Experimental conditions and plant growth. This study was developed from data collected in 233 commercial banana crops in the province of El Oro, Ecuador, between 2018 and 2020. All selected crops used the cultivars "Vallery" and "Williams" (triploid AAA group). This research was not conducted with endangered species and was carried out in accordance with the Declaration of the IUCN Policy on Research Involving Endangered Species. An average planting density of 1,500 plants ha− 1 was adopted. The climate of the region is AW (tropical savannah), according to the Köppen-Geiger classification. The soils in these areas originate from alluvial formation29 and are of the order inceptisol, according to the taxonomic classification of the United States Department of Agriculture (USDA)30, which is adopted in Ecuador. The cultural treatments carried out in areas cultivated with banana trees, including phytosanitary control and irrigation, followed the indications of Robinson and Galán-Saúco31.
Chemical analyses of leaves. An annual leaf sampling was carried out on ten healthy and representative plants between January and April 2018, 2019, and 2020, respectively. Leaf collection was performed considering the removal of the central portion (10 cm) of the third leaf (counted from the apex) at the beginning of flowering and in a succession plant (daughter plant) with a height of 1.5 m32. Then, the samples were dried in an oven with forced air circulation set to 65ºC until reaching a constant mass. Then, they were ground with a Wiley mill. Next, a chemical analysis was performed to determine the leaf contents of macronutrients (N, P, K, Mg, C, and S) and micronutrients (Cl, Fe, Mn, Cu, Zn, and B) following the methodology described by Bataglia et al.33. The banana productivity (PR) was obtained in each property by collecting fruits of ten plants of each plot. The result was expressed in t ha− 1, following the indications of Rodriguez and Rodriguez34.
Establishment of DRIS norms. The database containing results of leaf analysis and annual productivity was subdivided into populations of high and low productivity (HP and LP). In this context, to define HP, the production limit (PL) was calculated. It consisted of a value corresponding to the mean plus the standard deviation of PR20. After defining this parameter, only farms with a PR greater than PL were considered as HP.
The DRIS norms (N-DRIS) were calculated by transforming all 233 observations of leaf contents into % to homogenize the comparison criteria between them. Then, the values of nutrient content considered to be extreme were excluded. Subsequently, logarithmic transformations were applied to the data and the direct and inverse bivariate relationships between all nutrients were determined according to Beverly35.
To determine the functions of proportions of DRIS nutrients, the physiological diagnosis method and the simplified formula of Beaufils7. Subsequently, the Mean Nutritional Balance Index (NBIm) was calculated using the expression:
NBIm = │ I-DRIS A│ + │ I-DRIS B│ + │ I-DRIS C│ + ... + │ I-DRIS N│ / n
Where: I-DRIS A = DRIS index of any nutrient (A); n = number of DRIS indexes of nutrients included in the analysis.
The interpretation of the crop response potential to fertilization (PRF) was performed using the I-DRIS in three interpretations, sufficiency (S) when: I-DRIS ≤ NBIm, deficiency (D), when: NBIm < I-DRIS = negative and Toxicity (T), when NBIm < I-DRIS = positive18.
The means of high-production subpopulation indexes were considered to establish the nutrient limitation order. Nutritional deficiencies and excesses were obtained by negative and positive indexes, respectively, and the highest levels represented the most limiting nutrients21.
Experimental validation of established DRIS norms. The DRIS norms, were validated experimentally along a banana productive cycle, cultivar “Williams,” of the subgroup Cavendish (Musa AAA), from January 2019 to March 2020, in the experimental station Santa Inés, belonging to the Technical University of Machala (El Oro Province), Ecuador (3°17ʹ22'' S, 79°54'43'' W). The climate of the experimental area is tropical savannah (AW), according to the Köppen-Geiger classification.
The experiment considered randomized blocks with four replications in a 4 × 4 factorial design, being four doses of N (0, 200, 400, and 600 kg ha− 1) as ammonium nitrate (34% N) and four doses of K2O (0, 375, 750, and 1125 kg ha− 1) as potassium chloride (60% K2O). In addition, the crop received 50 kg ha− 1 of P2O5 as triple superphosphate (46% P2O5) and 64 kg ha− 1 of CaO and 60 kg ha− 1 of SO4 as calcium sulphate (23% CaO and 18% S). The experimental unit consisted of two rows of nine plants each spaced 2.2 m between rows and 1.7 m between plants, considering only the five central plants in the plot for nutritional and productivity assessment.
In the experiment, leaf samples were collected as indicated by Martin-Prevel32. Subsequently, the chemical analysis was carried out according to Bataglia et al.33 and the contents of macronutrients (N, P, K, Mg, Ca, and S) and micronutrients (Cl, Fe, Mn, Cu, Zn, and B) were determined. The PR was calculated by the multiplication of the mass of bunches harvested from plants by the population density expressed in t ha− 1. The harvest was carried out manually approximately 36 weeks after sowing. After obtaining the leaf contents and the PR, another database for DRIS calculation of the experiment was created and, together with the N-DRIS previously determined, the I-DRIS and NBIm was calculated according to Beaufils7, PRF according to Wadt18 and the nutrient limitation order according to Abebe et al.21.
The leaf nutritional diagnoses of N and K were evaluated by increases in PR (I% _Pr) based on the plant's response to fertilization with N and K2O in relation to a control condition considering increases or decreases equal to or above 10% in productivity20. The value was considered in nutritional sufficiency (S) when I_PR% ≤10%, deficiency (D) when I% _PR > 10%, and toxicity (T) when I% _PR <-10%16.
Accuracy of nutritional diagnoses. To model DRIS formulas, the variable F was introduced to interpret the indexes calculated by DRIS, adopting the value of F = 1.0, as described by Silva et al.20. Then, the accuracy of the nutritional status diagnosis for the nutrients N and K was determined. It was defined by two classes of interpretation, deficient (D) and sufficiency (S), using the DRIS norms created in this study.
The accuracy assessment consisted of verifying whether the nutritional diagnosis, obtained by the DRIS procedure, corresponded to the crop response depending on the PR variation, when N and K2O were applied in the experiment, always comparing the values with those of a control situation (without applying the two elements to the soil). In this context, the pairs of plots from a same experimental block were compared and received the same treatments, except for variations in nitrogen and potassium fertilizers. The diagnoses of the control situation were classified into D and S, as previously described, following the criterion for interpreting DRIS indexes using the PRF method18.
For the assessment of nutritional diagnoses, predictive diagnostic analyses for fertilization were used on a scale of 0 to 1, and contrasted with the seven accuracy measurements proposed by Wadt and Lemos17, considering three possible nutritional states: deficiency, sufficiency and toxicity.