Language change is neutral if the probability of a language learner adopting any given linguistic variant only depends on the frequency of that variant in the learner’s environment. Ruling out non-neutral motivations of change, be they sociolinguistic, computational, articulatory or functional, a theory of neutral change insists that at least some instances of language change are essentially due to random drift, demographic noise and the social dynamics of finite populations; consequently, it has remained little investigated in the historical and sociolinguistics literature, which has generally been on the lookout for more substantial causes of change. Indeed, recent computational studies have argued that a neutral mechanism cannot give rise to ‘well-behaved’ time series of change which would align with historical data, for instance to generate S-curves. In this paper, I point out a methodological shortcoming of those studies and introduce a mathematical model of neutral change which represents the language community as a dynamic, evolving network of speakers. With computer simulations and a quantitative operationalization of what it means for change to be well-behaved, I show that this model exhibits well-behaved neutral change provided that the language community is suitably clusterized. Thus, neutral change is not only possible but is in fact a characteristic emergent property of a class of social networks. From a theoretical point of view, this finding implies that neutral theories of change deserve more (serious) consideration than they have traditionally received in diachronic and variationist linguistics. Methodologically, it urges that if change is to be successfully modelled, some of the traditional idealizing assumptions employed in much mathematical modelling must be done away with.

The Constant Rate Hypothesis (Kroch 1989) states that when grammar competition leads to language change, the rate of replacement is the same in all contexts affected by the change (the Constant Rate Effect, or CRE). Despite nearly three decades of empirical work into this hypothesis, the theoretical foundations of the CRE remain problematic: it can be shown that the standard way of operationalizing the CRE via sets of independent logistic curves is neither sufficient nor necessary for assuming that a single change has occurred. To address this problem, we introduce a mathematical model of the CRE by augmenting Yang's (2000) variational learner with production biases over an arbitrary number of linguistic contexts. We show that this model naturally gives rise to the CRE and prove that under our model the time separation possible between any two reflexes of a single underlying change necessarily has a finite upper bound, inversely proportional to the rate of the underlying change. Testing the predictions of this time separation theorem against three case studies, we find that our model gives fits which are no worse than regressions conducted using the standard operationalization of CREs. However, unlike the standard operationalization, our more constrained model can correctly differentiate between actual CREs and pseudo-CREs-patterns in usage data which are superficially connected by similar rates of change yet clearly not unified by a single underlying cause. More generally, we probe the effects of introducing context-specific production biases by conducting a full bifurcation analysis of the proposed model. In particular, this analysis implies that a difference in the weak generative capacity of two com-

Quantifying the speed of linguistic change is challenging because the historical evolution of languages is sparsely documented. Consequently, traditional methods rely on phylogenetic reconstruction. Here, we propose a model-based approach to the problem through the analysis of language change as a stochastic process combining vertical descent, spatial interactions, and mutations in both dimensions. A notion of linguistic temperature emerges naturally from this analysis as a dimensionless measure of the propensity of a linguistic feature to undergo change. We demonstrate how temperatures of linguistic features can be inferred from their present-day geospatial distributions, without recourse to information about their phylogenies. Thus, the evolutionary dynamics of language, operating across thousands of years, leave a measurable geospatial signature. This signature licenses inferences about the historical evolution of languages even in the absence of longitudinal data.

Abstract. Event structural theories decompose verb meanings into an event template and idiosyncratic root. Many mainstream theories assume a bifurcation in the kinds of entailments contributed by roots and templates, in particular that lexical entailments of change of an individual in change-of-state verbs are only introduced by templates, not roots. We argue against such theories by comparing Levin's (1993) non-deadjectival vs. deadjectival change-of-state verb roots (e.g. crack vs. red roots). A broad-scale typological study reveals that red-type roots tend to have simple (e.g. non-deverbal) stative forms, but crack-type roots do not. Semantic studies of Kakataibo and English show that terms built on crack-type roots always entail change, while terms based on red-type roots may not. We thus suggest that crack-type roots entail change-of-state, contra Bifurcation.

One proposed mechanism of language change concerns the role played by second-language (L2) learners in situations of language contact. If sufficiently many L2 speakers are present in a speech community in relation to the number of first-language (L1) speakers, then those features which present a difficulty in L2 acquisition may be prone to disappearing from the language. This paper presents a mathematical account of such contact situations based on a stochastic model of learning and nonlinear population dynamics. The equilibria of a deterministic reduction of the model, describing a mixed population of L1 and L2 speakers, are fully characterized. Whether or not the language changes in response to the introduction of L2 learners turns out to depend on three factors: the overall proportion of L2 learners in the population, the strength of the difficulty speakers face in acquiring the language as an L2, and the language-internal utilities of the competing linguistic variants. These factors are related by a mathematical formula describing a phase transition from retention of the L2-difficult feature to its loss from both speaker populations. This supplies predictions that can be tested against empirical data. Here, the model is evaluated with the help of two case studies, morphological levelling in Afrikaans and the erosion of null subjects in Afro-Peruvian Spanish; the model is found to be broadly in agreement with the historical development in both cases.