Word formation is aware of morpheme family size

Words are built from smaller meaning bearing parts, called morphemes. As one word can contain multiple morphemes, one morpheme can be present in different words. The number of distinct words a morpheme can be found in is its family size. Here we used Birth-Death-Innovation Models (BDIMs) to analyze the distribution of morpheme family sizes in English and German vocabulary over the last 200 years. Rather than just fitting to a probability distribution, these mechanistic models allow for the direct interpretation of identified parameters. Despite the complexity of language change, we indeed found that a specific variant of this pure stochastic model, the second order linear balanced BDIM, significantly fitted the observed distributions. In this model, birth and death rates are increased for smaller morpheme families. This finding indicates an influence of morpheme family sizes on vocabulary changes. This could be an effect of word formation, perception or both. On a more general level, we give an example on how mechanistic models can enable the identification of statistical trends in language change usually hidden by cultural influences.