# Meta-analysis of the relationship between crop yield and soybean rust severity

#### Abstract

Meta-analytic models were used to summarize and assess the heterogeneity in the relationship between soybean yield (Y, kg/ha) and rust severity (S, %) data from uniform fungicide trials (study, k) conducted over nine growing seasons in Brazil. For each selected study, correlation (k = 231) and regression (k = 210) analysis for the Y-S relationship were conducted and three effect-sizes were obtained from these analysis: Fisher's transformation of the Pearson's correlation coefficient (Zr) and the intercept (β0) and slope (β1) coefficients. These effect-sizes were summarized through random-effect and mixed-effect models, with the latter incorporating study-specific categorical moderators such as disease onset time (DOT) (70%, moderate = >40 and ≤70%, and low = ≤40% S the check treatment), and growing season. The overall mean for r¯ (back-transformed Z¯r) was -0.61, based on the random-effects model. DOT and DP explained 14 and 25%, respectively, of the variability in Z¯r. Stronger associations (r¯ = -0.87 and -0.90) were estimated by mixed-effects models for the Zr data from studies with highest DP (DP > 70%) and earliest rust onset (DOT < R1), respectively. Overall means (based on a random-effect model) for the regression coefficients β¯0 and β¯1 were 2,977 and 18 kg/ha/%-1, respectively. In other words, S as low as 3% would reduce 60 kg/ha for an expected Y of 3,000 kg/ha. In relative terms, each unitary percent increase in S would lead to a 0.6 percentage point (pp) reduction in Y. The three categorical moderator variables explained some (5 to 10%) of the heterogeneity in β¯1 but not in β¯0. The estimated relative reduction in Y was 0.41 to 0.79 pp/%-1 across seasons. Highest relative yield reductions (>0.73 pp/%-1) were estimated for studies with DOT < R1 and DP > 70%; the latter possibly due to high fungicide efficacy when DP is low, thus leading to higher yield differences between fungicide-protected and nontreated plots. The critical-point meta-analytic models can provide general estimates of yield loss based on a composite measure of disease severity. They can also be useful for crop loss assessments and economic analysis under scenarios of varying DOT and weather favorableness for epidemic development.

*This paper has been withdrawn.*