Nutritional standards for cactus pear ‘Orelha de Elefante Mexicana’ by uni-, bi-, and multivariate methods¹

Normas nutricionais para palma forrageira ‘Orelha de Elefante Mexicana’ por métodos uni, bi e multivariados

ABSTRACT

The objective of this study was to establish nutritional standards and reference values for the cactus pear ‘Orelha de Elefante Mexicana’ using the Sufficiency Range (SR), Boundary Line (BL), Mathematical Chance (MCh), Diagnosis and Recommendation Integrated System (DRIS), Compositional Nutrient Diagnosis (CND), Kenworthy Balanced Index (KBI), and Critical Level by Reduced Normal Distribution (CLRiz), and to identify the most appropriate methods for nutritional diagnosis. The dataset containing nutrient concentration of cladodes and dry matter yield (DMY) derived from an experiment conducted in randomized blocks, with four replicates, in a split-plot scheme over time, with four planting densities (20,000, 40,000, 60,000, 80,000 plants ha^-1) arranged in the plots, and four evaluation cycles (2019-2021, 2021-2022, 2022-2023 and 2023-2024) in the subplots, totaling 64 sampling units, were divided into a low-yield (LYP) and a high-yield (HYP) populations, with HYP defined as DMY ≥ 25.23 Mg ha^-1 and n = 28. In the HYP, the order of macronutrient concentrations in the cladodes of Opuntia stricta ‘Orelha de Elefante Mexicana’ was K > Ca > Mg > N > P > S, whereas for micronutrients it was Fe > Mn > Na > B > Zn > Cu. Reference values increased with greater soil nutrient availability, and differences among diagnostic methods were mainly attributed to their conceptual foundations. The interpretive classes from SR, KBI, BL, MCh, and CND, along with the optimal concentrations from DRIS, KBI, and BL, proved to be the most suitable tools for the nutritional diagnosis of Opuntia stricta ‘Orelha de Elefante Mexicana’.

Key words:
Opuntia stricta ; cladode analyses; soil fertility; multinutrient diagnosis; reference values

HIGHLIGHTS

Potassium is the predominant macronutrient, while iron is the most abundant micronutrient, for cactus pear Opuntia stricta.

Reference values for nutritional diagnosis increase with greater availability of nutrients in the soil.

There is a difference between the interpretative classes generated by different nutritional diagnostic methodologies.

RESUMO

O objetivo desse estudo foi estabelecer normas e valores de referência nutricional para a palma forrageira ‘Orelha de Elefante Mexicana’, utilizando a Faixa de Suficiência (SR), Linha de Fronteira (BL), Chance Matemática (MCh), Sistema Integrado de Diagnose e Recomendação (DRIS), Diagnose da Composição Nutricional (CND), Índices Balanceados de Kenworthy (KBI) e Nível Crítico (CLRiz), e identificar as mais adequadas ao diagnóstico nutricional. O banco de dados contendo teores de nutrientes dos cladódios e produtividade de matéria seca (DMY) derivado de experimento conduzido em blocos casualizados, com quatro repetições, em parcelas subdivididas no tempo, sendo quatro densidades de plantio (20.000, 40.000, 60.000, 80.000 plantas ha^-1) nas parcelas, e quatro ciclos de avaliação (2019-2021, 2021-2022, 2022-2023 e 2023-2024), nas subparcelas, totalizando 64 unidades amostrais, foi dividido em populações de baixa (LYP) e alta (HYP) produtividades, sendo HYP com DMY ≥ 25,23 Mg ha^-1 e n = 28. A ordem de concentração dos macronutrientes nos cladódios da palma forrageira Opuntia stricta ‘Orelha de Elefante Mexicana’, na HYP, foi K > Ca > Mg > N > P > S; e de micronutrientes foi Fe > Mn > Na > B > Zn > Cu. Os valores de referência elevam com aumento da disponibilidade de nutrientes no solo e as diferenças entre os métodos foram mais associadas às suas concepções. As classes interpretativas geradas com SR, KBI, BL, MCh e CND, e os níveis ótimos gerados com DRIS, KBI e BL são mais adequados ao diagnóstico nutricional da Opuntia stricta ‘Orelha de Elefante Mexicana’.

Palavras-chave:
Opuntia stricta ; análises de cladódios; fertilidade do solo; diagnóstico multinutriente; valores de referência

Introduction

The cactus pear Opuntia stricta (Haw.) Haw. ‘Orelha de Elefante Mexicana’, a species native to Mexico, is widely used as a feed source for ruminants in the semiarid regions of Brazil (Matos et al., 2021). Cactaceae species exhibit high drought tolerance, conferred by their Crassulacean Acid Metabolism (CAM), which enhances adaptation to environments under water limitation (Santos et al., 2024); in addition, this cultivar is distinguished as it shows resistance to the carmine cochineal (Dactylopius opuntiae) (Silva et al., 2025), making it a promising alternative for forage production in areas prone to this pest, and, under irregular rainfall conditions, it consistently exhibits high yield potential when properly managed (Pereira et al., 2022; Santos et al., 2024), along with excellent palatability for livestock (Silva et al., 2017).

Crop yield, however, depends on a balanced nutrient supply, which is influenced by soil characteristics and climatic conditions. Factors such as cultivar selection (Teles et al., 2024), planting density (Soares et al., 2025), mineral fertilization (Lédo et al., 2021), and irrigation management (Santos et al., 2024) directly affect nutrient uptake and tissue concentrations, ultimately influencing crop performance. Therefore, assessing the crop’s nutritional status under different management systems is essential to guide effective fertilization strategies (Hernández-Vidal et al., 2021).

Plant tissue analysis is a fundamental tool in soil fertility management, as it provides an integrated assessment of the plant’s physiological condition within its growing environment and shows a strong correlation with yield (Donato et al., 2017). By integrating information from the soil–plant system, tissue analysis is widely recognized for its reliability and applicability in nutritional diagnosis. However, because nutrient interactions in plant tissues are dynamic and complex, techniques with varying degrees of analytical integration have been developed to address this complexity, ranging from univariate to more robust multivariate approaches (Attar et al., 2015).

Univariate methods, which assess each nutrient individually, include the Sufficiency Range (SR), Boundary Line (BL), Mathematical Chance (MCh), Kenworthy Balanced Index (KBI), and Critical Level by Reduced Normal Distribution (CLRiz). The Diagnosis and Recommendation Integrated System (DRIS) represent a bivariate approach that considers both direct and inverse relationships between nutrient pairs. The Compositional Nutrient Diagnosis (CND), in contrast, is a multivariate approach that simultaneously integrates all nutrients based on their geometric mean.

Among these methodologies, CND has been highlighted as the most accurate and robust because it accounts for multinutrient interactions, thereby providing a more comprehensive representation of the plant’s nutritional balance (Lima Neto et al., 2022), which is not always confirmed, as observed by Serra et al. (2010) and Camacho et al. (2012).

According to Santos et al. (2022a), diagnostic methodologies can be based on either dose–response experiments or large-scale commercial crop databases and have been widely applied to various crops. For cactus pear, studies conducted in Mexico by Blanco-Macías et al. (2009; 2010) applied the CND and BL methods; in Brazil, Donato et al. (2017) used SR and CLRiz to evaluate soil chemical properties; Alves et al. (2019a,b) applied MCh, SR, and CLRiz; while Teixeira et al. (2019; 2021; 2024) worked with DRIS, KBI, and BL. Although these studies significantly contributed to understanding the nutritional management of cactus pear, they focused on Opuntia ficus-indica. In Brazil, no studies have applied the CND method, which is recognized as theoretically more robust.

Thus, there is a clear need for studies aimed at monitoring nutritional status and applying predictive techniques to define appropriate fertilization strategies for cactus pear, particularly for O. stricta ‘Orelha de Elefante Mexicana’. Therefore, the objective of this study was to establish nutritional standards and reference values for the cactus pear ‘Orelha de Elefante Mexicana’ using the Sufficiency Range (SR), Boundary Line (BL), Mathematical Chance (MCh), Diagnosis and Recommendation Integrated System (DRIS), Compositional Nutrient Diagnosis (CND), Kenworthy Balanced Index (KBI), and Critical Level by Reduced Normal Distribution (CLRiz) approaches, and to identify the most appropriate methods for nutritional diagnosis.

Material and Methods

This study was conducted using a database derived from an experiment with the cactus pear Opuntia stricta (Haw.) Haw. ‘Orelha de Elefante Mexicana’, carried out in the Agricultural Sector of the Instituto Federal de Educação, Ciência e Tecnologia Baiano (IF Baiano) – campus Guanambi. The experimental area is located in the Ceraíma District, municipality of Guanambi, Bahia, Brazil, at 14° 17’ 45.87” S and 42° 41’ 43.56” W, with altitude of 545 m. The region’s climate is semi-arid, predominantly hot and dry. Historical averages indicate an annual precipitation of 673.6 mm and a mean temperature of 26 °C over the last 43 years (Soares et al., 2025).

The experiment was conducted from October 2019 to August 2024, covering four production cycles. The first harvest was carried out approximately 18 months after planting, as described by Soares et al. (2025), while the subsequent cycles were conducted at annual intervals. Meteorological data recorded during the experimental period by an automatic weather station installed near the study area indicated that, in the first cycle (October 29, 2019 – June 25, 2021), total precipitation was 1,328.02 mm. In the second cycle (June 26, 2021 – July 27, 2022), precipitation totaled 822.05 mm. In the third cycle (July 28, 2022 – June 21, 2023), precipitation was 591.55 mm. In the fourth cycle (June 22, 2023 – July 4, 2024), accumulated precipitation reached 857.49 mm.

The soil in the experimental area was classified as an Oxisol according to the USDA Soil Taxonomy (Soil Survey Staff, 2022), corresponding to a Latossolo Vermelho-Amarelo in the Brazilian Soil Classification System (Santos et al., 2025b), with a medium texture composed of 24% clay, 13% silt, and 63% sand. Chemical analyses of the soil reflect the cumulative effects of fertilization (Table 1).

Table 1.
Chemical attributes of the soil in the experimental area cultivated with Opuntia stricta ‘Orelha de Elefante Mexicana’, at the first harvest (18 months after planting) and after the second, third, and fourth annual harvests

Cycles	pH1	OM2	P3	K3	Na3	Ca4	Mg4	Al4	H+Al5	SB	eCEC
		dag kg-¹	mg dm-3	--------------------------------------- cmolc dm-3----------------------------------------
8 I – 2020	5.7	0.9	76.6	0.56	0.1	1.4	0.6	0.0	1.7	2.6	2.6
9 II – 2022	6.1	1.0	62.0	1.10	0.1	1.6	0.6	0.0	1.2	3.4	3.4
10 III – 2023	5.8	1.6	98.1	1.32	0.2	2.1	1.0	0.0	1.5	4.6	4.6
11 IV – 2024	6.3	2.2	133.9	1.08	0.2	3.3	1.6	0.0	1.3	6.1	6.1

Cycles	CEC	V	M	B6	Cu3	Fe3	Mn3	Zn3	P-res7	EC
	cmolc dm-3	---------%---------		----------------------mg dm-3---------------------					mg L-1	dS m-1
8 I – 2020	4.3	60	0	0.3	0.4	28.3	48.9	40.3	40.4	0.4
9 II – 2022	4.6	74	0	0.4	0.4	18.1	33.0	24.1	44.0	0.6
10 III – 2023	6.1	76	0	0.3	0.4	17.1	40.0	10.8	45.7	0.6
11 IV – 2024	7.4	82	0	0.4	0.6	17.2	49.7	5.7	45.9	0.7

• ¹
  pH in water;
• ²
  Colorimetry;
• ³
  Extractant: Mehlich-1;
• ⁴
  Extractant: 1 mol L^-1 KCl;
• ⁵
  SMP pH;
• ⁶
  Extractant: CaCl₂;
• ⁷
  Extractant: Ca(H₂PO₄)₂, 500 mg L^-1 P in 2 mol L^-1 HOAc (P equilibrium solution); SB – Sum of bases; eCEC – Effective cation exchange capacity; CEC – Cation exchange capacity at pH 7; V – Base saturation; m – Aluminum saturation; P-res – Residual phosphorus; EC – Electrical conductivity of soil saturation extract;
• ⁸
  Samples collected one year after planting;
• ^{9, 10 and 11}
  Samples collected after the harvests of the second, third, and fourth cycles, respectively

No soil analysis was performed immediately before planting in 2019; however, the history of land use and fertilization between 2011 and 2015 is reported in Lédo et al. (2020), and the initial attributes were: pH = 5.57; OM = 1.13 dag kg^-1; P = 23.57 and K = 0.46; Na = 0.10; Ca = 1.93; Mg = 0.90 and H + Al = 1.60; SB = 3.40; CEC at pH 7.0 = 4.97 (cmol_c dm^-3); V = 67.67%; B = 0.40; Cu = 0.40; Zn = 2.03; Fe = 35.93, and Mn = 50.20 (mg dm^-3); P-res = 39.10 mg L^-1 and ECse = 0.93 dS m^-1. Between 2016 and 2017, two additional production cycles were conducted without fertilization, and the area remained fallow from October 2017 to October 2019.

Organic matter content was classified as low in cycles I and II, moderate in cycle III, and very high in cycle IV. Soil P and K concentrations remained very high throughout all cycles. In contrast, Ca, Mg, and the sum of bases were very low in cycle I, low in cycle II, moderate in cycle III, and very high in cycle IV. Base saturation (V%) ranged from moderate in the first two cycles to high in cycles III and IV, according to the criteria established by Donato et al. (2017).

Planting was carried out in triple rows spaced 3.0 m apart, with 1.0 m between internal rows, and plant spacings of 0.30, 0.15, 0.10, and 0.075 m, according to the experimental design.

During the experimental setup, basal fertilization consisted of 150 kg ha^-1 of P₂O₅ (single superphosphate) and 30 Mg ha^-1 of cattle manure incorporated into the planting furrows. In the subsequent rainy season, 300 kg ha^-1 of K₂O (potassium chloride), 75 kg ha^-1 of N (ammonium sulfate), and 60 Mg ha^-1 of cattle manure were applied as topdressing at a distance of 0.20 m from the rows.

The fertilization strategy was standardized in the first production cycle, following the protocol described by Soares et al. (2025). Considering the organic and mineral fertilization applied at planting and as top-dressing during the first rainy season, as well as the fertilization with manure and K₂O (via potassium chloride) repeated during the second rainy season—still within the first cycle—the total amount of nutrients supplied was 930 kg ha^-1 of N, 1,770 kg ha^-1 of P₂O₅, and 1,050 kg ha^-1 of K₂O.

In the following cycles, after each harvest (I, II, and III), 90 Mg ha^-1 of cattle manure were applied approximately 30 days before the onset of the rainy season, along with 300 kg ha^-1 of K₂O applied during the rainy season, based on nutrient extraction estimates for the crop (Donato et al., 2017). After the third cycle, 1 Mg ha^-1 of dolomitic limestone (Effective Neutralizing Value of 82.02%), containing 29.00% CaO and 19.00% MgO, was applied to correct soil acidity and provide Ca and Mg.

The experimental design was a randomized complete block design, arranged in a split-plot scheme, with four replicates. Planting densities of 20,000, 40,000, 60,000, and 80,000 plants ha^-1 were assigned to the main plots, while production cycles (2019–2021, 2021–2022, 2022–2023, and 2023–2024) were assigned to the subplots, totaling 64 experimental units.

Cladode samples, specifically targeting third-order cladodes that were fully developed and physiologically mature, were collected from all experimental units, at the time of harvest for each cycle: in the first cycle at 18 months (600 days) after transplanting (Soares et al., 2025), and in the subsequent cycles—from the second to the fourth—at intervals of approximately one year. This procedure followed Donato et al. (2017), selecting one representative plant per plot from the central rows to avoid border effects. After harvesting, fresh mass and dry matter content were determined by drying samples in a forced-air oven at 65 °C to constant weight.

The dried samples were then sent to the laboratory of the Empresa de Pesquisa Agropecuária de Minas Gerais for determination of macronutrient (N, P, K, Ca, Mg, and S) and micronutrient (B, Cu, Fe, Mn and Zn) and Na concentrations, according to the analytical methods (Silva, 2009).

In each production cycle, green matter (GMY, Mg ha^-1) and dry matter (DMY, Mg ha^-1) yields were evaluated based on the harvest of whole cladodes from the usable plots, keeping the primary cladodes intact, and subsequent weighing on a field scale. Dry matter yield was obtained from the relationship between GMY and the dry matter content of the samples, following the harvesting and evaluation procedures described by Donato et al. (2017) and Soares et al. (2025).

Data on nutrient concentrations in the cladodes and DMY from the 64 experimental units were compiled and subjected to descriptive statistical analysis.

The experimental population was stratified into two groups based on DMY: low-yield (LYP) and high-yield (HYP) populations, using as the cutoff point the mean value of 25.23 Mg ha^-1 per cycle, corresponding to the average DMY of the cactus pear ‘Orelha de Elefante Mexicana’, with n = 28. Nutritional diagnosis methods were applied considering only the DMY for the following approaches: Sufficiency Range (SR), Mathematical Chance (MCh), Critical Level by Reduced Normal Distribution (CLRiz), Kenworthy Balanced Index (KBI), Diagnosis and Recommendation Integrated System (DRIS), and Compositional Nutrient Diagnosis (CND). The Boundary Line (BL) approach was applied considering the whole experimental population.

For the Sufficiency Range (SR), reference values were determined from HYP data using Eq. 1.

(1) $\text{SR}=\overline{x}\pm \text{ks}\overline{x}$

Where:

SR - nutrient sufficiency range in the cladodes;

X̅ - mean nutrient concentration in the HYP;

sX̅ - standard deviation of the mean; and,

k - a correction factor used to adjust interpretative classes and prevent excessively wide ranges (Santos et al., 2022a,b).

Thus, the following values were established: k = 1.0 for CV < 20%; k = 0.8 for 20.01% ≤ CV ≤ 40%; k = 0.6 for 40.01% ≤ CV ≤ 80%; and k = 0.4 for CV > 80%. Based on the Sufficiency Range (SR), nutrient contents in the cladodes were classified into five interpretative categories: deficient (DEF), when < (x̅ − 2ksx̅); tending to sufficient (TSF), when ≥ (x̅ − 2ksx̅) and < (x̅ − ksx̅); sufficient (SUF), when ≥ (x̅ − ksx̅) and < (x̅ + ksx̅); high (HIGH), when ≥ (x̅ + ksx̅) and < (x̅ + 2ksx̅); and tending to excess (TEX), when ≥ (x̅ + 2ksx̅).

For the BL approach, outliers below the lower limit and above the upper limit of the interquartile range (first to third quartile) were removed from the dataset comprising the whole experimental population (LYP and HYP). The DMY values were then related to the nutrient concentrations in cladodes using bivariate (X, Y) scatterplots. From these plots, points located along the upper boundary of the scatter were selected, representing the highest yields associated with specific nutrient concentrations. A potential response model regression equation (Santos et al., 2022a;b) was fitted to these threshold points to determine nutritional reference values.

The fitted BL equations were differentiated to identify the optimal nutrient concentrations (OC_BL) at the point of maximum DMY. By substituting these OC_BL values into the equations, the maximum DMY for each nutrient was estimated (Teixeira et al., 2024).

The interpretative categories of nutrient concentrations in cladodes were defined, based on their position relative to the point of maximum DMY: deficient, DMY < 70%, to the left of the maximum; tending to sufficient, 70% ≤ DMY < 90%, to the left of the maximum; sufficient, 90%, to the left of the maximum, ≤ DMY < 90%, to the right of the maximum; high, 90% > DMY ≥ 70%, to the right of the maximum; and tending to excess, DMY > 70%, to the right of the maximum.

The MCh approach (Wadt et al., 1998) was applied following the procedure described by Alves et al. (2019a,b). DMY and nutrient concentration data in the cladodes were arranged in ascending order and subsequently grouped into classes (i), the number of which was determined by the square root of the total number of observations (n). The amplitude of each class was obtained by dividing the data range by the number of classes. To select the fraction of HYP, the cutoff value was defined as the mean DMY of the HYP plus half of its sx̅, x̅ ± 0.5 sx̅ = 30.49 + (0.5 × 5.31) = 33.14 Mg ha^-1, designated as the highest-yield population (HTYP). Based on this criterion, eight plots (28.57%) composed the reference subpopulation, with a mean yield of 37.28 Mg ha⁻¹.

The mathematical chance for each class i (MCh_i) was determined using Eqs. 2, 3 and 4.

(2) ${\text{MCh}}_{\text{i}}={\left[\text{MCh}\left(\frac{\text{Ai}}{\text{A}}\right)\cdot \text{MCh}\left(\frac{\text{Ai}}{\text{Ci}}\right)\right]}^{0.5}$

Where:

MCh_i - represents the mathematical chance of class i;

Ai - total number of plots whose nutrient contents of class i (for i = 1 to n) are associated with the HTYP; the number of interpretation classes i is defined by the square root of the number of plots in the HYP. In this study, i ranged from 1 to 5, since the square root of n = 28, the number of HYP;

A - total number of plots in the class HTYP; and,

Ci - total number of plots whose nutrient i content falls within class i (for i = 1 to n).

(3) $\text{MCh}\left(\frac{\text{Ai}}{\text{A}}\right)=\text{P}\left(\frac{\text{Ai}}{\text{A}}\right)\cdot {\text{DMY}}_{\text{i}}$

Where:

P(Ai/A) - relative frequency of high-yield plots in class i relative to the total number of high-yield plots; and,

DMY_i - mean yield of class i.

(4) $\text{MCh}\left(\frac{\text{Ai}}{\text{A}}\right)=\text{P}\left(\frac{\text{Ai}}{\text{Ci}}\right)\cdot {\text{DMY}}_{\text{i}}$

Where:

P(Ai/Ci) - proportion of high-yield plots within class i.

The definition of the sufficiency range was based on the lower (LL) and upper (UL) limits of the classes that exhibited the highest MCh_i values. In addition, according to the criteria proposed by Santos et al. (2022a), the classes with the highest total frequency of plots and the greatest occurrence of highly productive plots (DMY ≥ x̅ + 0.5 sx̅) were also considered in defining the sufficient range.

After defining and selecting the sufficient classes, the optimal nutrient concentrations (OC_MCh) were calculated as the median of the limiting values (lower and upper) of the selected classes, while the critical levels (CL) corresponded to the lower limit (LL).

For the DRIS, the nutrient concentrations in the cladodes and the DMY of the HYP were used. Initially, all possible bivariate relationships among the nutrients were established, considering both direct (A/B) and inverse (B/A) forms.

The DRIS indices were then calculated for each nutrient following the procedure proposed by Beaufils (1973) and applied by Teixeira et al. (2021). For a given nutrient A, the DRIS index was obtained according to Eq. 5:

(5) $\text{IA}=\frac{{\displaystyle {\sum }_{i=1}^n\text{f}\left(\frac{\text{A}}{{\text{B}}_{\text{i}}}\right)}-{\displaystyle {\sum }_{j=1}^m\text{f}\left(\frac{{\text{B}}_{\text{j}}}{\text{A}}\right)}}{\text{n+m}}$

Where:

IA - DRIS index of nutrient A;

${\displaystyle {\sum }_{\text{I}=1}^{\text{n}}\text{f}\left(\frac{\text{A}}{{\text{B}}_{\text{i}}}\right)}$- sum of the functions in which the nutrient “A” is in the numerator;

${\displaystyle {\sum }_{\text{J}=1}^{\text{m}}\text{f}\left(\frac{{\text{B}}_{\text{j}}}{\text{A}}\right)}$- sum of the functions in which nutrient “A” is in the denominator;

n - number of times the nutrient appears in the numerator; and,

m - number of times the nutrient appears in the denominator.

The direct functions f(A/B) and inverse functions f(B/A) were obtained according to the formula by Jones (1981), which evaluates the dual relationship of the sample under diagnosis and the average obtained from the reference population, as Eq. 6.

(6) $\text{f}\left(\frac{\text{A}}{\text{B}}\right)\text{=}\frac{\left[\left(\frac{\text{A}}{\text{B}}\right)\text{-}\left(\frac{\text{a}}{\text{b}}\right)\right]}{\text{s}\overline{x}}$

Where:

A/B - dual relationship between the concentrations of nutrients A and B in the plot under diagnosis;

a/b - mean of the dual relationships between the concentrations of nutrients A and B in the HYP; and,

s - standard deviation of the dual relationships of nutrients A and B in the HYP.

The diagnostic classes of nutrient levels in cladodes were established based on the distributions of the DRIS indices of HYP, considering the x̅ and variations applied to the sx̅, according to criteria defined by Beaufils (1973), with modifications, namely: Deficient: < -4/3 sx̅; Tending to Sufficient: between -4/3 sx̅ and -2/3 sx̅; Sufficient: between -2/3 sx̅ and 2/3 sx̅; High: between 2/3 sx̅ and 4/3 sx̅; and Tending to Excess: ≥ 4/3 sx̅.

The optimal concentration (OC) was also estimated, based on the x̅ of the reference population and the CV, according to Eq. 7.

(7) ${\text{X}}_{\text{i}}={\overline{x}}_I\frac{\left({\text{CV}}_{\text{i}}-\text{DRISI}\right)}{\left({\text{CV}}_{\text{i}}-\text{100}\right)}$

Where:

X_i - nutrient i content at the lower or upper limit of the class;

CV_i - coefficient of variation of nutrient i;

x̅_i - average present in the standard of nutrient i; and,

DRISI - fixed DRIS indices to determine the lower or upper limits of the class.

Nutritional standards were defined using the KBI method based on HYP data. To achieve this, the x̅, sx̅, CV, and variance (s²) of the nutrient concentrations in the cladodes and the DMY were calculated. Following the methodology used by Teixeira et al. (2021), the standard indices Proportion (P), Influence (I), and Kenworthy Balanced Index (KBI) were expressed as a percentage and estimated based on the HYP. This approach considers both situations in which the nutrient content in the sample (y_i) is above and below the standard population mean (y̅). The procedure follows the method used by Teixeira et al. (2021), modified from the original proposal by Kenworthy (1961), according to Eqs. 8, 9 and 10.

(8) $\text{P=100}\left(\frac{\text{yi}}{\overline{y}}\right)$

(9) $\text{I=CV}\left({\text{y}}_{\text{i}}\text{-}\overline{y}\right)\text{/}\overline{y}$

(10) $\text{KBI}=\text{P-I}$

Where:

P - ratio between the nutrient content in the sample (yi) and the mean of the standard population (y̅);

I - influence of variation, weighted by the coefficient of variation of HYP;

CV - coefficient of variation of the nutrient in the reference population; and,

KBI - Kenworthy Balanced Index, expressing nutritional balance as a percentage.

The optimal concentration was calculated based on the average of the concentrations present in the normal class (KBI = 100%), according to Eq. 11.

(11) ${\text{X}}_{\text{i}}={\overline{x}}_i\frac{\left({\text{CV}}_{\text{i}}-\text{KBI}\right)}{\left({\text{CV}}_{\text{i}}-\text{100}\right)}$

Where:

X_i - concentration of nutrient i at the lower or upper limit of the class;

CV_i - coefficient of variation of nutrient i;

x̅_i - average present in the standard of nutrient i; and,

KBI - fixed values of KBI to determine the lower or upper limits of the class.

The CND method was established based on the arithmetic mean and standard deviation of the multinutrient variables obtained in the HYP, as described by Camacho et al. (2012) and Traspadini et al. (2018). The multivariate variables (VNutri_i) were calculated as the ratio between the concentration of each nutrient (vNutri_i), expressed in g kg⁻¹, and the geometric mean of the concentrations of the dry matter constituents (mGeo), as in Eq. 12.

(12) ${\text{VNutri}}_{\text{i}}=\frac{\left({\text{vNutri}}_{\text{i}}\right)}{\left(\text{mGeo}\right)}$

For i = 1 to n, representing the total number of nutrients considered, preliminary standards were used without applying a logarithmic transformation. The geometric mean (mGeo) was calculated as the n^th root of the product of the nutrient contents and the residual component (R), with the latter included in the set of variables, as in Eq. 13.

(13) $\text{mGeo}=\sqrt[\text{n+1}]{\text{vN}\times \text{vP}\times \text{vK}\times \text{vCa}\times \text{vMg}\times \text{vS}\times \text{vB}\times \text{vCu}\times \text{vFe}\times \text{vMn}\times \text{vZn}\times \text{vNa}\times \text{R}}$

The residual component R was estimated based on the difference between 1,000 g and the sum of the contents of the nutrients considered, according to Eq. 14.

(14) $\text{R}=\left(1000-{\displaystyle {\sum }_{\text{i=1}}^{\text{n}}{\text{vNutri}}_{\text{i}}}\right)$

Where:

n - total number of nutrients evaluated (N, P, K, Ca, Mg, S, B, Cu, Fe, Mn, Zn, and Na); vNutri_i - nutrient concentration, in g kg⁻¹; and,

R - fraction of dry matter that is not composed of the nutrients evaluated.

The 12 nutrients mentioned were considered, resulting in R. As described by Parent & Dafir (1992), R represents the residual dry matter content, excluding the essential nutrients. The standardization of the multinutrient variables was then performed by calculating the respective indices as in Eq. 15.

(15) ${\text{I}}_{{\text{Nutri}}_{\text{i}}}=\left[\frac{\left({\text{vNutri}}_{\text{i}}-{\text{vNutri}}_{\text{i}}\text{HYP}\right)}{{\text{sNutri}}_{\text{i}}\text{HYP}}\right]$

The definition of reference values was done in a manner analogous to the DRIS.

The CLRiz method was based on the nutrient contents of the cladodes and the DMY of the HYP (Santos et al., 2022a). The calculation was performed according to Eq. 16.

(16) ${\text{CLRiz}}_{\text{i}}=\frac{\left(\mathrm{1.281552.}{\text{s}\overline{x}}_1+{\overline{x}}_1\right)}{\left(\mathrm{1.281552.}{\text{s}\overline{x}}_2+{\overline{x}}_2\right)}$

Where:

CLRiz_i - critical level of nutrient i;

sx̅₁ - standard deviation of the DMY of the HYP;

x̅₁ - mean DMY of the HYP;

sx̅₂ - standard deviation of the quotient Q; and,

x̅₂ - mean quotient .

Q, defined as the ratio between DMY and the concentration of nutrient i, as per Eq. 17.

(17) $\text{Q=}\frac{\text{DMY}}{{\text{n}}_{\text{i}}}$

Where:

n_i - concentration of the nutrient in question.

To recommend the most appropriate nutritional diagnosis methods for the cultivar, the values of the lower limits (LL), upper limits (UL), and amplitude (AMP) of the sufficiency class for all nutrients were compared. These values were treated as response variables derived from the SR, BL, MCh, CND, KBI, and DRIS methods, which were analyzed as treatments. The same procedure was applied to select the most reliable methods for estimating optimal nutrient concentrations (OC).

To enhance the analytical robustness in identifying the most consistent methods, hierarchical cluster analysis was performed using the mean Euclidean distance as a measure of dissimilarity. The results were displayed in a dendrogram, where the vertical axis represents the degree of similarity and the horizontal axis displays the evaluated treatments. The analysis was conducted using SAEG software, through the “Hierarchical Clustering (1)” procedure (Ribeiro Júnior & Melo, 2009).

Results and Discussion

Among the 64 experimental units cultivated with cactus pear ‘Orelha de Elefante Mexicana’, 28 plots (43.75%) exhibited yield equal to or higher than the overall mean (≥ 25.23 Mg ha^-1), according to the dataset available in the Zenodo repository (Soares, 2025). These plots comprised the HYP, which served as the basis for generating reference values in the various diagnostic approaches evaluated. The only exception was the BL method, which considers the entire experimental population, that is, both the HYP and the LYP.

The amplitudes of the interpretative classes obtained through the SR approach were proportional to the observed CV (Table 2). This pattern is inherent to the methodology because it relies on the variability of the x̅ nutrient contents, taking into account both the sx̅ and the factor k, which adjusts the interpretative ranges according to the CV (Santos et al., 2022a).

Table 2.
Reference values generated by the Sufficiency Range (SR) approach, for nutritional diagnosis of Opuntia stricta ‘Orelha de Elefante Mexicana’

Nut	DEF1	TSF1	SUF1	HIGH1	TEX1	x̅	sx̅	CV(%)
	----------------------------------------------------- g kg-1 -----------------------------------------------------------------
N	<7.08	7.08 - 8.82	8.82 - 12.29	12.29 - 14.02	>14.02	10.55	2.17	20.54
P	<0.89	0.89 - 1.29	1.29 - 2.11	2.11 - 2.51	>2.51	1.70	0.51	29.95
K	<29.16	29.16 - 33.98	33.98 - 43.63	43.63 - 48.46	>48.46	38.81	4.83	12.43
Ca	<17.94	17.94 - 24.05	24.05 - 36.26	36.26 - 42.37	>42.37	30.15	7.63	25.31
Mg	<7.87	7.87 - 10.71	10.71 - 16.37	16.37 - 19.21	>19.21	13.54	3.54	26.16
S	<0.48	0.48 - 0.70	0.70 - 1.15	1.15 - 1.38	>1.38	0.93	0.28	30.16

	------------------------------------------------------ mg kg-1 -------------------------------------------------------------
B	<17.09	17.09 -20.54	20.54 -27.43	27.43 - 30.87	>30.87	23.98	3.45	14.37
Cu	<1.08	1.08 - 1.65	1.65 – 2.81	2.81 - 3.39	>3.39	2.23	0.96	43.13
Fe	<93.11	93.11 - 120.99	120.99 - 176.75	176.75 - 204.63	>204.63	148.87	34.85	23.41
Mn	<26.78	26.78 - 60.34	60.34 - 127.46	127.46 - 161.02	>161.02	93.90	55.93	59.56
Zn	<8.02	8.02 - 15.01	15.01 - 28.97	28.97 - 35.96	>35.96	21.99	8.73	39.70
Na	<29.84	29.84 - 46.26	46.26 - 79.09	79.09 - 95.51	>95.51	62.68	20.52	32.74

• Nut - Nutrient; x̅ - Mean, sx̅ - Standard deviation and CV - Coefficient of variation;
• ¹
  DEF - Deficient; TSF - Tending to sufficient; SUF - Sufficient; HIGH - High; and TEX - Tending to excess. Number of experimental plots, n = 28, considering the high-yield population (HYP)

Among the macronutrients, the smallest amplitude of the sufficiency range was observed for K, at 28.40%, with a CV of 12.43%, whereas the largest was recorded for S, at 64.29%, with a CV of 30.16%. For the micronutrients, B showed the smallest amplitude (33.54%) with a CV of 14.37%, while Mn showed the largest (111.24%) with a CV of 59.56%. Overall, micronutrients exhibited greater variability than macronutrients (Santos et al., 2024), particularly Mn, whose wide variation is related to the complexity of its dynamics within the soil–plant system (Rodrigues Filho et al., 2021a).

Although there are no specific sufficiency ranges in the literature for Opuntia stricta, several studies report nutritional contents in cladodes for this species. Alves et al. (2016), for example, recorded N concentration of 12.93 g kg^-1 for the cultivar ‘Orelha de Elefante Mexicana’ in Arcoverde, Pernambuco. Dubeux Jr. et al. (2021) also reported a similar value (12.90 g kg^-1). Conversely, Santos et al. (2024) observed a lower value, of 9.37 g kg^-1, in Guanambi, Bahia. These results, above or below the average obtained in the present study, can be explained by differences in management, soil fertility, climatic conditions, and plant genotype (Matos et al., 2021; Matos et al., 2024).

In the present study, the cultivar ‘Orelha de Elefante Mexicana’ exhibited lower N concentrations than those reported by Alves et al. (2019a) for O. ficus-indica ‘Gigante’, also evaluated using the SR approach and under the same environmental conditions. This difference is likely associated with the influence of high K concentrations in the soil and its additional input through fertilization, which may reduce N uptake by plants due to competitive inhibition. However, when compared with the Nopalea cochenillifera ‘Miúda’, the N values were higher, consistent with the findings of Souza et al. (2017), who reported variations from 9.5 to 11.2 g kg^-1 in São Bento do Una and from 5.19 to 8.25 g kg^-1 in Caruaru, under N application rates ranging from 0 to 600 kg ha^-1 per year, both in the state of Pernambuco. These results indicate a genotypic tendency of cactus pear ‘Orelha de Elefante Mexicana’ to accumulate higher N contents (Alves et al., 2016).

Regarding phosphorus (P), the values reported by Alves et al. (2016) (0.74 g kg^-1) and Santos et al. (2024) (0.45 g kg^-1) were lower than the mean of 1.70 g kg^-1 observed in the present study. This difference is attributed to the higher soil P availability, which ranged from 76.6 to 133.9 mg dm^-3 (Table 1), compared to the lower levels reported in previous studies.

For K, Alves et al. (2016) reported a value of 4.35 g kg^-1, considerably lower than the 38.81 g kg^-1 obtained in this study, a difference explained by variations in soil fertility and K input through fertilization. In contrast, Santos et al. (2024) observed a K concentration of 36.07 g kg^-1, even in soil with lower K availability. This was attributed to irrigation with treated wastewater, which contained 27.76 mg L^-1 of K, thereby contributing to the maintenance of elevated K concentrations.

At the same site as this study, Lédo et al. (2020) observed, in O. ficus-indica ‘Gigante’, K concentrations ranging from 30.70 to 44.00 g kg^-1, under conditions without fertilization and with the application of 600 kg ha^-1 per year of K₂O and 90 Mg ha^-1 of manure, respectively, in soils with 0.46 cmol_c dm^-3 of K. These data demonstrate that the K concentrations in the cladodes of the cultivars ‘Gigante’ and ‘Orelha de Elefante Mexicana’ (33.98 to 43.63 g kg^-1) are similar and strongly influenced by soil fertility, fertilization management, and the nutrient source used.

Regarding Ca and Mg, the levels obtained in this study of 30.15 and 13.54 g kg^-1, respectively, were higher than those recorded by Alves et al. (2016) of 13.46 and 6.15 g kg^-1 and by Santos et al. (2024) of 15.02 and 6.97 g kg^-1. This difference can be explained by the lower levels of these nutrients in the soil evaluated by Santos et al. (2024), 0.98 and 0.38 cmol_c dm^-3 for Ca and Mg, respectively, compared with 1.40 to 4.20 cmol_c dm^-3 for Ca and 0.5 to 2.1 cmol_c dm^-3 for Mg, observed between the first and fourth cycles of this study (Table 1). The increase in the concentrations of these nutrients in the soil, associated with fertilization and the application of limestone as a source of Ca and Mg, was reflected in the nutrient concentrations, corroborating Matos et al. (2021; 2024), who associate the nutritional levels and bromatological quality of cactus pear with soil fertility and the management adopted.

For S, the average value obtained in this study of 0.93 g kg^-1 was slightly higher than that reported by Alves et al. (2016) of 0.86 g kg^-1 and Santos et al. (2024) of 0.73 g kg^-1, even in soils with higher organic matter content and high manure input. However, for ‘Gigante’, in the same location, Lédo et al. (2020) observed S contents of 0.90 g kg^-1 without fertilization and 3.10 g kg^-1 when fertilized with 300 kg ha^-1 per year of N, P₂O₅ and K₂O. Similarly, Silva et al. (2012) reported S contents of 1.20 g kg^-1 without fertilization and 5.60 g kg^-1 with the annual application of 200 kg ha^-1 of N, 150 kg ha^-1 of P₂O₅, and 100 kg ha^-1 of K₂O, using ammonium sulfate and single superphosphate as sources, both rich in S.

For micronutrients, in general, the values were higher than those observed by Santos et al. (2024) for the same cultivar, which were: B = 16.33 mg kg^-1, Cu = 1.50 mg kg^-1, Fe = 72.17 mg kg^-1, Mn = 79.67 mg kg^-1, and Zn = 12.17 mg kg^-1, which can be attributed to differences in soil fertility and fertilizer management (Matos et al., 2021).

However, the cultivar ‘Orelha de Elefante Mexicana’ exhibits lower Zn and Mn accumulation compared to ‘Gigante’. Silva et al. (2012) reported average Zn contents of 65.37 mg kg^-1 and Mn contents ranging from 984.41 to 2,006.06 mg kg^-1 under the application of 200 kg ha^-1 of N, 150 kg ha^-1 of P₂O₅, and 100 kg ha^-1 of K₂O. Similarly, Lédo et al. (2020) observed Zn concentrations between 60.40 and 71.10 mg kg^-1 and Mn concentrations ranging from 137.00 to 2,558.30 mg kg^-1, with the highest values obtained following the application of 300 kg ha^-1 of N and P₂O₅ and 600 kg ha^-1 of K₂O. In both studies, ammonium sulfate was used as the N and S source; its application promotes rhizosphere acidification and, consequently, increases Mn availability in the soil, leading to higher absorption and accumulation in plant tissues.

For the cactus pear ‘Orelha de Elefante Mexicana’, significant quadratic equations were fitted between DMY and the nutrient contents in cladodes, based on the BL approach (Table 3). The coefficients of determination (R²) ranged from 0.72 to 0.90, and the adjusted coefficients (R²adj) ranged from 0.62 to 0.86 for S and K, respectively. The largest discrepancy between R² and R²adj was observed for N, with values of 0.76 and 0.65, respectively, indicating lower accuracy of the fitted model for this nutrient. For micronutrients, R² ranged from 0.78 to 0.99 and R²adj ranged from 0.70 to 0.98 for R²adj, with Fe and B showing the highest values, respectively.

Table 3.
Relationship between dry matter yield (DMY) and the concentrations of nutrients by the Boundary Line (BL) method, number of points used in regression (n), coefficient of determination (R²), adjusted coefficient of determination (R²adj), optimal content (OC_BL), and dry matter yield (DMY) for the optimal nutrient content in the cladodes of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

	Regression equation	N	R2	R2adj	OCBL (g kg-1)	DMY (Mg ha-1)
Macronutrient
N	DMY = -56.731274 + 17.440555* N – 0.832240*N2	7	0.76	0.65	10.48	34.64
P	DMY = 14.887508 + 20.424109**P – 5.520888**P2	9	0.89	0.86	1.85	33.78
K	DMY = -19.251139 + 2.631719**K – 0.032533**K2	9	0.90	0.86	40.45	33.97
Ca	DMY = -35.511356 + 4.993025*Ca – 0.086971*Ca2	7	0.80	0.70	28.71	36.15
Mg	DMY = - 16.061181 + 7.872020*Mg – 0.322182*Mg2	6	0.89	0.82	12.22	32.02
S	DMY = 1.705111 + 66.386792*S – 37.488798*S2	9	0.72	0.62	0.89	31.10

Micronutrient		N	R2	R2adj	OCBL (g kg-1)	OCBL (Mg kg-1)1
B	DMY = -71.345661 + 9.190786**B – 0.201242**B2	9	0.99	0.98	22.84	33.59
Cu	DMY = -19.782806 + 52.500919**Cu – 12.918651**Cu2	12	0.83	0.79	2.03	33.56
Fe	DMY = -16.529187 + 0.717096**Fe – 0.002572**Fe2	9	0.78	0.70	139.40	33.45
Mn	DMY = 16.606404 + 0.584830*Mn – 0.003562*Mn2	6	0.82	0.70	82.09	40.61
Zn	DMY = 7.335801 + 2.615015**Zn – 0.065776**Zn2	7	0.96	0.94	19.88	33.33
Na	DMY = 6.970686 + 0.892724**Na – 0.007603**Na2	8	0.87	0.82	58.71	33.18

• ^*
  Significant (p ≤ 0.05)
• ^**
  Significant (p ≤ 0.01) by t-test

The models were fitted considering points located in the upper-limit region of the scatter: six points for Mg and Mn; seven for N, Ca, and Zn; eight for Na; nine for P, K, S, B, and Fe; and twelve for Cu. Among these, the highest R² values and one of the smallest differences relative to R²adj were observed for K, evidencing its strong association with DMY. This behavior is related to the high K availability in the soil (Table 1), its contribution via fertilization, and the crop’s high nutrient demand, which leads to significant K export (Donato et al., 2017; Alves et al., 2019a).

Although Na is considered a beneficial or even toxic element for most crops, it is essential for species with Crassulacean Acid Metabolism (CAM), as it participates in the regeneration of phosphoenolpyruvate, a fundamental substrate in the first carboxylation step of this cycle. Its deficiency may cause chlorosis, necrosis, and floral malformation (Broadley et al., 2012). In this context, the OC_BL for Na estimated for ‘Orelha de Elefante Mexicana’ was 58.71 g kg^-1 for a DMY of 33.18 Mg ha^-1, indicating greater accumulation compared to the OC_BL of 45.76 g kg^-1 for a DMY of 35.76 Mg ha^-1 observed in ‘Gigante’ cactus pear (Teixeira et al., 2024). A similar pattern was observed for the OC_BL of P (1.85 g kg^-1) and K (40.45 g kg^-1), with corresponding HYP values of 33.78 and 33.97 Mg ha^-1, compared to 1.53 g kg^-1 and 35.46 g kg^-1, with HYP values of 36.27 and 37.98 Mg ha^-1, respectively, in ‘Gigante’ cactus pear.

These results suggest luxury consumption of P and K (Römheld, 2012), influenced by the high soil fertility and the nutrient supply provided through fertilization. Increases in OC_BL in response to elevated soil fertility have been previously reported for cactus pear (Blanco-Macías et al., 2010).

In contrast, the estimated OC_BL for N of 10.48 g kg^-1, with a DMY of 34.64 Mg ha^-1 in ‘Orelha de Elefante Mexicana’, was lower than that observed by Teixeira et al. (2024) in ‘Gigante’ (15.12 g kg^-1 and DMY of 37.42 Mg ha^-1), indicating lower N accumulation in the former (Souza et al., 2017). Competitive inhibition between K and N uptake may result from high soil fertility and K fertilization. Since K⁺ and NH₄⁺ both use uniport transport, they compete for the same binding sites; higher K⁺ concentrations favor its uptake over NH₄⁺, as observed in ‘Gigante’ cactus pear (Silva et al., 2012).

In the BL approach, the fitted models serve as the basis for defining the interpretative classes (Table 4). The x̅ nutrient contents and CV differ from those observed in the SR approach (Table 2), as the BL approach considers the entire evaluated population, while the SR uses only data from the HYP.

Table 4.
Reference values generated with the Boundary Line (BL) approach, for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

	DEF 1	TSF1	SUF1	HIGH1	TEX 1
Nut	(DMY < 70%)	(70% ≤ DMY< 90%)	(90% ≤ DMY< 90%)	(90% > DMY≥ 70%)	(DMY < 70%)	x̅	sx̅	CV (%)
	------------------------------------------------------------- g kg-1 --------------------------------------------------------------------
N	< 6.94	6.94–8.44	8.44–12.52	12.52–14.01	≥ 14.01	10.73	2.34	21.76
P	< 0.49	0.49–1.07	1.07–2.63	2.63–3.20	≥ 3.20	1.94	0.73	36.39
K	< 22.75	22.75–30.23	30.23–50.67	50.67–58.15	≥ 58.15	44.74	10.16	22.71
Ca	< 17.54	17.54–22.26	22.26–35.15	35.15–39.87	≥ 39.87	27.85	6.68	23.98
Mg	< 6.76	6.76–9.06	9.06–15.37	15.37–17.68	≥ 17.68	12.19	3.37	27.63
S	< 0.39	0.39–0.60	0.60–1.17	1.17–1.38	≥ 1.38	0.93	0.27	29.02

	------------------------------------------------------------- mg kg-1 ----------------------------------------------------------------
B	< 15.76	15.76–18.75	18.75–26.92	26.92–29.91	≥ 29.91	22.49	4.12	18.33
Cu	< 1.15	1.15–1.52	1.52–2.54	2.54–2.91	≥ 2.91	2.22	0.73	32.95
Fe	< 76.94	76.94–103.34	103.34–175.47	175.47–201.87	≥ 201.87	146.19	56.51	38.65
Mn	< 23.61	23.61–48.33	48.33–115.86	115.86–140.58	≥ 140.58	85.34	41.95	49.16
Zn	< 7.55	7.55–12.76	12.76–27.00	27.00–32.21	≥ 32.21	22.61	7.88	34.83
Na	< 22.53	22.53–37.82	37.82–79.60	79.60–94.89	≥ 94.89	51.41	19.29	37.52

• Nut - Nutrient; x̅ - Mean, sx̅ - Standard deviation and CV - Coefficient of variation
• ¹
  DEF - Deficient; TSF - Tending to sufficient; SUF - Sufficient; HIGH - High; and TEX - Tending to excess. Number of experimental plots, n = 64, considering the high- (HYP) and low- (LYP) yield population

The greatest variability among macronutrients in the comparison between SR and BL approaches was observed for K and P, whose CV were 12.43 and 29.95% in the SR approach, and 22.71 and 36.39% in the BL approach, respectively. Overall, higher CV values were observed for micronutrients than for macronutrients, corroborating Santos et al. (2025a).

The wider range of CVs obtained using the BL method resulted in broader interpretative classes compared to those generated with the SR approach. This behavior was also observed for the ‘Gigante’ cactus pear when comparing the results reported by Alves et al. (2019a), who applied the SR approach, with those of Teixeira et al. (2024), who employed the BL method.

Using the MCh, the sufficient class for the nutritional diagnosis of the cactus pear ‘Orelha de Elefante Mexicana’ was established based on five initial classes (Table 5).

Table 5.
Reference values generated with the Mathematical Chance (MCh) approach, for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

Nut	CL1	LLi	ULi	OCMCh	YLDi	P13	P24	MCh	Nut	LLi	ULi	OC	YLDi	P13	P24	MCh
		----- g kg-1 -----			Mg ha-1	------- % -------		Mg ha-1		----- Mg kg-1 -----			Mg ha-1	------- % -------		Mg ha-1
Nitrogen	1	12.02	13.90	12.02	33.31	62.50	50.00	18.62	Boron	28.29	31.26	26.80	31.66	25.00	50.00	11.19
	2	10.13	12.01		28.50	12.50	16.67	4.11		25.31	28,28		28.82	12.50	16.67	4.16
	3	8.24	10.12		28.51	0.00	0.00	0.00		22.34	25:30		31.79	37.50	50.00	13.76
	4	6.35	8.23		31.81	12.50	50.00	7.95		19.36	22.33		29.48	12.50	16.67	4.25
	5	4.46	6.34		29.36	0.00	0.00	0.00		16.38	19:35		29.68	12.50	50.00	7.42
Phosphorus	1	2.66	3.10	2.43	47.66	12.50	100.00	16.85	Copper	4.89	5.77	2.20	26.10	0.00	0.00	0.00
	2	2.21	2.65		31.21	37.50	60.00	14.80		3.99	4.88		26.89	0.00	0.00	0.00
	3	1.76	2.20		32.83	37.50	33,33	11.61		3.10	3.98		25.61	0.00	0.00	0.00
	4	1.31	1.75		28.35	12.50	9.09	3.02		2.20	3.09		28.47	37.50	42.86	11.41
	5	0.86	1.30		28.67	12.50	14.29	3.83		1.31	2.19		30.41	62.50	27.78	12.67
Potassium	1	45.58	49.80	39.23	26.89	0.00	0.00	0.00	Iron	210.17	241.31	194.59	47.66	12.50	100.00	16.85
	2	41.35	45.57		31.18	25.00	25.00	7.80		179.02	210.16		22.03	12.50	33,33	4.50
	3	37.12	41.34		31.33	37.50	33,33	11.08		147.87	179.01		27.74	37.50	30.00	9.30
	4	32.89	37.11		25.54	25.00	25.00	6.39		116.72	147.86		26.60	25.00	22,22	6.27
	5	28.66	32.88		30.32	0.00	0.00	0.00		85.57	116.71		24.46	12.50	20.00	3.87
Calcium	1	39.28	44.20	31.88	31.78	37.50	60.00	15.08	Manganese	218.58	265.42	101.45	25.86	0.00	0.00	0.00
	2	34,35	39.27		28.98	0.00	0.00	0.00		171.73	218.57		27.82	0.00	0.00	0.00
	3	29.42	34,34		34.03	37.50	50.00	14.74		124.88	171.72		34.14	37.50	50.00	14.78
	4	24.49	29.41		28.13	0.00	0.00	0.00		78.03	124.87		28.69	25.00	25.00	7.17
	5	19.56	24.48		29.46	25.00	25.00	7.37		31.18	78.02		30.47	37.50	25.00	9.33
Magnesium	1	16.74	19:30	15.45	31.88	37.50	50.00	13.80	Zinc	36.30	42.86	23.14	35.89	12.50	33.33	7.33
	2	14.17	16.73		28.77	12.50	25.00	5.09		29.72	36.29		33.27	12.50	50.00	8.32
	3	11.60	14.16		31.43	37.50	30.00	10.54		23:15	29.71		30.75	37.50	42.86	12.33
	4	9.03	11.59		28.23	0.00	0.00	0.00		16.57	23.14		25.70	25.00	25.00	6.42
	5	6.46	9.02		31.81	12.50	50.00	7.95		10.00	16.56		29.12	12.50	12.50	3.64
Sulfur	1	1.22	1.40	1.12	36.40	37.50	60.00	17.27	Sodium	97.85	115.59	62.35	31.26	12.50	50.00	7.81
	2	1.03	1.21		29.56	25.00	33,33	8.53		80.10	97.84		27.66	0.00	0.00	0.00
	3	0.84	1.02		29.68	12.50	33,33	6.06		62.36	80.09		31.72	25.00	28.57	8.48
	4	0.65	0.83		28.72	12.50	11,11	3.38		44.61	62.35		31.06	50.00	44.44	14.64
	5	0.46	0.64		24.46	12.50	20.00	3.87		26.86	44.60		29.82	12.50	16.67	4.30
CV (%)	DMY		N	P	K	Ca	Mg	S		B	Cu	Fe	Mn	Zn	Na
	17.42		20.54	29.95	12.43	25.31	26.16	30.16		14.37	43.13	23.41	59.56	39.70	32.74

• ¹
  CL - Classes; LL_i - Lower limit of class i; UL_i: Upper limit of class i; OC_MCh - Optimal concentration in the optimal range (median values in the range) of MCh; YLDi - of plots in class i
• ³
  P1 - Probability or frequency of high-yield plots in class i in relation to the total number of high-yield plots P(Ai/A)
• ⁴
  P2 - Probability or frequency of high-yield plots in class i in relation to the total number of plots in class i. Nut - Nutrient; MCh - Mathematical chance of the factor in class i; DMY - Dry matter yield; CV - Coefficient of variation for DMY ≥ 33.14 Mg ha ^-1 and nutrients. Number of experimental plots, n = 28, considering the high-yield population (HYP) and n = 8 considering the reference subpopulation, the highest-yield population, HTYP

The lower (LL) and upper (UL) limits of nutrient contents that define the sufficient class – i.e., the intervals with the highest MCh value, the greatest frequency of high-yield plots, and presence in the HTYP – were, respectively, for macronutrients (g kg^-1): N (10.13–13.90), P (1.76–3.10), K (32.89–45.57), Ca (29.42–34.34), Mg (11.60–19.30), and S (0.84–1.40); and for micronutrients (mg kg^-1): B (22.34–31.26), Cu (1.31–3.09), Fe (147.87–241.31), Mn (31.18–171.72), Zn (16.57–29.71), and Na (44.61–80.09). Compared with the other approaches, the MCh generated lower LLs for Cu and Mn, and higher LLs for N, P, Ca, Mg, S, B, Fe, and Zn. It also generated lower ULs for Ca, and higher ULs for N, P, Mg, S, B, Cu, Fe, Mn, and Na.

The nutrient concentrations increased progressively from class 1 to class 5. For macronutrients, the sufficient classes corresponded to classes 1 and 2 for N; 1 to 3 for P, Mg, and S; class 3 for Ca; and 2 to 4 for K. The selection of classes with the highest K contents is consistent with the greater K export rate by the crop (Lédo et al., 2021).

For micronutrients, the sufficient classes were 1 to 3 for B and Fe, 3 and 4 for Zn and Na, 3 to 5 for Mn, and 4 and 5 for Cu. Class 5, which had the highest concentrations, coincided with Cu, the least exported micronutrient by cacti (Silva et al., 2016). This pattern may be related to the subjectivity inherent in defining the sufficient class using the MCh approach, as it depends on the researcher’s interpretation (Alves et al., 2019a,b; Santos et al., 2022a,b).

The values of LL_i UL_i and the OC_MCh obtained by MCh for the cactus pear ‘Orelha de Elefante Mexicana’ were lower for N and S, and higher for P, K, Ca, and Mg, compared with those reported for ‘Gigante’ cactus pear (Alves et al., 2019a). For instance, the OC_MCh values in this study were: N (12.02 g kg^-1), P (2.43 g kg^-1), K (39.23 g kg^-1), Ca (31.88 g kg^-1), Mg (15.45 g kg^-1), and S (1.12 g kg^-1), whereas ‘Gigante’ showed 17.63, 1.09, 36.73, 27.03, 10.71, and 1.44 g kg^-1, respectively. The higher OC_MCh values for P and K are justified by the greater soil availability of these nutrients (Table 1) and their elevated contribution through fertilization. Thus, it is possible to notice the influence of soil fertility on the increase in optimal nutrient limits (Blanco-Macías et al., 2010).

Conversely, the lower OC_MCh of N may be related to the competitive inhibition between K⁺ and NH₄⁺, intensified by high soil fertility and the K supply (Alves et al., 2016). Such competition stems from uniport competitive uptake, in which excess K⁺ limit N uptake by the plant (Silva et al., 2012).

In the comparison between OC_MCh and the optimal levels estimated by BL (OC_BL), the slightly lower value for K (39.23 vs. 40.45 g kg^-1) and higher values for N (12.02 vs. 10.48 g kg^-1), P (2.43 vs. 1.85 g kg^-1), Ca (31.88 vs. 28.71 mg kg^-1), Mg (15.45 vs. 12.22 g kg^-1), S (2.24 vs. 0.89 g kg^-1), B (26.80 vs. 22.84 mg kg^-1), Cu (2.20 vs. 2.03 mg kg^-1), Fe (194.59 vs. 139.40 mg kg^-1), Mn (101.45 vs. 82.09 mg kg^-1), Zn (23.14 vs. 19.88 mg kg^-1) and Na (62.35 vs. 58.71 mg kg^-1). These discrepancies arise from methodological differences, as MCh considers only the HYP and HTYP plots, while the BL approach uses the entire population, which tends to increase variability.

Additionally, OC_MCh is the median of the sufficient class, while OC_BL is the nutrient concentrations associated with the maximum DMY (Teixeira et al., 2024). Furthermore, MCh involves a greater degree of subjectivity in the definition of interpretative classes (Wadt et al., 1998), since its delimitation depends directly on the criterion adopted by the researcher (Santos et al., 2022a,b).

The lower (LL_i) and upper (UL_i) limits of the nutritional diagnosis classes established using DRIS for the cactus pear ‘Orelha de Elefante Mexicana’ were quite narrow (Table 6), a result similar to that observed for ‘Gigante’ (Teixeira et al., 2021). This appears to be related to the design of the method. Although smaller amplitudes are desirable because they indicate greater precision (Serra et al., 2010), excessively narrow ranges can compromise the practical applicability of nutritional diagnosis.

Table 6.
Reference values and the optimal concentrations of nutrients (OC_DRIS), generated with the Diagnosis and Recommendation Integrated System (DRIS) approach for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

Nut	DEF1	TSF1	SUF1	HIGH1	TEX1	OCDRIS	x̅	sx̅	CV(%)
	------------------------------------------------------------ g kg-1 ---------------------------------------------------------------
N	< 9.71	9.71 – 10.13	10.13 – 10.97	10.97 – 11.39	≥ 11.39	10.49	10.55	2.17	20.54
P	< 0.81	0.81 – 1.26	1.26 – 2.14	2.14 – 2.59	≥ 2.59	1.69	1.70	0.51	29.95
K	< 37.95	37.95 – 38.38	38.38 – 39.24	39.24 – 39.67	≥ 39.67	38.59	38.81	4.83	12.43
Ca	< 29.42	29.42 – 29.79	29.79 – 30.52	30.52 – 30.89	≥ 30.89	29.95	30.15	7.63	25.31
Mg	< 12.86	12.86 – 13.20	13.20 – 13.88	13.88 – 14.22	≥ 14.22	13.45	13.54	3.54	26.16
S	< 0.15	0.15 – 0.54	0.54 – 1.32	1.32 – 1.70	≥ 1.70	0.92	0.93	0.28	30.16

	----------------------------------------------------------- mg kg-1 -------------------------------------------------------------
B	< 23.12	23.12 – 23.55	23.55 – 24.42	24.42 – 24.85	≥ 24.85	23.84	23.98	3.45	14.37
Cu	<1.24	1.24 – 1.74	1.74 – 2.73	2.73 – 3.22	≥ 3.22	2.21	2.23	0.96	43.13
Fe	< 147.84	147.84 – 148.36	148.36 – 149.39	149.39 – 149.91	≥ 149.91	147.90	148.87	34.85	23.41
Mn	< 92.71	92.71 – 93.30	93.30 – 94.50	94.50 – 95.09	≥ 95.09	92.74	93.90	55.93	59.56
Zn	< 20.93	20.93 – 21.46	21.46 – 22.52	22.52 – 23.05	≥ 23.05	21.81	21.99	8.73	39.70
Na	< 61.48	61.48 – 62.08	62.08 – 63.27	63.27 – 63.87	≥ 63.87	62.21	62.68	20.52	32.74

• Nut - Nutrient; x̅ - Mean, sx̅ - Standard deviation and CV - Coefficient of variation
• ¹
  DEF - Deficient; TSF - Tending to sufficient; SUF - Sufficient; HIGH - High; and TEX - Tending to excess. Number of experimental plots, n = 28, considering the high-yield population (HYP)

For example, for K, the nutrient most exported by cactus pear, with a coefficient of variation (CV) of 12.43%, the lower (LL_i) and upper (UL_i) limits, as well as the amplitude (AMP) of the sufficient class, were 38.38, 39.24, and 0.86 g kg^-1, respectively. These LL_i and UL_i values have no practical applicability for nutritional diagnosis. Similarly, for Mn, the nutrient with the greatest variability (CV = 59.56%), the LL_i, UL_i, and AMP of the sufficient class were 93.30, 94.50, and 1.20 mg kg^-1, respectively, which compromises the adequacy of the diagnosis, rendering it technically unfeasible.

The OC_DRIS values, considering HYP, were very similar to those of OC_BL, generated based on the entire population. However, they differed from the OC_MCh, also derived from the HYP. This indicates that the differences among methods arise primarily from their theoretical assumptions rather than from variability within the populations analyzed. Compared with OC_BL, the OC_DRIS values were lower for P and K and higher for other nutrients. Conversely, OC_DRIS values exceeded those of OC_MCh only for Cu, being lower for the remaining nutrients.

Overall, the mean nutrient concentrations in the HYP were equivalent or very close to the OC_DRIS values, validating the normal distribution of dual relationships and supporting the assumption that the mean approximates the median, as reported by Teixeira et al. (2021). For instance, OC_DRIS values represented between 98.76% (Mn) and 99.43% (N and K) of the mean concentrations observed in the HYP. On the other hand, the OC_BL values, derived from equations relating nutrient concentrations to maximum DMY (Santos et al., 2022a,b; Teixeira et al., 2024), exhibited wider variations, ranging from 113.03% for Mg to 49.14% for S relative to the mean of the HYP and LYP.

In contrast, the OC_MCh values defined as the median between the LL_i and UL_i limits of the sufficient class established based on the HYP, are more susceptible to subjectivity (Santos et al., 2022a;b), which explains the more pronounced deviations observed. For example, OC_MCh values ranged from 98.65% for Cu to 142.94% for P relative to the mean nutrient concentrations in the HYP, highlighting the greater dispersion.

The OC_DRIS values estimated for the cactus pear ‘Orelha de Elefante Mexicana’ were lower for N, B, Mn, and Zn, and higher for Fe and Na, compared with those obtained for ‘Gigante’ (Teixeira et al., 2021), remaining similar for the other nutrients. Among macronutrients, noteworthy OC_DRIS values were observed for N (10.49 g kg^-1), P (1.69 g kg^-1), and K (38.59 g kg^-1), compared with 15.62, 1.46, and 37.95 g kg^-1, respectively, reported by those authors. The higher OC_DRIS values for P and K reflect the elevated soil concentrations of these nutrients and their contribution via fertilization, which promote higher tissue concentrations and luxury consumption (Römheld, 2012), as previously demonstrated (Blanco-Macías et al., 2010). Conversely, the lower OC_DRIS for N may be associated with competitive inhibition between K and N, caused by the high K concentrations and inputs.

Among the micronutrients, the lower OC_DRIS values for Mn (92.74 mg kg^-1) and Zn (21.81 mg kg^-1) are noteworthy compared with those estimated for ‘Gigante’ (388.88 and 46.21 mg kg^-1, respectively), representing 23.85 and 47.20% of the values reported by Teixeira et al. (2021). This difference can be attributed to the higher soil pH observed in the present study, which reduces the availability of metal cations such as Mn and Zn due to the formation of inner-sphere complexes with high adsorption energy, thereby limiting their uptake by plants (Silva et al., 2012; Lédo et al., 2020).

For all interpretative classes and nutrients analyzed, the reference values obtained through the KBI approach (Table 7) exhibited wider ranges compared to those estimated by the DRIS method (Table 6). These findings are consistent with Teixeira et al. (2021) regarding the comparison between both methods. The means and standard deviations of the nutrient concentrations in the HYP constitute the KBI standards, with the means representing the Optimal concentration (OC_KBI) values.

Table 7.
Reference values and standards generated with the Kenworthy Balanced Indices (KBI) approach, for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

Nut	DEF1	TSF1	SUF1	HIGH1	TEX1	x̅	sx̅	CV (%)
	------------------------------------------------------------------ g kg-1 -----------------------------------------------------------
N	< 3.91	3.91 – 8.30	8.30 – 12.81	12.81 – 17.19	≥ 17.19	10.55	2.17	20.54
P	< 0.49	0.49 – 1.29	1.29 – 2.11	2.11 – 2.91	≥ 2.91	1.70	0.51	29.95
K	< 16.65	16.65 – 31.27	31.27 – 46.34	46.34 – 60.97	≥ 60.97	38.81	4.83	12.43
Ca	< 9.97	9.97 – 23.29	23.29 – 37.02	37.02 – 50.34	≥ 50.34	30.15	7.63	25.31
Mg	< 4.37	4.37 – 10.42	10.42 – 16.66	16.66 – 22.71	≥ 22.71	13.54	3.54	26.16
S	< 0.26	0.26 – 0.70	0.70 – 1.15	1.15 – 1.59	≥ 1.59	0.93	0.28	30.16

	----------------------------------------------------------------- mg kg-1 ----------------------------------------------------------
B	< 9.98	9.98 – 19.22	19.22 – 28.75	28.75 – 37.99	≥ 37.99	23.98	3.45	14.37
Cu	< 0.27	0.27 – 1.56	1.56 – 2.90	2.90 – 4.19	≥ 4.19	2.23	0.96	43.13
Fe	< 51.69	51.69 – 115.83	115.83 – 181.92	181.92 – 246.06	≥ 246.06	148.87	34.85	23.41
Mn	< 0.00	0.00 – 54.42	54.42 – 133.38	133.38 – 210.01	≥ 210.01	93.90	55.93	59.56
Zn	< 3.76	3.76 – 15.79	15.79 – 28.19	28.19 – 40.22	≥ 40.22	21.99	8.73	39.70
Na	< 16.08	16.08 – 46.83	46.83 – 78.52	78.52 – 109.27	≥ 109.27	62.68	20.52	32.74

• Nut - Nutrient, x̅ - Mean, OC_KBI - Optimal concentration, sx̅ - Standard deviation and CV - Coefficient of variation
• ¹
  DEF - Deficient; TSF - Tending to sufficient; SUF - Sufficient; HIGH - High; and TEX - Tending to excess. Number of experimental plots, n = 28, considering the high-yield population (HYP)

The DRIS approach is, in principle, more efficient in identifying plots with nutritional imbalance compared to the KBI. This is because DRIS reference values tend to be proportionally lower than the standard deviation of the mean nutrient concentrations in HYP. According to Teixeira et al. (2021), the KBI method is less sensitive in estimating nutrients with CV greater than 30%, particularly for detecting deficiencies. This limitation arises because the ranges originally proposed by Kenworthy (1961) assume an average variability of 20% for each nutrient, a statistically arbitrary definition that can compromise diagnostic accuracy, especially for Cu, Mn, Zn, and Na.

Nevertheless, the excessively narrow lasses generated by DRIS often hinder diagnosis, regardless of the CV. For the nutrient with the lowest variability in the HYP, K (CV = 12.43%), the sufficient class values were as follows: DRIS: LL_i = 38.38, UL_i = 39.24, and AMP = 0.86 g kg^-1; KBI: LL_i = 31.27, UL_i = 46.34, and AMP = 15.07 g kg^-1. For the nutrient with the greatest variability, Mn (CV = 59.56%), the corresponding values were: DRIS: LL_i = 93.30, UL_i = 94.50, and AMP = 1.20 mg kg^-1; KBI: LL_i = 54.42, UL_i = 133.38, and AMP = 78.96 mg kg^-1. Additionally, the amplitudes of the sufficient classes estimated by the SR and BL approaches for K were 9.65 and 20.44 g kg^-1, respectively, and for Mn, 67.12 and 67.53 mg kg^-1, showing closer agreement with the KBI method.

The OC_DRIS values, approximating the population median (Teixeira et al., 2021), were very close to the OC_KBI, varying from 99.43% for K to 98.76% for Mn. In contrast, the OC_BL values, which are associated with the maximum DMY of the HYP and LYP (Teixeira et al., 2024), differed more markedly from the OC_KBI, ranging from 113.03% for Mg to 49.14% for S. The OC_MCh values were even more distant from the OC_KBI, as they represent the median between the LL_i and UL_i limits of the sufficient class defined based on the HTYP.

When comparing the CND standards and reference values (Table 8) with those derived from the KBI approach (Table 8), noticeable differences were observed. This divergence arises because the KBI standards are based on the natural means and standard deviations of nutrient concentrations in the HYP, whereas the CND standards are derived from the multivariate. approach that considers the multinutrient variable. Like this, all nutrients contribute to the individual standards, since the CND incorporates the geometric mean, reflecting the joint influence of all nutrient concentrations, and the R value, which represents the difference between total dry matter and the sum of all analyzed nutrients.

Table 8.
Standards and reference values generated using the Compositional Nutrient Diagnosis (CND) approach for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

Nut	DEF1	TSF1	SUF1	HIGH1	TEX1	x̅CND	sx̅CND	CVCND (%)
	---------------------------------------------------------- g kg -1 --------------------------------------------------------------
N	< 9.90	9.90 – 11.00	11.00 – 13.30	13.30 – 14.40	> 14.40	12.13	1.69	13.94
P	< 1.40	1.40 – 1.70	1.70 – 2.20	2.20 – 2.40	> 2.40	1.93	0.37	18.88
K	< 36.70	36.70 – 41.00	41.00 – 49.50	49.50 – 53.80	> 53.80	45.27	6.39	14.12
Ca	< 28.90	28.90 – 31.60	31.60 – 37.00	37.00 – 39.80	> 39.80	34.32	4.09	11.92
Mg	< 12.00	12.00 – 13.70	13.70 – 17.20	17.20 – 18.90	> 18.90	15.45	2.55	16.52
S	< 0.80	0.80 – 0.90	0.90 – 1.20	1.20 – 1.30	> 1.30	1.05	0.17	15.86

	---------------------------------------------------------- mg kg -1 -----------------------------------------------------------
B	< 22.40	22.40 – 25.20	25.20 – 30.70	30.70 - 33.40	> 33.40	27.94	4.13	14.79
Cu	< 1.60	1.60 – 2.00	2.00 – 3.00	3.00 – 3.40	> 3.40	2.50	0.70	27.98
Fe	< 129.20	129.20 – 150.60	150.60 – 193.40	193.40 – 214.80	> 214.80	172.01	32.09	18.65
Mn	< 36.50	36.50 – 69.30	69.30 – 135.00	135.00 – 167.90	> 167.90	102.18	49.29	48.24
Zn	< 15.70	15.70 – 20.10	20.10 – 29.10	29.10 – 33.60	> 33.60	24.63	6.71	27.27
Na	< 35.50	35.50 – 54.90	54.90 – 93.70	93.70 – 113.10	> 113.10	74.31	29.11	39.17

The CND standards showed higher values for macronutrients compared to the KBI standards. For instance, for N, x̅KBI = 10.55 g kg^-1 and VNutri_iHYP = 12.13 g kg^-1; for P, x̅KBI = 1.70 g kg^-1 and VNutri_iHYP = 1.93 g kg^-1. Among micronutrients, the CND standards were also higher: for B, x̅KBI = 23.98 mg kg^-1 and VNutri_iHYP = 27.94 mg kg^-1; and for Na, x̅KBI = 62.68 mg kg^-1 and VNutri_iHYP = 74.31 mg kg⁻¹.

Hernández-Vidal et al. (2021), when estimating CND standards for O. ficus-indica cv. Rojo Pelón grown for fruit production, found nutrient levels of N (9.58 g kg^-1), P (3.18 g kg^-1), K (35.07 g kg^-1), Ca (42.28 g kg^-1), and Mg (14.41 g kg^-1). The values were higher for P, Ca, and Mg, and lower for N and K levels compared with the present study, due to evaluated species, production objectives, soil fertility, and climatic conditions of the study region, which exhibits milder temperatures.

The decreasing order of the amplitudes of the sufficient ranges across the evaluated methods showed that, for most nutrients, the CND approach produced narrower ranges than those obtained with MCh, KBI, BL, and SR, but wider than those generated by DRIS, whose ranges were extremely narrow. Among the six methods analyzed, CND presented the fifth smallest amplitude for N, K, Mg, B, Fe, Mn, and Zn (exceeding only DRIS); the fourth smallest for Ca (larger than MCh and DRIS); the smallest amplitude for P, S, and Cu; the second largest amplitude for Na.

The values of the Critical Levels estimated by CLRiz method (Table 9) were lower for all nutrients compared to the values of OC_BL (Table 3), OC_MCh (Table 5), OC_DRIS (Table 6), and OC_KBI (Table 7).

Table 9.
Critical concentration generated with the Critical Level by Reduced Normal Distribution (CLRiz) approach, for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’

N	P	K	Ca	Mg	S	B	Cu	Fe	Mn	Zn	Na
---------------------------------- g kg-1-----------------------------------						---------------------------------- mg kg-1---------------------------------------
8.86	1.48	37.30	26.39	10.68	0.76	22.31	1.67	130.91	47.61	16.22	46.49

In the CLRiz approach, the critical value is calculated based on the ratio between the mean plus the standard deviation of dry DMY and the mean plus the standard deviation of Q, the quotient between DMY and nutrient concentration (Santos et al., 2022a). In CLRiz, since the nutrient standard deviation appears in the denominator of the formula for calculating estimated concentrations, greater variability (higher standard deviation) results in values lower than the population average of the HYP. For instance, among the macronutrients, the greatest variation between CLRiz and the mean concentration was observed for K, the nutrient with the lowest coefficient of variation (CV = 12.43%), where CLRiz corresponded to 96.11% (37.30 g kg^-1) of the average HYP concentration (38.81 g kg^-1). In contrast, for S, with a higher CV (30.16%), CLRiz represented only 86.02% (0.80 g kg^-1) of the mean concentration (0.93 g kg^-1). Regarding OC_BL, the greatest percentage deviation occurred for Mg (106.82%, or 12.22 g kg^-1, relative to a mean of 11.44 g kg^-1), while the smallest was for S (95.70%, or 0.89 g kg^-1, relative to a mean of 0.93 g kg^-1).

Among micronutrients, the highest CLRiz percentage relative to the mean concentration was observed for B (CV = 14.37%), corresponding to 92.99% (22.30 mg kg^-1) of the mean value (23.98 mg kg^-1). The lowest was for Mn, with a high CV (59.56%), yielding 50.69% (47.60 mg kg^-1) of the mean concentration (93.90 mg kg^-1). In contrast, for OC_BL, Na exhibited the greatest positive deviation (118.41%, or 58.71 mg kg^-1, relative to a mean of 49.58 mg kg^-1), while Zn showed the lowest (89.19%, or 19.88 mg kg^-1, relative to a mean of 22.29 mg kg^-1).

The CLRiz of nutrient, whether in plant tissue or soil, is defined as the concentration beyond which no significant yield increase occurs. However, this value varies according to the diagnostic method, plant species, crop age, and nutrient availability in soil, which in turn depend on factors such as adsorption–desorption dynamics and spatial variability. Specifically, both in soils (Donato et al., 2017) and in plants (Alves et al., 2019a), CLRiz tends to be strongly influenced by nutrient variability and may be underestimated when the CV is high, as often occurs with micronutrients.

For example, for P, the estimated CLRiz was 1.48 g kg^-1, with a CV of 29.85%, in soil with high P concentrations ranging from 76.6 to 133.9 mg dm^-3 between the first and fourth production cycles (Table 1). The value of remaining P (P-res), a measure of the soil’s phosphorus buffering capacity, ranged from 40.4 to 45.9 mg L^-1, classified as low to high (Donato et al., 2017), indicating increased P desorption and availability in the soil. In contrast, Alves et al. (2019a) estimated the CLRiz for the ‘Gigante’ cactus pear at 0.93 g kg^-1 (CV = 45.71%) in soil with an average P concentration of 16.3 mg dm^-3 and P-res values between 39.8 and 47.6 mg L^-1. The lower nutrient availability and greater variability in this case resulted in a reduced CLRiz value, consistent with the soil’s lower P-res.

For K, estimated CLRiz for the cactus pear ‘Orelha de Elefante Mexicana’ was 37.30 g kg^-1 (CV = 12.43%) in soils with high K concentration, ranging from 0.56 to 1.04 cmol_c dm^-3 across cycles. In comparison, Alves et al. (2019a) reported a CLRiz of 31.86 g kg^-1 (CV = 20.69%) for cactus pear ‘Gigante’ in soils containing 0.29 cmol_c dm^-3 of K, indicating that higher CLRiz values are associated with greater K availability in soil and fertilization inputs.

For micronutrients, the CLRiz values for Mn and Zn in ‘Orelha de Elefante Mexicana’ were 47.61 mg kg^-1 (CV = 59.56%) and 16.22 mg kg^-1 (CV = 39.70%), respectively. In contrast, Alves et al. (2019b) reported values of 110.67 mg kg^-1 for Mn (CV = 80.71%) and 30.27 mg kg^-1 for Zn (CV = 42.14%) in ‘Gigante’. The lower CLRiz values observed in ‘Orelha de Elefante Mexicana’ can be attributed to higher soil pH values (5.7–6.3) compared to those under ‘Gigante’ (5.5–6.1) (Padilha Júnior et al., 2020). Soil pH is a key factor controlling the availability of metallic cations, as higher pH promotes the formation of inner-sphere complexes with high adsorption energy, thereby reducing their availability, plant uptake, and cladode concentrations (Silva et al., 2012; Lédo et al., 2020).

Regardless of the diagnostic method, increases in estimated reference values for a given species or cultivar are closely related to nutrient availability in the soil (Santos et al., 2022a). This is influenced by intrinsic soil fertility, nutrient fertilization, and by meteorological and management conditions that directly affect nutrient flow in the soil–plant system and root uptake dynamics (Rodrigues Filho et al., 2021b; Santos et al., 2025a).

In general, the order of macronutrient concentrations in the cladodes of the cactus pear ‘Orelha de Elefante Mexicana’ within the evaluated population (HYP) was K > Ca > Mg > N > P > S. This sequence largely agrees with the findings of Donato et al. (2017) and Lédo et al. (2021) for ‘Gigante’, except for Mg and N, whose positions were reversed. For micronutrients, the observed order was Fe > Mn > Na > B > Zn > Cu, differing from that reported by Teixeira et al. (2021) for ‘Gigante’ (Mn > Fe > Na > Zn > B > Cu).

To define the most appropriate methods, the means of LL_i, UL_i and AMP of the sufficient nutritional diagnostic classes, as well as the optimal nutrient concentrations estimated by each approach for the cactus pear ‘Orelha de Elefante Mexicana’, were subjected to dissimilarity analyses to assess the convergence or divergence between the sufficient classes and the optimal nutrient levels established by each diagnostic approach (Figure 1).

Figure 1
Dissimilarity analyses between the approaches used to generate sufficient diagnostic classes and the optimal nutrient concentrations generated by different approaches for nutritional diagnosis of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’, with dendrogram illustrating the mean Euclidean distance dissimilarity measure between the methods SR, BL, MCh, CND, KBI and DRIS (A), and between the methods BL, KBI, DRIS, MCh and CLRiz (B)

The dendrogram (Figure 1A), representing the average Euclidean distance among the methods, revealed three major discontinuities, suggesting the formation of four homogeneous clusters: SR and KBI (high similarity); BL alone; MCh, and CND (high similarity); and DRIS alone, showing the greatest dissimilarity. Smaller vertical jumps in the dendrogram indicate higher similarity among methods. This analysis reinforces the pronounced divergence of DRIS compared to the others, emphasizing its practical limitations for the nutritional diagnosis of this crop when defining diagnostic classes.

The results indicate that, although DRIS theoretically provides greater diagnostic precision due to its narrow ranges, these intervals were excessively restrictive in practice. Furthermore, its low convergence with the other methods, identified by the dissimilarity test, limits its applicability. These findings highlight the need to balance statistical precision with agronomic relevance when selecting diagnostic methods, avoiding ranges that are either too restrictive or too broad.

Figure 1B shows the hierarchical clustering analysis identifying four distinct clusters: Group 1 - BL isolated; Group 2 - KBI and DRIS, with high similarity; Group 3 – MCh, isolated; and Group 4 - CLRiz, with greater dissimilarity.

Finally, the standards and reference values established in this study provide valuable tools for decision-making in the nutritional assessment of the cactus pear ‘Orelha de Elefante Mexicana’, particularly when applying the diagnostic methods identified as the most suitable. However, even refined and crop-specific interpretative guidelines, as well as isolated tissue or soil analyses, are insufficient for an accurate nutritional diagnosis without complementary information. A comprehensive evaluation must include the crop’s anamnesis, prevailing meteorological conditions, and the soil’s physical, hydraulic, and biological properties, all of which regulate nutrient dynamics within the soil–plant–atmosphere system.

Conclusions

1. The order of nutrient concentrations in the cladodes of the cactus pear Opuntia stricta ‘Orelha de Elefante Mexicana’ was K > Ca > Mg > N > P > S for macronutrients and Fe > Mn > Na > B > Zn > Cu for micronutrients.

2. Reference values increased with greater availability of nutrients in the soil, and the differences observed among methods were primarily associated with their theoretical foundations rather than population variability.

3. Among the evaluated methods, Sufficiency Range (SR), Kenworthy Balanced Index (KBI), Boundary Line (BL), Mathematical Chance (MCh), and Compositional Nutrient Diagnosis (CND) generated more reliable interpretative diagnostic classes, while Diagnosis and Recommendation Integrated System (DRIS), KBI, and BL provided the most consistent optimal nutrient concentrations compared with MCh and Critical Level by Reduced Normal Distribution (CLRiz).

¹

Research developed at Instituto Federal de Educação, Ciência e Tecnologia Baiano, Guanambi, BA, Brazil. Paper derived from the first author´s doctoral thesis

Financing statement:

This research was funded by the National Council for Scientific and Technological Development (CNPq), the Coordination for the Improvement of Higher Education Personnel (CAPES, Funding Code 001), the Agricultural Research Company of Minas Gerais (EPAMIG Norte), and the Federal Institute Baiano – Guanambi Campus.

Data Availability Statement:

The authors declare that the data underlying this article are available in the Zenodo repository at: https://doi.org/10.5281/zenodo.17805342

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Editors:

Ítalo Herbet Lucena Cavalcante & Walter Esfrain Pereira

*

Corresponding author - E-mail: [e-mail]

Conflict of interest:

The authors declare that there are no conflicts of interest, whether financial, personal, or institutional, that could have influenced the results or the writing of this work.

Publication Dates

• Publication in this collection
  28 Sept 2026
• Date of issue
  2026

History

• Received
  10 Nov 2025
• Accepted
  01 July 2026
• Published
  14 Sept 2026