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Interval estimates of language divergence times

It is often convenient to construct a branching diagram to represent the relationships between languages belonging to the same language family (for example, between Romance languages such as Rumanian, Italian, French and Spanish). It is desirable that the diagram should illustrate both the closeness of the relationships (that is, which pairs of languages have an immediate common ancestor and which are more remotely related) and the relative chronology of the languages. In this paper, the problem of estimating the time since two languages had a common ancestor and were the same is considered. Interval estimates are sought since, in general, consistent point estimates may be impossible; a numerical example is given to illustrate this.