Benchmarking the response of grain yield to plant population density across environments and management: A case study for faba bean

Agronomic experiments to establish the relationship between yield and plant population density (PPD) are widespread but remain inconclusive because management and environmental conditions modulate the responses. We analysed and synthesised yield-to-PPD responses in faba bean (Vicia faba L.), with a focus on Australia. We compiled a database of 204 yield-to-PPD responses from 77 Australian experiments and included 33 experiments from other regions for comparison. Our framework comprises two steps: 1) estimate the plant population density required to achieve 95% of the grain yield asymptote (critical PPD) in each yield-to-PPD response, 2) explain variation in critical PPD with environmental and agronomic variables. Median critical PPD was 34 plants m-2, with an interquartile range of 21 to 49 plants m-2. Critical PPD decreased with higher environmental yield, with higher soil pH, and for indeterminate cultivars compared with determinate ones, factors that favour yield, and decreased with hot springs and low in -season rainfall, factors that do not favour yield. Grain yield, seed number, pod number, branch number, and biomass increased to an asymptote with plant population density at the crop -level, and decreased following a power model at the plant -level; seed size, seeds per pod and crop height did not vary with plant population density. Compared to the current standard of 20 plants m-2, the profit-to-PPD response for Australian experiments was more negative at 10 and 15 plants m-2 than positive at 25 and 30 plants m-2. This supports the standard recommendation but highlights the risk of reduced profitability when establishment is compromised. Our framework can be used to tailor faba bean plant population density recommendations to local conditions and can be adapted for other crops.