Frans Matthias Thon , Caroline Müller, Meike J. Wittmann

Plants harbour an astonishing amount of chemodiversity, i.e., diversity of specialized metabolites, at different scales. For instance, individual plants can produce a large number of different specialized metabolites and individuals in a population can differ in their metabolite composition. Given the ecological and economic importance of plant chemodiversity, it is important to understand how it arises and is maintained over evolutionary time. For other types of biodiversity, i.e., species diversity and genetic diversity, quantitative models, that is, mathematical models and computer simulations, have long played an important role in addressing such questions. Here we review models and hypotheses for the evolution of plant chemodiversity and, in particular, explore what quantitative models have been proposed so far and what gaps there are in quantitative modeling of chemodiversity. For each model or hypothesis we review its ingredients, i.e., the biological processes that are assumed to shape chemodiversity, the scales at which the model explains or claims to explain chemodiversity, and the extent to which the model has been formalized as a mathematical or simulation model. From this review, a mixed picture emerges. We identified a small number of quantitative models for the evolutionary dynamics of plant chemodiversity. In addition we found a number of models that use equations to derive an optimal defense, but are not dynamic. Many influential models, however, have remained verbal so far. Furthermore, we identify some quantitative models used for genetic variation that have not been used for chemodiversity so far, but could be easily extended to do so. We end by outlining our vision for future model building for the evolution of plant chemodiversity.