Quantifying the evolutionary dynamics of language

Abstract

Human language is based on grammatical rules. Cultural evolution allows these rules to change over time. Rules compete with each other: as new rules rise to prominence, old ones die away. To quantify the dynamics of language evolution, we studied the regularization of English verbs over the past 1,200 years. Although an elaborate system of productive conjugations existed in English's proto-Germanic ancestor, Modern English uses the dental suffix, '-ed', to signify past tense. Here we describe the emergence of this linguistic rule amidst the evolutionary decay of its exceptions, known to us as irregular verbs. We have generated a data set of verbs whose conjugations have been evolving for more than a millennium, tracking inflectional changes to 177 Old-English irregular verbs. Of these irregular verbs, 145 remained irregular in Middle English and 98 are still irregular today. We study how the rate of regularization depends on the frequency of word usage. The half-life of an irregular verb scales as the square root of its usage frequency: a verb that is 100 times less frequent regularizes 10 times as fast. Our study provides a quantitative analysis of the regularization process by which ancestral forms gradually yield to an emerging linguistic rule.

Figure 1

Irregular verbs regularize at a rate that is inversely proportional to the square root of their usage frequency. a, The evolution of 177 verbs from Old English (green) over time, through Middle (red) and Modern English (blue). The fraction remaining irregular in each bin decreases as the frequency decreases. Frequency shown is that of the modern descendant, and was computed using the CELEX corpus. Error bars indicate standard deviation and were calculated using the bootstrap method. b, The regularization rate of irregular verbs as a function of frequency. The relative regularization rates obtained by comparing Old vs. Modern English (green) and Middle vs. Modern English (red) scale linearly on a log-log plot with a downward slope of nearly one-half. The regularization rate, and the half-life, scale with the square root of the frequency.

Figure 2

Irregular verbs decay exponentially over time. a, Specifying approximate dates of Old and Middle English allows computation of absolute regularization rates. Regularization rates increase as frequencies decrease, but are otherwise constant over time. b, Absolute rates of regularization are shown as a function of frequency. Error bars indicate standard deviation and were calculated using the bootstrap method. The square-root scaling is obtained again.

Figure 3

Extrapolating forward and backward in time using the observation that regularization rate scales as the square root of frequency. The differential system is exactly solvable and the solution fits all three observed distributions. As we move backward in time, the distribution of irregular verbs approaches the Zipfian distribution characteristic of random sets of words. The distribution for exceptions to the -ed rule became non-random because of frequency dependent regularization due to selective pressure from the emerging rule.