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Do Languages Spread Solely By Diffusion?

Submitted by on October 19, 2012 – 8:36 pm 2 Comments |  
(Note: This post is jointly written by Martin Lewis and Asya Pereltsvaig; we thank Vitaliy Rayz for his help with this post)

While earlier GeoCurrents posts focused on incomplete and faulty data fed into the computational model of Bouckaert et al., as well as the erroneous results therefore produced, we have barely tackled the central assumptions behind the Science article. In the previous post, we critiqued their key postulate that linguistic evolution is so similar to biological evolution that the two processes can be modeled in the same manner. The current post addresses the issue of language spread, questioning whether it occurs by way of diffusion only, as modeled by Bouckaert et al. Instead, we suggest that a different transport phenomenon, that of advection,  should be incorporated in order to provide an adequate mathematical model of language expansion.

According to the standard definition, diffusion is a phenomenon that results in mass transport without bulk motion. The process of diffusion, for instance, of small particles suspended in a fluid, is described by the theory of Brownian motion, which Bouckaert et al. refer directly on p. 10 of their Supplementary Materials; the paths that such particles take as they diffuse are modeled in terms of a random walk (which is a mathematical formalization of a path that consists of a succession of random steps). Take, for example, a scenario in which a drop of cream is diffused in a cup of coffee. Initially, the cream particles are clumped in one area of the cup, typically on the top. As the particles diffuse, they randomly move through the medium, which would eventually lead to a uniform distribution of cream throughout the cup of coffee. Importantly, diffusion in this sense eventually results in a state where the two substances can no longer be separated; once the cream has spread, it can no longer be removed without elaborate filtration. In the process of diffusion, cream particles move through the medium without the bulk of coffee moving anywhere. As you may know from your experience, the process is rather slow. May I suggest a stirrer? As you stir the coffee, flow patterns are created, resulting in the bulk motion of coffee that in turn moves the cream particles around, speeding up the process. The relevant transport mechanism, in which a substance moves in fluid due to the fluid’s bulk motion, is known as advection. A number of transport phenomena are best described by combinations of these two mechanisms, with one or the other generally prevailing: paint dropped into the standing waters of a lake spreads by diffusion, while paint dropped into the running waters of a river spreads mostly by advection. So which form of transport provides the best analogy for language spread: diffusion or advection?

As it turns out, some geolinguistic phenomena are best described as occurring through diffusion, whereas for others advection offers a better model. In particular, diffusion seems to be an especially apt analogy for the mixing of languages in border zones and for the penetration of small groups of speakers of one language into the spatial area of another language. Such processes, like diffusion in general, are slow, random, and uniform; they are also extremely common, especially in times and places where state borders are not significant. For example, Belgium can be divided roughly into two linguistic zones: a Flemish-speaking north and a French-speaking south (we are ignoring the German-speaking zone in the east and the multilingual Brussels). But the actual linguistic situation on the ground is much more complex than a simple line on the map would indicate: some Flemish-speaking communities are found south of the line and a few French-speaking communities are located in the Flemish-speaking north. An example of the latter is a small suburban town Wemmel, which is technically on the Flemish-speaking side of Belgium, but which has become home to many French speakers fleeing the urban hustle and bustle of Brussels. Swedish-speaking communities in the neighboring Finland and Finnish-speaking communities in Sweden are also example of language spread by diffusion. As mentioned above, the diffusion of substances results in the creation of an inseparable mixture; likewise, diffusion of languages results in a high degree of linguistic admixture in the form of individual and communal bilingualism.

One can also see diffusion at play in language contact phenomena such as borrowing, the formation of a Sprachbund (or a linguistic convergence area), and substratum influences. When speakers of two languages are in contact through war and conquest, economic activities such as trade, plantation agriculture, or servitude, or cultural exchanges, elements of one language, such as words, sounds, or grammatical patterns, may be adopted by speakers of the other. For example, the conquest of England by the Normans (itself decidedly not a case of diffusion, but more on that later) led to a massive influx of Norman French words into English; much later the French adopted numerous English terms such as le weekend and le hotdog via cultural exchanges with English speakers.

Alongside lexical borrowing, grammatical patterns too can be adopted via a process that can be modeled as diffusion. However, grammatical borrowing is more common in Sprachbund situations, where certain unrelated or distantly related languages come to share each other’s grammatical features through prolonged contact. A classical example of a Sprachbund is the Balkan Peninsula, where Bulgarian, Romanian, Greek, and Albanian converged on numerous grammatical properties that diffused from one language into the others. For instance, Bulgarian is unlike other Slavic languages in using analytical rather than synthetic forms for future and perfect tenses (e.g. shte ucha ‘I will study’, səm uchil ‘I have studied’); this feature has resulted from diffusion from Greek. The use of suffixed definite article in Bulgarian (e.g. kniga-ta ‘book-the’) and Romanian (e.g. lup-ul ‘wolf-the’) probably stems from diffusion from Albanian (cf. mik-u ‘man-the’), as neither Slavic nor Romance languages outside the Balkans exhibit this pattern. Likewise, a substratum language may leave a trace on the superstratum language via diffusion: thus, the do-support phenomenon in English (i.e. the use of do in questions and negative sentences) is now believed by many scholars to have diffused from an older form of the now-extinct Cornish language. This diffusion pattern can be traced in the gradual, slow—over a matter of centuries—and random spread of do-support, seen first in manuscripts from southwestern England and gradually making its way into later manuscripts produced further to the east and north. As with other instances of diffusion, grammatical borrowing often creates an inseparable mix whereby a grammatical pattern from one languages fuses with a pattern from another.

But while diffusion is a useful analogy for describing such language contact phenomena, not all language spread can be portrayed as a slow, random, and uniform mixing process. Bouckaert et al. make a specific caveat that their model cannot adequately describe “the rapid expansion of a single language” (Supplementary Materials, p. 19); however, relatively rapid expansions of linguistic groups are far too common in the history of the Indo-European family, and of other families as well, to be simply ignored. Examples from modern history abound: Russian spread over its huge present-day territory in less than 200 years, displacing indigenous languages of Siberia.* European languages—English, Spanish, Portuguese, and to a lesser extent Dutch and French—have established themselves in Africa, South and Southeast Asia, Australia, and the Americas in record time as well. Such rapid language spread is not solely an artifact of modern transportation technology. Latin spread over a vast territory in the span of a few hundred years, as did Germanic-speaking peoples after the fall of Rome. Among the latter group were Anglo-Saxons who settled in the British Isles; the later conquest of England by Romance-speaking Normans was fast as well. Outside the Indo-European family, Quechua expanded over the large expanse of the Incan Empire in decades. The Magyars, who brought an Ugric tongue to present-day Hungary, migrated from the Pontic Steppes en mass in the late ninth century. The spread of the Turkic and Bantu languages was also rapid. In many instances the speed at which a certain linguistic group expands can be assessed from historical records or archeological evidence, but the geospatial distribution of languages too bears witness to the swiftness of such expansions: very often speakers of other languages are engulfed rather than gradually displaced from their original territory, creating pockets of one language (or language family) inside a larger zone occupied by another. Examples include pockets of Munda (or Austro-Asiatic) languages in northeastern India; Brahui, a Dravidian language, in Pakistan; and Hadza and Sandawe, two Khoisan languages spoken in Tanzania and surrounded by Bantu languages. Arguably, such rapid expansions are better modeled by the process of advection rather than diffusion. As in the physical world, advection is typically accompanied by diffusion in the newly created border zones, but advection remains the predominant mechanism, whether cream is stirred into coffee or a certain language or language cluster expands rapidly and non-randomly.

The rapid spread of the Turkic languages in the first millennium of the common era was associated with equestrianism, as was the displacement of the Magyar language from the Pontic Steppes to Carpathian Basin. Horse riding, and the pastoral nomadism that is often associated with it, lends itself to rapid movement and even to wholesale population relocation. The jostling of different tribes and confederation and the competition for grazing grounds often led entire peoples to undergo migrations of thousands of miles; such is the stuff of Eurasian history. Example would include the relocation of the Mongolian-speaking Kalmyks from Central Asia to the lower Volga region in the 1600s and the movement of the Turkic-speaking Yakuts (Sakha) to central Siberia in the 1200s. According to the steppe hypothesis, supported by a significant body of evidence, the proto-Indo-European speakers, and most of the immediate descendents, were accomplished horse-breeders, and thus would have had the means to have engaged in such wide-ranging movements, spreading their languages in a largely advectional manner.

Mass movements of entire linguistic communities, however, do not require horses, or any other particular technologies or ways of life, as is abundantly evident when one considers the linguistic geography of indigenous North Americans. Almost all of the major languages families of North America were characterized by highly discontinuous patterns. Consider, for example, the Na-Dene languages, depicted on the map to the left. Most of these languages are found in the northwestern portion of the continent as would be expected, considering the fact that the ancestors of the Na-Dene speakers almost certainly migrated to North America over the Bering Land Bridge long after other Amerindian groups. But note that Na-Dene languages are (or were) also found in Northwestern California, the U.S. Southwest, and the Great Plains. According to a diffusional model, their ancestors would have had to have slowly moved southward, occupying all of the intermediate areas on the map before reaching what is now Texas. One would thus have to hypothesize subsequent diffusions of other language families into the Na-Dene zone that supplanted these languages across most of the western half of what is now the United States, yet left pockets of Na-Dene speakers in the Southwest in areas that were somehow “immune” to the diffusional process. Archeological and ethnohistorical evidence, however, shows that the ancestors of the Navahos and Apaches, the main Na-Dene-speaking groups of the American Southwest, migrated into the region from the north sometime after 1000 CE, their language thus moving by way of an advectional rather than a diffusional process.

The migrating ancestors of the Apaches and Navahos were hunter-gatherers, but similar patterns obtained in regard to languages spoken by the agricultural peoples of pre-Columbian North America. The Siouan- and Iroquoian-speaking peoples were farmers at the time of contact (although many Siouan groups later abandoned the practice in favor of Bison hunting), as were many of the Algic and Uto-Aztecan groups. As can be seen in the maps posted here, these major language families were also characterized by pronounced spatial discontinuity. Admittedly, some of the fractionated nature of Amerindian language families resulted from populations fleeing the encroachment of European settlers, but the basic patterns had been established well before colonization; the maps presented here, moreover, aim to depict the pre-contact situation. In same cases, multiple long-distance migrations occurred; in that of the Tuscarora, the second movement entailed a return to the homeland. The Tuscarora are an Iroquoian-speaking group whose ancestors left the Great Lakes region and resettled in what is now North Carolina well before English settlers arrived. After suffering a major defeat at the hands of the North Carolina Militia in 1713, a large contingent of the Tuscarora returned to the Great Lakes area, where they were welcomed into the Iroquois League as the group’s sixth nation, a standing that they retain to this day.

Considered together, the spatial patterns visible on the six language maps of North America posted here would be almost impossible to explain by way of diffusion. They are easily explained, however, by advectional processes of migration, processes that are well attested by archeological and ethnohistorical lines of evidence. Such migrational scenarios, moreover, are vastly more parsimonious than the alternative, that of a series of spatially overlapping, temporally offset, and always incomplete diffusions of multiple language families over most of North America. If one is to follow Occam’s razor, one would avoid modeling the spread of any of these language groups just on the basis of diffusion.

The speed of many instances of language expansion and the discontiguous nature of many language families are not the only reasons to opt for an advectional rather than a diffusional model. As mentioned above, diffusion is necessarily random, while language expansion—whether due to the migration of a linguistic group or to a language shift—rarely is. Some migrations are a result of a conscious choice on the part of an individual or a group; the high degree of communal multilingualism in the Silicon Valley, the home of GeoCurrents, is a result of such non-random migrations. But in other cases, numerous factors involving physical and human geography act as abstract currents creating flow patterns that guide language spread. In some instances, these features are actual currents in water bodies, which—contrary to Bouckaert et al.’s assumption that water acts as a barrier to migration—have often propelled human groups over vast distances. For example, eastwards currents arising in central Pacific during El Niño episodes brought Austronesian speakers into the depths of the Polynesian triangle. But such currents can also be of a more abstract nature. Features of physical geography, such as waterways, stretches of fertile land, or habitat zones of useable flora and fauna often serve as conduits for human migration. Physical barriers to easy movement, such as mountains, rugged coastlines, and bog lands, may funnel movement into strips of relatively easy passage, thus indirectly creating migration paths. Consider, for example, the spread of Turkic languages from their homeland roughly in northern Mongolia, which largely followed the steppe zone of central Eurasia. The map of American English dialects reproducedabove highlights the important role of Mississippi in the spread of certain Southern dialects.

Google Earth Image of Darial Gorge, Georgia and North Ossetia

Another good example is the Darial Gorge, the only easy passage through the Great Caucasus Range (except the Derbent Pass, much further east, near the Caspian shore), which resulted in Ossetian being the only language found both north and south of the Caucasus crest (again, except in the eastern Caucasus). Numerous additional examples from around the world could be used to illustrate this phenomenon.

But factors of physical geography alone do not typically determine the spread of human groups and as a result that of languages. Political, social, economic, and cultural factors of human geography play an important role in generating non-random migratory currents. The abovementioned Magyar migration was caused in large part by pressures from Turkic-speaking groups such as the Pechenegs. The expulsion of Jews from Spain in 1492 and their acceptance by the Ottoman Sultan Bayazid II led to the spread of Judeo-Spanish (Ladino) into areas that today are parts of Greece, Turkey, and the former Yugoslavia. The fact that some speakers of Judeo-Spanish could be found in Portugal or North Africa was not a result of gradual diffusion across the Spanish-Portuguese border and the Strait of Gibraltar, but of the “advection” caused by the 1492 expulsion as well. Likewise, Yiddish did not diffuse from its homeland in southern Germany in a random fashion; if it did, Yiddish would have been spoken in France and Italy as well as in Poland. Instead, Jews in what are now France and Italy spoke Judeo-French (in northern France), Judeo-Comtadine (in the historical region of Comtat-Venaissin, present-day department of Vaucluse), Judeo-Provençal (in Nice and Marceille), and a number of Judeo-Italian dialects, some of which, such as bagito in Livorno and Pisa, were quite distinctive (see chapter 12 of Languages of the World: An Introduction for more details). All of these various mixed Jewish languages are themselves a result of grammatical mixing that can be modeled in part on the basis of diffusion (e.g. Yiddish absorbed certain grammatical patterns and large chunks of its lexicon from Slavic languages), but the spatial distribution of the Jewish diaspora is a result of advectional processes determined by such factors as religious persecutions and economic opportunities. Often such non-random migrations were generated by an invitation extended by a single ruler, as in the case of Bayazid II, mentioned above, or of the Grand Duke of Lithuania Vytautas the Great who resettled nearly 400 Karaim-speaking families from Crimea to the town of Trakai (Troki) in Lithuania in the last decade of the 14th century; to this day, more speakers of Karaim live in Lithuania than in Crimea. Similarly, the current distribution of Northwest Caucasian languages, spoken more extensively through the Middle East than in the Caucasian homeland, is a result of advection caused by two factors: expulsion by the Russians and acceptance by the Ottomans.

As we advocate an introduction of an advection factor into computational equations for language expansion, we realize that using advection to model population migrations is not an entirely novel idea. The next GeoCurrents post will examine one such study that uses both diffusion and advection to model population distribution.


* Some indigenous groups, such as the Itelmen, have completely or almost completely abandoned their original language in favor of Russian. Such a process of language shift requires relatively intimate language contact: while some Siberian peoples switched to Russian, unsurprisingly none switched to Abkhaz or Zulu. Crucially, this process is not random and hence cannot be modeled as diffusion, but it is not clear whether advection is the right mechanism either. Since Bouckaert et al. model Indo-European spread in terms of population movement rather than language shift (i.e. cultural innovation), we will largely ignore language shift as well.

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  • annoyed

    What’s wrong with the HTML of your site that makes it impossible to enlarge the font? I’d like to read these posts but it’s just too hard to even see the letters.

    • Asya Pereltsvaig

      Sorry about this. What browser do you use? Apparently, some browsers don’t allow to enlarge the font, but Mozilla Firefox works just fine. Or try using the Print/PDF button at the top of the post. We are working on fixing this problem.