The rapid development of mechanistic, trait-based models has resulted in increasingly reliable predictions of the functional diversity of individuals in populations and communities. However, a focus on individuals’ traits differs from the prevailing focus on species in much of community ecology. We sought to identify correlative links between species richness and size diversity, focusing on size diversity as one component of functional diversity. These links could be used to extend individual, size-based models to predict patterns of species richness. We used the distribution of the sizes of individuals in a community – the individual–size distribution (ISD) – as a measure of size diversity, and constructed Bayesian regression models with species richness as the response variable and ISDs as the predictor variables. We used two methods to include ISDs in our analyses. First, we summarized the ISD with five common diversity indices and used these indices as predictor variables in our analyses. Second, we used functional data analysis to include the entire ISD (a continuous function) as a predictor variable in our analyses. Analyses of diversity indices identified consistent, positive associations between species richness and size diversity. Analyses of entire ISDs revealed that these associations were driven by numbers of small- and medium-sized individuals. In general, a combination of diversity indices predicted species richness as well as or better than continuous ISDs. However, models with ISDs as predictor variables were less sensitive to technical details of model fitting (e.g. discretization method) than those based on diversity indices, and the use of ISDs avoids the arbitrary selection of one or several diversity indices. Our use of functional data analysis allows any trait distribution to be included as a variable in statistical analyses, and has the potential to reveal new diversity patterns in ecology.