The relationship between biodiversity and ecosystem functioning is central to ecology. The quest to elucidate this relationship has motivated some of the largest experiments in ecology, and touches all corners of the field, from fundamental theory to conservation applications. In this area, the connection between phylogenetic/functional diversity and productivity has special relevance. A large body of ecological theory suggests that in competitive communities, functional similarity should be predictive of productivity. Where functional diversity is high, niche overlap, and consequently strength of competition, is expected to be lower, leading to more productive communities. Assuming some degree of niche conservatism, phylogeny should be similarly predictive. However, there is an active debate in the literature regarding the connection between phylogenetic/functional diversity and productivity. Efforts to resolve it have been stymied by the need to develop statistical models that are sufficiently powerful and tractable to discern the effects of phylogeny in noisy data, and by the difficulty of translating between molecular phylogenies and traits that are relevant for species interactions. Here, we overcome both of these issues by introducing a new statistical framework for analyzing biodiversity-ecosystem functioning data. Our framework is explicitly derived from models of population dynamics, and allows us to naturally include effects of phylogenetic relatedness. Additionally, we develop a computional approach to fitting these models that is informed by the phylogenetic topology, but is agnostic about the mapping between phylogeny and competitive traits.