Color

Values of L, a and b of the CIE L*a*b* color system were obtained with a colorimeter (Hunter Lab D25-PC2; Reston, Virginia, USA) at two opposite points on the equatorial zone of the fruit; subsequently, these values were used to calculate the hue angle with the formula: hue (º) = tan^-1 (b/a), while brightness was obtained directly with the colorimeter (^{McGuire, 1992}).

Lycopene

Using the equation proposed by ^{Arias et al. (2000)}, the concentration of lycopene (in mg kg^-1 FF) was calculated indirectly using the a and b values, which are chromaticity coordinates for a* = red/green coordinate and b* = yellow/blue coordinate, obtained in the fruit color measurement described above.

Firmness

Before making the chemical determinations and after measuring the color, the firmness was measured at two opposite points in the equatorial zone of the fruit using a texture analyzer (FDV-30, Greenwich, Connecticut, USA) adapted with an 8 mm diameter conical strut. Two punctures were made in the fruit, and the corresponding values were reported in Newtons of force (N) (^{San Martín-Hernández et al., 2012}).

Yield

The yield, reported in g per plant, was evaluated in the second, fourth and sixth clusters. Tomato plants were grown to four fruits per cluster, with the remaining fruits pruned when the fourth established fruit was between 1 and 2 cm in size.

Statistical analysis

To investigate the relationship between the study factors (N and K) and the response variables, the following model was used, adapted to a completely randomized design with a split-plot arrangement.

Where: Y _ijk = response variable for the ijk experimental unit, µ = overall mean, N _i = effect of the i^th level of N, Ԑ _a = experimental error of large plot, K _j = effect of the j^th level of K, N × K _ij = effect of the N × K interaction, Ԑ _ijk = random experimental error. Ԑ _a ~ NI(0, σ_a² ) and Ԑ _ijk ~ NI(0, σ²) are assumed to be normal, independent, with zero mean and common variance σ².

An analysis of variance (ANOVA) was performed and means were compared with the Tukey HSD test (P ≤ 0.05). The verification of the assumptions of the model was performed using the Bartlett’s test, the Shapiro-Wilk normality test and the Durbin-Watson statistic, which were reasonably normal, with homogeneity of variances and independence. All statistical calculations were carried out using the SAS Ver. 9 software.

Hue

Both N and K affected fruit color (Table 2). In tomato, an increase in N fertilization from 0 to 250 kg ha^-1 resulted in delayed fruit maturity and adverse effects on fruit color development (^{Parisi et al., 2006}). These responses fully agree with those detected in this study, since hue in fruits of the first (42.8°) and third (35.8°) clusters was the lowest at the lowest level of N, and increased by 5.6 and 5.9 % when changing the level of N from 10 to 14 and from 10 to 16 mol_c m^-3 respectively. These increases in hue caused by the increase in N are due to the reduced red color in the fruits according to the L*c*h* color space (^{McGuire, 1992}); on the contrary, the increase in K concentration from 5 to 13 mol_c m^-3 induced a reduction of 7, 10 and 11 % in the hue angle compared to the hue in fruits of the first (45.3°), third (38.8°) and fifth (37.0°) clusters, observed with the lowest level of K tested (Table 4). The increasing of K fertilization in field-grown tomatoes improved the value of the hue angle (^{Hartz et al., 2005}), which is in full agreement with the results obtained in this research, since the K treatments increased the reddish hue of fruits.

Brightness

The effects of N on brightness were observed only in fruits of the first cluster, and those of K in the first and third clusters (Table 2). The highest mean for brightness was observed with the highest concentration of N. Similar results were observed in apple fruits when increasing doses of N (from 9 to 105 g per plant) were applied (^{Wang and Cheng, 2011}). Regardless of the K added to the nutrient solution, fruit brightness gradually decreaed in fruits from the first to the fifth cluster; however, when K increased from 5 to 13 mol_c m^-3, the brightness proportionally increased by 5 % from the minimum values recorded in the first and third clusters, with K concentrations ≥ 11 mol_c m^-3 being the most appropriate to increase fruit brightness (Table 4); conversely, when increasing K fertilization from 0 to 800 kg ha^-1 in field-grown tomatoes, a 7 % reduction in brightness was observed, while the highest value (44) was observed with the lowest K dose applied (^{Hartz et al., 2005}).

Lycopene

The study factors influenced lycopene concentration in the fruit: N altered the synthesis of this pigment in the first and third clusters, while K, influenced the three clusters (Table 2). As N increased from 10 to 14 mol_c m^-3 in the nutrient solution, lycopene concentrations decreased by 8 and 6 % compared to the maximum values detected in the first and third clusters respectively, both with N at 10 mol_c m^-3 (Table 4).

Results showed that a low N concentration can improve lycopene concentration in tomato. Lycopene decreased from 68 to 38 mg kg^-1 in fresh fruits due to increases in N of 1, 12.9 and up to 15.8 mol_c m^-3 (^{Dumas et al., 2003}). On the other hand, when tomato is nourished with increasing K, lycopene concentrations significantly increase. In this experiment, when K concentration increased from 5 to 13 mol_c m^-3, the lycopene concentration increased considerably by 10, 12 and 13 % in the first, third and fifth clusters, respectively (Table 4). The lowest lycopene concentration was observed in plants treated with the lowest K, while the highest concentration was observed with K at 13 mol_c m^-3, in the three clusters evaluated (Table 4). Lycopene content of tomato can increase by 35 % when the concentration of K increases from 8 to 9 mol_c m^-3 (^{Ramírez et al., 2012}). Potassium is involved in the activation of several enzymes, being phytoene synthase and phytoene desaturase those associated with phytoene and phytofluene, both intermediates in the biosynthesis of lycopene (^{Taber et al., 2008}).

Firmness

In fruits of the fifth cluster, firmness was significantly affected by nitrogen supply (Table 1). By increasing the nitrogen supply from 10 to 16 mol_c m^-3, the firmness in fruits of the fifth cluster decreased by 16 % (Table 5). Small increases in the concentration of N during tomato cultivation increase fruit firmness, but when the N supply exceeds 30 mol_c m^-3, this attribute decreases (^{Frías-Moreno et al., 2020}) as observed in this investigation. The nitrogen to calcium ratio (N/Ca) is a crucial factor determining fruit firmness in different plant species (^{Khalil and Hammoodi, 2021}; ^{Torkashvand et al., 2017}), while decreases in accumulation of Ca in the fruit result in loss of cellular integrity and reduced firmness (^{Zhang et al., 2020}).

Yield

The application of N at the vegetative stage and its N × K interaction did not affect fruit yield analyzed in three clusters; instead, the increase in the level of K at the reproductive stage of the crop affected fruit yield in the second, fourth and sixth clusters (Table 1); in fact, positive relationships between K supply and fruit yield have been previously reported (^{Taber et al., 2008}).

Increasing the concentration of K in the nutrient solution from 5 to 13 mol_c m^-3 improved yield, but the maximum increases, with 11, 10 and 15 % were obtained at 11 mol_c m^-3 in fruits of second, fourth and sixth clusters, respectively (Table 5). In an experiment conducted under field conditions, the 125 % K-based soil test application via polysulphate surpassed all the other treatments in terms of growth and yield parameters (^{Navitha et al., 2019}).

Likewise, fruit weight exhibited a similar trend as yield. The highest average weight per fruit, with 287, 255 and 200 g, corresponding to the second, fourth and sixth clusters, were obtained when K was supplied at 11 mol_c m^-3. Potassium plays an important role in the mobilization of carbohydrates from source to sink organs (^{Engels et al., 2012}). Equivalent increases of up to 33 % in fruit weight have been reported when potassium fertilization changed from 0 to 141.1 kg ha^-1 in tomato crop (^{Sultana et al., 2015}).

Soluble solids, acidity, color, pigment concentrations, sugars and titratable acidity are the result of interactions of a set of pre-harvest factors; these factors include genetics, environmental elements such as solar radiation, temperature (^{Gautier et al., 2005}), humidity, crop management and fertilization levels (^{Wang and Xing, 2017}), as observed in this study. Regarding plant nutrition, N plays a key role as a constituent of most of the essential organic molecules, such as nucleic acids, purines, amino acids, some vitamins, proteins and enzymes (^{Beatty et al., 2016}), while N deficiency may reduce yield, its excess favors vegetative growth to the point of causing toxic effects (^{Leghari et al., 2016}). In tomato, a high supply of N during cultivation worsens the chemical quality attributes of fruits, including pH, soluble solids content, glucose, fructose and the sugars/total solids ratio (^{Parisi et al., 2006}).

Potassium is an essential element involved in vital physiological and biochemical processes, including plant signaling, osmoregulation, maintenance of cation-anion balance, cytoplasmic pH regulation, enzyme activation and protein and starch synthesis (^{Rogiers et al., 2017}). It is important to know that K is involved in fruit development (^{Almeselmani et al., 2009}) and sucrose accumulation in tomato (^{Caretto et al., 2008}). Although K is not a structural component of plant cells, it is absorbed in large amounts by most crop species, influencing product quality parameters and yield parameters. Fruit quality attributes such as TA, TSS, concentration of citric and malic acids, sugars and carotenoids have been found to be positively associated with increasing K doses, while K deficiencies cause fruits with heterogeneous maturity due to low contents of lycopene (^{Çolpan et al., 2013}; ^{Ramírez et al., 2012}; ^{Rebouças Neto et al., 2016}). The results reported herein are in full agreement with those aforementioned due to the manipulation of N and K during the vegetative and reproductive stages of tomato, respectively. In addition to the effects attributed to the nutrient management implemented, different trends in each cluster were observed in each cluster, since TSS, reducing sugars and lycopene concentration increased from the first to the fifth cluster (Tables 3 and 4), whereas color attributes such as hue and brightness decreased (Table 4). Titratable acidity showed an irregular response, presenting its maximum value in the first cluster (Table 3).