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Automatic feeder productivityTable 1 and Figs. 4, 5 and 6 show the automatic feeder productivity as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the automatic feeder productivity increases with increasing feed pellets size, air flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the automatic feeder productivity significantly increased from 11.16 to 13.87 (by 19.54%) kg min−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the automatic feeder productivity significantly increased from 11.02 to 14.03 (by 21.45%) kg min−1, while the automatic feeder productivity significantly increased from 3.33 to 21.46 (by 84.48%) kg min−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 1 Automatic feeder productivity at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 4Automatic feeder productivity at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 5Automatic feeder productivity at different feed pellet sizes and air flow rates.Full size imageFigure 6Automatic feeder productivity at different rotational speeds of screw and flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to increase the automatic feeder productivity from 3.04 to 3.79, 6.23 to 8.92, 11.86 to 14.10, 15.27 to 18.94 and 19.42 to 23.62 kg min−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the automatic feeder productivity increased from 3.04 to 19.42, 3.16 to 21.36 and 3.79 to 23.62 kg min−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 4.From statistical analysis, there were no significant different between feed pellets sizes 1 and 2 on the automatic feeder productivity, meanwhile, there were significant differences between feed pellets size 3 and sizes 1 and 2 on the productivity. Regarding the effect of air flow rate, there were significant differences between air flow rates on the automatic feeder productivity, the same trend was happened with the effect of rotational speed of screw on productivity. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 1.Regarding the effect of feed pellet size and air flow rate on the automatic feeder productivity, the results indicate that the automatic feeder productivity increases with increasing the feed pellets size and flow rate. It increased from 9.53 to 12.37, 11.23 to 13.82 and 12.73 to 15.43 kg min−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the automatic feeder productivity increased from 9.53 to 12.73, 11.16 to 13.92 and 12.37 to 15.43 kg min−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 5.The results also indicate that the automatic feeder productivity increased from 2.26 to 4.54, 6.39 to 8.90, 11.76 to 14.56, 15.25 to 18.68 and 19.44 to 23.45 kg min−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the automatic feeder productivity increased from 2.26 to 19.44, 3.19 to 21.50 and 4.54 to 23.45 kg min−1 at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 6.Multiple regression analysis was carried out to obtain a relationship between the automatic feeder productivity as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ Pr_{actual} = – 8.457 + 1.354PS + 0.301FR + 0.025RS{text{ R}}^{{2}} = 0.98{ ,} $$
(13)
where PS is the feed pellets size, mm; FR is the air flow rate, m3 min−1; RS is the rotational speed of screw, rpm.This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Automatic feeder efficiencyTable 2, Figs. 7, 8 and 9 show the automatic feeder efficiency as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that, when the feed pellets size increased from 1 to 3 mm, the automatic feeder efficiency significantly increased from 65.30 to 82.14 (by 20.50%) %. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the automatic feeder efficiency significantly increased from 62.58 to 85.07 (by 26.44%) %, while the automatic feeder efficiency significantly increased from 61.58 to 78.69 (by 21.74%) % when the rotational speed of screw increased from 180 to 900 rpm.Table 2 Automatic feeder efficiency at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 7Automatic feeder efficiency at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 8Automatic feeder efficiency at different feed pellet sizes and air flow rates.Full size imageFigure 9Automatic feeder efficiency at different rotational speeds of screw and air flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to increase the automatic feeder efficiency from 55.79 to 69.41, 57.10 to 81.78, 72.48 to 86.13, 69.96 to 86.81 and 71.19 to 86.58% at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the automatic feeder efficiency increased from 55.79 to 71.19, 57.98 to 78.29 and 69.41 to 86.58% at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 7.The statistical analysis showed that the differences between the obtained data of automatic feeder efficiency due to the effect of feed pellets size (A) and air flow rate (B) were significant. Regarding the effect of rotational speed of screw, there were significant differences between rotational speeds of screw 1, 2 and 3, meanwhile, there were no significant differences between rotational speeds of screw 3, 4 and 5. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 2.Regarding the effect of feed pellet size and air flow rate on the automatic feeder productivity, the results indicate that the automatic feeder efficiency increases with increasing the feed pellets size and flow rate. It increased from 53.91 to 70.69, 65.23 to 81.19 and 76.78 to 94.54% for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the automatic feeder efficiency increased from 53.91 to 76.78, 63.14 to 83.89 and 70.69 to 94.54% at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 8.The results also indicate that the automatic feeder efficiency increased from 41.37 to 83.28, 58.53 to 81.54, 71.85 to 84.96, 69.88 to 85.59 and 71.27 to 85.98% at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the automatic feeder efficiency increased from 41.37 to 71.27, 58.53 to 80.82 and 83.28 to 85.98% at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 9.Increasing the parameters seams to increase the productivity but regarding the efficiency, results show that the efficiency increases with increasing this parameter at (540 rpm) started to be constant and 720–900 rpm decreased in all treatments under study (Figs. 7, 9). It is concluded that efficiency with the parameters increased, became constant and decreased.Multiple regression analysis was carried out to obtain a relationship between the automatic feeder efficiency as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ eta = 9.566 + 8.417PS + 2.249FR + 0.025RS{text{ R}}^{{2}} = 0.89{ ,} $$
(14)
where this equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Specific energy consumptionTable 3, Figs. 10, 11 and 12 show the specific energy consumption of automatic feeder as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the specific energy consumption of automatic feeder decreases with increasing feed pellets size, air flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the specific energy consumption of automatic feeder significantly decreased from 8.93 to 6.74 (by 24.52%) W h kg−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the specific energy consumption of automatic feeder significantly decreased from 10.83 to 5.42 (by 49.95%) W h kg−1, while the specific energy consumption significantly decreased from 9.08 to 6.55 (by 27.86%) W h kg−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 3 Specific energy consumption at different feed pellets sizes, air flow rates and rotational speeds of screw.Full size tableFigure 10Specific energy consumption at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 11Specific energy consumption at different feed pellet sizes and air flow rates.Full size imageFigure 12Specific energy consumption at different rotational speeds of screw and air flow rates.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to decrease the specific energy consumption from 9.87 to 7.94, 9.18 to 7.63, 9.14 to 7.30, 8.65 to 6.63 and 7.79 to 4.20 W h kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the specific energy consumption decreased from 9.87 to 7.79, 9.42 to 7.65 and 7.94 to 4.20 W h kg−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 10.From statistical analysis, there were no significant differences between feed pellets sizes 1 and 2 on the specific energy consumption, meanwhile, there were significant differences between feed pellets size 3 and 1 and 2 on the specific energy consumption. Regarding the effect of air flow rate, there were significant differences between air flow rates and specific energy consumption. Regarding the effect of rotational speed of screw, there were significant differences between rotational speeds of screw 1, 2, 4 and 5 on the specific energy consumption, meanwhile, there were no significant differences between rotational speeds of screw 2 and 3 on the specific energy consumption. The analysis showed also that the interaction between both ABC was non-significant. On the other hand, the interaction between the effect of both AB, AC and BC on the data was significant as shown in Table 3.Regarding the effect of feed pellet size and air flow rate on the specific energy consumption, the results indicate that the specific energy consumption decreases with increasing the feed pellets size and flow rate. It decreased from 12.05 to 9.07, 8.81 to 6.56 and 5.92 to 4.59 W h kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the specific energy consumption decreased 12.05 to 5.92, 11.37 to 5.75 and 9.07 to 4.59 W h kg−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 11.The results also indicate that the specific energy consumption decreased from 12.31 to 6.18, 11.43 to 5.63, 11.21 to 5.63, 10.38 to 5.21 and 8.81 to 4.46 W h kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the specific energy consumption decreased from 12.31 to 8.81, 8.75 to 6.37 and 6.18 to 4.46 W h kg−1 at 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown Fig. 12.
Multiple regression analysis was carried out to obtain a relationship between the specific energy consumption of automatic feeder as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:-$$ SEC = 20.045 – 1.095PS – 0.541FR – 0.003RS{text{ R}}^{{2}} = 0.92 , {.} $$
(15)
This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw.Total costs of automatic feederTable 4, Figs. 13, 14 and 15 show the total cost of automatic feeder as affected by the different feed pellets sizes (1, 2 and 3 mm), air flow rates (10, 15 and 20 m3 min−1) and rotational speeds of screw (180, 360, 540, 720 and 900 rpm). The results indicate that the total cost of automatic feeder decreases with increasing feed pellets size, flow rate and rotational speed of screw. It indicates that when the feed pellets size increased from 1 to 3 mm, the total cost of automatic feeder significantly decreased from 0.15 to 0.11 (by 26.27%) EGP kg−1. It also indicates that when the air flow rate increased from 10 to 20 m3 min−1, the total cost of automatic feeder significantly decreased from 0.16 to 0.09 (by 43.75%) EGP kg−1, while the total cost of automatic feeder significantly decreased from 0.16 to 0.10 (by 37.50%) EGP kg−1 when the rotational speed of screw increased from 180 to 900 rpm.Table 4 Total cost of automatic feeder at different feed pellets sizes, air flow rate and rotational speeds of screw.Full size tableFigure 13Total cost of automatic feeder at different feed pellet sizes and rotational speeds of screw.Full size imageFigure 14Total cost of automatic feeder at different feed pellet sizes and air flow rates.Full size imageFigure 15Total cost of automatic feeder at different rotational speeds of screw and air flow rate.Full size imageIt could be noticed that increasing the feed pellets size from 1 to 3 mm, tends to decrease the total cost of automatic feeder from 0.18 to 0.14, 0.16 to 0.12, 0.15 to 0.11, 0.13 to 0.09 and 0.12 to 0.08 EGP kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively. The results also indicate that the total cost of automatic feeder decreased from 0.18 to 0.12, 0.17 to 0.10 and 0.14 to 0.08 EGP kg−1 at 1, 2 and 3 mm feed pellets sizes, respectively when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 13.From statistical analysis, there were no significant differences between feed pellets sizes 1 and 2 on the total cost of automatic feeder, meanwhile, there were significant differences between feed pellets size 3 and 1 and 2 on the total cost of automatic feeder. Regarding the effect of air flow rate, there were significant differences between air flow rates and specific energy consumption. Regarding the effect of rotational speed of screw, there were no significant differences between rotational speeds of screw 1 and 2, also 3 and 4 on the total cost of automatic feeder, meanwhile, there were significant differences between rotational speeds of screw 2 and 3 on the total cost of automatic feeder.Regarding the effect of feed pellet size and flow rate on the total cost of automatic feeder, the results indicate that the total cost of automatic feeder decreases with increasing the feed pellets size and air flow rate. It decreased from 0.18 to 0.13, 0.16 to 0.11 and 0.10 to 0.08 EGP kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the feed pellets size increased from 1 to 3 mm. The results also indicate that the total cost of automatic feeder decreased from 0.18 to 0.10, 0.16 to 0.10 and 0.13 to 0.08 EGP kg−1 at 1, 2 and 3 mm feed pellets size, respectively, when the air flow rate increased from 10 to 20 m3 min−1 as shown in Fig. 14.The results also indicate that the total cost of automatic feeder decreased from 0.22 to 0.11, 0.18 to 0.10, 0.16 to 0.10, 0.13 to 0.09 and 0.12 to 0.07 EGP kg−1 at 180, 360, 540, 720 and 900 rpm rotational speed of screw, respectively, when the air flow rate increased from 10 to 20 m3 min−1. The results also indicate that the total cost of automatic feeder decreased from 0.22 to 0.12, 0.16 to 0.11 and 0.11 to 0.07 EGP kg−1 for 10, 15 and 20 m3 min−1 air flow rate, respectively, when the rotational speed of screw increased from 180 to 900 rpm as shown in Fig. 15.
Multiple regression analysis was carried out to obtain a relationship between the total costs of automatic feeder as dependent variable and different of feed pellets size, air flow rate and rotational speed of screw as independent variables. The best fit for this relationship is presented in the following equation:$$ TC = 0.315 – 0.020PS – 0.006FR – 8.8 times 10^{ – 5} RS{text{ R}}^{{2}} = 0.87{,} $$
(16)
where: TC is the total cost of automatic feeder, EGP kg−1.This equation could be applied in the range of 1 to 3 mm feed pellets size, 10 to 20 m3 min−1 air flow rate and from 180 to 900 rpm of rotational speed of screw. More

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The surveyed, rainfed commercial soybean fields were spread across the U.S. north-central region (Supplementary Fig. S1 online) with a latitudinal gradient evident for maturity group (MG). The number of fields (n) was distributed evenly across the three years (2014: n = 812, 2015: n = 960, 2016: n = 966). Among the 2738 fields, 833 (or 30.4%) were sprayed with foliar fungicides. Out of the 833 fields sprayed with foliar fungicides, 623 (74.8%) had also been sprayed with foliar insecticides.A t-test estimate of the yield difference between all fields sprayed with foliar fungicides and those which were not was 0.46 t/ha (95% confidence interval [CI] of 0.39 to 0.52 t/ha). When t-tests were applied to fields within TEDs (the 12 TEDs with the most fields), half of the 95% CIs included zero, indicative of possibly no yield increase due to foliar fungicides over unsprayed fields in those TEDs (Supplementary Fig. S2 online). A linear mixed model with random slopes and intercepts for the fungicide effect within TEDs returned an estimated yield gain of 0.33 t/ha due to foliar fungicide use. A simpler model without random slopes for foliar fungicide was a worse fit to the data. Together these basic tests were indicative of heterogenous effects concerning foliar fungicides and yield gain, implying other global (regional) and local (field specific) conditions may be involved as factors.A tuned random forest (RF) model fitted to the entire dataset (all 2738 observations) overpredicted soybean yield at low actual yields, and underpredicted at the high-yield end (Supplementary Fig. S3 online). However, as 99% of the residual values were less than or equal to |0.25 t/ha| which corresponded to less than 7% of the average yield, we proceeded with the interpretation of the fit RF model. The mean predicted soybean yield (global average) was 3.79 t/ha (minimum = 1.13 t/ha, maximum = 6.02 t/ha, standard deviation = 0.81 t/ha, root mean squared error between the observed and predicted yields = 0.1 t/ha).At the global model level, location (latitude; a surrogate for other unmeasured variables) and sowing date (day of year from Jan 01) were the two variables most associated with yield (Fig. 1), consistent with the central importance of early planting to soybean yield5,13. Soil-related properties (pH and organic matter content of the topsoil) were also associated with yield (Fig. 1). Management-related variables such as foliar fungicide, insecticide and herbicide applications were of intermediate importance, and other management variables (row spacing, seed treatments, starter fertilizer) were on the lower end of the importance spectrum in predicting soybean yield (Fig. 1). Insecticide and fungicide seed treatments were poorly associated with soybean yield increases as has been previously shown8,40. The relatively lower importance of row spacing is consistent with previous analyses of this variable from soybean grower data6. The dataset we analyzed did not contain enough observations to include artificial drainage as a variable, which has been shown to influence soybean yield, presumably by allowing earlier sowing14.Figure 1Importance of management-based variables in a random forest model predicting soybean yield. Feature importance was measured as the ratio of model error, after permuting the values of a feature, to the original model error. A predictor was unimportant if the ratio was 1. Points are the medians of the ratio over all the permutations (repeated 20 times). The bars represent the range between the 5% and 95% quantiles. Sowing date was the number of days from Jan 01. Growing degree days and the aridity index were annualized categorical constructs used within the definition of technology extrapolation domains (TEDs). Foliar fungicide or insecticide use, seed treatment use, starter fertilizer use, lime and manure applications were all binary variables for the use (or not) of the practice. Iron deficiency was likewise binary (symptoms were observed or not). Topsoil texture, plant available water holding capacity in the rooting zone, row spacing, and herbicide program were categorical variables with five, seven, five, and four levels, respectively.Full size imageThe strongest pairwise interactions included that between sowing date and latitude. Delayed sowing at higher latitudes decreased yield by about 1 t/ha relative to the highest yielding fields sown early in the more southerly locations (Supplementary Fig. S4 online). Further examination of the interactions showed that the yield difference between sprayed and unsprayed fields increased with later sowing, indicative of a greater fungicide benefit in later-planted fields (Fig. 2). This would seem to conflict with the results of a recent meta-analysis in which soybean yields responded better when foliar fungicides were applied to early-planted fields27, but in that study there was also the confounding effect of higher-than-average rainfall between sowing and the R3 growth stage. With respect to latitude, the global difference in yield between sprayed and unsprayed fields decreased as one moved further north (Fig. 2), suggesting that foliar fungicides were of more benefit when applied to the more southerly located fields, which do tend to experience more or prolonged conditions conducive to foliar diseases than the northern fields22,24.Figure 2Two-way partial dependence plots of the global effects of (i) foliar fungicide use and sowing date (left panel), and (ii) foliar fungicide use and latitude (right panel) on soybean yield. The black plotted curves are the yield differences between fields that were sprayed or not sprayed with foliar fungicides. Smoothed versions of the curves are shown in blue.Full size imageFocusing on model interpretation at the local level, we examined the Shapley φ values (see the “Methods” section for more information) associated with foliar fungicide applications for different subsets (s) and cohorts (c) of fields within the data (see Supplementary Table S1 online). The 1st subset (s1) was comprised of the 20 highest-yielding fields among those sprayed with foliar fungicides (s1c1) and the 20 highest-yielding fields among those which were not sprayed (s1c2) in each of the 12 technology extrapolation domains (TEDs) in the data matrix with adequate numbers of fields for comparisons (see also Supplementary Table S2 online; Supplementary Fig. S5 online maps the field locations within these 12 TEDs). A TED is a region (not necessarily spatially contiguous) with similar biophysical properties41. Predicted yields within these cohorts were mainly above the global average of 3.79 t/ha, except in TED 602303 (Fig. 3), which corresponded to fields in North Dakota (Supplementary Fig. S5). In most cases Shapley φ values for foliar fungicide use exhibited a positive contribution to the yield above the global average. If these cohorts of fields represented high-yielding environments within each TED, then foliar fungicide sprays contributed positively up to 0.3 t/ha in the yield increase above the global average in s1c1. However, among high-yielding fields in s1c2, the penalty for not spraying was less than 0.1 t/ha. This finding supports the contention that fungicide sprays are most worthwhile in high-yielding environments. Supplementary Fig. S6 online complements Fig. 3 by summarizing the Shapley φ values in another visual format. The overall mean predicted yield for the unsprayed (s1c2) fields was slightly higher (by 0.1 t/ha) than that for the sprayed (s1c1) fields (Supplementary Fig. S6 online). This difference may have been driven by the higher variability in yields among the two cohorts (particularly for TEDs 403603, 602303, 403703, and 303603), or underlying differences in other management factors. Also, the number of sprayed fields in each of these four TEDs was at the target sampling boundary of 20 fields per TED (Supplementary Table S2 online).Figure 3Shapley phi values attributed to foliar fungicide use for two cohorts of fields within the 12 technology extrapolation domains (TEDs) with the most fields. Within each TED, the cohorts are the 20 highest-yielding fields among those sprayed with foliar fungicides and the 20 highest-yielding fields among those which were unsprayed.Full size imageThe Shapley φ values for fungicide use were well-separated among the four cohorts of fields of s2 (Fig. 4, Supplementary Table S1 online). The fields within s2 were selected across the entire dataset and not by TED membership. The lowest-yielding fields (s2c2 & s2c4) were all below the global yield average, whereas the converse was true of the highest-yielding fields (s2c1 & s2c3). Among the lowest-yielding fields, foliar fungicides were mainly associated with a positive, but less than 0.2 t/ha, effect on yield (s2c2), and other factors were responsible for dropping a field’s yield to below the global average. Amongst the highest-yielding fields (s2c1), foliar fungicides were associated with between 0.15 and 0.35 t/ha of the yield above the global average. These Shapley φ values for the contribution of foliar fungicides are consistent with estimates of the yield response to foliar fungicides from a meta-analytic perspective27. Given that the individual yields in s2c1 & s2c3 were 1 to 2 t/ha above the global average, other location-driven factors such as early sowing (Fig. 1) were the larger drivers of yield in these cases. However, there was only a negligible or small ( More

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