The critical role that biodiversity plays in ecosystem functioning has motivated many studies of the mechanisms that sustain biodiversity, a notable example being cyclic competition. We extend existing models of communities with cyclic competition by incorporating variable community evenness and resource dependence in demographic processes, two features that have generally been neglected. In this way, we align previous approaches more closely with real-world microbial ecosystems. We demonstrate the existence of a trade-off between increasing biomass production and maintaining biodiversity. This supports experimental observations of a net negative biodiversity effect on biomass productivity, due to competition effects suffered by highly productive species in diverse communities. Our results also support the important role assigned by microbial ecologists to evenness in maintaining ecosystem stability, thus far largely overlooked in in silico approaches.