A distributional approach to assessing conditional yield risk in pure-line and hybrid winter barley

Increasing climate variability elevates the probability of extreme low yields, highlighting the need for analytical approaches that characterize distributional risk beyond mean‑based metrics. We introduce a distribution‑focused framework using empirical cumulative distribution functions (CDFs) to evaluate conditional technological yield risk across genotype × management × environment (G×M×E) combinations. Conditional technological yield risk is defined here as the probability of obtaining yields below a specified threshold within a given G×M×E combination. A five‑factor factorial field experiment (cultivar, sowing density, nitrogen rate, growth regulation, disease control) was conducted over three contrasting seasons—wet, dry, and near‑normal. For each season–cultivar combination, empirical CDFs were constructed and cultivars were compared using first‑order stochastic dominance and two‑sample Kolmogorov–Smirnov tests. Across seasons, the hybrid cultivar exhibited quasi–first‑order stochastic dominance over the pure‑line cultivar: the probability of yields ≤ the overall annual mean (9.62 Mg·ha⁻¹) was 0.40 for the hybrid versus 0.62 for the pure‑line ( P = 0.0002). Differences were most pronounced in the lower tail, indicating a substantially reduced risk of extreme low yields for the hybrid under both drought and excess‑rain conditions. Optimized management combinations further reduced conditional risk to 0.09 (pure‑line) and 0.24 (hybrid). The CDF‑based approach captures risk characteristics that variance‑based metrics cannot and provides a practical tool for cultivar evaluation and technology design aimed at minimizing exposure to low yields.