Lexicostatistical tree reconstruction incorporating borrowing

A persistent concern of lexicostatistics has been to eliminate all meanings susceptible to borrowing from the test-list used in family-tree reconstruction for a group of related languages. However, it is not clear that any meanings exist which are completely immune to borrowing, especially in situations of large-scale language contact. There are also considerable statistical advantages in the use of a longer test-list. Thus lexicostatistical tree reconstruction methods can be improved by incorporating borrowing rates as well as replacement rates in the reconstruction process. The system of differential equations necessary for this reconstruction (where the replacement rate r and the borrowing rate b are known) will be presented, together with a computer simulation of the divergence of a language family in which both lexical replacement and borrowing are involved. The results of comparisons of the reconstructed trees with the computer-generated trees for different lengths of test-list and for different values of r and of b show that a high degree of accuracy, both in the topology of the tree and in its relative branch lengths, can be obtained, even for values of rand b considerably higher than those found in natural language.