Potential nutrient-response curves and sufficiency ranges for ‘Prata-Anã’ banana cultivated under two environmental conditions

Proper plant nutrition is critical to increasing the yield of bananas. The objective was to establish the potential nutrient-response curves and sufficiency ranges using the boundary line approach (BLA) and the method proposed by Kenworthy (MK) to assess the nutritional status of ‘Prata-Anã’ bananas cultivated under two environmental conditions. The study was carried out using a database comprising leaf nutrient concentrations and banana yields grown at Missão Velha, Ceará, and Ponto Novo, Bahia, Brazil. The reference population consisted of high-yielding plants with yields greater than the mean yield plus 0.5 standard deviation. The database was divided into two datasets. One contained 253 leaf analysis results and a reference population with a mean yield greater than 39.81 t ha–1 yr–1 at Missão Velha. The other contained 147 samples and a reference population with a mean yield greater than 41.69 t ha–1 yr–1 at Ponto Novo. The sufficiency ranges obtained by the BLA for ‘Prata-Anã’ banana in Bahia and Ceará, respectively, are: a) for macronutrients (g kg–1): N (19.3-22.0) and (19.9-22.1); P (1.4-2.0) and (1.4-1.6); K (22.6-32.2) and (24.0-31.3); Ca (4.6-6.5) and (5.3-5.8); Mg (1.8-2.6) and (2.1-2.7); S (1.3-2.0) and (1.3-1.5); b) for micronutrients (mg kg–1): B (8.4-13.0) and (13.7-16.4); Cu (5.6-8.4) and (4.4-5.2); Fe (54.2-77.6) and (39.0-55.0); Mn (140.1-222.8) and (64.0-91.0); Zn (13.5-18.3) and (12.4-14.5). The sufficiency ranges obtained by the BLA are more assertive when assessing the nutritional status for ‘Prata-Anã’ banana.


Introduction
Leaf tissue analysis as a tool for assessing plant nutritional status has been widely used to improve fertilizer rate recommendations and crop management practices. Reference values are conventionally established in calibration tests in which genetic and environmental factors and the interplay between nutrients are controlled; however, the nutritional composition of plant tissues is highly influenced by several environment-and crop-related factors (Iheshiulo et al., 2019). Indiscriminate extrapolations of sufficiency ranges established in diverse environmental conditions may lead to inaccurate nutritional diagnoses; thus, determining site-and cultivar-specific sufficiency ranges is a preferable course of action.
The boundary line approach (BLA) is an alternative to calibration experiments because this method uses nutrient concentration data from commercial crop fields (Maia and Morais, 2016). The approach consists of relating nutrient concentrations to yield data, so that the optimum concentration of a given nutrient can be determined. Moreover, it permits the estimation of the highest attainable yield from observational data (Ali, 2018).
Bananas demand large amounts of nutrients and are sensitive to nutritional imbalances. Thus, periodically, nutritional diagnoses should be adopted as a routine procedure on banana plantations (Silva, 2015) based on specific norms established using data from commercial fields (Lafond, 2013).
The objective of this study was to establish potential nutrient-response curves for determining sufficiency ranges using the BLA and the method proposed by Kenworthy to assess the nutritional status of 'Prata-Anã' bananas cultivated under two environmental conditions.

Experimental conditions
he study was carried out using data from 'Prata-Anã' banana production systems under two environmental conditions. The first farm is located at Missão Velha, in the state of Ceará (CE), Brazil (7°35'90" S, 39°21'17" W, altitude of 442 m). Data were collected from plants averaging 12 years of age at the beginning of data collection and 19 by the end of it. The climate of the region is Aw -tropical savanna climate with a dry winter season and a rainy summer season (Köppen-Geiger) (Alvares et al., 2013). Mean annual rainfall and temperature are 942 mm and 25.8 °C, respectively. The soil was sandy and classified predominantly as a Red-Yellow Latosol (SiBCS) (Santos et al., 2018). On this farm, there are 57 plots averaging 3.26 ha in size of fertigated 'Prata-Anã' banana spaced at 2.8 × 2.8 m (1,275 plants ha -1 ).
The second farm is located at Ponto Novo, in the state of Bahia (BA), Brazil, (10°51'46" S, 40°08'01" W, and altitude of 342 m). Data collection began when bananas were eight years old and ended when they were ten. The climate is also Aw (Köppen-Geiger) (Alvares et al., 2013) with a mean annual rainfall of 697 mm and temperature 24.1 °C. The predominant soil at the site is a sandy Yellow Latosol (SiBCS) (Santos et al., 2018). On this farm, there are 100 plots averaging 4.53 ha in size of fertigated 'Prata-Anã' banana spaced at 2.8 × 2.8 m (1,275 plants ha -1 ).
Fertilizer rates recommended for both sites were based on their respective soil test results and followed Silva (2015) with adaptations. Table 1 and 2 show soil test results and climate data for both sites, respectively. Climate data are the year 2016, when weather stations were installed at the sites.

Database
The results of the analysis of the leaf tissue and the yields recorded in a database belonging to the experimental area were used. Leaf tissue sampling was performed twice a year, every six months, and followed the    recommendations of Costa et al. (2019). The mid-portion of the third leaf lamina, counting from the apex, was collected when the inflorescence had two or three open clusters of male flowers. Samples were processed and analyzed as to leaf macro-(N, P, K, Ca, Mg and S) and micronutrient (B, Cu, Fe, Mn and Zn) contents, which were determined as follows: N -Kjeldahl method; P, S, Ca, Mg, Fe, Mn, Cu, Zn, B, Al -nitric-perchloric acid digestion and determination by ICP-OES; Knitric-perchloric digestion and determination by flame photometer as described by Deus et al. (2018a).
Yields were estimated as t ha -1 yr -1 by weighing hands of harvested bunches. Relative yield (RY) was determined based on the highest recorded yield (100 %) as recorded by Deus et al. (2018b).
The database was divided into two site-specific datasets. A dataset was from the farm located at Missão Velha, CE, and comprised annual yields and leaf analysis results relative to the years from 2010 to 2017. The initial sample containing 804 recordings, mean ± standard deviation of 35.91 ± 7.8 t ha -1 yr -1 , was subdivided into low-and high-yielding populations; the latter was the reference population, defined as having yields above the average plus 0.5 standard deviation, as used by Alves et al. (2019), which corresponded to 39.81 t ha -1 yr -1 (73 % maximum relative yield) (n = 253).
The other dataset was from the farm located at Ponto Novo, BA, and contained leaf analysis results from samples collected twice a year and annual yields recorded between 2014 and 2016. The initial sample consisting of 481 recordings, mean ± standard deviation of 34.89 ± 13.59 t ha -1 yr -1 , was subdivided into low-and high-yielding populations. The reference population had a yield greater than average plus 0.5 standard deviation, corresponding to 41.69 t ha -1 yr -1 (57 % maximum relative yield) (n = 147).

Determination of potential nutrient-response curves, reference values and sufficiency ranges by the Boundary Line Approach (BLA)
Relative yields (RY), on the y-axis, were plotted against leaf nutrient concentrations, on the x-axis, forming a scatter diagram. Data points located on the upper edge of the scatter diagram were selected by drawing a line confining all data, forming a boundary line. Each data point on the upper boundary line represents the highest yield at a corresponding nutrient concentration. A regression equation fitted to the boundary line was used to determine sufficiency ranges.
A boundary line can be determined through different approaches (Deus et al., 2018a). The line around the scatter of data points can be drawn either by hand (Maia and Morais, 2016) or by using computer applications, such as Boundary Fit, developed by the Federal University of Viçosa (UFV) (Lima Neto et al., 2020). In this study, a nonparametric boundary regression (NPBR) package in R (R Development Core Team, 2012) was used as a routine for determining the boundary line.

Original Method proposed by Kenworthy (MK orig )
The mean and variability of leaf nutrient concentrations were obtained from the reference population of each site ( Table 3). Percent of standard (P) (ratio of sample nutrient concentration to standard concentration), influence of variation (I) and coefficient of variation (CV) were calculated. The results were expressed in the form of a percentage. The following equations were used to calculate Kenworthy's balance indices (BIKW): where: P is the ratio of sample nutrient concentration (yi) to standard concentration (Ŷ ) (%); I is the influence of variability (%); CV is the coefficient of variation (%) of nutrient concentrations in the reference population; and BIKW is the balance index proposed by Kenworthy.

Modified Method proposed by Kenworthy (MK mod )
The ranges originally proposed by Kenworthy (1961) for apple trees may not be adequate because the author consistently used a mean variability of 20 % for every nutrient. This poses a problem when dealing with micronutrients because their leaf contents tend to have a variability higher than 20 %. Thus, the BLA was used to obtain nutrient-specific interpretive classes based on RY (Lima Neto et al., 2020) After obtaining the BIKW for each nutrient studied using site-specific norms, RY was plotted against the BIKM to form a scatter of data points. Data points located on the upper boundary of the scatter diagram were selected, and were used to determine regression equations, with which the nutrient-specific interpretive classes were determined based on the following: deficient (RY < 70 %), tending to sufficient (70 ≤ RY < 90 %), sufficient (90 ≤ RY < 100 %), high (100 > RY ≥ 90 %, to the right of the maximum), tending to excessive (90 ≤ RY < 70 %, to the right of the maximum) and excessive (RY < 70 %, to the right of the maximum).

Results and Discussion
The original methodology proposed by Kenworthy (1961), MK orig , is based on the assumption that each nutrient limits crop yield equally; however, when using the BLA, the relationship between the RY and the BIKW (Figures 1A-K and 2A-K) yielded different interpretative classes (Table 4) for each nutrient, which  contradicts Kenworthy's approach. Differences across sufficiency ranges are mainly due to how yield-limiting the nutrient is when its concentration in plant tissues is at its lowest. Apparently, the interpretive classes originally proposed by Kenworthy were based on a mean variability of 20 % for macro-and micronutrients alike. As micronutrient concentrations vary greatly in banana leaves, misleading interpretations are more likely to arise owing to their complex dynamics within the soilplant system (Li et al., 2007;Rengel, 2015).
For each nutrient, regression equations were fitted to a boundary line fitted to the relationship between the RY and the BIKW of 'Prata-Anã' banana grown in CE and BA (Figures 1A-K and 2A-K) with high R 2 (0.92 to 0.97). The regression equations were used to obtain nutrientspecific interpretive classes used for discriminating the BIKW (Table 4).
The BLA allowed for the fitting of significant quadratic regression equations with high R 2 (0.91 to 0.98) to the upper boundary of the relationship between the RY and leaf nutrient concentrations in 'Prata-Anã' grown in CE ( Figure 3A-K) and BA ( Figure 4A-K). Sufficiency ranges were then estimated by regression equations (Table 5).
Sufficiency ranges obtained by MK mod for 'Prata-Anã' grown in CE and BA are in Table 6 while sufficiency ranges obtained by MK orig for CE and BA are in Table 7.
The sufficient N concentration range established by the BLA for 'Prata-Anã' grown in CE was 19.2-22.0 g kg -1 (Table 5); very similar to that obtained by MK mod , 19.3-21.9 g kg -1 , ( Table 6) and close to MK orig , 17.9-21.9 g kg -1 (Table 7). For BA, the sufficient N concentration range obtained by the BLA was 19.9-22.1 g kg -1 (Table  5), with only the upper limit similar to that determined by MK mod , 16.4-22.2 g kg -1 ( Table 6). The range was somewhat different from that proposed by MK orig , 18.5-23.0 g kg -1 (Table 7). |The sufficient N concentration ranges for Missão Velha, CE, are similar to that reported by Deus et al. (2018b) (18.0-26.8 g kg -1 ) for the same site and different from that reported by Silva (2015) for the same cultivar grown in northern Minas Gerais, Brazil (25.0-29.0 g kg -1 ). This difference was due to differences in soil organic matter levels and crop management.
Bananas grown on soils with medium-to-high organic matter content (> 16 g kg -1 ), such as those in this study (Table 1),are not likely to respond to N fertilization, and yields may even decrease as a result of excessive N Sufficiency ranges for 'Prata-Anã' banana Sci. Agric. v.78, Suppl., e20200158, 2021 applications (Silva, 2015). In addition, nutrient cycling plays a major role in replenishing the soil with N; up to 83 % of N returns to the soil after the harvest (Hoffmann et al., 2010). The increased N level in the soil resulted in a narrower sufficient N range than that reported by Silva (2015) and similar to that found by Deus et al. (2018b) in conditions akin to those of this study. This reduction in leaf N concentration was also observed by Damatto Junior et al. (2011), who reported a decrease in leaf N concentrations in 'Prata-Anã' banana subject to an increase in N supply.
The lower sufficient N concentration ranges reported in this study, in comparison with those reported by Silva (2015), agree with previously proposed reductions in N fertilizer rates (Deus et al., 2018a). In 1999, the recommended N fertilizer rate for 'Prata-Anã' grown in northern Minas Gerais ranged from 200 to 400 kg ha -1 yr -1 , a rate range much greater than previous N recommendations, which ranged from 90 to 220 kg ha -1 yr -1 (Silva, 2015).
The sufficient P concentration range obtained by the BLA for 'Prata-Anã' grown in CE was 1.4-2.0 g kg -1 (Table 5); equal to the range found by MK mod (Table 6) and close to MK orig , 1.3-1.7 g kg -1 (Table 7). For BA, the sufficient range obtained by the BLA was 1.4-1.6 g kg -1 (Table 5), the same range determined by MK mod (Table  6) and very close to the range obtained by MK orig , 1.3-1.6 g kg -1 (Table 7). Similarly, Deus et al. (2018b) and Silva (2015) found the ranges 1.5-1.7 g kg -1 and 1.5-1.9 g kg -1 , respectively; their lower variability is consistent with how banana plants respond to P (Silva, 2015).
Phosphorus is the macronutrient that accumulates the least in leaves of 'Prata-Anã' banana (Hoffmann et al., 2010). Increased leaf P concentrations may limit the yield due to imbalances in other nutrients, particularly Zn. Although soil P availability increases, leaf P concentration remains virtually unchanged (Damatto Junior et al., 2011). It has been reported that 'Prata-Anã' bananas only respond to P fertilization in the first cycle, even when grown on soils with low P levels (Silva, 2015).
The sufficient K concentration range obtained by the BLA for CE was 22.6-32.2 g kg -1 ( Table 5). The range limits are closer to that found by MK mod , 22.3-32.3 g kg -1 (Table 6) than by MK orig , 26.9-34.0 g kg -1 (Table 7). For BA, the sufficient K concentration range obtained       by the BLA was 24.0-31.3 g kg -1 (Table 5); different from the range determined by MK mod , 27.3-36.2 g kg -1 (Table 6) and similar to MK orig , 24.5-31.4 g kg -1 ( Table 7). The range established by Silva (2015), 27.0-35.0 g kg -1 , was closer to that obtained by MK orig while Deus et al. (2018b) reported a narrower, higher range, 32.0-37.4 g kg -1 , which reflects how K moves within the soil-banana system, with greater variations in tissue concentration as a result of biochemical and geochemical cycling (Silva et al., 2015). Although bananas demand large amounts of K, up to 86 % of the K taken up by banana plants is reutilized (Hoffmann et al., 2010) when plant residues left on the soil surface after the crop harvest break down. Nevertheless, K deficiency may reduce the relative growth of 'Prata-Anã' banana by 44 % (Silva et al., 2014).
The sufficient Mg concentration established by the BLA for CE was 1.8-2.6 g kg -1 (Table 5); very close to MK mod and MK orig , 1.9-2.6 g kg -1 (Table 6) and 1.9-2.4 g kg -1 (Table 7), respectively. For BA, the sufficient Mg concentration range obtained by the BLA was 2.1-2.7 g kg -1 (Table 5), which is similar to that determined by MK mod and MK orig , 2.0-2.6 g kg -1 (Table 6) and 2.3-2.7 Sufficiency ranges for 'Prata-Anã' banana Sci. Agric. v.78, Suppl., e20200158, 2021 g kg -1 (Table 7), respectively. The sufficient Mg range determined by Silva (2015) was 2.4-4.0 g kg -1 , whose lower limit is close to the upper limit of the sufficient Mg concentration ranges found in this study. Narrower ranges for Mg might be associated with the high K supply via fertigation to a soil containing high K levels (8.4 mmol c dm -3 ). Thus, the K/Mg ratio increased, which limited Mg uptake (Silva, 2015;Deus et al., 2018b).
Banana is a monocot and thus has low root cation exchange capacity, which means the plant can take up more monovalent cations to the detriment of divalent cations. Similarly,,high soil Ca levels, particularly in CE, contribute to decreases in Mg uptake by competitive inhibition. In a pot experiment withholding Mg, 'Prata-Anã' reduced growth by 67 % (Silva et al., 2014); therefore, one should be careful when supplying Mg to banana plants grown on soils containing high K levels, especially when the plants are under stress because Mg and K play an important role in alleviating plant stress (Marschner, 2012).
The sufficient B concentration range established by the BLA for 'Prata-Anã' cultivated in CE was 8.4-13.0 mg kg -1 (Table 5), while by MK mod and MK orig , the ranges were 6.4-11.6 mg kg -1 (Table 6) and 7.9-11.1 mg kg -1 (Table 7), respectively. For BA, the sufficient B concentration range obtained by the BLA was 13.7 to 16.4 mg kg -1 ( Table 5). The range differs from those determined by MK mod and MK orig , 11.5-15.5 mg kg -1 (Table 6) and 11.7-14.7 mg kg -1 , respectively. The sufficient B concentration range established for CE is lower than those proposed by Silva (2015), 12.0-25.0 mg kg -1 , whose lower limit has the same value as the corresponding upper limit reported herein. The sufficient range established for BA was different, but within the range proposed by Silva (2015).  1.9-2.6 2.6-3.4 3.4-4.0 ≥ 4.0 S < 0.9 0.9-1.3 1.3-1.9 1.9-2.6 2.6-3.0   The sufficient Cu concentrations obtained by the BLA for 'Prata-Anã' grown in CE ranged from 5.6 to 8.4 mg kg -1 (Table 5), which is similar to the range determined by MK mod , 5.3-8.8 mg kg -1 (Table 6), but different from that obtained by MK orig , 4.5-6.2 mg kg -1 ( Table 7). The sufficient Cu concentration range determined by the BLA for BA was 4.4-6.2 mg kg -1 (Table 5), whose limits are different from those determined by MK mod , 2.9-4.7 mg kg -1 (Table  6), and equal to the MK orig , 4.2-5.3 mg kg -1 (Table 7). Silva (2015) reported a sufficiency range of 2.6-8.8 mg kg -1 , whose lower limit is different from those determined in CE by the BLA and MK mod , and altogether different from limits obtained by MK orig . For BA, all sufficient Cu ranges except the one obtained by MK mod were different from the range proposed by Silva (2015).
Manganese is the most variable element in both CE (CV = 51.8 %) and BA (CV = 38.0 %). If leaf nutrient concentrations in a population have a CV higher than 30 %, the sufficiency ranges obtained by MK orig are less precise in detecting nutrient deficiencies. Moreover, Silva (2015) found a wider sufficient Mn range because the author did not use a correction factor (k) that is needed to narrow the range down (Alves et al., 2019) in the event of highly fluctuating tissue nutrient levels, mostly micronutrients with a CV higher than 20 %. The sufficient Zn concentration range obtained by the BLA for CE was 13.5-18.3 mg kg -1 (Table 5), similar to the range determined by MK mod and MK orig , 12.9-18.3 mg kg -1 (Table 6) and 13.1-16.5 mg kg -1 (Table 7), respectively. For 'Prata-Anã' grown in BA, the sufficient Zn concentration range obtained by the BLA was 12.4-14.5 mg kg -1 (Table 5), similar to ranges obtained by MK mod and MK orig , 12.2-14.7 mg kg -1 (Table 6) and 12.0-14.8 mg kg -1 (Table 7), respectively. Proposed ranges for CE are close to that established by Silva (2015), 14.0-25.0 mg kg -1 , despite the latter's higher upper limit. As for BA, the upper limits were identical to the lower limits proposed by Silva (2015).
The sufficient ranges for micronutrients are less consistent with the literature than for macronutrients. Micronutrient concentrations in leaves are associated with their dynamic within the soil-plant system. Their availability in the soil is governed by pH, organic matter content, clay content, soil source rock, and, specifically for Fe and Mn, by the reduction potential (Li et al., 2007;Rengel, 2015). These factors can interfere with element uptake, thereby affecting leaf micronutrient concentrations.
For example, in CE, soil pH averaged 7.3, at which metal cations, such as Cu, Fe, Zn and Mn, as well as B, are considerably less available. In general, soil pH has a major impact on Mn availability in the soil (Marschner, 2012). Therefore, sufficient ranges established for 'Prata-Anã' were higher for Cu, Fe, Mn and Zn in CE compared with BA, but lower for B, which is associated with the higher fertility of soils in CE. However, a higher soil availability of Fe and Mn may cause temporary toxicity in plants in the case of heavy rain and may precipitate a rise in reducing conditions, especially in soils containing high Mn levels.
The results highlight the importance of this study. The advantages of using the BLA to obtain sufficiency ranges include taking into account the site specificities, climate, soil, cultivar, and management, which increase the degree of precision in assessing the nutritional status of 'Prata-Anã' bananas by preventing miscalculated extrapolations.
Potential response curves and sufficiency ranges for leaf macro-and micronutrient concentrations and BIKW were established. They allow for an improved assessment of the nutritional status of fertigated 'Prata-Anã' bananas under different environmental conditions, which is a refinement to be incorporated into production systems.

Conclusions
The sufficiency ranges obtained by the BLA for 'Prata-Anã' banana in BA and CE, respectively, are: a) for macronutrients (g kg -1