Correlations of soybean yield with soil porosity and bulk density of an Oxisol 1

determine the potentialities, fragilities and limitations of each environment, and should be considered for a sustainable biomass production. This means that the farther the agricultural ecosystem is from its natural state, the more dependent a sustainable production will be on human management actions. With the intensification of agricultural mechanization, cultivation is often carried out under conditions that compromise the conservation

PALAVRAS-CHAVE: Glycine max L.; compactação do solo; aeração do solo; geoestatística; sistema plantio direto.Correlations of soybean yield with soil porosity and bulk density of an Oxisol e-ISSN 1983-4063 -www.agro.ufg.br/pat-Pesq.Agropec.Trop., Goiânia, v. 48, n. 4, p. 476-485, Oct./Dec.2018 of edaphic resources, leading, for example, to a soil compaction process and its advancement in extensive regions of the country, with impacts on agricultural yield.Thus, mapping the soil physical attributes of an agricultural area is of utmost importance, both for the recommendation of management practices and for the evaluation of agricultural effects on environmental quality (Andreotti et al. 2010).
In geostatistics, maps made from estimates of a studied variable can represent the spatial variability.Studies related to soil compaction, which use its bulk density as an indicator attribute, have shown that its increase may cause, in general, a decrease in agricultural yield (Lima et al. 2007, Queiroz et al. 2011).In view of that, this study aimed to compare methods for determining soil porosity and density, as well as to analyze correlations between soybean grain yields with some attributes of soil mass-volume relationships, in order to indicate those that were more efficiently related to soybean yield, as well as to study the spatial variability of soil attributes and yield components of this crop.

MATERIAL AND METHODS
The study was carried out in Selvíria, Mato Grosso do Sul state, Brazil (20º18'05"S and 20º18'28"S; 52º39'02"W and 52º40'28"W), where the precipitation and average annual temperature are 1,300 mm and 23.7 ºC, respectively (Figure 1).The climate is Aw, characterized as humid tropical, with a rainy season in the summer and dry in the winter.The experiment was cultivated under a no-tillage system for five years, with successive sowings of corn in the first two years (2005/2006 and 2006/2007), and, in the last three years, sorghum in the second crop and soybean in the summer, respectively.
Soybean of the commercial variety Conquista was sown on December 21 and 22, 2009, with a space of 0.45 m between rows and density of 18 seeds m -1 , fertilized at sowing with 300 kg ha -1 of the formulation 00-20-20 (N-P-K).The soybean seeds were previously inoculated with Bradyrhizobium japonicum, using the commercial liquid inoculant Masterfix ® , containing SEMIA 5079 and SEMIA 5019 strains (minimum concentration of 5 × 10 9 viable cells mL -1 ).
The statistical mesh was established in an area of 10 ha using the x and y directions of the Cartesian coordinate system in the largest launcher of the crop, performing random staking of the mesh at the time of planting and soil data sampling.In the direction of the x-axis, 18 lines were spaced at 39.0 m apart, with the number of 18 variable sample points in each of them and distances ranging between 18.0 m and 21.0 m in the direction of the y-axis, so that within the area 99 sampling points were distributed, obtaining an average of 10 sampling points per hectare.
The soybean yield components and soil physical attributes were collected around each sampling point.For the collection, 10 plants positioned in the central part of the points and their surroundings were used for the analysis of the soybean yield components.For the determination of grain yield, all the plants of the useful area were harvested, which, after dried, were submitted to manual tracking and, then, the mass of these grains, corrected to 13 % of humidity, was determined.The useful area of each sampling point was the result of the harvesting of four sowing rows, spaced at 0.45 m, totaling a width of 1.80 m and a length of equal value, totaling 3.24 m 2 .The soybean yield components were the following ones: grain yield (GY), number of pods per plant, number of grains per pod, mass of 100 grains, grain mass per plant (GMP), plant population and plant height.
The statistical analysis was performed using the SAS software (SAS Institute 2010).The descriptive analysis of the attributes was performed by calculating the average, median, minimum and maximum values, standard deviation, coefficient of variation, kurtosis, skewness and frequency distribution analysis, using the Shapiro & Wilk test at 1 % of error probability.The soil attributes variability and soybean yield components were classified according to the magnitude of their coefficients of variation (CV), which, according to Pimentel-Gomes & Garcia (2002), are classified as low (CV < 10 %), average (10 % < CV < 20 %), high (20 % < CV < 30 %) and very high (CV > 30 %).The correlation matrix was built among all the attributes studied, containing all the possible matched combinations, in order to detect the existence of significant correlations between the components of plant yield (dependent variables) and soil attributes (independent variables).The geostatistical analysis was done using the Gamma Design Software 7.0 (GS + 2004).For each attribute, the spatial dependence was analyzed by means of semivariogram calculation.The aim was to analyze correlations between soybean yield and soil, seeking to select which attribute was correlated with yield, as well as to study the spatial variability of the soil attributes and the yield components of this crop.

RESULTS AND DISCUSSION
According to Pimentel-Gomes & Garcia (2002), the yield components, regarding the number of soybean grains per pod and mass of 100 grains, indicated a low variability, with coefficient of variation values of 5.7 % and 6.4 %, respectively, whereas plant height, plant population and grain yield indicated an average variability (11.3 %, 12.2 % and 19.9 %); in turn, grain mass per plant and number of pods per plant indicated a high variability (22.6 % and 23.5 %) (Table 1).The values determined for number of pods per plant, number of grains per pod, grain mass per plant and plant population agreed with the magnitude of those obtained by Dalchiavon et al. (2011), except for grain yield, which showed an average variability of the data (19.9 %) and the aforementioned high variability (21.8 %).
When any statistical variable has a frequency distribution of the normal type, the most suitable central tendency measure to represent it should be the average.On the other hand, it should be represented Correlations of soybean yield with soil porosity and bulk density of an Oxisol e-ISSN 1983-4063 -www.agro.ufg.br/pat-Pesq.Agropec.Trop., Goiânia, v. 48, n. 4, p. 476-485, Oct./Dec.2018 by the median or by the geometric average, in case it is lognormal (Dalchiavon et al. 2011).Therefore, except for the number of pods per plant, number of grains per pod and plant population, the components indicated a frequency distribution of the normal type and had their respective central tendency measures represented by the average (Table 1).
For the yield components, the average values for number of pods per plant, number of grains per pod, mass of 100 grains, grain mass per plant, plant population and plant height were, respectively, 25, 2.0, 15.8 g, 6.9 g, 36.5 plants m -2 and 75.8 cm, different from those obtained by Dalchiavon et al. (2011), who evaluated the soybean grain yield under no-tillage, in the region of Selvíria, and lower in terms of number of pods per plant, number of grains per pod and grain mass per plant attributes, whose values corresponded, respectively, to 72.2 g, 2.2 g and 23 g.The number of pods per plant was lower than that of 36.6 obtained by Queiroz et al. (2011), who studied the soybean grain yield in an Oxisol, in a crop rotation with brachiaria pasture, and of 72.2 observed by Dalchiavon & Carvalho (2012), evaluating soybean grain yield cultivated in a Oxisol under no-tillage.Possibly, the number of pods per plant was lower due to the increase in the soil bulk density, since, under stress conditions, the plant formed few grains in the pods, because the main biological objective of the crop is the dissemination of the species (Carvalho et al. 2004).
The mass of 100 grains (15.8 g) was very close to that of 15.9 g obtained by Lovera (2015) and less than the 16.4 g obtained by Carvalho et al. (2004), studying the effect of soybean cultivated under notillage in an Oxisol, because, according to the authors, the mass of 100 grains is the one that presents the lowest percentage variation due to changes in the growing environment.The plant height (75.8 cm) was higher than that of 68.0 cm verified by Queiroz et al. (2011).It is noteworthy that, when it exceeds 65 cm, it is indicated as the desired height of plants for mechanical harvesting (Bonetti 1983).
Grain yield was low (Table 1), with an average value of 2,659 kg ha -1 , lower than the national average of 3,362 kg ha -1 (Conab 2017) and also lower in relation to that reported by Rosa Filho et al. ( 2009) of 3,317.5 kg ha -1 , by Queiroz et al. (2011) of 3,270 kg ha -1 and by Dalchiavon et al. (2011) of 4,639.4kg ha -1 .However, it is much higher than that of 1,215 kg ha -1 found by Lovera (2015), all carried out in the same soil under no-tillage in the region of Selvíria.It should be noted that the soybean sowing took place in late December and it was summer throughout the crop cycle, both of which were determinants for the low grain yield.Despite the total rainfall of 645 mm, there was an irregular distribution of rainfall, with 72 % of the total concentration in the months of December and January.Considering that the rainfall levels in the months of February and March were, respectively, 76.7 mm and 72.9 mm (Figure 1), and based on the soil water requirement for soybean from 7 mm day -1 to 8 mm day -1 in the period of the flowering-grain filling, there were hydric deficits in the period, since rainfall levels of 196 mm and 248 mm would be necessary for the mentioned months.
The variability of soil bulk density and particle density attributes, in the two layers evaluated, were low, with coefficient of variation values between 3.9-7.2% and 1.9-3.0%, respectively (Table 2).The coefficient of variation data for soil bulk density were of the same magnitude as those obtained by Santos et   (2015), evaluating an Oxisol in the region of Selvíria, which ranged between 3 % and 10 %.The variability of the soil bulk density values was affected by the crop soil management, which is essentially mechanized.The pressure exerted on the soil by the machines and the implements used in the cultivation and harvesting of soybean may generate additional compaction of the soil in certain regions in the place, mainly when under conditions of high soil moisture.Regarding particle density, the low variability of the data attested by the variation coefficient between 1.9 % and 3.0 % agreed with the findings of Santos et al. ( 2006) with values of 2.5-3.0 %, and Montanari ( 2009) with 4.6-5.5 %.The lower variability of the particle density data is consistent, because the soil pore volume is not considered in its determination, only that of the solid fraction, what makes it impossible to detect changes in the soil structure (Brady 1990) due to crop management.Probably, the variability of the particle density is more related to errors due to its determination than to the variations of the constituents of the solid fraction of the soil.
In general, the total soil porosity presented a low variability, corroborating the findings of Andreotti et al. (2010) and Lovera (2015), with coefficients of variation of 1-6.5 % and 6.9-8.9 %, respectively (Table 2).However, the attributes TP1 and TP3 indicated the average variability of the data, with coefficients of variation of 11 % and 10.5 %, respectively, agreeing with those found by Montanari (2009), with values of 11.5-14.3%.It should be noted that the same considerations made to base the variability of the data determined from soil bulk density are plausible for the total soil porosity attribute, whose calculation considers the pore space in the soil.
The average values of the soil physical attributes were different in the layers, with an increase in the soil bulk density when determined by the ring method (BD1 and BD2) and in particle density for the evaluated methods (PD1 and PD2, PD3 and PD4) (Table 2).The average values were 1.442 kg dm -3 and 1.460 kg dm -3 for BD1 and BD2, respectively, and 1.545 kg dm -3 and 1.539 kg dm -3 for BD3 and BD4, respectively.This indicates a soil compaction in the studied layers, since they are larger, in relation to those determined by Oliveira & Moniz (1975) for a Dystroferric Oxisol under natural forest (0.980 kg dm -3 and 1.130 kg dm -3 ).The bulk density values found in the present study were higher than those observed by Lovera (2015) of 1.359 kg dm -3 and 1.411 kg dm -3 , respectively at the 0.00-0.10m and (a) BD1 and BD2 and BD3 and BD4 are respectively the bulk densities determined by the methods of the ring and clod; PD1 and PD2 and PD3 and PD4 are respectively the particle density determined by the methods of the volumetric flask and modified volumetric flask; and TP1 to TP8 are respectively the total porosities of the soil determined by the abovementioned methods, sampled at the 0.00-0.10m and 0.10-0.20 m layers (respectively indicated by even an odd numbers). (b) FD = frequency distribution; UN = undetermined; NO = normal; LN = lognormal.
Attribute (a)   Descriptive statistical measures 0.10-0.20 m layers, in the same area and the same soil classification as in the present study, indicating that, maybe, there was an increase in soil compaction due to the no-tillage system.The higher soil compaction in the superficial layer for the no-tillage system, as a consequence of the movement of machines in the area, without the subsequent rotation, could increase the degree of packing of particles, thus reducing the volume of voids and increasing the soil bulk density (Portugal et al. 2012, Sales et al. 2016).The higher soil bulk density values obtained using the paraffin-coated clod method (BD3 and BD4), if compared to those using the ring method, have been reviewed in the literature (Pires et al. 2011).The penetration of paraffin in small cracks in the clod and in the macropores, besides the loss of them during the clod sampling, are among the probable causes of the higher values obtained by the analysis method.According to Van Remortel & Shields (1993), the values are generally 0.07-0.09kg dm -3 higher than those determined by the volumetric ring method.In the present study, they were higher at 0.103 kg dm -3 and 0.079 kg dm -3 for the layers of 0.00-0.10m and 0.10-0.20 m, respectively.Pires et al. ( 2011) found an increase of 0.15 kg dm -3 of the clod method, in relation to the volumetric ring, due to the procedure of clod collecting, in which only the denser ones had a structure to be prepared and analyzed in the laboratory.The total soil porosity was lower than that recommended as ideal, which is of 0.500 m 3 m -3 of its total volume (Kiehl 1979), indicating a compaction of the layers evaluated by the mechanized activities in the area.The values ranging from 0.398 m 3 m -3 (TP7) to 0.441 m 3 m -3 (TP1 and TP2) were lower than those determined by Lovera (2015) of 0.489 m 3 m -3 and 0.467 m 3 m -3 , respectively in the layers of 0.00-0.10m and 0.10-0.20 m.However, the reduction of total soil porosity did not result in lower grain yields, since they were superior to those obtained by Lovera (2015).
According to Dalchiavon (2010), when between any two attributes, there is a high and significant Pearson's correlation coefficient and both result in a semivariogram, and co-kriging will certainly exist.However, if they present a low and non-significant Pearson's correlation coefficient and both present a semivariogram, co-kriging may or may not exist.In this context, Table 3 displays the parameters of the cross-semivariograms adjusted between some attributes of grain yield.
In Figure 2, which represents the map of the grain yield simple kriging, the highest values for grain yield were found in the southwest and northeast regions, ranging from 2,623 kg ha -1 to 3,069 kg ha -1 in the form of halos of light color.On the other hand, the northwest and southeast regions of the map presented the lowest values for grain yield (2,027-2,474 kg ha -1 ) in the form of halos of dark color.
The cross-semivariograms and the co-kriging maps between soybean yield components (plant versus plant) and between soybean yield components and soil attributes (plant versus soil) are shown in Figure 4. Thus, of the co-kriging attested by the coefficient of spatial determination (r 2 ), the GMP = f(BD1) presented a variographic adjustment of the direct Gaussian type (Table 3; Figure 4e) and a higher value of r 2 , indicating that 78.6 % of the spatial variability of the grain mass per plant could be explained by the spatial variability of BD1.In other words, from a spatial point of view of the searched areas, in the halos in which BD1 presented values between 1.46 kg dm -3 and 1.54 kg dm -3 , the grain mass per plant of soybean of the commercial variety Conquista, planted in late December, ranged between 7.10 g and 8.16 g.However, in those where the BD1 ranged from 1.35 kg dm -3 to 1.43 kg dm -3 , the soybean mass of 100 grains ranged between 5.67 g and 6.74 g.A direct relationship was also observed for co-kriging between the grain mass per plant and soybean grain yield (Table 3; Figure 4a).Thus, in the halos of the map in which the soybean grain mass per plant presented values between 7.10 g and 8.16 g, the soybean grain yield varied between 2,623 kg ha -1 and 3,069 kg ha -1 .
The co-kriging of BD1 with soybean grain yield (Table 3; Figure 4b), with a direct relation to the spherical variographic adjustment indicated in the halos of the map in which BD1 presented the highest values, ranged between 1.46 dm -3 and 1.54 kg dm -3 , and the soybean grain yield increased, ranging between 2,623 kg ha -1 and 3,069 kg ha -1 , corroborating the fact that the increase between soil and root caused by higher BD1 was not sufficient to affect the soybean grain yield.According to Favaretto et al. (2006), nutritional and water stresses are necessary to plants between the emergence and maturation periods to affect the plant growth, what was not observed in the present study.Lovera (2015), who evaluated some soil physical attributes and soybean yield components in the same area as that of the present study, also verified such a direct behavior between the soil bulk density co-kriging and soybean grain yield.The variographic adjustment was of the Gaussian type, with r 2 = 0.813 and a reach of 35.0 m.
The co-kriging of TP3 and TP2 with grain yield (Table 3; Figures 4c and 4d) was adjusted to the Gaussian model and showed an indirect relation between them, indicating that the increase of total soil porosity resulted in a decrease of soybean grain yield.Thus, the co-kriging GY = f(TP3) (Table 3; Figure 4d

Figure 1 .
Figure 1.Maximum and average rainfall and temperature, during the evaluation period of the experiment.

Table 1 .
Descriptive analysis of the crop production components of soybean in an Oxisol.

Table 3 .
Parameters of cross-validation semivariograms adjusted for some attributes of the soybean grain yield (GY) and Oxisol.