Beaufils Ranges to assess the Cotton nutRient status in the southeRn Region of Mato gRosso(1)

the relationships between nutrient contents and indices of the Diagnosis and Recommendation integrated system (DRis) are a useful basis to determine appropriate ranges for the interpretation of leaf nutrient contents. the purpose of this study was to establish Beaufils ranges from statistical models of the relationship between foliar concentrations and DRis indices, generated by two systems of DRis norms – the f value and natural logarithm transformation and assess the nutritional status of cotton plants, based on these Beaufils ranges. Yield data from plots (average acreage 100 ha) and foliar concentrations of macro and micronutrients of cotton (Gossypium hirsutum r. latifolium) plants, in the growing season 2004/2005, were stored in a database. the criterion to define the reference population consisted of plots with above-average yields + 0.5 standard deviation (over 4,575 kg ha-1 seed cotton yield). the best-fitting statistical model of the relationship between foliar nutrient concentrations and DRis indices was linear, with R2 > 0.8090, p < 0.01, except for n, with R2 = 0.5987, p < 0.01. the two criteria were effective to diagnose the plant nutritional status. the diagnoses were not random, but based on the effectiveness of the chi-square-tested method. the agreement between the methods to assess the nutritional status was 92.59–100 %, except for s, with 74.07 % agreement.

intRoDuCtion to interpret the results of traditional chemical analyses of plant tissue for the assessment of the nutritional status of cotton plants, the methods critical level and sufficiency range are used.they are called univariate methods, because only the individual concentration of the nutrients in leaf tissue is taken into consideration while no information about the nutritional balance is provided.the Diagnosis and Recommendation integrated system (DRis) (Beaufils, 1973) is an alternative to these traditional appraoches. it relates the nutrient contents in dual ratios, enabling the evaluation of the nutritional balance of a plant, ranking the nutrient levels in relative order, from the most deficient to the most excessive.
underlying the DRis is the concept of nutrient balance in plant tissue (Baldock & schulte, 1996).to be able to determine the nutritional balance, the DRis index must be determined for each element in the chemical analysis of plant tissue.the indices are derived from the arithmetic mean of the DRis functions in which the element is involved.the calculated deviation between the dual ratios of the sample and the same ratios of DRis norms is positive or negative, depending on the direction of the dual ratios in relation to the norm.When the values of these indices approach zero, the dual ratios of the sample are similar to the DRis norms, in other words, the closer to zero the indices, the lower is the nutritional imbalance (Beaufils, 1973).
since the optimal nutrient content corresponds to a DRis index of zero, statistical models can be adjusted to determine the appropriate nutrient ranges.Beaufils (1973) stated that the standard deviation (s) of the normal nutrient ranges would be between -4/3 and 4/3; levels below the minimum are considered deficient and above the maximum, excessive.this method is defined in the literature as Beaufils ranges.
the development of normal nutrient ranges for each production region is of utmost importance, since it is observed that farmers use tables based on sufficiency ranges of regions other than the production site.Beaufils ranges are useful because farmers can determine the nutritional status of a crop in a simple way, based on leaf analysis, comparing the foliar contents with the Beaufils ranges.
the purpose of this study was to develop Beaufils ranges based on statistical models of the relationship between foliar concentrations and DRis indices, generated by two systems of DRis norms -the f value and natural log transformation -and use these Beaufils ranges to assess the nutritional status of cotton in southern region of Mato grosso.

MateRials anD MethoDs
this study was performed with data from commercial cotton fields, of the growing season 2004/2005, in southern region of Mato grosso, (approximately 12 o 41' s, 45 o 40' W, average altitude 497 m asl).the soil of the study area was predominantly oxisol (embrapa, 2006).Yield data of the conventionally tilled varieties Deltaopal, DeltaPenta, DeltaPine acala 90, CnPa ita 90, and fiberMax 966 were compiled in a database.
to constitute the database, 108 samples of complete leaves (blade + petiole), of which each consisted of 30 single samples, were randomly selected in each commercial plot (average acreage 100 ha).one sample per plant was taken from the fifth leaf on the main stem (Malavolta, 2006), during flowering of the crop (stages f1 to f4), according to the classification of Marur & Ruano (2001).the samples were dried in a forced-air oven at 65 °C to constant weight, ground and sieved (60 mesh cm -2 ). the seed cotton yield was evaluated at the end of the cycle, after harvesting the plots with a combine harvester.
in the leaf samples, the total contents of n, P, K, Ca, Mg, s, B, Zn, Cu, Mn, and fe were determined by the method described by Malavolta et al. (1997).the information stored in the database and used for DRis were the total leaf contents of macronutrients (g kg -1 ) and micronutrients (mg kg -1 ) and seed cotton yield (kg ha -1 ). the database was divided into two subpopulations, using the mean + 0.5 standard deviation as criterion to separate the populations (silva et al., 2005; urano et al., 2006, 2007) into a high-yielding group (over 4,575 kg ha -1 (mean + 0.5 standard deviation) and one with seed cotton yield below 4,575 kg ha -1 .two methods were used to choose the norms (mean and standard deviation of the ratios between nutrients in the reference population), and the method determined by the f value (Jones, 1981;letzsch, 1985letzsch, , Walworth & sumner, 1987) ) and transformation by natural log (nl) of the ratios between the nutrient concentrations (urano et al., 2006, 2007, serra et al., 2010a,b).
the determination of the ratio (a/B or B/a) to establish the norm by the variance ratio method, the f value, was defined as the variance ratio of the low-yielding (non-reference) and high-yielding population (reference), and the order of the ratio with the highest value was chosen among the variance ratios (Jones, 1981;letzsch, 1985;Walworth & sumner, 1987).
the second approach consisted of the natural log transformation (nl) of the ratios between nutrient contents in the reference population, directly using the ratios between nutrients (a/B), since, when nl is used for the dual ratios, be it the direct (a/B) or the inverse form (B/a), both have the same numerical value, changing only the sign (+ or -).
in each sample to be assessed, the deviations (DRis functions) of these sample from the average values of the same ratios in the reference population were determined according to Jones (1981), in units of standard deviation (s) using an adjustment factor (c) = 1, as suggested by alvarez V. & leite (1999): the DRis indices were calculated following the general formula proposed by Beaufils (1973), where for nutrient a: n = number of DRis functions involved in the analysis.
after the individual assessment of the model fitting of regression equations between foliar nutrient concentrations and DRis indices, by the two determination methods of the DRis norms (f value and nl), the identity of the methods was tested.the approach based on the f value was considered standard (Y 1 ), and then compared with the alternative method nl (Y j ). for the identity test, the statistical procedure proposed by leite & oliveira (2002) was used.
the above procedure was used to test the identity of two analytical methods (Y 1 Y j ), using a combination of the f statistic [f(h 0 )], as modified by graybill (1976), test of the mean error (t ) and of the linear correlation coefficient (r Y1Yj ).
Based on these statistics, we propose a decision rule for testing the hypothesis of identity between any two analytical methods, ie, groups of values.the identity between Y1 and Yj was tested by the model Y j = bb 0 + bb 1 Y 1 + e i .the hypothesis H 0 : bb 0 = 0 e bb 1 = 1 was adjusted and then tested by comparison with the f(H 0 ) statistic of graybill (1976) with the tabulated value f 0,01 (2, n-2) and the Msres (residual mean square of the regression); the condition set for identity between the methods was: f(h 0 )s < f 0,01 (2, n-2), = 0 (non-significant) and r YjY1 > (1-| |); it was assumed that the result would be Y j = Y 1 for a significance level of 1 %, where: to test the hypothesis h 0 : = 0, the statistic was used with ; adopting n-1 degrees of freedom and a = 1 %.if t ≥ t a (n-1), the hypothesis h 0 is rejected.on the other hand, if t < t a (n-1), the hypothesis h 0 is accepted, indicating that the observed difference between the two methods was random and that the approaches are identical, however, the decision of the identity test equations must be based on the other criteria, f(h 0 ) and r YjY1 , as well.
for both methods, the hypothesis whether the frequency at which each nutrient appeared as deficient had been randomly attributed was tested.for this purpose, the chi-square test (χ 2 ) of Pearson was applied at 1 % probability, with n-1 degrees of freedom (n = number of analyzed nutrients).if the hypothesis were true, the observed frequencies for all nutrients would be statistically equal to each other (urano et al., 2006; serra et al., 2010a).the expected (EF) and observed frequencies (OF) were calculated as follows: the assessment of the nutritional status by the two methods was compared by the frequency of coincident diagnoses obtained by the norms defined by the f value and those obtained by natural log transformation (nl).statistical analysis was performed using the program saeg 9. 1 (Ribeiro Junior, 2001), and the other DRis calculations with excel ® ( 2010) spreadsheets (Microsoft Corporation, 2010).

Results anD DisCussion
the relationship between DRis index and foliar nutrient allowed two fittings of equations, linear and quadratic (figures 1, 2, 3, and 4).  the micronutrients had a greater coefficient of determination (R 2 ) than the macronutrients, (over 0.90, p < 0.001), except for Zn (figure 3c,d), which shows that there is greater dependency of the DRis indices on the content the element itself than on the other nutrients involved in the calculation of DRis indices (figures 3 and 4). it was noted that the relationship between DRis indices and foliar concentrations was significant (p < 0.01) for all nutrients.lowest DRis indices were associated with the lowest leaf levels, increasing the reliability of the DRis norms, since the approaches indicated the nutritional limitations correctly (figures 1, 2, 3 and 4).however, n was the nutrient with the lowest R 2 (figure 1a,b).
Reis Júnior et al. (2002) found a strong positive correlation (p < 0.01) between foliar concentrations and the DRis index, confirming the hypothesis that the system effectively diagnoses the nutritional status.however, they observed the lowest correlation coefficients (0.47 and 0.55, respectively) for the nutrients n and s. in addition, silveira et al. the coefficient of determination (R 2 ) is an important parameter to indicate the model fitting of regression equations, however, this parameter alone is not sufficient to define whether two tested methods are identical or not.thus, the hypothesis of identity was tested for the two analytical methods, as proposed by leite & oliveira (2002). in the identity test (table 1), the f(h 0 ) value was between 6.24 ** and 91.85 **, significant at 1 % probability.this test result for f(h 0 ) showed that the hypothesis H 0 : b 0 = 0 e b 1 = 1 was rejected, accepting the alternative hypothesis that b 0 and b 1 are different from 0 and 1, respectively.in the test of mean error (t ), no significance was found, in other words, the observed differences between methods were caused randomly, however, the value of r YjY1 ≥ (1-| |) was higher in most cases, except for Zn.taking into account the parameters of the identity test proposed by leite & oliveira (2002) for decision making, it was concluded that the two tested methods of choice for DRis norms, f value and nl, result in different DRis indices, which are not coincident (table 1).therefore, according to leite & oliveira (2002), the projected values of DRis indices would be coincident if: f(h 0 were not significant at 1 % probability; t not significant at 1 % probability, and r YjY1 ≥(1-| |).since no such situation occurred, it was concluded that the tested methods were not identical.taking into account that the plant is nutritionally balanced when the DRis indices are close to zero (Walworth & sumner, 1987;Beverly, 1991), the leaf nutrient concentrations were established according to this point of nutritional balance.
Based on the relationship between DRis indices and nutrient contents in leaf samples of the highyielding population, it was possible to determine the normal nutrient ranges, the so-called Beaufils ranges.the best-fitting statistical model was linear, p < 0.01 (table 2) and used to generate the ranges (table 3), following the recommendations of Beaufils (1973).
the two ways of calculating the norms resulted in similar Beaufils ranges, not dissenting from each other (table 3). the coefficient of determination (R 2 )  was higher than 0.8090, p < 0.001, for most nutrients except n, which had the lowest R 2 [0.6097 (nl) and 0.5987 (f value)] but was significant (p < 0.01) (table 3). the hypothesis of randomness of the results diagnosed as deficient was tested by chi-square (table 4). the test was effective (p < 0.01) to prove that the results were not random but that the  (1) according to the method proposed by leite & oliveira ( 2002). (2)natural logarithm (nl).** significant at 1 %.ns: not significant.e 1 Y Y j r calculation of the DRis system, using two criteria norms, was effective in diagnosing the nutritional status, rejecting the hypothesis that the deficiency had been randomly diagnosed by DRis. urano et al. (2006) reported similar results in an evaluation of the nutritional status of soybean and serra et al. (2010a, b) in an assessment of the nutritional status of cotton plants by the methods  (1)  ef (1)  (of-ef) 2 /ef of (1)  ef (1)  (of-ef)

DRis and CnD (Compositional nutrient Diagnosis).
in the analysis of the nutritional status of the plots, Zn was most frequently diagnosed as deficient, followed by Ca and n (table 6), with agreement between the criteria of norm establishment.however, s had the highest percentage of deficiencyprone plots (table 5).
these tables of ideal nutrient ranges are only recommended in the regions where they were developed, for their use in other regions can produce unfavorable results.the same is true for the DRis norms, because the Beaufils ranges are derived from statistical models based on DRis procedures, indicated for specific regions.so far it has been observed that specific norms for each climate and soil region are more efficient than general norms for different regions. in view of the absence of universal norms, silva et al. ( 2005) suggested the use of specific rather than of general norms.the percentage of agreement of the diagnosed nutritional status was 74.07-100 % among the plots evaluated (table 6).Coincidence was lowest between the methods for s (74.07 %).however, the percentage of plots in which s deficiency was diagnosed was higher by the f value (7.41 %) than by the other criterion (2.78 %).
silveira et  al. (2005a)  stated that the best-fitting model was linear and logarithmic, as also reported by guindani et al.(2009).

figure 1 .figure 2 .
figure 1. Relationship between the primary macronutrient (reference and non-reference population) and their respective DRis indices (DRis i), generated by the norms based on the criterion of natural log transformation (nl) (a, c and e) and the norms determined by the f value (b, d and f).** indicates p < 0.01.

figure 4 .
figure 4. Ratio between the levels of micronutrients (reference and non-reference population), manganese (Mn) and iron (fe) and their respective DRis indices (DRis i), generated by the norms based on the criterion of natural log transformation (nl) (a and c) and the norms defined by f value (b and d).** p < 0.01.
ademar Pereira serra et al.