S-curves and the mechanisms of propagation in language change

Abstract

A variety of mechanisms have been proposed in sociolinguistics for the propagation of an innovation through the speech community. The complexity of social systems makes it difficult to evaluate the different mechanisms empirically. We use the four-way typology of mechanisms proposed by Baxter and colleagues (2009), and define them mathematically in such a way that the effects of different mechanisms in the trajectory of a change can be modeled. The model suggests that the widely observed empirical pattern of an S-curve temporal trajectory of change can be captured only if the mechanisms for propagation include replicator selection, that is, differential weighting of the competing variants in a change, except under highly specialized circumstances that probably do not hold in speech communities in general

How many qualitatively distinct possible mechanisms of language change are there? And how can we decide among them, or at least determine which mechanisms are necessary and/or sufficient for explaining language change? Of course, empirical confirmation or disconfirmation is the most obvious and best way to answer these questions. But some questions are very difficult to address empirically. (p. 270)

For instance, collecting data on interlocutor frequencies (the Bloomfield-inspired mechanism) is extremely difficult, and it is not clear whether we would be able to decide between interlocutor frequencies vs. associated social values as the best or only explanation for the propagation of a novel variant. The system of social behavior is so complex that empirical analysis can be very challenging. (p. 270)

There is another approach that offers the opportunity to address some—though certainly not all—of the theoretical issues of the mechanisms of language change in society, namely mathematical modeling of social systems and linguistic behavior. Mathematical modeling offers two significant advantages. First, it demands that we provide precise mathematical definitions of the proposed mechanisms that allow those mechanisms to be incorporated into a model. These definitions allow us to sharpen our theoretical tools for analyzing language change. We provide sharpened definitions for mechanisms of language change in §3. Second, the model of various mechanisms can be applied to empirically supported patterns of language change, and some mechanisms can be ruled out, or ruled in, based on the ability of the model to capture the empirical pattern with or with out those mechanisms. We present results of this application in §§6-7. (p. 270)

Our modeling indicates that language changes that follow an S-curve almost certainly involve at least differential valuation of linguistic variants. None of the other mechanisms, alone or in concert, produce an S-curve trajectory of language change except under highly specialized circumstances that are unlikely to hold in speech communities in general. (p. 270)

The Sturtevant-inspired mechanism is characterized by differential valuation of the specific variants. Because the variants are the replicators in language change, Baxter and colleagues describe this as replicator selection. (p. 272)

The replicator selection mechanisms for propagation proposed by sociolingu all social. Other linguists have proposed other mechanisms for propagation, i phonetic biases and morphological analogy favoring some variants over ot sound change, and structural or functional biases favoring some variants over ot grammatical and lexical change (e.g. Haspelmath 1999, Nettle 1999). These explanations would also be instances of replicator selection, since one variant 𝑤 weighted differentially over another. Croft argues, however, that these phonetic, structural, and/or functional biases are mechanisms for the generation of variation trast to biological evolution, in which the generation of variation appears to be Croft 2000:8) (p. 273)

Our mathematical model cannot decide among these various social, functional tural, or phonetic weightings of variants, or indeed any other differential weig variants (on the use of prestige in sociolinguistics, see Labov 2001:24 and 2004:153; on the use of acts of identity, see Trudgill 2008). But all of these the instances of replicator. (p. 273)

The other mechanism described in the intro duction, the Bloomfield-inspired mechanism, operates in a very different way. Language change is simply driven by the frequency of interaction with one’s interlocutors. As we observed in §1, no social valuation of the variants used plays a role, nor does any social valuation of the speaker using the variant(s). All that matters is how often one converses with one interlocutor as opposed to another, and which variants those interlocutors produce in the conversational interaction. For this mechanism, the variants are symmetrical: if one replaced variant A with variant B in the manner described above, then variant B would have the same path of propagation as variant A: all that matters is who is talking to whom. (p. 273)

The terminology ‘neutral interactor selection’ emphasizes that it is the properties of the interactors, the interlocutors, that drive the diffusion process rather than properties of the replicators. (p. 273)

It is of course possible for a speaker’s linguistic behavior to be more strongly affected by one speaker over another, and in particular, for a speaker 𝑖 to have a greater influence on another speaker 𝑗 than 𝑗 has over 𝑖.

In this case, the symmetry defining neutral interactor no longer applies.

Weighted interactor selection can be identified in another model of propagation discussed by Milroy and Milroy (1985). (p. 274)

Finally, Labov suggests that some sound changes occur without any social mechanisms operating at all: a theory invoking a social mechanism such as his own ‘does not apply to most mergers and other changes which their course without taking on symbolic value of any kind’ (Labov 2001:517). What Labov is suggesting here is that language change can happen without any social process being involved. This is an example of invoking the last mechanism described by Baxter and colleagues—neutral evolution. Neutral evolution, also known as ‘drift’ in biological evolution (see §2), is change that results from the random fluctuations in replicator frequencies in a finite population: these fluctuations may go to 0%, leading to extinction of the replicator, or 100%, leading to fixation of the replicator. (p. 275)

Neutral evolution is related to neutral interactor selection in that neither mechanism involves any differential weighting of either interactors (speakers) or replicators (variants). Not surprisingly, neutral evolution as a mechanism for language change has not been examined in detail by sociolinguists, as it has no social dimension to it. Neutral evolution’s independent role in evolutionary change can only be inferred in models with a ‘flat’ network structure, in which all individuals have an equivalent position within the social structure. For example, models in which speakers have equal proba bility of interacting with all other individuals (i.e. all individuals are directly connected, and there are no differences in tie strength between individuals) fall into this category. Examining such models mathematically demonstrates that the likelihood of fixation (propagation to 100%) of a replicator (e.g. linguistic variant) is proportional to its fre quency in the population. Hence Trudgill’s observation that the majority variant in the input to New Zealand English is generally the one that became fixed for the New Zealand English dialect (Trudgill 2004:113-15) is probably a consequence of the oper ation of neutral evolution rather than neutral interactor selection. (p. 276)

In our analysis of the mechanisms of propagation of change, the salient properties of the different mechanisms are whether their effects on replicators and interactors are symmetric or not. In replicator selection, the replicators are nonsymmetric (i.e. not necessarily symmetric, though for replicators of equal weighting, of course, they will be interchangeable). In weighted interactor selection, replicator behavior is symmetric, but the interactors (speakers) are nonsymmetric: speaker A may weight the language produced by speaker B more heav ily, but not vice versa. In neutral interactor selection, replicator behavior and interactor behavior are symmetric; all that matters is interaction frequency, which may be unequal (speaker A may interact more with speaker B than with speaker C). Finally, neutral evolution is the behavior found with no interaction inequalities, and symmetric interactor and replicator behaviors. (p. 276)

Theories of language change may and do involve multiple mechanisms of more th one type, though there is sometimes unclarity about what mechanisms are involved (p. 277).

The results from the modeling imply that replicator selection, that is, differential weighting of linguistic variants, is almost certainly essential mechanism for language changes that follow an S-curve, specifically, when a competing variant replaces a previously established conventional variant. Since the language changes of this type that have been quantitatively documented over their life-times follow an S-curve or are compatible with an S-curve, our results suggest that most if not all such changes involve differential weighting of linguistic variants. That is, the Sturtevant-inspired mechanism plays a central role in language change. (p. 293)