During the Ordovician Radiation, domination of benthic marine communities shifted away from trilobites, toward articulated brachiopods, and, to a lesser degree, toward bivalves and gastropods. Here, models are formulated that mathematically represent alternative hypothesized causes of this transition. These include models in which per-genus origination or extinction probabilities were constrained to be (1) constant, (2) diversity-dependent, (3) productivity-dependent, or (4) jointly dependent on productivity and diversity. Using a method adapted from capture-mark-recapture (CMR) population studies, we estimate origination, extinction, and sampling probabilities jointly in order to avoid confounding patterns in turnover probabilities with temporal variation in the quality of the fossil record. Using Akaike's Information Criterion (AIC), we assessed the fit of the alternative causal models relative to one another, and relative to a noncausal “phenomenological” alternative that placed no constraints on the pattern of temporal variation in origination or extinction. There were differences among taxa in the relative fit of these models, suggesting that the effects of productivity and diversity varied among higher taxa. In the aggregate, however, there was strong support for diversity-dependent origination. For extinction, poor fit of the alternative causal models suggests that we lack a good explanation for extinction patterns. These analyses support the hypothesis that diversity-dependent origination, particularly in trilobites, contributed to the Ordovician faunal transitions. By contrast, the effects of increased productivity, if indeed they were large enough to influence global diversification patterns, did not proceed in the hypothesized manner.