Variability and spatial correlation of soil micronutrients and organic matter with macadamia nut production

: Soil fertility is the key to agricultural production. The spatial correlation and location of nutrients may significantly affect the yields. The objective of this work was to evaluate the variability and spatial correlation of iron (Fe), copper (Cu), manganese (Mn), zinc (Zn), and organic matter (OM) with macadamia nut yield. The study was conducted in an Oxisol cultivated for 20 years with macadamia nut in São Mateus, state of Espírito Santo, Brazil. A 100 point grid was used comprising an area of 144 × 140 m with a minimum distance between points of 5 m, in which a single composite soil sample was collected from 0-0.20 m layer for chemical analysis of Fe, Cu, Mn, Zn and OM. Nuts under the canopy’s projection were harvested from February to June, 2015. The data were evaluated by geostatistical analysis using semivariograms, and kriging was used to map spatial distributions of nutrients and nut yield. All evaluated attributes showed strong or moderate spatial dependence structure. The OM was correlated positively with micronutrients, but only Zn was positively correlated with nut yield. Crossed semivariograms adequately explained the maps of Zn and Mn; and Fe showed opposite tendency for macadamia nut yield.


Introduction
Macadamia (Macadamia integrifolia Maiden and Betche) is a fruit tree that belongs to the Proteaceae family and is indigenous to Australia. Plants of the Macadamia genus have good development in tropical and sub-tropical climates; this genus comprises four species, but Macadamia integrifolia is the only commercially planted species (Schneider et al., 2012). Macadamia nut has high international commercial value and good acceptance by consumers; thus, most nuts produced in Brazil is intended for export. Brazil is among the countries with higher potential for plantation and production of macadamia nuts (Rodrigues et al., 2015).
Floral abortion is one of the main problems that contribute to yield reduction, which may be correlated with the plants' nutritional imbalance (Perdoná et al., 2014). Organic matter has practically all the essential elements required by the plant, especially micronutrients (Oliveira et al., 2016), which affect plant development and the quality of the nuts produced (Huichun et al., 2015).
Brazilian soils present, in general, acidity and low fertility and organic matter content, which may limit productions due to nutritional deficiencies (Melo et al., 2015). In addition, the high nutritional requirements of macadamia plants show the importance of studies that indicate more efficient ways of fertility management for macadamia nut plantations.
Geostatistical studies using semivariograms have shown spatial dependence of soil micronutrients. Kriging is an adequate method to evaluate spatial distribution of the nutrients through mapping, as used by Gontijo et al. (2012).
The objective of this study was to evaluate the spatial variability of soil micronutrients (Fe, Cu, Mn, and Zn) and organic matter, and their spatial correlation with macadamia nut yield in an Oxisol.

Material and Methods
The experiment was conducted in a 20-year-old plantation of macadamia plants of the HAES344 variety, in São Mateus, ES, Brazil. The trees had been planted with spacing of 8.0 × 5.0 m (250 plants ha -1 ) under a micro-sprinkler irrigation system. The plantation area was at the UTM coordinates (24S) 388.106.00 m E, 7.934.570.38 m S, at an altitude of 86 m, and had a 4% mean slope. The soil was classified as Oxisol, which is common in the Coastal Tableland region of northern Espírito Santo. The climate of the region is Aw, tropical humid climate, with dry winter and rainy summer, according to the Köppen classification. The mean annual rainfall is 1.200 mm, concentrated in November and January. The annual mean temperature is 23 ºC, with maximum of 29 ºC and minimum of 18 ºC (Alvares et al., 2013).
The macadamia plantation was intercropped with Coffea canephora plants in alternated rows with spacing of 4.0 × 2.0 m. Soil acidity was corrected using 3.000 kg of dolomitic limestone (total neutralizing power of 85%), and localized fertilization was performed before planting, using 300 g of simple superphosphate. In the first year, 30 g of urea per plant were applied during 60 days; and in the second year, 200 g of NPK (25-05-20) were applied per plant during 60 days between August and March. The macadamia plants continued to receive fertilization as in the second year up to the eighth year. In the ninth year, coffee plants were removed and macadamia plants were fertilized annually (between September and March) with 150 kg of N, 80 kg of P 2 O 5 , and 160 kg of K 2 0. Liming was performed annually in May with 2.000 kg of dolomitic limestone (total neutralizing power of 85%).
A 100-point grid comprising an area of 144 × 140 m (20.160 m 2 ) was used, with a minimum distance between points of 5 m (Figure 1). The area was georeferenced using a pair of geodesic receptors (Spectra Precision ProMark ® 220). The coordinates were established and the data were processed by the Brazilian Network for Continuous Monitoring of the Brazilian Institute of Geography and Statistics, with precision of 10 mm + 1 ppm. Four soil sub-samples of the 0-0.20 m layer were collected in each sampling point in the area, under the macadamia canopy projection, using a probe-like soil sampler, making a composite sample for chemical analysis of micronutrients (Fe, Cu, Mn and Zn) and organic matter, according to EMBRAPA (2017).
Macadamia fruits were harvested from February to June 2015 by collecting the fruits under the canopy projection, which was delimited by the division of the distance between plants. The macadamia nuts were collected manually after they dropped from the trees in four harvests, and the yield of each plant was determined by weighing them, considering the economically viable fruits. Economically unviable macadamia fruits and carpels were discarded, which represented 35% of the production; therefore, 65% of the production was considered for evaluation. The yield obtained in kg per plant was transformed into Mg ha -1 .
An exploratory analysis of data was performed through descriptive statistics, obtaining the following parameters: arithmetic mean, median, standard deviation, sample variation, maximum and minimum values, coefficient of variation, coefficient of asymmetry and kurtoses. The frequency distribution of the data was analyzed to verify their normal distributions, using the Shapiro-Wilk test at p ≤ 0.05 probability and the Assistat 7.7 Beta program (Silva & Azevedo, 2016).
Geostatistical analysis was used to define the spatial variability model of the evaluated soil attributes by generating semivariograms and mapping each chemical attribute through ordinary kriging. The spatial dependence was analyzed by calculating the sample semivariances, using the GS+ 7 Figure 1. Sketch of the experimental area program (Gamma Design Software, 2004) and following the mathematical expression described by Vieira et al. (2000), as showed in Eq. 1: variables showed some distance to the mean and median (Table  1), indicating asymmetric distributions, with central measure tendencies presenting atypical values. However, Zn, OM and yield showed symmetrical data when tested by the Shapiro-Wilk test at p ≤ 0.05.
Data normality does not constitute a requisite in geostatistics. The fact that some variables do not follow a normal distribution has no influence on the analysis. This denotes the importance of using geostatistics to represent variability. The use of geostatistics is recommended when considering the soil as heterogeneous, and the variables as independent of each other and not arbitrary, representing data with normal distribution. According to the preliminary exploratory analysis, it was assumed that distributions were symmetric enough and long tailed. It was also assumed a nonoccurrence of proportional effect, enabling the development of well-defined semivariograms.
According to the classification of Warrick & Nielsen (1980), coefficients of variation (CV) were regular (12 < CV < 62%) for chemical attributes and nut yield. Gontijo et al. (2012) evaluated the same soil type and found regular CV for Fe, Cu, Mn, Zn and OM.
The lower the CV, the homogeneous the data set. Consequently, the low CV found for OM is explained by the normality found among its data through the Shapiro-Wilk test. The high CV values found for some attributes indicate high heterogeneity close to the mean, as in the case of available Fe (CV = 48%). This may be explained by the heterogeneity of the soil use and fertility.
The C/(Co + C) ratio for Zn, Mn, MO and yield ( Table  2) showed these variables with moderate spatial dependence (25% < GD < 75%); while Fe and Cu showed strong spatial dependence (<25%), according to classification suggested by Cambardella et al. (1994). Similar results were found by Chig et al. (2016) for Fe and Mn in a swampy environment.
Values of the range of the semivariograms are considerably important in determining the spatial dependence limit; thus, samples that show distances between them higher than the value of the range have random distributions and are independent from each other, with no restrictions for the use of classic statistics (Chaves & Farias, 2009 The nugget effect (Co) is a parameter of the semivariogram that shows the non-explained variability, which may occur due to measurement errors or non-detected variation by the sampling scale. The structural component (C) corresponds to the difference between the sill and the nugget effect and represents the spatially structured semivariance (Cambardella et al., 1994). The nugget effect was expressed in relation to the sill to simplify the comparison of the spatial dependence degree of the studied variables. The spatial dependence ratio was calculated as the proportion (percentage) of the nugget effect in relation to the sill (Eq. 2), which, according to Cambardella et al. (1994), can be classified as: (a) strong spatial dependence, < 25%; (b) moderate spatial dependence, 25 to 75%; and (c) weak spatial dependence, > 75%. *Normal distribution by the Shapiro-Wilk test at p ≤ 0.05 Table 1. Descriptive statistics of data of soil micronutrients, organic matter and macadamia nut yield, obtained from 100 samples where: DD -spatial dependence degree; C o -nugget effect; and, C o + C -sill.
Pearson's correlation was used to perform simple linear correlations for the combinations -two by two -between yield and soil attributes, using the Action 3 program.

Results and Discussion
The results for Cu, Zn, OM and yield were close to the mean and median, showing symmetric distributions. All other Table 2. Models and parameters estimated by experimental semivariograms for micronutrients, organic matter and macadamia nut yield SPH -Spherical model; DD -Degree of spatial dependence; R² -Coefficient of determination; SSR -Sum of squared residues; CVRC -Cross-validation regression coefficient  Figure 2). Contrastingly, low range values may affect negatively the quality of the estimations, since few points are used to perform the interpolation (Lima et al., 2013).
The nutrients presented R 2 higher than 0.795, i.e., more than 79.5% of the variation of estimated semivariance values are explained by the models, denoting that the semivariogram models satisfied the requirements of spatial interpolation. Similar results were reported by Santos et al. (2014), who evaluated Conilon coffee plantations in an Oxisol and found a high fitting degree of the dependent variable by independent variables. Spatial dependence was found for all evaluated attributes, expressed by means of the fitting to semivariogram models ( Figure 2). The soil chemical attributes and macadamia nut yield fitted to the spherical model (Table 2 and Figure 2). Similarly, Marques Júnior et al. (2015) found predominantly spherical mathematical model in soil science studies.
The cross-validation regression coefficient (CVRC) varied from 55.7 to 98.8% for the macadamia nut yield and Fe, respectively. In this analysis, after obtaining the variogram model, each original value was removed from the spatial domain and, using the other ones, a new value was estimated for that point. Thus, a graphic showing the relation between real and estimated values was developed. Cross validation does not prove that the selected model is the most correct, but rather that such model is not entirely incorrect. The CVRC for Fe shows that its estimate in the soil, using kriging, has a lower error and, therefore, it is more reliable (Landim, 2007). The cross-validation method measures the uncertainty of data prediction, i.e., it verifies the reliability of the variogram model, which will reflect in the interpolation of the data and, consequently, in the mapping by kriging. Faraco et al. (2008) evaluated diverse criteria for soil attributes validation and concluded that cross validation was an adequate method to select the best fit.
The maps in Figure 3 show a general tendency of higher iron concentrations at northeast and zinc and manganese concentrations in the central area.
Regions with spots of high nut yield are in areas with high Zn and Mn contents (Figure 3). The highest macadamia nut yield found (5.1 Mg ha -1 ; 20.4 kg plants -1 ) was higher than that found by Perdoná et al. (2012) for the same cultivar (10.7 kg plant -1 ).
Micronutrients and OM showed close relation (Figure 3). The available Fe increased as the OM increased, confirming the results found by Huichun et al. (2015). This may be due to the OM decomposition, complexation and chelatization, the dissolution of the organic and humic acids produced during the decomposition process, and the transformation of the soil active OM, which increase Fe availability (Bernardi et al., 2015). The chelated micronutrient becomes more soluble and its availability increases in the soil solution. Zn presented similar behavior; however, in areas with high OM concentrations (> 2.20 dag dm -3 ), Zn concentrations were regular (1.0 to 2.2 mg dm -3 ).
The differences found indicate that the use of different doses of soil amendments, sub-dividing the area into management units, optimizes the use of agricultural inputs and, consequently, increases the crop yield. The definition of soil management units, which represent homogeneous regions regarding soil attributes that affect plant development, is one of the most challenging stages in precision agriculture (Santos et al., 2012). The developed maps denoted, in general, favorable conditions for plant development. Therefore, soil fertilization and tillage affect the spatial variability of soil nutrients.
The yield map showed higher yields in areas with high Zn concentrations, as confirmed by their positive correlation (Table 3)  The linear correlation between macadamia nut yield and Zn concentration was weak, according to Dancey & Reidy (2005). The OM correlated positively with all evaluated nutrients; this attribute is an indicator of soil quality in agricultural areas and an important component of the soil, which is responsible for soil structuration and the supply of macro and micronutrients (Zanão Júnior et al., 2010). The presence of OM in the soil is associated with the availability, quantity and retention of some micronutrients in the soil, such as Fe, Cu, Mn and Zn, since these micronutrients are released with the decomposition of OM (Silveira & Cunha, 2002).

Conclusions
1. Spatial dependence was found for all evaluated soil chemical attributes, except for Cu, with strong and moderate degrees of spatial dependence.
2. Higher range of spatial dependence was found for organic matter (133.3 m), and lower range for iron (34.4 m).
3. The contrasts in the Zn and Mn maps showed the correlation of these nutrients with yield, which was not found for Fe.
4. The organic matter had significant correlation with all micronutrients, and Zn had significant correlation with yield.  Table 3. Simple linear correlation between macadamia nut yield and soil chemical attributes in an Oxisol