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Abstract— A method for reconstructing the history of a host-parasite assemblage is described. This method has the advantage of making explicit the relationship between the host and parasite trees, and it allows a visually intuitive representation of that history. It also enables host switches to be incorporated as an explanation of the observed pattern of host-parasite associations, without the spurious overestimates of the number of host switches that can be obtained using Brooks parsimony analysis (BPA). Reconstructions that maximize the number of cospeciation events have the greatest explanatory power and are hence preferred over reconstructions with fewer cospeciation events. A heuristic algorithm to find a single maximal reconstruction, and an exact algorithm to find all such reconstructions are presented. Two empirical applications of the method are given.