Soil analysis

At the beginning of the study (May 2006), 10 trees were randomly selected in each orchard and from each one a sample composed of four subsamples (one for each cardinal point) was obtained from the tree’s drip zone, from 0-30 cm deep, since it is where there is the greatest abundance of fine roots (^{Salazar-García, Ramírez-Murillo, & Gómez-Aguilar, 1993}). From the 40 sub-samples, a composite sample was obtained and analyzed for its physical and chemical characteristics in a laboratory accredited by the North American Proficiency Testing (NAPT) program of the Soil Science Society of America. Soil properties determined were: texture; pH (1:2 water) (^{McLean, 1982}); organic matter by the method of Walkley and Black (^{Nelson & Sommers, 1982}); N-inorganic (^{Dahnke, 1990}); P-Bray (^{Bray & Kurtz, 1945}); K, Ca, Mg and Na extracted with ammonium acetate (^{Doll & Lucas, 1973}); Fe, Zn, Cu and Mn by the DTPA method (^{Lindsay & Norvell, 1978}), and B by the hot water method and Azometina-H (^{Bingham, 1982}). Nutrients were quantified with an atomic absorption spectrophotometer (Thermo Series S, Madison, Wisconsin, USA), with the exception of P and B, which were determined in a spectrophotometer (Genesys™ 20, Thermo Scientific, Madison, Wisconsin, USA).

Leaf sampling

In each orchard, trees were identified that, according to the grower, had an annual production ≥ 100 kg, which surpasses the current average (11 t·ha^-1) of mango in the region (^{Servicio de Información Agroalimentaria y Pesquera [SIAP], 2016}). Of these trees, 20 were randomly selected and in each one 20 shoots of each vegetative flush were tagged in a bud-breaking stage (zero day). In each mango cultivar, two vegetative flushes were studied. Their starting dates were: January 5 for the SpVF (Ataúlfo, Kent and Tommy Atkins), June 22 for the SuVF (Ataúlfo and Kent) and September 21 for the AVF (Tommy Atkins). Once the zero day was established, the days after leaf sprouting (DALS) were counted until abscission.

Monthly leaf samplings were made for each vegetative flush, alternating between odd- and even-numbered trees (10 trees per sampling date), which started when the leaf was ≥ 5 cm long and ended when senescence and abscission occurred. To avoid contamination of the leaves by the soil, they were attached from the petiole, with a cotton thread, to the shoot that held them. In each sampling, 20 healthy, complete (lamina + petiole) leaves were collected per tree from the six and seven basipetal positions. In total, 15 leaf samplings of the SpVF were performed in the three mango cultivars (from February 2006 to April 2007), 12 samplings from the Ataúlfo and Kent cultivars of the SuVF (from August 2006 to July 2007) and 12 samplings from the Tommy Atkins cultivar of the AVF (October 2006 to September 2007). Additionally, in each sampling the length of the lamina of 10 leaves from each tree was measured.

The leaves were washed and dried in a forced-air oven at 65 °C for 48 h. Subsequently, they were ground in a stainless-steel mill (MF10, IKA^®), sieved in mesh no. 1.0 (35 holes·cm^-2) and sent to the aforementioned laboratory to determine the concentrations of N-total, NO₃, P, K, Ca, Mg, S, Fe, Cu, Mn, Zn and B. N-total was determined by the semi-microKjeldahl method (^{Alcántar-González, & Sandoval-Villa, 1999}; ^{Bremner & Mulvaney, 1982}), which is based on the wet oxidation of organic matter using sulfuric acid and a catalyst, while for NO₃ the nitration method with salicylic acid was used (^{Alcántar-González, & Sandoval-Villa, 1999}; ^{Etchevers et al., 2000}). The K was extracted with distilled water and quantified in an atomic absorption spectrophotometer (ICE 3000™, Thermo Scientific) (^{Alcántar-González, & Sandoval-Villa, 1999}; ^{Etchevers et al., 2000}). The P and S were determined using the vanadate-yellow molybdate and turbidimetry methods, respectively. The B was determined by the azomethine-H calcination method (^{Enríquez, 1989}) with a spectrophotometer (Genesys™ 20, Thermo Scientific, Madison, Wisconsin, USA). For Ca, Mg, Cu, Fe, Mn and Zn, the HNO₃+HCl microwave digestion method was used (^{Alcántar-González, & Sandoval-Villa, 1999}; ^{Etchevers et al., 2000}). These last nutrients were quantified by atomic absorption in a spectrophotometer (ICAP 7200™, Thermo Scientific).

Determination of appropriate leaf sampling period

In this determination, the procedure described by ^{Salazar-García et al. (2015)} was used. For each orchard and vegetative flush, mathematical functions were generated using DALS as an independent variable and the concentrations of each nutrient as dependent variables. The general equation was: Nutrient = β₀ + β₁D + β₂D² + β₃D³ + β₄D⁴ + β₅D⁵; where D are the days after sprouting and β the mathematical coefficients. Subsequently, for each nutrient, the best mathematical function was selected by order of response (from the first to the sixth order) with the "Stepwise" procedure of the Statistical Analysis System (^{SAS Institute, 2009}). The criteria for choosing the best functions were: 1) highest R² value, 2) lowest mean squared error (MSE) and 3) Mallows's Cp value (^{Draper & Smith, 1981}; ^{Neter, Li, & Kutner, 1985}). Once the best functions were identified, their mathematical coefficients (β₀,…, βn) were calculated by the REG procedure (^{SAS Institute, 2009}). The predicted values for each day of the nutrient evolution were calculated by substituting the DALS value in the general equation.

Once the best mathematical functions of each nutrient were selected, the derivatives for each day were calculated. The values obtained were plotted in SigmaPlot (^{Systat Software Inc., 2006}) to identify the periods of least variation, referred to here as having greater stability, of each nutrient. The values can be positive or negative, and as they approach zero the rate of change in the concentration of each nutrient is lower; therefore, the criterion to determine the ALSP was that the result of the derivative was equal or close to zero (^{Granville, Smith, & Longley, 1963}). Then, for each mango cultivar, a table was prepared with the periods of greatest stability for macro and micronutrients, as well as the ALSP for each vegetative flush.

Soil properties

There were some differences in the soil characteristics of the mango orchards where the study was carried out (Table 2). The Chacala and Atonalisco orchards had the most clayey textures. Soil pH varied from 4.7 in Chacala to 6.7 in Las Palmas, and in the 'Tommy Atkins' and 'Kent' (Buenavista) orchards it was within the limits in which mango thrives (5.0 to 6.5) (^{Chávez-Contreras, Vega-Piña, Tapia-Vargas, & Miranda-Salcedo, 2001}). On the other hand, in the 'Ataúlfo' orchards, the most acidic pH values were recorded (4.7 to 4.9); this type of soil tends to favor leaf nutrient deficiencies, mainly Ca and Mg (^{Salazar-García, 2002}). No salinity problems were detected. As for organic matter, only in the Buenavista orchards was the content very low. Additionally, low and very low concentrations of Ca, Mg, Zn and B were evident, and that of Mn was classified as moderately high to very high.

Appropriate leaf sampling period

As the results of leaf analysis vary with vegetative flush and sampling time, ^{Rajput et al. (1985)} suggest establishing an adequate sampling period for each flush to avoid erroneous results. In the present work, the periods of leaf nutrient stability (PLNS) showed differences among the mango cultivars, as well as among their corresponding vegetative flushes (Table 3).

‘Ataúlfo’. In the SpVF, the PLNS for N, P, K, Ca and Mg was from 249 to 331 DALS (Table 3; Figure 1A), and for S from 175 to 226 DALS. In the case of micronutrients, PLNS occurred between 276 and 236 DALS (Table 3; Figure 1B). Although the Mn concentration did not present stability, this period applies to this nutrient. Therefore, for both macro and micronutrients, the ALSP was delimited from October 8 to December 2 (276 to 331 DALS).

Figure 1 Leaf length, value of the derivative and periods of nutrient stability (space between the vertical lines) for macro (A and C) and micronutrients (B and D) in 'Ataúlfo' mango. Data from two orchards. 

For the SuVF, macronutrients stabilized between 94 and 170 DALS (Table 3; Figure 1C) and micronutrients between 100 and 160 DALS (Table 3; Figure 1D). In both cases, the ALSP was from September 30 to November 29 (100 to 160 DALS; Table 3). In this case, as in the SpVF, the PLNS of the micronutrients was fitted to Mn even though in this nutrient there was not a period of stability.

For the 'Manila' mango grown in Veracruz, Mexico, leaf sampling is recommended in June-July or August-September, when the spring leaves are four to seven months old (^{Mosqueda-Vázquez et al., 1996}). When comparing these results with those obtained from cv. Ataúlfo no coincidence was found, since in 'Ataúlfo' the ALSP for the SpVF was when the leaves were from nine to eleven months of age. The foregoing evidences the need to obtain specific information for each mango cultivar and cultivation condition.

‘Kent’. In this cultivar, the PLNS in the SpVF for macronutrients was from 241 to 316 DALS (Table 3; Figure 2A) and for micronutrients between 215 and 318 DALS (Table 3; Figure 2B). As in 'Ataúlfo', S did not show a PLNS that coincided with the other macronutrients; however, between 241 and 316 DALS the value of its derivative showed a lower change rate. The instability of S could be caused by the frequent chemical sprayings that contain this element to control diseases such as anthracnose and powdery mildew (^{Espinoza-Aburto et al., 2006}).

Figure 2 Leaf length, value of the derivative and periods of nutrient stability (space between the vertical lines) for macro (A and C) and micronutrients (B and D) in 'Kent' mango. Data from three orchards.  

In the SuVF, the PLNS for macro and micronutrients was between 96 and 150 DALS and 75 to 157 DALS, respectively (Table 3; Figures 2D and 2C). According to the above, the ALSP was from September 26 to November 19 (96 to 150 DALS) (Table 3). Leaf samplings are appropriate with leaf ages between eight to ten months (spring leaves) and three to five months (summer leaves). These results do not coincide with those reported by ^{Benítez-Pardo et al. (2003)}, who for the same mango cultivar, but in the state of Sinaloa (located north of Nayarit), recommend analyzing leaves from two to four months of age, although they did not specify the type of vegetative flush studied; in addition, this sampling period was proposed with a visual (graphic) criterion, not a mathematical one.

‘Tommy Atkins’. The PLNS of the SpVF for macronutrients occurred from 195 to 370 DALS and from 261 to 365 DALS for micronutrients (Table 4; Figures 3A and 3B). For the AVF, the PLNS for macro and micronutrients was from 256 to 282 DALS and 258 to 284 DALS, respectively (Table 4; Figures 3C and 3D). Accordingly, the ALSP of the SpVF was from September 23 to January 5 (261 to 365 DALS) and from June 6 to 30 (258 to 282 DALS) for the AVF (Table 4). This last result differs from that mentioned by ^{Rajput et al. (1985)}, since they suggest that in subtropical climates the month for sampling AVF leaves is October (April in the northern hemisphere).

Figure 3 Leaf length, value of the derivative and period of nutrient stability (space between the vertical lines) for macro (A and C) and micronutrients (B and D) in 'Tommy Atkins' mango. Data from two orchards.  

No information was found available on sampling periods for mango SuVF leaves, probably because the SpVF, which occurs after flowering, is the most important in most mango-producing regions.