Three-dimensional cost-matrix optimization and maximum cospeciation

In recent years, event-based approaches have been gaining ground in coevolutionary and biogeographical inference. Unlike pattern-based methods, event-based protocols deal directly with evolutionary events, such as dispersals and host switches. Three protocols have been proposed to date: (1) a coevolutionary method based on optimization of a standard two-dimensional cost matrix; (2) dispersal-vicariance analysis, based on optimization of a three-dimensional cost matrix; and (3) the maximum cospeciation method, thus far not considered a cost matrix method. I describe here general three-dimensional cost matrix optimization algorithms and how they can be applied to the maximum cospeciation problem. The new algorithms demonstrate that all existing event-based protocols, as well as possible future methods based on more complicated process models, can be incorporated into the three-dimensional cost matrix optimization framework. (C) 1998 The Willi Hennig Society.