Modern comparative lexicostatistics
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The problem most often dealt with in comparative lexicostatistics is to reconstruct a family tree for a family of dialects by comparing their lexicons (in a carefully chosen manner). A second problem (often distinguished by the name glottochronology) is to estimate the time at which branchings of the tree occurred. The fundamental data have this form: For a specified meaning, is the word in Dialect A cognate or not cognate to the word in Dialect B. This determination must be made by a highly-skilled linguist who has extensive knowledge of the dialect family, and is of course subject to error like any other measurement process.
Earlier work in comparative lexicostatistics treated the replacement rates for different meanings as equal, although many authors have pointed out the likelihood and effects of varying replacement rates. More recent work has dispensed with this equality assumption. Replacement rates have been explicitly estimated (by maximum likelihood) for hundreds of meanings in three different language families, and the rates have been used to estimate branching times in a tree of 84 Indoeuropean dialects.