Simulated and experimental species mixtures. BPM (biodiversity effects of partial density monocultures) are calculated from the differences between the partial density monoculture yield of more competitive species and total yield expected from species relative yields and full density monoculture yields (see competitive exclusion in Table S1 and Table S2 for detailed calculations).

Under the competitive hypothesis, more competitive species gain size (biomass or volume) and less competitive species lose size in mixture relative to their full density monocultures. The magnitude of competitive growth responses (i.e., proportional changes in individual size) increases with relative competitive ability (proportional deviations of species competitive ability from community average) from a minimum of 0 (at community average) to a maximum of Wp/Wf – 1 for more competitive species and -1 for less competitive species in competitive exclusion. The changes may not be linear, greater near community average and smaller with deviations of competitive ability (Gaudet & Keddy, 1988) or recourse availability (e.g., light, see Brüllhardt et al. 2020) away from community averages. Wf represents for individual size in full density monocultures and Wp represents for individual size in partial density monocultures.

Partitioning net biodiversity effects (changes in stand volume in mixtures relative to monocultures) with competitive (a and b) and additive (c and d) partitioning models for 20- to 80-year-old mixed trembling aspen and white spruce with varying species compositions from nearly pure aspen (90% aspen) to nearly pure spruce (90% spruce) on average medium productivity sites in western Canada. The growth and yield data (Table 1) are generated with GYPSY (Huang et al., 2009) and calculations of biodiversity components with this figure are detailed in Table S1.

Partitioning net biodiversity effects (changes in aboveground biomass, g) with competitive and additive partitioning models using experimental data (Table 1) from a grassland diversity–productivity study (Mahaut et al., 2020). Calculations are detailed in Table S2.