**5. Compositional modeling of C mineralization of organic residues in soils**

The carbon, nitrogen, phosphorus and sulfur cycles are interconnected in agroecosystems and often expressed using stoichiometric rules [4]. The ratio between total C and total N is the most simplified rule used in C mineralization studies but the Corganic/Norganic and lignin/ Norganic ratios are also common. However, several biochemical components of organic matter are omitted in most studies, resulting in loss of information on the system. There are few studies on the relationship between labile or recalcitrant C and the biochemical composition of organic residues added to soil. [70] analyzed ash and N contents as well as four C frac‐ tions in organic residues representing pools of increasing resistance to decomposition. In this section, we related labile C in organic residues to this 6-part compositional vector of or‐ ganic residues. The components were expressed as fractions on dry weight basis to compute a biological stability index using multiple linear regression models. The compositional vec‐ tor was defined as follows:

(a) (b)

**Figure 15.** Ternary diagrams showing K treatments applied to a K-deficient soil at rates of 0, 50, 100 and 150 kg K ha-1

**Figure 16.** General view of plant ionomes in P and K deficient soils moving toward the reference ellpse for highly pro‐

ductive agroecosystems as P (blue) and K (red) fertilizers are added.

(rates increasing as red circles enlarged (a) zoomed on proportions and (b) centered and scaled.

104 Soil Fertility

$$\mathcal{S}^{\mathcal{A}} \triangleq \mathcal{C} \{ \text{SOL } \text{ }, \text{ HEM }, \text{CEL } \text{ }, \text{ LIG } \text{N }, \text{ Ash }\} \tag{10}$$

Where SOL = soluble matter, HEM = hemicellulose, CEL = cellulose, L IG= lignin, and N = total nitrogen.

Because scale dependency induces spurious correlations [71, 72, 73] and linear regression models are solved based on correlations between variables, the interpretation of regression coefficients is scale-dependent. To illustrate the problem of spurious correlations, chemical fractions were scaled on organic mass basis and analyzed using multiple linear regression.

The balance scheme reflected the C/N ratio and the order of decomposability of biochemical components (Figure 17). The SOL fraction was isolated from other biochemically labile frac‐ tions because its composition is complex, possibly including sugars, amino-sugars, aminoacids, and polypeptides as well as more recalcitrant or bacteriostatic easily solubilized polyphenols such as fulvic acids, tannic substances, resins, intermediate products, etc. The balance scheme was formalized by SBP as shown in Table 4.


**Table 4.** Sequential binary partition of the biochemical composition of organic residues in Thuriès et al. (2002)

**Figure 17.** Graphical representation of the balances for the sequential binary partition defined in Table 3. SOL = solu‐ ble matter, HEM = hemicellulose, CEL = cellulose, LIG = lignin, N = total nitrogen, and ash.

The linear regression models relating labile C to bio-chemical fractions or balances showed R2 values between 0.86 and 0.92 (Figure 18). For the 6-part (dry mass basis) and 5-part (or‐ ganic matter basis) models, variation in labile C mesaured as evolved CO2 was explained in part by total N and SOL as follows:

$$\mathbf{C\_{lubble}} = 0.0773 + 0.5202 \,\text{SOL} \quad \text{- } 0.2515 \,\text{HEM} \text{ - } 0.3372 \,\text{CEL} \text{ - } 0.2882 \,\text{LIG} + 2.3884 \,\text{N}\_{\text{total}} \tag{11}$$

$$C\_{\text{labile}} = -0.1776 + 0.5585SOL \quad + 0.1909HEM + 2.0187N\_{\text{total}} \tag{12}$$

**Figure 18.** Regression analysis of C mineralization on dry matter (six raw components) or organic matter (five compo‐

Pearson correlation coefficient Dry matter basis (including ash)

Nutrient Balance as Paradigm of Soil and Plant Chemometrics

http://dx.doi.org/10.5772/53343

107

Organic matter basis (loss on ignition)

**Component SOL HEM CEL LIG Ash**

Total N 0.241 0.354 -0.462 -0.320 -0.184 SOL -0.115 -0.232 -0.669 -0.027 HEM -0.292 -0.293 -0.340 CEL 0.465 -0.495

Total N 0.466 0.067 -0.637 -0.475 - SOL -0.194 -0.425 -0.756 - HEM -0.409 -0.383 - CEL 0.376 -

**Table 5.** Scale dependency of the correlations between biochemical components in Thuriès et al. (2002); for 17

SOL = soluble substances; HEM = hemicelluloses; CEL = cellulose; LIG = lignin and cutin

observations, r = 0.468 at P = 0.05 and r = 0.590 at P = 0.01

nents) basis and using balances that reflects the order of decomposability of b

However, Equations 11 and 12 were subcompositionally incoherent. The intercept and the β coefficient for HEM showed opposite signs in equations 11 and 12 while CEL and LIG were absent in Equation12. This incoherence is attributable to spurious correlations (Table 5). Pearson correlation coefficients among raw proportions were not consistent in terms of val‐ ue, significance or sign whether the proportions were expressed on the dry mass of the or‐ ganic product (including ash) or on organic matter (LOI) basis.

**Figure 18.** Regression analysis of C mineralization on dry matter (six raw components) or organic matter (five compo‐ nents) basis and using balances that reflects the order of decomposability of b


SOL = soluble substances; HEM = hemicelluloses; CEL = cellulose; LIG = lignin and cutin

**Figure 17.** Graphical representation of the balances for the sequential binary partition defined in Table 3. SOL = solu‐

The linear regression models relating labile C to bio-chemical fractions or balances showed

 values between 0.86 and 0.92 (Figure 18). For the 6-part (dry mass basis) and 5-part (or‐ ganic matter basis) models, variation in labile C mesaured as evolved CO2 was explained in

*Clabile* =0.0773 + 0.5202*SOL* - 0.2515*HEM* - 0.3372*CEL* - 0.2882*LIG* + 2.3884*Ntotal* (11)

However, Equations 11 and 12 were subcompositionally incoherent. The intercept and the β coefficient for HEM showed opposite signs in equations 11 and 12 while CEL and LIG were absent in Equation12. This incoherence is attributable to spurious correlations (Table 5). Pearson correlation coefficients among raw proportions were not consistent in terms of val‐ ue, significance or sign whether the proportions were expressed on the dry mass of the or‐

*Clabile* = - 0.1776 + 0.5585*SOL* + 0.1909*HEM* + 2.0187*Ntotal* (12)

ble matter, HEM = hemicellulose, CEL = cellulose, LIG = lignin, N = total nitrogen, and ash.

ganic product (including ash) or on organic matter (LOI) basis.

R2

106 Soil Fertility

part by total N and SOL as follows:

**Table 5.** Scale dependency of the correlations between biochemical components in Thuriès et al. (2002); for 17 observations, r = 0.468 at P = 0.05 and r = 0.590 at P = 0.01

On the other hand, the labile C pool was largely explained by the *ilr* balances between C sources and total N, a surrogate of the C/N ratio, the balance between labile and refractory C sources, and between two labile C pools, one being more labile (HEM) than the other (CEL). The equation was as follows:

**Author details**

, L.E. Parent1

tro, Registro, São Paulo, Brasil

, D.E. Rozanne2

Raton FL: CRC Press, 2000. p. D-113-D-153.

derland MA: Sinauer Ass. Inc.; 2005.

MI: Ann Arbor Press; 1999.

NY: Wiley Intersci.; 1986.

Biology 2003;12(3) 247–249.

Science 2012;175(2) 236-244.

ronmental Quality 2004;33: 2333-2342.

1215–1221.

\*Address all correspondence to: Leon-Etienne.Parent@fsaa.ulaval.ca

, A. Hernandes3

1 Department of Soils and Agrifood Engineering, Université Laval, Québec (Qc), Canada

2 Departamento de Agronomia, Unesp, Universidade Estadual Paulista, Campus de Regis‐

3 Departamento de Solos e Adubos, Unesp, Universidade Estadual Paulista, Jaboticabal, São

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and W. Natale3

Nutrient Balance as Paradigm of Soil and Plant Chemometrics

http://dx.doi.org/10.5772/53343

109

S.É. Parent1

Paulo, Brasil

**References**

$$\begin{array}{l} \text{\(\mathcal{C}\_{\text{label}} = 0.3065\text{–}0.1251\text{\[\]SOL\\_HEM, CEL\\_LIG\\_I\\_I\\_)-0.0301\text{\[]SOL\\_IEL\\_IIL\\_IIG\\_I\\_I\\ \text{\(\!+0.0019\text{\[]SOL\\_IEL\\_J\\_I-0.1063\text{\[}\]HEM\\_IEL\\_I\\_I\\_I\\_I)-0.0301\text{\[}\]HEM\\_I} \end{array}} \tag{13}$$

Equation 13 shows that labile C increases with total N and higher proportions of more labile over more recalcitrant C forms. These findings indicate that the *ilr* coordinates provide a co‐ herent interpretation of the C dynamics of organic products. The *ilrs* are not redundant, scale-invariant and free from spurious correlations.
