Cultivar factors and plant density

There was no significant effect in any of the variables evaluated for the factors: cultivars and plant density, nor for any of the interactions; there was only a significant effect for the stratum factor of the plants in the hydroponic system. Therefore, the results presented correspond to this factor.

Stratum factor

Development variables: between 8 and 19 SDT the plants showed vegetative behavior, with no difference between treatments in the four strata. After 20 SDT the differences began for: number of leaves (Figure 2), crown diameter (Table 1), fruit diameter (Table 2) and number of fruits (Table 3).

The plants of the upper stratum had a greater number of leaves (Figure 2A). According to the regression analysis, after week 30, the number of leaves increased in the upper stratum, contrary to what was observed in the lower strata (Figure 2B).

Figure 2 Number of leaves per greenhouse strawberry plant produced in four different strata in a production system with a pyramidal structure. 2A) the curves connect the means, data evaluated by analysis of variance (General Linear Model, SAS); 2B) curves calculated by linear regression. ^ns, ^*, ^**, ^*** not significant and significant at p< 0.05, 0.01 and 0.001, respectively. 

In the upper stratum, the number of leaves was 13 leaves at 30 SDT; this value is less than the 16 leaves per plant reported by ^{Juárez-Rosete et al. (2007}) in a horizontal NFT system at 10 SDT, where he mentions that the NFT being a circulating (closed) system is given a constant supply of nutrients unlike open substrate systems. In addition to this, ^{Díaz-Pérez (2013}) mentions that under shade the productivity of crops can be reduced.

This agrees with our results where fewer leaves and a reduction in crown diameter were observed in the shaded strata. The inclination of the pyramidal system could cause the plants to be shaded to a greater extent in the intermediate strata. The smaller size of the intermediate strata causes that the plants of the lower strata had greater exposure to light, since the inclination prevents the plants with less growth, in this case the plants of the intermediate strata, from affecting the development of the plants in the lower stratum.

At 26 SDT, a decrease in the number of leaves was observed, this due to the sanitation pruning that was given to stimulate the formation of new foliage and flowers, thereby avoiding the formation of stolons, since it is one of the reasons why the plant strawberry loses nutrients and photosynthesized compounds (^{Avitia-García et al., 2014}).

The regression analysis showed an increase in the number of leaves in the upper stratum compared to the three lower strata, it is the only one that shows an increasing behavior, with an R²= 0.9606. The results of the diameter of the crown agree with the behavior of the number of leaves, in most cases, the largest diameter was presented in the upper stratum of the plants with a 77% increase compared to the intermediate strata, where it was lower (Table 1).

The diameter of the crown in the upper stratum ranged from 2.43 cm in week 20 to 3.09 cm in week 30, with an average growth per week of 0.06 cm, greater than that reported by ^{Tariq et al. (2013}) where he obtained diameters from 1.06 to 1.4 cm testing different densities of plants and substrates in strawberry hydroponics, where the largest diameter was obtained with a mixture of sand, manure and silt substrates (1:1:1) with a density of plants of 22 plants·m^-2. In the upper middle stratum, an increase in the diameter of the crown of 0.03 cm per week was observed, which corresponded to half the average in the plants of the high stratum, and in the lower middle stratum the same size was maintained among these 10 weeks (20-30 SDT).

In the same way as in the variable number of leaves, light could influence (^{Díaz-Pérez, 2013}) the size of the diameter of the crown, since, the lower the number of leaves, the less the thickness of the crown in the strawberry plant. Flowering started 20 SDT. However, ^{Hidaka et al. (2017}) report that strawberry flowering begins at 6 SDT. In this study, the delay in flowering could be attributed to the high temperature and a long photoperiod, since the low temperature and short days induce flower differentiation (^{Miyoshi et al., 2013}).

Inside the greenhouse, the average maximum temperature (TMaxP) during the months of March to June was 35 °C and the average minimum (TminP) 15 °C, from July to October the TMaxP was 32 °C and the TMinP 14.5 °C. The minimum and maximum recorded throughout the crop cycle were 4 °C to 38 °C, respectively. ^{Neri et al. (2012}) mention that the development of flower buds in an early stage is carried out in an optimal temperature range of 26.7 °C day/15.6 °C night, so that high temperatures partially inhibit flowering (greater than 26 °C) or totally (greater than 30 °C).

Fruit quality and yield variable: these variables registered behavior similar to that described in number of leaves and crown diameter; that is, only the stratum factor had a significant effect. The plants located in the upper part with respect to the plants of the medium-high and medium-low stratum presented greater fruit diameter (Table 2). The plants of the high stratum produced statistically the same number of fruits (Table 3), that those of the low stratum in the 22 and 24 SDT, with a tendency to be higher in the high stratum. In the medium-low stratum the diameter of the fruits was smaller than the upper stratum from 22 to 30 SDT.

The yield was higher in the upper stratum of the pyramid, except in week 30 where the plant yield was similar to the low stratum (Figure 3A). The plants of the low stratum had an upward trend in yield, while the curve of the high stratum had a decreasing behavior at the end of the experiment (Figure 3B). According to ^{Ledesma et al. (2008}), the temperature and the length of the day play a fundamental role that affects the production of fruits. ^{Ledesma and Kawabata (2016)} mention that there is a decrease in fruit size and weight caused by high temperatures (greater than 32 °C for more than 4 h) in strawberry cultivars, temperatures less than 2 °C and greater than 35 °C for prolonged periods, cause devitalization of pollen, floral abortion and fruit malformations.

Figure 3 Cumulative yield of greenhouse strawberry fruits produced in four different strata of production system with pyramidal structure. 3A) the curves connect means; data evaluated by analysis of variance (General Linear Model, SAS); 3B) curves calculated by linear regression. ^{ns, *}, ^**, ^*** not significant and significant at p< 0.05, 0.01 and 0.001, respectively. 

Probably the ‘Festival’ and ‘San Andreas’ cultivars responded favorably to high temperature stress, since from July to October there were maximum temperatures of 38 °C, but lasting less than 4 h. ^{Caruso et al. (2011}) report that the duration of high temperature stress in strawberry affects the number of fruits. These authors mention that the period in which the plant is cultivated has great relevance for strawberry production, since cold hours are crucial for strawberries, in agreement with our study, since probably the excessive accumulation of cold hours also prevented the plant will develop in better conditions.

The total soluble solids were only different in the 24, 26 and 30 SDT in the treatment with the high and low stratum where the highest values (better quality) are had, although statistically the values of the medium high and medium low stratum were not different of the lower stratum (Table 4).

The total soluble solids were higher when the yields increased (Figure 4), the yield also increased when the incidence of solar radiation increased. Solar radiation is associated with the content of soluble solids in the fruit. ^{Díaz-Pérez (2014}) reported that the amount of total soluble solids decreases when the shade level increases in bell pepper (Capsicum annuum L.). Thus, by having greater shading in the medium-high and medium-low strata, there is a lower amount of soluble solids in the fruit, stratified in the same way as the other variables observed.

Figure 4 Relationship between total soluble solids and yield as a result of four strata with horizontal bags in a pyramidal hydroponic system; through, linear regression analysis. A= high, B= medium high, C= medium low, D= low. 

The yields obtained per plant agree with the trend in the variables: number of fruit and diameter of fruit, since the high, medium-high and medium-low stratum has the same decreasing behavior in yield per plant, adjusting to the probability that the shadow acted on the system by making a pattern over the three strata in which it shows us that the variability of light that affected the system affected the plants as a whole, this agrees with that reported by ^{Wang and Wang (2014}) as it mentions that light intensity is a key factor in improving strawberry production in a hydroponic system.

The production results in this study were low compared to those presented by ^{Miranda et al. (2014}) in a hydroponic system in bags and coconut fiber channels since they obtained 684 and 1 407 g plant^-1 handling a density of 10 and 13 plants m^-2, respectively. However, the total yield was higher in this study. Since using a density of 43 plants m^-2, a production of 23.5 kg m^-2 was obtained in the upper stratum of the pyramidal system (Table 5), therefore, one of the benefits of the pyramidal system is the ability to increase the plant density per square meter and space optimization.

The results obtained in this study were also higher than that reported by ^{Paranjpe et al. (2003}), in this case per square meter, since it reported a yield of 7 to 9 kg m^-2 in a hydroponic system, in a greenhouse with climate control, with production in the winter months in Florida, USA.