This is not a competition: modeling interactions between word senses in a diachronic polysemy dataset using replicator dynamics

This is the preprint of our paper: Olbrich, M., & Baumann, A. (in review). This is not a competition: Modeling interactions between word senses in a diachronic polysemy dataset using replicator dynamics. 

Abstract: The relative frequencies of a word's senses change over time as a reflex of interactions between them. Although lexical semantic change has been extensively studied from both theoretical and, more recently, computational perspectives, the nature of interactions between individual word senses and how they evolve has not yet been systematically investigated.
Here, we model this evolutionary interplay within the framework of Evolutionary Game Theory using replicator dynamics, a system of ordinary differential equations modeling scenarios such as competition, predation, and cooperation, governed by a matrix of interaction coefficients. To estimate these coefficients from empirical data, we employ methodology based on nonlinear least-squares optimization for fitting the evolutionary model to observed trajectories of word-sense frequencies. 
Our experiments show that cooperation is the most common interaction type for words with two senses, whereas predation dominates among words with three senses. Surprisingly, direct competition is not the prevailing interaction type, despite being one of the most frequently discussed mechanisms in theories of lexical semantic change.