Optimizing Directed Acyclic Graphs via Simulated Annealing for Reconstructing Human Segmental Duplications

Segmental duplications, relatively long and nearly identical regions, prevalent in the mammalian genome, are successfully modeled by directed acyclic graphs. Reconstructing the evolutionary history of these genomic regions is a non-trivial, but important task, as segmental duplications harbor recent primate-specific and human-specific innovations and also mediate copy number variation within the human population. Using novel models derived by Kahn and Raphael, we formalize this reconstructon task as an optimization problem on the space of directed acyclic graphs. We employ a simulated annealing heuristic and describe an efficient way to use the technique to solve the optimization problem in general. We apply the heuristic to both maximum parsimony and maximum likelihood evolutionary models. We use these models to analyze segmental duplications in the human genome and reveal subtle relationships between these blocks.