Mathematical approaches to comparative linguistics‡

The inference of the evolutionary history of a set of languages is a complex problem. Although some languages are known to be related through descent from common ancestral languages, for other languages determining whether such a relationship holds is itself a difficult problem. In this paper we report on new methods, developed by linguists Johanna Nichols (University of California, Berkeley), Donald Ringe and Ann Taylor (University of Pennsylvania, Philadelphia), and me, for answering some of the most difficult questions in this domain. These methods and the results of the analyses based on these methods were presented in November 1995 at the Symposium on the Frontiers of Science held by the National Academy of Sciences.

Genes, peoples, and languages

The genetic history of a group of populations is usually analyzed by reconstructing a tree of their origins. Reliability of the reconstruction depends on the validity of the hypothesis that genetic differentiation of the populations is mostly due to population fissions followed by independent evolution. If necessary, adjustment for major population admixtures can be made. Dating the fissions requires comparisons with paleoanthropological and paleontological dates, which are few and uncertain. A method of absolute genetic dating recently introduced uses mutation rates as molecular clocks; it was applied to human evolution using microsatellites, which have a sufficiently high mutation rate. Results are comparable with those of other methods and agree with a recent expansion of modern humans from Africa. An alternative method of analysis, useful when there is adequate geographic coverage of regions, is the geographic study of frequencies of alleles or haplotypes. As in the case of trees, it is necessary to summarize data from many loci for conclusions to be acceptable. Results must be independent from the loci used. Multivariate analyses like principal components or multidimensional scaling reveal a number of hidden patterns and evaluate their relative importance. Most patterns found in the analysis of human living populations are likely to be consequences of demographic expansions, determined by technological developments affecting food availability, transportation, or military power. During such expansions, both genes and languages are spread to potentially vast areas. In principle, this tends to create a correlation between the respective evolutionary trees. The correlation is usually positive and often remarkably high. It can be decreased or hidden by phenomena of language replacement and also of gene replacement, usually partial, due to gene flow.