We tested four maize hybrids (H1–H4) with relative maturity between 118 and 125. Genotypes are the result of a single cross between a common female of one heterotic pool and four males with different backgrounds of a second heterotic pool of KWS Group breeding program. Genotype H1 is commercially known as KM3800 (relative maturity 118), H2 is KM4200 (relative maturity 122), H3 is KM4321 (relative maturity 123), and H4 is KM4500 (relative maturity 125).

Field experiments were conducted in the year 2014 in Zavalla, Santa Fe, Argentina (33° 2′ 24.75″ S, 60° 53′ 11.76″ W). Plots were eight rows with 6 m long and 0.52 m row spacing. Plots were kept free of weeds, insects, and diseases. Weeds were controlled using standard agronomic practices and manually removed whenever necessary. Soil was Vertic Argiudoll, Roldan series. One shading experiment was conducted at Campo Experimental Villarino, Facultad de Ciencias Agrarias, Universidad Nacional de Rosario (named Env 1). Sowing date was September 27 and was conducted under no till and rainfed conditions. All plots were oversown and hand-thinned at V2 (Ritchie and Hanway, 1982) to 8 plants m^–2. A second shading experiment was conducted at KWS Experimental Station (named Env 2). Sowing date was December 20 and was managed under tillage and rainfed conditions. Plots were hand-planted at three seeds per hill and hand-thinned to one plant per hill at V2 (Ritchie and Hanway, 1982), resulting in a final stand density of 5.5 plants m^–2.

In both experiments, all the hybrids were shaded during periods of 7 days with 80% reduction of incident photosynthetic active radiation. Five shading treatments were centered around the flowering period. Shading treatments went from 14 to 7 days previous to anthesis (named S−7), from 7 days preanthesis to anthesis (named S0), from anthesis to 7 days after anthesis (named S + 7), and from 7 days after anthesis to 14 after anthesis (named S + 14). A control treatment without shading (named T0) was also evaluated, and in Env 1 an additional treatment starting 21 days before anthesis and ending 14 days before anthesis was also tested (named S−14). The experimental design of both shading experiments was a randomized complete block with three replicates. Shading cloth blocked 80% natural light intensity and was suspended above canopy.

Three additional field experiments testing hybrid response to stand density were conducted at KWS Experimental Station. The three experiments were sown on September 23, October 20, and November 20, 2014, and named Env 3, Env 4, and Env 5, respectively. They included the same four hybrids used in Env 1 and Env 2. Experiments were managed under tillage and rainfed conditions. Plots were four rows with 6 m long and 0.52 m row spacing. Hybrids H1–H4 were tested at four stand densities (5, 7, 9, and 11 plants m^–2). Plots were oversown and hand-thinned to the desired stand density at V2 (Ritchie and Hanway, 1982). Experiments were fertilized with 40 kg N ha^–1 before sowing plus an additional 120 kg N ha^–1 at V6. Plots were kept free of weeds, insects, and diseases. Each stand density experiment had a randomized complete block design of hybrids and stand densities with three replicates.

In both shading experiments, yield was calculated from harvesting all ears of two central rows per plot at harvest maturity. Individual kernel weight (KW) was determined after weighting 400 kernels per plot, and KNP was calculated using yield and stand density. Yield and individual KW are reported with 145 g kg^–1 moisture. Relative yield (RY) was calculated as the ratio between the yield of any shade treatment and the control plot from the same genotype and block.

In the shading experiment of Campo Experimental Villarino, 15 consecutive plants per plot were tagged at V8 in center rows. These plants were used for describing plant growth and kernel number differences across treatments.

At the pre- and postflowering stages, non-destructive allometric models were used to estimate shoot biomass and partitioning at the individual plant level (Vega et al., 2000; Echarte et al., 2004; Gambín et al., 2008). The preflowering model was based on the linear regression between shoot biomass and stem volume (Vega et al., 2001; Gambín et al., 2008). Stem volume was calculated from plant height (ground level up to the uppermost leaf collar) and stem diameter at the base of the stalk. The preflowering biomass sample was done 15 days before 50% anthesis, and the postflowering one was done 15 days after anthesis. In each plot, two plants from border rows were used to develop the allometric preflowering and postflowering models (Vega et al., 2001). All plant samples were determined after cutting plants and drying them in a forced-air oven at 65°C for at least 7 days. The r² values for the preflowering model ranged from 0.79 to 0.91 (p < 0.01; n = 27) across hybrids.

The postflowering biomass sample was done using a multiple linear regression model with stem volume and maximum ear diameter from all ears having extruded visible silks (Vega et al., 2001; Gambín et al., 2008). The r² values for this model ranged from 0.81 to 0.98 (p < 0.01; n = 27) across hybrids. In the postflowering biomass sample, we also estimated the ear biomass 15 days after anthesis by fitting a linear regression between ear biomass and the square of ear diameter (similar to Hernández et al., 2014).

Plant growth rate around flowering (mg plant^–1°C d^–1) was calculated as the ratio between the plant biomass (mg plant^–1) difference and the thermal time accumulated from pre- to postflowering samples in each specific plot. Daily thermal time values were calculated using a base temperature of 8°C. PGR was determined for each tagged plant and the values were presented as an average individual PGR, and its plant-to-plant variability was expressed as the coefficient of variation of PGR (CVPGR) for each genotype × treatment combination.

Barrenness was calculated as the percentage of barren plants per plot. Plants with less than 10 kernels at harvest maturity were considered barren (Tollenaar et al., 1992). For each individual plot, we also calculated the partition efficiency (PEF) as the ratio between EB and the total plant biomass 15 days after anthesis, and the seed set efficiency (SSEF) as the ratio between KNP and the accumulated EB.

For comparing hybrids, we fitted the relationship between KNP and EB 15 days after anthesis, and between EB and PGR around flowering, similar to Hernández et al. (2014). Both relationships were described by a hyperbolic function with their specific parameters [Figure 1; Eqs. (1–4)]. Descriptive parameters of the models are PGR_b, IS_EB, C_EB, EB_b, IS_KN, and C_KN (Figure 1). Models were fit to each genotype × replicate combination and included in the same curve the five shading treatments utilized within each replicate; so the parameters were estimated for genotype × replicate combinations. Replicates were used for an ANOVA test, and r² values ranged from 0.41 to 0.92 (p < 0.01).

where in Eq. (2) IS_EB is the initial slope of the relationship between EB and PGR, PGR_b is the base PGR for ear growth, and C_EB is the curvilinearity of the hyperbolic function (curvature) of the relationship between EB and PGR. In Eq. (4) IS_KN is the initial slope of the relationship between KNP and EB, EB_b is the base ear biomass for initial kernel set, and C_KN is the curvilinearity of the hyperbolic function (curvature) of the relationship between KNP and EB. All these parameters are considered genotypic coefficients. Applying these coefficients uniformly to all the plants is supported by several studies that show a consistent relationship between ear growth and PGR around flowering across environments (Andrade et al., 1999; Vega et al., 2001; Borrás et al., 2007). All curves were fitted using the GraphPad Prism version 5.0 (Raduschev, 2007) iterative optimization technique.

Yield was calculated after harvesting all ears from 3 m² in central rows at harvest maturity in all genotype × stand density × environment combinations. Yield is reported with 145 g kg^–1 moisture.

Data were analyzed separately for each experiment (shading or stand density) in R software (R Core Team, 2020). We used a randomized complete block design with three replications in all the trials. Sources of variation were environment (sowing date), hybrids, treatment (shading or stand density), and blocks. Main or interaction effects were tested with ANOVA. Treatment marginal means were estimated with “emmeans” function from EMMEANS R package (Russell, 2021). Tukey test was done for pairwise comparisons of estimated means.

Environments, hybrids, and shading treatments all showed significant yield differences (p < 0.001; Table 1). A hybrid × shading × environment treatment interaction (p < 0.001; Table 1) was also significant, showing that shading stress responses were different among hybrids and environments (p < 0.001; Table 1). In both environments, the effects of shading treatments S−14, S + 7, and S + 14 on yield did not differ across hybrids, but large hybrid yield differences were observed in the treatments closer to anthesis (S−7 and S0 treatments; Supplementary Table 1). In Env 1 the S−7 treatment hybrids H1, H2, H3, and H4 yielded 13.0, 11.9, 8.7, and 14.2 Mg ha^–1, respectively (Supplementary Table 1), and in the S0 treatment genotypes H1, H2, H3, and H4 yielded 11.6, 4.6, 8.2, and 12.7 Mg ha^–1, respectively (Supplementary Table 1). These genotype differential yield responses were even more evident in Env 2.

When analyzed in relative terms (here called relative yield), the interaction environment × hybrid × shading treatment was significant (p < 0.05; Table 1), illustrating that yield reductions associated with shading treatments were different depending on the particular hybrid and environment. For example, the relative yield of H1 and H4 in Env 1 did not differ among shading treatments, but the shading treatment finishing at anthesis (S0) applied to H1 had a 26% relative yield, whereas it did not reduce H4 relative yields in Env 2 (Supplementary Table 1, contrast p < 0.001). Likewise, hybrids H2 and H3 showed significant relative yield reductions when the shading treatment S0 was applied to both the environments (Supplementary Table 1).

In a second round of experiments, we tested how these same hybrids responded to stand density changes, and a stand density × hybrid experiment was repeated across three environments.

Yield results showed that all three main effects (hybrids, stand densities, and environments) were highly significant (p < 0.001), and that the interactions hybrid × stand density and hybrid × environment were also statistically significant for yield (p < 0.05; Table 4). The significant interaction hybrid × stand density showed that hybrids responded differently to changes in stand density.

Analyzing hybrids across densities, H4 produced highest yields in all densities, yielding 12.4, 15.0, 14.9, and 14.2 Mg ha^–1 for stand densities 5, 7, 9, and 11 plants m^–2, respectively. Hybrid H1 also presented its highest yields in the highest stand densities, with 14.1 and 14.0 Mg ha^–1, at 9 and 11 plants m^–2, respectively (Table 4). Contrary to this response, hybrids H2 and H3 did not maximize their yields at the highest densities and showed a significant decline in their yields at the highest stand density of 11 plants m^–2. Hybrids H2 and H3 showed that the maximum yields were achieved at the lower stand densities of 9 and 5 plants m^–2, respectively (Table 4). This differential yield response to stand the density of hybrids H2 and H3 compared to H1 and H4 was more evident in the lowest yield environment Env 5 (Supplementary Table 3).