Statistical analysis

An exploratory analysis, scatter plots and Pearson correlation matrix was performed. An unsupervised statistical analysis of principal components (ACP) with standardized values was made. PCA has many advantages (^{Broschat, 1979}), is a technique that reduces the dimensionality of a set of multivariate data, removes existing interrelationships between variables, organizes data in orthogonal vectors where each of the variables within the vector behaves in a similar manner based on their correlations, each of these vectors is called a principal component. The first components express most of variance of orthogonal data and are a useful tool to simplify the analysis and interpretation of large amount of variables considered in an exhaustive assessment. Calculations were performed with the language and environment for statistical computing R version 3.1.1 (James et al., 2014).

Dynamics of chemical variables over time for different crops

By observing nutritional dynamics of the different variables of soil solution over time (Figures 1-5) it can be appreciated in the different sites similar patterns in behavior regarding time and values and concentrations of different variables. In all cases pH values fluctuated, but always keeping a positive trend as samplings advanced, the values ranged from 5 to 7.8. EC showed a negative trend versus time for avocado, cranberry and pepper with initial levels of 0.8, 1.74 and 1.41 respectively, decreasing towards final stages to values of 0.4 dSm^-1for avocado and cranberry and 1 dSm^-1 for pepper. For strawberry and papaya the trend in EC was positive initiating with of 0.6 and 0.87 to 1.4 and 1.8 respectively. The concentration of Na⁺ and K⁺ showed a decreasing trend for all crops, showing fluctuations in certain samplings; for avocado, cranberry and strawberry Na⁺ values remained on an average range of 154 to 15 mg L^-1 and K⁺ levels for the three cases showed increases in their early sampling dates of up to 296 mg L^-1 as for cranberry, K⁺ levels decreased from 231, 296 and 76 to 17, 84 and 28 mg L^-1 respectively. For papaya and pepper Na⁺ range was higher, taking values of 487 and 475 to 43 and 136 mg L^-1, respectively, while K⁺ showed a milder decrease, starting in concentrations of 190 to 29 mg L^-1 for papaya and from 62 to 2 mg L^-1 for pepper. Ca²⁺ and NO₃^- showed the same dynamic pattern, decreasing in all crops except where papaya levels reached 580 and 620 mg L^-1 respectively. For the rest of the crops Ca²⁺ and NO₃^- concentration in soil solution decreased showing ranges from 381 to 34 mg L^-1 and 418 to 112 mg L^-1 (avocado), 250 to 18 mg L^-1 and 430 to 65 mg L^-1 (cranberry), 180 to 59 mg L^-1 and 547 to 271 mg L^-1 (strawberry) and from 430 to 27 mg L^-1 and 360 to 45 mg L^-1 (pepper).

Figure 1 Dynamics of chemical variables over time for growing avocado, at the bottom of the graphs the Pearson correlation coefficient indicated. 

Figure 2 Dynamics of chemical variables over time for growing blueberry, at the bottom of the graphic Pearson correlation coefficient indicated. 

Figure 3 Dynamic chemical variables over time for the strawberry crop, at the bottom of the graphs the Pearson correlation coefficient indicated. 

Figure 4 Dynamic chemical variables over time for growing papaya, at the bottom of the graphs the Pearson correlation coefficient indicated. 

Figure 5 Dynamics of chemical variables over time for the pepper crop, at the bottom of the graphic Pearson correlation coefficient indicated. 

The results found for NO₃^- in soil solution for most crops can be given by leaching processes and radical absorption (^{Navarro-Blaya and Navarro-García, 2003}). Both processes may be associated not only with decreased NO₃^- but also with other ions (K⁺, Ca^2+, Na⁺) and in general EC of soil solution.

For papaya (Figure 5) an opposite behavior in EC apparently associated to an increase in Ca²⁺ and NO₃^- present in soil solution was observed (^{Charley and McGarity, 1964}; ^{Menguel and Kirby, 2001}).

For strawberry (Figure 3) the highest concentration of NO₃^- and K⁺ in soil solution is present in early stages, which was described by the absorption curves studied by ^{Molina et al. (1993)}, who pointed out that in its early stages the absorption is very low, increasing simultaneous to fructification. The increasing dynamics from pH of soil solution, observed in all cultures studied, could be due to the alkalizing effect of nitrates from fertilizers applied (^{Snakin, 2001}). Decreases in Ca²⁺ and K⁺ ions in soil solution is probably due to increased absorption as the crop passes from the vegetative stage to flowering and fruit set, this due to a preference in the absorption of these ions by avocado plants (Figure 1) (^{Maldonado-Torres et al., 2007}), cranberry (Figure 2) (^{Ferreyra et al., 2001}) and papaya (Figure 4) (^{Fallas, 2014}).

This decreasing effect on ions present in the soil solution could be related to an increase in the absorption rate of nutrients as the crop grows as observed in strawberry case (Figure 3) (^{Avitia-Garcia et al., 2014}) and pepper (Figure 5) (^{Rincón et al., 1995}).

For cranberry another factor possibly involved in the reduction of ions in the soil solution (Figure 2), would on one hand the fixation in soil particles or in the case of sandy soils through leaching (^{Hancock and Draper, 1989}). For decreasing Na⁺ in the soil solution (Figure 2) it has been reported that cranberry tends to absorb it in high levels in leaf tissue, this because it lacks a mechanism of regulating the uptake of this element (^{Spiers, 1983}).

First principal component analysis

Data obtained in the study from the dynamics of the composition of soil solution for five different crops, underwent an unsupervised multivariate statistical analysis called principal component. Consisted in the creation of new variables called principal components from the original variables (NO₃^-, K⁺, Ca2⁺, Na ⁺, pH and EC). With this method accomplished to create a linear function with which was possible to explain the multivariate behavior of the system comprised by the soil solution. For this purpose the values of the principal components were obtained and defined using only the first principal component which groups the highest variance. For avocado groups 50%, cranberry 40%, strawberry 40%, papaya 33% and pepper 62%.

The load vectors obtained for the first principal component (Table 2) were identified the highest absolute value for each crop studied, determining with this which variable contributed the most to the variation of the first component. For avocado and cranberry was the most important variable was K⁺, for strawberry pH, for papaya NO₃^- and pepper Na⁺. These characters of the soil solution could rule as conditioning variables (independent variables) (Jenny, 1994), in the dynamic behavior of the system and presumably are different in each culture for being different soils and geographical sites.

Table 2 Vectors standardized load the first principal component of the different variables evaluated for different crops. 

Despite soil and crops diversity, it was found in the behavioral set of load vectors a pattern in all crops: the values of load coefficients were positive for pH and negative for most of the remaining cases (Table 2). This result indicates that in all cases pH tends to rise during crop growth, indicating a deficit in the protonation of soil solution, possibly resulting from the absence of a suitable concentration of organic matter, which is known to be the repository for exchanging e-/H⁺ (^{Menguel and Kirby, 2001}) and the aforementioned effect of alkalinization by applying NO₃^- in fertilizers (^{Snakin, 2001}). The rest of the coefficients, of negative sign, indicate the trend towards decline in the availability of mineral nutrients in soil solution. A possible explanation for this would be insufficient capacity of the solid phase of the soil to provide the necessary nutrients in the soil solution (^{Menguel and Kirby, 2001}) to cover all crops needs, this despite the contribution of fertilizers via fertigation.

By observing the dynamic behavior of the first principal component it can be seen the variability of the observations versus time or samples number, finding that the dynamics of the first principal component was similar to the six crops, with a clear upward trend (Figure 6). This rising trend is largely governed by the variables with greater weight in the first principal component.

Figure 6 Performance of the first principal component over time for different crops studied. 

These variables, through load coefficients, are negative for avocado, cranberry and pepper, while for strawberry and papaya are positive. A possible answer to this similarity would be given by pH of the soil solution over time, which as mentioned previously, for all cases showed positive correlation (Figure 1, 2, 3 and 5) and is associated in a very similar way to the principal component (Figure 6) over time. This happens for all crops except papaya (Figure 4), where NO₃^- plays a key role in the rising behavior of the principal component. In all cases the first component shows a positive trend over time, which indicates the possible presence of a temporal pattern in joint dynamics of the attributes of the soil solution.

These results seem to suggest on one hand the effectiveness of the first principal component in shaping joint dynamics of soil solutions in different crops; in particular, it is an integration of the results presented above in univariate analysis of different ions for different crops over time.

On the other hand, the dynamics described indicates the plausibility of modeling the behavior of a complex system such as soil solution, while not using any single variable or group of variables analyzed individually, but a linear function of the variables determined in soil water. It is possible that increasing the number of variables determined in the soil solution the modeling power is higher to predict the joint dynamic behavior. Such studies should be performed to verify if the study of the soil solution can be a useful supplement to traditional studies in the solid phase of the soil.

From Dokuchaev times raised that the knowledge of soils is the mean to dominate and lead them with goals applied to agriculture (^{Hernandez-Jimenez et al., 2006}). Based on the findings of this research can be inferred that it is possible to predict nutrient dynamics of soil solution in soils with agricultural management. This behavior could be modified by changing crop management and/or land use and therefore have consequences on the pattern of the principal component. This effect in modifying the soil solution has been reported by ^{Snakin et al. (2001)}, who indicates that in forest soils without human intervention the variability of the solution tends to decrease, which could make the predictive study of the soil solution easier.

The author indicates that human activities could create dynamic heterogeneity additional to that arising naturally in certain soil characteristics. The latter supports the findings in this study where agricultural soils on the one hand seem to show a similar multivariate dynamic that seems to suggest common patterns of behavior in different systems, but with specific heterogeneities in the case of each crop and surely comes from each specific combination soil - plant species- agronomic management. Also have been reported results of a daily cyclical behavior of pH, redox potential and calcium in the soil solution in forests (^{Snakin, 1983}), but without finding similar trends in the different soils. Currently there is no information on the composition dynamics of the soil solution over time for crops as well as for multivariate statistical analyzes that attempt to explain or predict the behavior of the soil solution system.

It is essential to continue with these types of studies and repeat them in subsequent years adding more variables as well as other ions (NH₄⁺ Mg²⁺, H₂PO₄^-, SO₄^2-, CO₃^2- Mn^{2 +}, Fe^{2 +}, Cu^{2 +}, H₃BO₃, Zn^{2 +}, MoO₄^2-, Si(OH)₄, Al^{3 +}, etc.), oxide reduction potential (ORP), concentration of organic acids (malate, citrate, lactate, etc.), titratable acidity, populations and species of bacteria, fungi and protists or metagenomic studies thereof, among others. It would also be of great importance to perform such work under natural conditions without human intervention or in rainfed, reduced tillage or organic farming areas, to determine if in spite of the different soil conditions exist common patterns among them as those are described in this study.

This study explores the broad picture about soil composition and its behavior. It offers the prospect of evaluating the soil solution as a complement to classical physicochemical determinations performed on samples of the soil solid phase.

From the methodological point of view, this paper illustrates the usefulness of principal component analysis, as a useful tool for the descriptive study of the soil solution, as being a complex and dynamic system it consists of many elements that govern their behavior both individually and collectively. Studying the individual components separately without an integrative dimension reduction tool, would fail in exploring joint dynamics from soil solution systems, where not only considers the behavior of individual attributes, but the system as a whole that emerges from the components connected by its interactions and interdependencies.