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SPATIAL DISTANCE AND LEXICAL REPLACEMENT L. L. Cavalli-SforzaWilliam S-Y. Wang Stanford UniversityUniversity of California, Berkeley The 'stepping-stone' model has been used to study genetic similarity of peoples as a function of the geographical distances separating them. A gene is represented by one of several alleles, much as a meaning is represented by one of many words. Based on this parallel, the stepping-stone model is here applied to a body oflinguistic data from a chain of Micronesian islands. The logarithm of the lexical similarity, when plotted against geographical distance, shows a pronounced upper concavity not found in the genetic investigations. This deviation from linearity is largely caused by non-homogeneity of replacement rates in the words studied. Another contributing factor is that the effect of distance on lexical similarity is much greater for the eastern islands in the group. Rates of replacement in space, computed here, show a significant positive correlation with those in time, computed for a related language or for different groups oflanguages.* 1. Introduction. When two speech communities are separated, their languages develop in different ways. The rate at which differences accumulate depends largely on the extent to which the populations continue to interact. The less the interaction, the more rapidly the two languages diverge. Nowadays , contact is greatly enhanced by mass media and fast transportation. But until very recent times, it was the movement of populations and of individuals that generated these interactions. Population movement can affect linguistic change in many ways. For instance , mass movements are important, especially for the macro-geographic distribution of languages. The relocation of a group (or a splinter of a larger group) to a new area is part of the history of settlement of that area, and of the origin of the local language. Usually, however, the history of settlement is complicated and poorly known; pre-existence or later arrival of groups with different languages adds complexity to the picture. But local linguistic differentiation at a micro-geographic level must be affected especially by migration of single individuals or families. Individual migration is a constant phenomenon in all societies, including traditional ones—though it is usually more intense in economically more advanced societies. Relocation of individuals can result from marriage, or can be related to work or other causes; and travel without relocation can be a common event. In earlier times, individual movement must have provided an important social exchange for language. Following the classic work of Hägerstrand 1967, geographers have shown that social exchanges of all sorts tend to decrease regularly with increasing distance. Quantitative study usually supports the validity of simple mathematical functions for the dependence of social contact on spatial distance. Because individual migration is usually maximal at short distances, one can expect * This manuscript was completed while the authors were Fellows at the Center for Advanced Study in the Behavioral Sciences. We are grateful for financial support provided by NIH grant GM 20467, NSF grant BNS 76-22943, an Exxon Education Foundation grant, and Alfred P. Sloan Foundation grant 82-2-10. 38 SPATIAL DISTANCE AND LEXICAL REPLACEMENT39 it to exercise most of its influence on linguistic differentiation at a micro-geographic level. According to the classical 'wave theory' of diffusion of linguistic change, innovations spread from their place of origin in concentric, circular waves, generating the 'isoglosses' which have been so frequently described in linguistic geography. If each new, independent innovation spreads independently from earlier ones, the result should be a highly varied set of intersecting isoglosses. Geographic, political, or social barriers which generate discontinuities in social (and therefore also linguistic) exchange put constraints on this free variation; and specific patterns of isoglosses may emerge in response to orographic, hydrographie , or political geography. But wherever these constraints do not dominate the picture, there should be greater similarities, on average, between two languages spoken at a shorter geographic distance. This expectation was recognized early by the proponent of wave theory, J. Schmidt, in 1872. A succinct statement of the theory was given by Bloomfield (1933:317): 'Schmidt showed that special resemblances can be found for any two branches of Indo-European , and that these special resemblances are most numerous in the case...

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