Linguistic diversification as a long-term effect of asymmetric priming

An adaptive-dynamics approach

in Language Dynamics and Change
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Abstract

This paper tries to narrow the gap between diachronic linguistics and research on population dynamics by presenting a mathematical model corroborating the notion that the cognitive mechanism of asymmetric priming can account for observable tendencies in language change. The asymmetric-priming hypothesis asserts that items with more substance are more likely to prime items with less substance than the reverse. Although these effects operate on a very short time scale (e.g. within an utterance) it has been argued that their long-term effect might be reductionist, unidirectional processes in language change. In this paper, we study a mathematical model of the interaction of linguistic items that differ in their formal substance, showing that, in addition to reductionist effects, asymmetric priming also results in diversification and stable coexistence of two formally related variants. The model will be applied to phenomena in the sublexical as well as the lexical domain.

Linguistic diversification as a long-term effect of asymmetric priming

An adaptive-dynamics approach

in Language Dynamics and Change

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Figures

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    Figure 1

    Gaussian function underlying the asymmetric competition term with 354

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    Figure 2

    (a) Asymmetric competition terms with 355 and 356 assuming strong (left; 357) and weak (right; 358) priming effects, respectively. (b) Evolutionary trajectory of formal substance 359 based on the canonical equation of adaptive dynamics assuming 360. If priming effects are strong, items undergo formal reduction thereby approaching an optimal degree of formal substance (left). Under weak priming effects, diversification occurs followed by stable coexistence of two items occurs that differ as to their degree of formal substance (right).

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    Figure 3

    Intrinsic growth rate 361 as a function of 362, where 363. Solid light gray curve: 364, 365, i.e. perceptual effort dominates. Dashed dark gray curve: 366, 367, i.e. articulatory effort dominates. In both cases, 368.

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    Figure 4

    Bifurcation plots of the evolutionary singularity 369 depending on the similarity threshold 370 and priming strength 371. Dark areas denote BPs, lighter areas denote CSSs. Plots are shown for different values of articulatory effort 372 (rows) and perceptual effort 373 (columns).

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    Figure 5

    (a) Evolutionary trajectory of 374 before and after branching. Substance s proceeds towards a BP, subsequently followed by branching and coexistence of a shorter (morphonotactic, ‘mpt’) and a longer (lexical, ‘lex’) variant (only every 100th point displayed). (b) Frequency trajectories of both variants (dashed: lexical; solid: morphonotactic) after evolutionary branching (375).

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    Figure 6

    Empirical developments of four word-final consonant-diphone types retrieved from Middle and Early Modern English corpus data. Circles and crosses denote normalized frequencies (p.m.) of morpheme-internal (lexical) and boundary-spanning (morphonotactic) diphones, while dashed and solid lines denote LOESS trajectories fitted to the lexical and morphonotactic data points, respectively.

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    Figure 7

    Evolution of formal substance 376 in grammaticalization under asymmetric formal priming and (a) Zipfian intrinsic growth. (b) Items undergo unidirectional reduction and become increasingly frequent (frequency 377 measured on the vertical axis; 378).

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    Figure 8

    Evolution of the degree of grammaticality 379 in grammaticalization under asymmetric priming among words 380 and (a) a positive relationship between 381 and intrinsic growth rate: 382. (b) After a period of increasing grammaticality (and decreasing formal substance), the dynamics lead to stable coexistence of two words that differ with respect to their degree of grammaticality 383 and frequency 384. The more grammatical word is more frequent and more reduced than its more lexical cousin. Both trajectories exhibit sigmoid shapes (385; only every 100th point displayed). (c) Diachronic trajectories of grammaticalized (solid) and lexical (dashed) variants. On the left: attributive (grammaticalized) and verbal (lexical) instances of fucking (search queries: fucking _j* + fucking _nn* (attributive) vs. fucking_v* (verbal)). On the right: auxiliary (grammaticalized) and verbal (lexical) instances of going to (search queries: [going to _v?i*] vs. [going to]-[going to _v?i*]). The data was retrieved from the Corpus of Historical American English.

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