper for ACG in BMC Bioinformatics