# Quantifying the evolutionary dynamics of language

Lieberman, E., Michel, J. B., Jackson, J., Tang, T., & Nowak, M. A. 于2007年在《自然》杂志上发表了题为 Quantifying the evolutionary dynamics of language. Nature的论文。1

Human language is based on grammatical rules1–4. Cultural evolution allows these rules to change over time5.

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 tense6.

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.

Irregular verbs regularize at a rate that is inversely proportional to the square root of their usage frequency.

F1b则告诉我们动词时态被规则化使用的比例反比于这个词语的使用频率的平方根（-0.48，-0.51）。

The relative regularization rates obtained by comparing Old versus Modern English (green) and Middle versus 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.

We can estimate actual half-lives of the irregular verbs in different frequency bins. Irregular verbs that occur with a frequency between $10^6$ and $10^5$ have a half-life of about 300 years, whereas those with a frequency between $10^4$ and $10^3$ have a half-life of 2,000 years.

If we fit half-life versus frequency with a straight line in a log–log plot, we obtain a slope of 0.50, which again suggests that the half-life of irregular verbs is proportional to approximately the square root of their frequency (Fig. 2b).

Our study provides a quantitative analysis of the regularization process by which ancestral forms gradually yield to an emerging linguistic rule.

# 参考文献

1. Lieberman, E., Michel, J. B., Jackson, J., Tang, T., & Nowak, M. A. (2007). Quantifying the evolutionary dynamics of language. Nature, 449(7163), 713-6.

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