Both linguistic and genetic evolution involve copying and mutation of variants. The simplest copying process assumes that variants are reproduced at a rate equal to their current frequency, exemplified by Kimura's stepping stone model of neutral evolution, and the voter model. In this case, spatial patterns are driven by noise. In the linguistic context, an alternative possibility is that speakers preferentially select variants which are already popular, yielding patterns driven by surface tension, exemplified by the Ising model. In this paper, we model language change using a spatial network of speakers, inspired by the Hopfield neural network. The model's universality class-Voter or Ising-is determined by speakers' learning function. We view maps generated by the Survey of English Dialects as samples from our network. Maximum likelihood analysis, and comparison of spatial auto-correlations between real and simulated maps, indicates that the underlying copying processes is more likely to belong to the conformity-driven Ising class.

We introduce a stochastic model of language change in a population of speakers who are divided into social or geographical groups. We assume that sequences of language changes are driven by the inference of grammatical rules from memorised linguistic patterns. These paths of inference are controlled by an inferability matrix which can be structured to model a wide range of linguistic change processes. The extent to which speakers are able to determine the dominant linguistic patterns in their speech community is captured by a temperature-like parameter. This can induce symmetry breaking phase transitions, where communities select one of two or more possible branches in the evolutionary tree of language. We use the model to investigate a grammatical change (the rise of the phrasal possessive) which took place in English and Continental North Germanic languages during the Middle Ages. Competing hypotheses regarding the sequences of precursor changes which allowed this to occur each generate a different structure of inference matrix. We show that the inference matrix of a "Norway hypothesis" is consistent with Norwegian historical data, and because of the close relationships between these languages, we suggest that this hypothesis might explain similar changes in all of them.

This paper examines individual differences in constraints on linguistic variation in light of Labov's (2007) proposal that adult change (diffusion) disrupts systems of constraints and Tamminga, MacKenzie, and Embick's (2016) typology of constraints. It is shown that, in pooling data from multiple speakers, some of the complexity in structured community variation may be overlooked. Data on rhoticity from speakers of Bristol English are compared to 34 previous studies of rhoticity in varieties of English around the world. Constraints found to be consistent across varieties are also found to be consistent across speakers of Bristol English, whereas those that differ between varieties also differ between individuals, implying that only those which differ are truly part of the grammar, and that these are indeed disrupted by diffusion.

Work in historical sociolinguistics can broadly be divided into quantitative work which examines population-level trends in past language use, and qualitative work which documents and explains the usage of individuals or within particular texts. In this paper, we argue for an approach which combines both of these. Using mixed methods we can achieve all the advantages of both qualitative and quantitative approaches, revealing the complexity of language use in real social contexts but situating it in a well-described view of the historical processes at play. We demonstrate our approach with an exploration of the rise of 'broken' forms of the first person singular nominative pronoun in the history of Norwegian. We chart the overall progression and social patterning of the change using kernel density estimation, regression and geographically weighted regression. We then explore the wealth of fascinating local and ephemeral patterns by examining usage of particular individuals and texts.

Tracing the diffusion of linguistic innovations in space from historical sources is challenging. The complexity of the datasets needed in combination with the noisy reality of historical language data mean that it has not been practical until recently. However, bigger historical corpora with richer spatial and temporal information allow us to attempt it. This paper presents an investigation into changes affecting first person non-singular pronouns in the history of Norwegian: first, individual changes affecting the dual (vit > mit) and plural (vér > mér), followed by loss of the dual-plural distinction by merger into either form or replacement of both by Danish-Swedish vi. To create dynamic spatial visualisations of these changes, the use of kernel density estimation is proposed. This term covers a range of statistical tools depending on the kernel function. The paper argues for a Gaussian kernel in time and an adaptive uniform (k-nearest neighbours) kernel in space, allowing uncertainty or multiple localisation to be incorporated into calculations. The results for this dataset allow us to make a link between Modern Norwegian dialectological patterns and language use in the Middle Ages; they also exemplify different types of diffusion process in the spread of linguistic innovations.