It has recently been proposed (Doebeli & Ispolatov 2010, Science 382:494-497) that, on theoretical grounds, one should expect a positive correlation between organismal complexity and diversity. This conclusion is based on the finding that in a Lotka-Volterra competition model, so-called evolutionary branching points are more likely to exist the more quantitative traits determine the carrying capacity function and the competition coefficient of an evolving species. We present two results elaborating on this finding. First, the prediction can also be derived in a model independent manner based on properties of the fitness landscape in a multidimensional trait space. Second, in order to get a more mechanistic understanding of this finding we analyze an explicit Lotka-Volterra consumer-resource model in which consumers and resources are both characterized by several quantitative traits and in which the fitness landscape emerges from the interaction between these traits. This analysis supports the results by Doebeli and Ispolatov and our generalization with the addition that not only increasing consumer complexity but also increasing resource complexity facilitates evolutionary branching.