Pattern identification in biogeography

Identifying common patterns among area cladograms that arise in historical biogeography is an important tool for biogeographical inference. We develop the first rigorous formalization of these pattern-identification problems. We develop metrics to compare area cladograms. We define the maximum agreement area cladogram (MAAC) and we develop efficient algorithms for finding the MAAC of two area cladograms, while showing that it is NP-hard to find the MAAC of several binary area cladograms. We also describe a linear-time algorithm to identify if two area cladograms are identical