This research was carried out during the period 2015-2016 in the municipality of Armero-Guayabal, located in the northern region of Tolima, Colombia. Ten sowing dates (SD), a SD per month, were established on November, December, January, February, March, April, May, June, July, and August. The cultivar used was Oryzica 1, this cultivar was selected because it has been sown for 34 years in this region due to its good productivity and high grain quality.

The experiment was carried out in soil formed by volcanic flows with a sandy loam texture. Plots were established in a completely randomized block design in a divided strips arrangement, where the stripes corresponded to the sowing dates. Each strip comprised 2500 m² divided into three blocks. Similar agronomic management was carried out for the ten sowing dates, where irrigation was provided by gravity with a frequency of two days per week. The control of pests, diseases, and weeds were carried out according to weekly sampling, using chemical synthesis products. The nutritional supply was made using five edaphic fertilizations, during the different phenological stages according to the nutritional requirements for the extraction of potential yield of 10,000 kg ha^-1.

Growth variables and trends were estimated, as follows: Leaf area index (LAI) and dry matter (DM) above the soil was determined following the methodology described by Degiovanni et al. (2010) and Garcés and Restrepo (2015), respectively. Phenology stages were characterized according to the BBCH scale (Lancashire et al., 1991), and plant height was also measured. These variables were evaluated in all the plants that were in an area of 625 cm², from the phenological stage 11 to 99. Once the phenological stage 99 was reached, harvest index and plant components were estimated. Moreover, with data obtained from the panicle number per square meter, weight of 1,000 grains, the percentage and weight of filled grains, green paddy yield in kg ha^-1 was calculated according to Garcés and Restrepo (2015). The yield was estimated with a grain humidity of 22%.

Climatological variables were collected using a weather station (Davis Vantage Pro 2, San Francisco, California) located 500 meters far from the study area. These data were divided into 12 parts according to the BBCH scale, and the following variables were obtained: maximum diurnal temperature, maximum night temperature, minimum night temperature, accumulated solar radiation (SR), accumulated precipitation and average relative humidity according to each of the 12 parts considered.

In the SD of April, May, June, July, and August, photosynthesis rate, stomatal conductance and transpiration, in the phenological stages 49 (i.e., first awns visible), 65 (i.e., 50% of flowers), and 75 (i.e., milky ripe) were estimated in the youngest completely expanded leaf, using a portable open photosynthesis-meter system (LI-6400 XT Li-Cor Lincoln, Nebraska, U.S.A.). The photosynthetic photon flux density of 1600 μmol photons m^-2 s^-1, the concentration of CO₂ inside the chamber was set at 400 μmol CO₂ mol^-1, and the vapor pressure deficit remained between 1.5 and 1.7 kPa; data were taken after reaching stable state equilibrium (~10 min). The area of the leaf inside the chamber was measured in order to correct with the real data area.

Growth trends, as well as growth, development, yield components and, climatic variables, were analyzed with the automatic learning methodology using tree decision algorithms (Delerce et al., 2016). In order to use this technique, it is necessary to previously filter the variables considering their correlation with predictors (Hastie et al., 2009); therefore, these variables were filtered by partial least squares regression using the NIPALS model (Geladi and Kowalski, 1986). Furthermore, the criteria considered were the variables of importance that presented a coefficient >0.8 and a correlation with the predictor variable. Once important variables were identified through the trees and photosynthesis analysis, contour plots were made with yield as a response variable. This analysis was done with the objective of identifying optimal points where performance is maximum (Figueroa, 2003). Besides, a multivariate analysis of variance with a Hotelling’s significance test was performed with yield component data. Data analyzes were carried out with the software RStudio Inc., version 3.5.1.

The SD of December and May presented the highest yields (Table 1), agreeing with the results found by various authors (Datt et al., 2012; Sameera et al., 2016; Dong et al., 2017). Moreover, the number of panicles and the percentage of full grains have a high correlation with yield (Table 2) where a significant correlation is observed between these variables. This correlation explains the high yields found in the SD of December and May, the results obtained were similar to those reported by Thippani et al. (2017). However, no relationship was observed between the weight of 1,000 grains and the number of grains per panicle with yield (Table 2), what differs from what was found by Díaz et al. (2000), where they stated that these are variables that significantly influence yield and are closely related to grain length. Possibly this correlation was not observed because only one variety was evaluated, and it is probable that no variability in this character would occur, so in future studies, this variable should be considered.

Table 1

Table 2

According to the tree method, the LAI variable in the stage 49 (i.e. maximum panicle swelling stage), plant height in the phenological stage 41 (i.e. beginning of panicle swelling), and accumulated DM in the stage 37 (i.e. elongation of the stem), are the variables that are mostly associated with rice yield, moreover, together they explain this with an R ² of 0.92 (Figure 1A). Maximum yield is reached when the LAI is between 10 and 11 (Figure 2A), which are similar to values found by Mae et al. (2006), who observed a linear relationship between LAI and yield, finding the maximum crop yield with a LAI between 10 and 12. Garcés and Restrepo (2015) conducted a similar study in the southern area of Tolima, where they found that maximum yield was reached with a LAI of 7; this difference can be attributed to the fact that different varieties were used. The highest yield is reached with a plant height between 0.30 and 0.40 m, while yield is significantly reduced when it is less than 0.30 m (Figure 2A). These differences are present because higher plants allow better ventilation and better location of the leaves inside the canopy. On the contrary, plants with lower height generate lower ventilation and wrong leaf location, which generate a reduction in the photosynthesis rate of the canopy in 60 to 80%, and yield is reduced by approximately 2,000 kg ha^-1 (Setter, 1997; Peng et al., 2008). Therefore, to obtain a high yield, it is necessary to reach a LAI between 10 and 11 and a plant height between 0.30 and 0.40 m, both between plant development stages 41 and 49, which allows the plant to have a better solar radiation uptake.

Figure 1

Figure 2

SR that is received by crops from stages 30 to 89 has a decisive influence on crop yield (Yoshida and Parao, 1976). According to the tree methodology, the climatic factors that are the most associated with yield is SR in the phenological stage 51 to the 77, with an R ² of 0.88 (Figure 1B). Maximum yield is reached when SR presented values between 4,000 and 4,500 cal cm^-2 d^-1 between stages 51 to 59 (i.e., inflorescence emergence), and greater than 4,500 cal cm^-2 d^-1 between stages 71 and 77 (i.e., development of fruit) (Figure 2B). The relationship found between SR and yield is due to a direct relationship between global and intercepted SR and accumulation of DM; and therefore, with yield (Garcés and Restrepo, 2015; Huang et al., 2016).

However, for SR to be converted into DM, it must be intercepted, and this is defined by plant LAI and architecture (Ying et al., 1998; De Costa et al., 2006; Zhang et al., 2009). These physiological factors are decisive because it allows SR, that cannot be absorbed by the leaves of the upper third, to penetrate and be intercepted by the middle and lower third leaves, where 70% of the leaf area is found, which contributes to a photosynthetic rate of approximately ~47% of the canopy (Song et al., 2013). Furthermore, to have a high efficiency in the conversion of SR into carbon skeletons, it is necessary that the photosynthetic apparatus does not show climatic stress limitations, which can be generated by high diurnal (>40 °C) and nocturnal (>30 °C) temperatures (Sánchez et al., 2014; Alvarado et al., 2017). However, these temperatures were not found in any sowing date (data not shown).

The photosynthesis rate has a close relationship with yield because as it increases, photosynthate supply increases from leaves to grains (Fu and Lee, 2008). However, no clear relationship was found between yield and this variable. SD with the highest yield does not coincide with a high photosynthesis rate in any of the three phenological stages evaluated (Figure 3). This lack of relationship is contradictory to the direct relationship between photosynthesis rate and yield found by other authors (Hidayati et al., 2016). This result is explained because the photosynthesis rate was not evaluated at the canopy level but on a single leaf, and it was also estimated at the saturation point and not the real photosynthesis rate on different phenological moments. Therefore, the influence of SD in the photosynthesis rate of the canopy should be studied further in depth, through daily curves, which allow seeing the real capacity of carbon fixation and its relationship with the yield.

Figure 3