The impact of biodiversity on the stability of ecological communities has been debated among biologists for more than a century. Recently summarized empirical evidence suggests that biodiversity tends to enhance the temporal stability of community-level properties such as biomass; however, the underlying mechanisms driving this relationship remain poorly understood. Here, we report the results of a microcosm study in which we used simplified systems of freshwater microalgae to explore how the phylogenetic relatedness of species influences the temporal stability of community biomass by altering the nature of their competitive interactions. We show that combinations of two species that are more evolutionarily divergent tend to have lower temporal stability of biomass. In part, this is due to negative ‘selection effects' in which bicultures composed of distantly related species are more likely to contain strong competitors that achieve low biomass. In addition, bicultures of distantly related species had on averageweaker competitive interactions, which reduced compensatory dynamics and decreased the stability of community biomass. Our results demonstrate that evolutionary history plays a key role in controlling the mechanisms, which give rise to diversity–stability relationships. As such, patterns of shared ancestry may help us predict the ecosystem-level consequences of biodiversity loss.