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they evolve. We describe our analysis of an Indo-European (IE) dataset (originally assembled by Ringe and Taylor) based on this new model. Our study shows that this new model fits the IE family well and suggests that the early evolution of IE involved only limited contact between distinct lineages. Furthermore, the candidate histories we obtain appear to be consistent with archaeological findings, which suggests that this method may be of practical use. The case at hand provides no opportunity to explore the problem of conflict between network optimization criteria; that problem must be left to future research.* 1. INTRODUCTION. Languages differentiate and divide into new languages by a pro- cess roughly similar to biological speciation:1 communities separate (typically geo- graphically), the language changes differently in each of the new communities, and in time people from separate communities can no longer understand each other.2 While this is not the only way in which languages change, it is this process that is referred to when we say, for example, 'French and Italian are both descendants of Latin'. The evolution of families of related languages can be modeled mathematically as a rooted tree in which internal nodes represent ancestral languages at the points in time at which they began to diversify and the leaves represent attested languages. Reconstructing this process for various language families is a major endeavor within historical linguistics, but it is also of interest to archaeologists, human geneticists, and physical anthropolo- gists, for example, because an accurate reconstruction of how particular families of languages have evolved can help answer questions about human migrations, the times at which new technologies were first developed, when ancient people began to use

Perfect Phylogenetic Networks: A New Methodology for Reconstructing the Evolutionary History of Natural Languages