Plant density and size, which represent plant survival and growth respectively, are key determinants of yield but have rarely been analysed explicitly in the context of biodiversity–productivity relationships. Here, we derive equations to partition the net, complementarity, and selection effects of biodiversity into additive components representing diversity-induced changes in plant density and size. Applying this new method to empirical datasets revealed contrasting ways in which density and size regulate yield in species mixtures. In an annual plant diversity experiment, overyielding was largely explained by selection effects associated with the increased size of highly productive species. The pattern of constant final yield, which has been well documented in plant population ecology, was also observed in species mixtures. In a tree diversity experiment, the driver of overyielding shifted from enhanced tree growth to reduced mortality resulting from complementary use of canopy space during stand development. Both monoculture and mixture stands followed the -3/2 self-thinning law. These results highlight the capability of our new method to resolve crucial, yet understudied, demographic links between biodiversity and productivity.