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Sites description and field operationsA total of six field studies were conducted in two different regions over two seasons. Four studies (two dryland and two irrigated) were in Kansas, United States (dryland: 39°4′30″ N, − 96°44′43″ W, irrigated: 39°4′25″N, − 96°43′12″ W) during the 2019 and 2020 growing seasons (hereafter referred to as USDry19, USIrr19, USDry20, and USIrr20 studies). The remaining two studies (dryland) were in Entre Rios, Argentina (31°50′49″ S; 60°32′16″ W) during the 2018/2019 and 2019/2020 growing seasons (hereafter referred to as Arg19 and Arg20 studies). The soils were Fluventic Hapludolls [silt loam, 40% sand, 13% clay, 47% silt, organic matter (OM) 1.7%, 7.7 pH, 31.1 ppm P (Bray−1)] at the US dryland studies, and Pachic Argiudolls [silty clay loam, 10.1% sand, 30.6% clay and 59.3% silt, OM 3.2%, 6.8 pH, 34.7 ppm P (Bray−1)] at the US irrigated studies. At the Argentinian studies soil was a Vertic Argiudoll in 2019 [silty clay loam to clay loam, 3.9% sand, 27.6% clay, 67.9% silt, OM 2.65%, 7.2 pH, 12.5 ppm P (Bray−1)] and an Acuic Argiudoll in 2020 [silt loam to silty-clay-loam, 5.6% sand, 28.6% clay, 65.8% silt, OM 3.33%].The US dryland and irrigated studies were sown on June 4, 2019, and May 20, 2020. In 2019, the dryland study was replanted on June 29 due to poor emergence after the first sowing. The studies in Argentina were sown on December 5 in 2018 and November 20 in 2019. At all six studies, plots were kept free of weeds, pests, and diseases through recommended chemical control.The genotypes used in the US were P40A47X (MG 4.0) and P39A58X (MG 3.9) (Corteva Agriscience, Johnston, IA, USA) in 2019 and 2020, respectively. Both varieties are tolerant to glyphosate and dicamba herbicides (RR2X) and have low lodging probability. For the northeast region of Kansas, recommended sowing dates range from May 15 to June 15 along with MG 421. In addition, recommended seeding rates are between 270 and 355 thousand seeds ha−1 for low-yielding environments and 190 to 285 thousand seeds ha−1 for medium- and high-yielding environments13. In Argentina, the genotype AW5815IPRO (MG 5.8, Bayer, Leverkusen, Germany) was used both in 2020 and 2021, it is tolerant to glyphosate and sulfonylureas, and has low lodging probability. Recommended sowing dates for Entre Rios considering soybeans as a single crop range from October 20 to December 10, and MG usually range from 4 to 6; lastly, seeding rate recommendations are between 200 and 250 thousand seeds ha−1 in the region22.Study designThe studies carried out in the US were arranged as a split plot design with three replicates in both 2019 and 2020. In 2019, the main plot treatment factor was planter type with two levels [John Deere (Moline, Illinois, US) Max Emerge planter (ME, 12 rows), and John Deere Exact Emerge Planter (EE, 16 rows)], and the split-plot treatment factor was seeding rate with two levels (160 and 321 thousand seeds ha−1). In 2020 the main plot treatment factor was also planter type with two levels (ME and EE), and the split-plot treatment factor was seeding rate with four levels (160, 215, 270 and 321 thousand seeds ha−1). Planting speed was 7 km h−1 in both studies and years, plots were 24 and 32 rows wide when planted with ME and EE, respectively, with 0.76 m row spacing. Plot length was 80 m in the dryland studies and 160 m in the irrigated studies. The studies in Argentina were arranged as a single replicate of each seeding rate (100, 230, 360 and 550 thousand seeds ha−1) in both years. Planting speed was 5.5 km h−1 in both years, and plots were 10 rows wide with 0.52 m row spacing and 350 m in length.All treatment factors in US studies were evaluated with the overall goal of producing substantial variation in the variable of interest, plant-to-plant spatial uniformity, rather than to make an inference of their effect on yield. The Argentinian studies were only used for selection of stand uniformity variables due to the single replicate. Plant spatial uniformity variables were first fitted using the data from US studies (details below), and then the best explanatory metrics were selected to re-fit the relationships combining both data sets from US and Argentina. Finally, sowing dates, maturity groups, and seeding rates evaluated in this study at both locations (Arg and US) were aligned with those recommended for each region.Data collection and spacing uniformity variablesTwo segments of 2 m in length were established early in the season inside each plot. At the V5 (US studies) and R1 (Arg studies) soybean development stage23, the cumulative distance of the plants within each segment was measured and then used to calculate multiple derived variables. Plant spacing (cm) was calculated as the average distance between neighboring plants. In addition, the distance from a plant to each neighboring plant was classified as shorter or longer than the plant spacing (named nearest and farthest neighbor distance, respectively). Achieved versus Target Evenness Index (ATEI, dimensionless) was calculated as the ratio between the observed plant spacing and the theoretical plant spacing (TPS, cm), where TPS is the expected plant spacing derived from a specific seeding rate and row width (Eq. 1).$$ATEI = frac{Spacing;(cm) }{{TPS;(cm)}}$$
(1)
The ATEI index was designed to account for the proximity of the observed plant spacing to the TPS. Values closer to 1 indicate that the plant spacing is close to the TPS and values that are below or above 1 indicate that the plant spacing is lower or higher than the TPS, respectively; thereby departing from an ideal plant spacing. Hence, ATEI values greater than 1 depict both (i) non-uniform plant-to-plant spacing distribution and (ii) plant densities below the target (seeding rate). To further understand the meaning of ATEI, the relative density (rd) was calculated as the ratio between plant density (based on the number of plants in the 2 m segment) and seeding rate.To account for the unevenness of distance from a plant to both neighboring plants within the row, we used the Evenness Index (EI, dimensionless), calculated as the ratio between the distance to the nearest neighbor (cm) and the plant spacing (cm) of a given plant (Eq. 2). The Evenness Index values range from 0 to 1, a value closer to 1 indicates that a plant is equidistantly spaced to both of its neighboring plants within the row, if zero then those plants are occupying the same position (as doubles). It is important to note that EI does not provide information on the spacing (in distance, cm) or how close the spacing is compared to the TPS, but only describes the unevenness distance of a plant to its neighboring plants within a row.$$Evenness ;Index; (EI) = frac{nearest; neighbor ;(cm)}{{Spacing; (cm)}}$$
(2)
In addition, the distance from a plant to its preceding neighboring plant, and the TPS were used to classify the position of each plant into one of eight classes (Fig. 1). Plants were classified in classes ranging from “double” (preceding plant distance  Double-skip) as a function of seeding rate, planter type and their interaction (fixed effects), and block nested in site-year (random effect) (Tables 1 and 2). Independent models for each of the 4 US studies were built assessing the effects of planter type, seeding rate, and their interaction (fixed effects), and seeding rate nested in planter type, and in block (random effects) on the same variables previously mentioned (Supplementary Table 1). The models were run using the lmer function from lme4 package in R (R Core Team, 2021). In addition, the US and Arg studies were combined to evaluate the effect of site-year on yield, plant density, and all stand uniformity variables (Supplementary Fig. 1) using the lm function from package stats. Means separation were performed using Fisher’s LSD (Least Significance Difference) test (alpha = 0.05) with emmeans function from package emmeans.Table 1 Effect of planter type, seeding rate, and their interaction on variables from plant position classification for all US studies. References: percentage of perfectly spaced plants (Perfect), percentage of plants misplaced by 66% (Mis 66), percentage of plants misplaced by 33% (Mis 33), percentage of double plants (Double), percentage of short skips plants (Short-skip), percentage of long skip plants (Long-skip), percentage of double skips plants (Double-skip), and percentage of greater than double skip plants ( > Double-skip).Full size tableTable 2 Effect of planter type, seeding rate, and their interaction on yield and stand uniformity variables for all US studies. References: Spacing between plants standard deviation (Spacing sd), achieved versus targeted evenness index mean and standard deviation (ATEI and ATEI sd, respectively), and evenness index mean and standard deviation (EI and EI sd, respectively).Full size tableCommunity-scale data from the four US studies were combined and fitted to bivariate linear regression models with yield as the response variable and each of the stand spatial uniformity variables as the explanatory variable. Significant models (alpha = 0.05) were further evaluated by calculating the coefficient of determination (R2) and root mean squared error (RMSE) (Fig. 2). Models with the lower RMSE and higher R2 were selected as those that best captured the effect of non-uniform stands on soybean yield. After variables were selected, both US and Arg data sets were combined and the linear regressions between the selected variables and yield were re-fitted to assess the consistency of the relationships when an independent data set was included. Community-scale yield from US and Arg studies was modelled as a function of the selected stand uniformity variable, country (US and Arg), and their interaction (fixed effects) (Fig. 3). The spatial uniformity metric showing the most consistent relationship for both US and Arg studies (i.e., non-significant interaction between stand uniformity metric and country), was selected to continue the analysis. The bivariate linear regression models were run with function lm.Figure 2Relationship between stand uniformity variables and soybean yield for US studies. ATEI mean and sd achieved versus targeted evenness index mean and standard deviation, EI mean and sd evenness index mean and standard deviation, Perfect percentage of perfectly spaced plants, R2 coefficient of determination, RMSE root mean square error. All stand uniformity variables presented a significant slope at alpha = 0.05.Full size imageFigure 3Relationship of spacing standard deviation (Spacing sd, cm) and achieved versus targeted evenness index standard deviation (ATEI sd) to soybean yield. Different colors and line types denote different countries (Argentina, Arg—full line, red points; United States, US—dashed line, blue points). R2 coefficient of determination, RMSE root mean square error.Full size imageDifferent environmental conditions and seeding rate levels may modify the effect of plant spatial uniformity on yield. To explore this, each of the studies from Arg and US were separated into low- (USDry19 and ArgDry20, mean of 2.7 Mg ha−1), medium- (USIrr19, USDry20 and ArgDry19, mean of 3.0 Mg ha−1), and high- (USIrr20, mean of 4.3 Mg ha−1) yield environments based on the effect of site-year on yield (Supplementary Fig. 1). Additionally, the tested seeding rates were separated in low ( 300 thousand seeds ha−1) levels based on the current optimal seeding rate for medium yielding environments (235 thousand seeds ha−1, 4 Mg ha−1)13 and the extreme values proposed by Suhre et al.11 (148 and 445 thousand seeds ha−1). This classification was used to model yield as a function of (i) the selected stand uniformity metric, yield environment, and their interaction, and (ii) the selected stand uniformity metric, seeding rate levels, and their interaction. These models were tested to obtain a robust conclusion on the overall effect of yield environment and seeding rate levels, and their interactions (all treated as fixed effects) with plant-to-plant spatial uniformity relative to the response variable, soybean yield. The Akaike information criteria (AIC) was used to compare the full (with interactions) relative to the reduced models (single effects).Ethics declarationsExperimental research and field studies on plants including the collection of plant material, complied with relevant institutional, national, and international guidelines and legislation. More

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