Description of the study site

The experiment was carried out in an 8-year-old litchi cv “Brewster” plantation, located in the common “Cerro of Tigre”, which is located at coordinates 21° 36’ 04” north latitude, 104º 56’ 47.5” longitude west, at an altitude of 700 m. The topological arrangement of the plantation is in real frame with distance of 6 x 6 m. According to the climate classification of Köppen modified by ^{García (1981)}, the climate is a (A) e (W2) a (i), which corresponds to a semi-warm (subtropical sub-humid), which is the warmest of the tempered (c); the average annual precipitation is greater than ≥1 300 mm. The plantation has drip irrigation infrastructure.

Initial diagnosis of soil and plants to define fertilization dose

Within the plantation, seven tree lines were randomly selected, in each of them 10 trees were randomly selected, which resulted in a total of 70 trees. To define the doses that would be evaluated, prior to the establishment of the experiment, composite samples were taken, both soil and foliar component. The procedures of the collection are detailed below:

Soil sampling

Soil samples were taken at the four cardinal points of the base of each of the 10 trees of the selected lines, at a distance of 0.5 m and at -40 cm depth. Each of these samples was mixed homogeneously to obtain a single sample for each selected tree. This exercise was replicated in the 10 trees of each line. The 10 samples were mixed to obtain a composite sample for each line. In all the surface of the experimental area seven composite samples were obtained. Once collected, they were taken to the soil, plant tissue and water analysis laboratory of the Agricultural Academic Unit of the Autonomous University of Nayarit.

The analyzes contemplated to diagnose the state of soil fertility were: pH, MO, N, P, K, CIC, CE and interchangeable bases, which were developed by the methods recommended by the Official Mexican Standard PROY-NOM-021- RECNAT-2000 (^{DOF, 2000}).

Diagnosis of edaphic fertility

The soil of the orchard under study has the following characteristics: clay texture, bulk density (g cm³) of 1.2, P Bray (22.22 mg kg^-1), interchangeable K (300 mg kg^-1), interchangeable Ca (2 300 mg kg^-1), exchangeable Mg (300 mg kg^-1), pH 6.4 and CE (dS m^-1) of 0.14. The foliar nutritional concentration in the trees was N (1.43%), P (0.14%), K (0.86%), Ca (1.91) and Mg (0.26%), these concentrations are within the optimum range indicated by ^{Menzel and Simpson (1987)}, for the litchi culture, with the exception of potassium that are in a lower level, these authors indicate 1.2% as optimal.

Sampling of the foliar component

In each tree of each line, two pairs of complete leaflets of the fourth leaf were identified and collected at each cardinal point, according to the methodology of ^{Menzel and Simpson (1987)}. The samples were placed in paper bags and taken to the laboratory, where they were washed with running water and later with distilled water; they were dried in a forced air oven at 60 °C for 48 h until constant weight was obtained, and ground in a stainless-steel mill. To determine the initial contents of nutrients, an extraction was made in wet digestion following the procedures established by ^{Alcantar and Sandoval (1999)}. For the case of N, a mixture of sulfuric acid with salicylic acid was used for Ca, Mg, P and K, this mixture was with nitric acid and perchloric acid.

Estimation of fertilization dose

Based on the results of the soil analysis, equation 1 was developed, proposed by ^{Volke et al. (1998)} by which it is possible to determine the optimal dose of each nutrient.

Where: DON= optimum nutrimental dose; demand= is the quantity of the nutrient that the crop requires to complete its physiological processes and to reach to produce a certain production goal; supply= is the quantity of the nutrient that the soil is capable of supplying to the crop; ERF= fertilizer recovery efficiency (ERF). With the application of the equation the optimum doses of N. P, K. were calculated.

Estimation of N dose

To estimate the demand for this nutrient, a production goal of 50 kg of fruit per tree^-1 was set. With the results of the fertility diagnosis that was made, the supply of N was set at 31 g tree^-1, said value results from considering a content of organic matter in the soil (MOS) of 3.7%, an annual mineralization rate of 2%, an N content of 5% in the MOS and a root exploration area at a distance of 75 cm from the base of the tree and a depth of 40 cm, as well as an apparent density of 1.2 Mg m^-3. If it is taken into account that for the production of fruit per tree per year^-1, 110 g are extracted for the fruit component and for leaf 282 g (calculated from a dry matter production in the foliar component of 23.5 kg year^-1, determined through preliminary evaluations), the demand of N per tree per year^-1 is 392 g of N. The recovery efficiency of nitrogen fertilizer (ERFN) is 60%. Therefore, the N annual dose was 600 g tree^-1.

Phosphorus dose estimation

The nutritional extraction for the fruit is estimated at 2.2 kg of P₂O₅ per ton of fruit (^{Galan, 1987}). Therefore, for a production of 50 kg of fruit (yield goal) the demand is 48.4 g of P. As for the case of N, at this value the nutrient extraction of the foliar component was added, which considers a concentration of P of 0.18%, which results in a demand of 42.3 g of P in said component. From the sum of these two values resulted a demand of 90.7 g of P (tree annual^-1). The results of the diagnosis of soil fertility indicated that the supply of P was 18.66 g per tree. While the efficiency of phosphate fertilizer recovery was 30%, so the annual dose of P was 240 g tree^-1.

Potassium dose estimation

The nutritional extraction for the fruit is estimated at 5.5 kg of K per ton of fruit (^{Galán, 1987}), what the demand for a yield goal of 50 kg of fruit tree^-1 is 275 g of K, at this value the extracted K per leaf was added, which was 282 g, so the demand for K per tree was calculated at 557 g. The soil analysis reported 300 mg kg^-1 of exchangeable K, so the supply of K was estimated at 252 g tree^-1. If a recovery efficiency of 50% potassium fertilizer is considered. The dose of K was 600 g tree^-1 year^-1. The resulting NPK dose expressed in g tree^-1 year^-1 was 600-240-600.

Experimental design/treatments

The experiment was established as completely random blocks, with factorial arrangement 3 x 2, where the factor A consisted of three levels of K, the B factor in two levels of banding. Six treatments emerged from this arrangement. The intermediate dose was considered calculated from equation 1. The levels of N and P remained fixed. The details of the treatments are presented in Table 1.

The resulting treatments were evaluated with 10 repetitions. As an experimental unit, it was considered a tree. Nutrient sources were potassium nitrate, MAP, potassium sulfate and urea.

Establishment and management of the experiment

Once the designation of the treatments in the field was made, the corresponding trees were annealed, this practice consisted of making a ring-shaped incision of approximately 0.8 cm in width in 70% of tree branches. At the same time, 30% of the fertilization dose was applied, while the remaining 70% was dosed by fertigation to the emission of the reproductive shoots, which occurredsix months after the first fertilization. During the whole production cycle, the crop was watered twice a week, applying 100 liters of water per tree, suspending said irrigation 20 days before harvesting.

Response variables

Determining variables of performance

The results show an individual effect of factor A (potassium levels), factor B (banding levels), as well as their interaction, on the variables total yield (RT). It can be seen that the B factor plays a more important role on the variables fruit width (AF), fruit length (LF) and fruit production per tree (PFA), with respect to the factor A. Therefore, treatment six which combines a higher dose of K (900 g tree^-1) with the presence of ringing was the one with the highest fruit yield (Table 3).

The effect of factor A and B, as well as their interaction on fruit yield, is due to higher fruit production per tree (PFA), since as can be seen in the same table, both the dimensions of the fruits, as the proportions of husk, pulp and seed between the treatments, do not denote statistically significant differences. Other investigations had already documented similar results. ^{Pathak and Mitra (2010)}, indicate that the supply of K favorably affects the yields in litchi trees, due to a higher photosynthetic rate activity, stoma conductance as well as greater efficiency in the use of water. Although this increase in yield, it is not necessarily due to a positive modification in the anatomical constitution of the litchi fruit, derived from the application of increasing doses of K (^{Rai et al., 2002}).

In spite of the documented evidences, the effect that the K has on the yield and quality of fruit cannot be generalized, since the hydric condition to which the trees are subjected, is an important factor in this answer, mainly because the K has a specific physiological role in the opening and closing of stomata through its influence on the osmotic potential of guard cells (^{Havlin et al., 1999}). Due to the variability of this condition, research has been conducted in which the effect of K is equal to or lower than that of other nutrients. ^{Reza et al. (2007)} and ^{Joo-Pérez et al. (2017)} indicate that under irrigation conditions, the requirement of K in the litchi culture is lower than those of N and P. Although in the case of this investigation, the above is only congruent in the treatments without banding, since in the treatments that were ringed, there was a response to increasing doses of K (Table 3).

Various investigations have established that ringing in litchi trees and other fruit trees causes an accumulation of carbohydrates (^{Gaete, 2007}), which probably caused an increase in the demand for K, since this nutrient intervenes in the processes of synthesis and transport of sugars and starches (^{Liu et al., 2017}), which is why those treatments with rings that received higher levels of K, were those that expressed higher fruit yields.

Determining variables of fruit quality

The analysis of the effects of factors A and B, as well as their interaction on most of the variables related to fruit quality did not show statistically significant differences. Except in the variable pH, which is affected mainly by the factor B. From the above it follows that the fruits of treatments 4, 5 and 6 recorded a higher pH (3.64), with respect to those from trees that they lacked the incision (3.41) (treatment 1, 2 and 3). According to ^{Çolpan et al. (2013)}, the supply of K can cause an increase in the pH of the fruit due to the synergy that this element presents with others such as Ca, which is reflected in an increase in the levels of °Brix, caused by the increase in the amount of total soluble solids (SST) in the juice. However, in the present investigation, these variables were not substantially affected by factors A and B, nor by their interaction (Table 4).

An effect of factor A on the variable fruit weight loss (PPF) is observed. However, this effect is not totally clear and forceful. Although it is necessary to advance in this physiological phenomenon, it is proposed that the dose of 600 g tree^-1 of K is the most adequate to maintain the turgor of the fruits for longer, since both the low dose (300 g^-1 of K) as the high dose (900 g^-1 of K), have a higher PPF, being the low dose of (300 g tree^-1 of K) where there is a higher PPF (Table 4). The results obtained in this investigation suggest that the K applied to the litchi trees, improve the water supply to the fruits, which caused a dilution effect in the juice, so the SST: water ratio, as well as the Levels of °Brix did not present significant statistical differences, nor for the individual effects of factors A and B, as well as those of their interaction.