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Diagnosis of nutrient composition in fruit crops: Major developments
C H A P T E R
12 Diagnosis of nutrient composition in fruit crops: Major developments Leon Etienne Parenta,*, Danilo Eduardo Rozaneb, Jose Aridiano Lima de Deusc, William Nataled a
Department of Soil and Agri-food Engineering, Universite Laval, Quebec, QC, Canada b Sa˜o Paulo State University, UNESP, Registro, Brazil c Institute of Technical Assistance and Rural Extension of Parana´ (EMATER-PR), Curitiba, Brazil d Federal University of Ceara´, Fortaleza, Brazil *Corresponding author. E-mail: [email protected] O U T L I N E 1 Introduction
145
2 Diagnostic methods 2.1 Early evidence of physiological balances between nutrients 2.2 Critical nutrient concentrations and concentration ranges 2.3 Weighted nutrient diagnosis
146 146 146 147
3 Nutrient balances as dual or stoichiometric ratios 147 3.1 Nutrient ratios 147 3.2 Diagnosis and recommendation integrated system 147 4 Compositional nutrient diagnosis 4.1 Centered log ratios 4.2 Isometric log ratios
148 148 150
5 Data partitioning
151
6 New lines of research 6.1 Customized nutrient balance designs 6.2 Total analysis versus extracted forms 6.3 Box-Cox coefficients 6.4 How physiologically meaningful is nutrient numerical ordering? 6.5 What is the minimum nutrient dosage to recover from nutrient imbalance? 6.6 Ionomics, biofortification, and fruit quality 6.7 Big data, machine learning, and artificial intelligence
152 152 152 152
References
154
Web reference
156
Further reading
156
153 153 153 154
1 Introduction Because the roots of fruit trees can explore soil layers well below the sampled layers, plant tissue analysis is a useful means to diagnose the nutrient status of fruit crops (Smith et al., 1997). Tissue nutrient concentrations are thought to integrate growth factors under the prevailing ecological conditions affecting crop response to fertilization (Munson and Nelson, 1990). Where one nutrient is supplied in insufficient amounts or in inappropriate combination with other nutrients to support plant growth, agroecosystems cannot be sustainable. At the other extreme, the overuse of fertilizers and inefficient nutrient uptake leads to luxury consumption (Nowaki et al., 2017; Deus et al., 2018), biochemical and physiological disorders, yield losses (Prado and Caione, 2012), wastage of fertilizers, and environmental damage (Das and Mandal, 2015). A.K. Srivastava, Chengxiao Hu (eds.) Fruit Crops: Diagnosis and Management of Nutrient Constraints https://doi.org/10.1016/B978-0-12-818732-6.00012-5
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© 2020 Elsevier Inc. All rights reserved.
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12. Diagnosis of nutrient composition in fruit crops: Major developments
K
FIG. 12.1
Representation of the change in NPK balance in the potato diagnostic leaf in response to P fertilization, projected into a Lagatu and Maume (1934) center-scaled ternary diagram (N + P + K ¼ 100%). Nutrients move along the line as P dosage increased with spot size. The gray blob encloses the NPK composition of high-yielding crops, and Parent, L.E., the central spot is blob centroid. Reproduced with permission from Parent, S.-E., Rozane, D.E., Hernandes, A., Natale, W., 2012. Nutrient balance as paradigm of soil and plant chemometrics. In: Issaka, R.N. (Ed.), Soil Fertility. IntechOpen Ltd., London, pp. 83–114. https:// doi.org/10.5772/53343.
N
P
To diagnose plant nutrient status, total, soluble, or extractable nutrients are quantified in a selected tissue collected at a specific developmental stage (Bould et al., 1960). Cost-effective sampling procedures have been developed for each species (Benton Jones et al., 1991). Tissue analysis includes sample preparation, digestion, and quantification. The basis for nutrient expression is generally tissue dry matter but could be also fresh matter (Clements, 1957), petiole sap (Vitosh and Silva, 1994), or nitrogen (Ingestad, 1987). Quantified plant nutrients and undetermined tissue components are intrinsically multivariate and interrelated parts. Tissue compositions should thus be diagnosed holistically as nutrient combinations rather than as collections of nutrients addressed separately (Deus et al., 2018). In this chapter, we examine the science behind plant nutrient diagnosis from earlier methods that diagnosed nutrients separately under the laws of the minimum and the optimum to modern tools of compositional nutrient diagnosis that address nutrient combinations impacting fruit yield and quality.
2 Diagnostic methods 2.1 Early evidence of physiological balances between nutrients In the 1830s, Jean-Baptiste Boussingault advanced the idea that nutrient balances were more important for plant growth than nutrients examined separately (Epstein and Bloom, 2005). Lagatu and Maume (1934) represented Boussingault’s inkling as a blob or domain delineating optimum NPK combinations in potato leaves. To validate their theory, they used a ternary diagram, an old concept dating 1704 but widely used in many fields of science to synthesize three variables adding up to 100% (Howarth, 1996). Lagatu and Maume (1934) showed (Fig. 12.1) that Carl Sprengel’s Law of the Minimum popularized by Justus von Liebig (Epstein and Bloom, 2005) was based on overoptimistic assumptions for not accounting for nutrient interactions. Their brilliant demonstration of nutrient interactions remained unattended for nearly 50 years.
2.2 Critical nutrient concentrations and concentration ranges Macy (1936) was the first to define adequate concentration ranges in line with Georg Liebscher’s Law of the optimum stating that a growth-limiting factor contributes more to production the closer other production factors are to their optimum (De Wit, 1992). Ulrich (1952) set critical concentration values at 90%–95% maximum yield. Percentage of maximum yield was designed to remove the location-to-location variability due to factors other than the nutrient being studied, but this has serious agronomic (absolute profitability vs nutrient dosage) and statistical (variance heterogeneity and negligible interactions assumed) limitations (Nelson and Anderson, 1984). There is luxury consumption, accumulation, or contamination without yield loss above sufficiency range (Ulrich, 1952). At the far end of the response curve, a slow yield decrease indicates nutrient excess due to nutrient antagonism or toxicity. To establish nutrient concentration ranges, a gradient of nutrient doses must be planned in controlled experiments where the effect of target nutrient on yield is not altered by any harmful effect of another factor (Ulrich and Hills, 1967). Nutrient concentration ranges can also be computed from crop surveys as confidence intervals of nutrient
3 Nutrient balances as dual or stoichiometric ratios
147
concentrations at high-yield level. However, the assumptions behind the law of the optimum are rarely met under field conditions where factor levels vary widely. Critical concentration ranges are easy to interpret (Benton Jones et al., 1991). However, confidence intervals diagnose nutrients in one dimension and two nutrients in 2-D rectangles or squares delineated by the intervals (Nowaki et al., 2017). The 2-D scheme expands to hyperrectangles or hypercubes as more nutrients are added. Assuming normal (ellipsoidal) data distribution at high-yield level, the success across nutrient-by-nutrient diagnosis is conceptually low (Nowaki et al., 2017). Indeed, the volume of a hypersphere is small compared with that of a hypercube across several intervals.
2.3 Weighted nutrient diagnosis Running fertilizer experiments to delineate nutrient concentration ranges is expensive. Using both crop surveys and experimental data, Kenworthy (1967) suggested to standardize nutrient concentrations as percentages of mean values for “normal” crops and then to weight the result by the coefficient of variation V to account for variation in the data. A balance index B relative was computed as follows: If X < Std, ðX=StdÞ 100 ¼ P;ð100 PÞ ðV=100Þ ¼ I;P + I ¼ B If X > Std, ðX=StdÞ 100 ¼ P;ðP 100Þ ðV=100Þ ¼ I;P I ¼ B where X is tissue concentration of nutrient X, Std is standard nutrient concentration for “normal” crops, P is percentage of standard value, and I reflects the variation in standard values. Because Kenworthy’s equations were set symmetrical about 100, they allowed assessing relative shortage (<100) or excess (>100) of nutrients. However, the Kenworthy model did not address nutrient interactions.
3 Nutrient balances as dual or stoichiometric ratios 3.1 Nutrient ratios Interactions are important where one nutrient competes with or dilutes another one close to its deficiency threshold (Marschner, 1986). Nutrient interactions are reported as dual (Bergmann, 1988; Walworth and Sumner, 1987; Wilkinson, 2000) or stoichiometric (Ingestad, 1987) ratios. Selected ratios must reflect physiological functions such as protein synthesis (N and S) and plant-available energy (P) (Epstein and Bloom, 2005) or guide nutrient applications relative to nitrogen (Ingestad, 1987). Nutrient ratios assume sometimes erroneously that pairs of elements are linearly related (Kenworthy, 1967). Ratios can return similar values within deficiency, sufficiency, or toxicity ranges, confusing the interpretation of dual ratios if concentration values are not examined concomitantly (Marschner, 1986).
3.2 Diagnosis and recommendation integrated system The DRIS is an appealing diagnostic method that integrates dual ratios and functions into nutrient indices and arranges nutrients in the order of their limitation to yield (Beaufils, 1973). Dual ratios used to compute DRIS functions are as follows (Walworth and Sumner, 1987): ðA=BÞ κ 1 , if ðA=BÞ > ða=bÞÞ, f ðA=BÞ ¼ ða=bÞ cv ða=bÞ κ f ðA=BÞ ¼ 1 , if ðA=BÞ < ða=bÞÞ, ðA=BÞ cv f ðA=BÞ ¼ 0, if ðA=BÞ ¼ ða=bÞÞ, where A/B and a/b are dual nutrient ratios in diagnosed and reference compositions, respectively, and cv is coefficient of variation (standard deviation divided by mean) of the reference dual ratio. Factor κ accounts for differential measurement units. The ratio expressions (X/Y or Y/X) are selected from the highest variance ratio between the low- and high-yielding subpopulations. However, such selection procedure is questionable because false-positive specimens (high yield despite nutrient imbalance) may result from luxury consumption or contamination.
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12. Diagnosis of nutrient composition in fruit crops: Major developments
The DRIS indices IA, IB, and IC are computed across nutrients A, B, and C by averaging DRIS functions after multiplying DRIS functions by (+1) if the nutrient is at numerator or (1) otherwise, as follows (Walworth and Sumner, 1987): IA ¼
f ðA=BÞ + f ðA=CÞ f ðA=BÞ f ðC=BÞ f ðA=CÞ + f ðC=BÞ ; IB ¼ ; IC ¼ 2 2 2 IA + IB + IC ¼ 0 jIA j + jIB j + jIC j ¼ NII
where NII is nutrient imbalance index. Because DRIS indices are symmetrical, their sum is constrained to zero (Beaufils, 1973). The DRIS was claimed wrongly to diagnose nutrient status irrespective of plant age and location (Walworth and Sumner, 1987; Epstein and Bloom, 2005). The DRIS has been modified empirically at several occasions, including nutrient products to account for nutrients accumulating in opposite directions with time and a dry matter index to delineate nutrient shortage from excess (Walworth and Sumner, 1987). The symmetry of DRIS indices was lost using nutrient products. The dry matter basis was viewed erroneously as a component rather than a scale of measurement. Beverly (1987a,b) suggested to log transform nutrient ratios to facilitate deriving DRIS norms. Indeed, the advantages of log transformations are as follows: • It is common to use a logarithmic scale where ratios are greater than 104 (Budhu, 2010). • ln(A/B) and log(B/A) are reflective because ln(A/B) ¼ ln(B/A); therefore, the variance is the same between both expressions. • The geometric mean is the most appropriate centroid to conduct statistical analyses on ratios (Fleming and Wallace, 1986). DRIS was a major step forward combining nutrients for diagnostic purposes. Nonetheless, the assumed additivity of DRIS functions and indices led to conceptual errors compared with the unbiased compositional data analysis methods (Parent and Dafir, 1992; Parent et al., 2012b).
4 Compositional nutrient diagnosis 4.1 Centered log ratios Aitchison (1986) used a ternary diagram to illustrate the closure problem of three-part geochemical compositions, where any change in the proportion of one part must resonate on others. The negative covariance inherent to resonance distorts the results of linear multivariate analysis and may lead to wrong conclusions. Nutrient interactions (synergism and antagonism), luxury consumption, nutrient excess or toxicity, and contamination are sources of resonance specific to the closed space of the tissue measurement unit (e.g., 1000 g/kg on a dry mass basis). To control resonance, Aitchison (1986) derived log-ratio transformations from the multinomial Dirichlet distribu p tion function across proportions and the logistic function ln 1p closed to one for probability p, (1 p) being the filling value to one. Because ln(A/B) ¼ ln (A) ln (B), a log ratio is a log contrast between two quantities. To close system space to 1000 g/kg in tissue dry matter, the filling value Fv in a D-part composition is computed by difference between measurement unit and the sum of proportions or concentrations as follows: XD1 Xi Fv ¼ 1000 i¼1 where Xi is the ith proportion or concentration. A compositional simplex comprising 12 components of which 11 are nutrients is described as follows on dry matter basis: 9 8 N, S, P, K, Mg, Ca, B, Fe, Mn, Zn, Cu, F ; v > > > > = < N > 0; S > 0; P > 0; K > 0; Mg > 0; Ca > 0; ; S12 ¼ B > 0; Fe > 0; Mn > 0; Zn > 0; Cu > 0; Fv > 0 > > > > ; : N + S + P + K + Mg + Ca + B + Fe + Mn + Zn + Cu + Fv ¼ 1000 g kg1 Aitchison (1986) proposed to express relationships among components as centered log ratios scaled on the geometric mean, as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðci Þ ¼ 12 N S P K Mg Ca B Fe Mn Zn Cu Fv
149
4 Compositional nutrient diagnosis
TABLE 12.1
clr
Centered log-ratio (clr) standards (mean and standard deviation (SD)) of Brazilian fruit crops. Guava
Mango
Grape
Atemoia
Psidium guajava
Mangifera indica
Vitis vinifera
Annona squamosa
Mean
SD
Mean
SD
Mean
SD
Mean
SD
N
2.831
0.190
2.541
0.129
2.761
0.160
3.294
0.164
P
0.435
0.236
0.075
0.227
0.652
0.164
0.070
0.616
K
2.689
0.186
2.175
0.198
1.981
0.208
2.606
0.117
Ca
2.074
0.164
2.978
0.203
2.085
0.178
2.497
0.232
Mg
0.744
0.182
0.620
0.178
0.531
0.147
0.947
0.285
S
0.870
0.174
0.253
0.145
0.718
0.111
0.452
0.220
B
3.499
0.330
3.718
0.273
3.953
0.257
2.934
0.215
Cu
3.310
0.911
4.072
0.650
4.956
0.152
4.795
0.463
Fe
2.827
0.386
2.807
0.287
2.719
0.228
2.549
0.342
Mn
2.790
0.259
0.782
0.344
1.263
0.246
2.596
0.540
Zn
3.972
0.188
3.950
0.336
2.148
0.322
3.677
0.624
Santos, E.M.H., 2013. Programa de computador: Instituto Nacional da Propiedade Industrial—INPI: Courtesy from Rozane, D.E., Natale, W., Parent, L.E., Parent, S.-E., BR5120130003806. Universidade Estadual Paulista “Júlio de Mesquita Filho”; Universite Laval. 2013. http://www.registro.unesp.br/%23!/sites/cnd/ (Accessed 10 December 2018). (in Portuguese, Spanish, English and French).
The clr is much easier to compute than DRIS indices, as follows:
Xi ¼ lnðXi Þ lnðGÞ clrXi ¼ ln G where Xi is the ith nutrient concentration, G is geometric mean, and clr is a log contrast between Xi and G. The clr is a linear combination of dual ratios as follows:
1 N N 12 12 clrN ¼ ln ¼ ln N P K Mg Ca B Fe Mn Zn Cu Fv G
1 N N N N N N N N N N N 12 ¼ ln N P K Mg Ca B Fe Mn Zn Cu Fv ¼ ln
N N N N N N N N N N + ln + ln + ln + ln + ln + ln + ln + ln + ln P K Mg Ca B Fe Mn Zn Cu Fv
As a result, each component is adjusted to every other, avoiding optimistic assumptions on optimum levels of other nutrients under the law of the optimum or equal levels of other nutrients under the law of the minimum. Parent and Dafir (1992) proposed to compute clr indices as follows: Iclri ¼
clri clr∗i , s∗clri
where clri is clr value of the ith component of the composition being diagnosed, clr∗i is clr mean of the ith component of the reference composition, and s∗clri is standard deviation of the ith component of the reference composition. Positive and negative Iclri values can be ranked on a histogram to illustrate nutrient limitations as shortage or excess. The clr standards (clr∗i and s∗clri) of some Brazilian fruit crops are presented in Table 12.1. The difference between any two compositions X and Y can be computed as Euclidean distance 2 as follows (Aitchison, 1986): XD ðclrXi clrYi Þ2 ¼ ðclrXi clrYi ÞI 1 ðclrXi clrYi Þ 2¼ i¼1 where I is the identity matrix and X and Y refer to compositions X and Y, respectively. The clr and the ordinary log transformation return identical Euclidean distances if and only if geometric means are identical.
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12. Diagnosis of nutrient composition in fruit crops: Major developments
As a means to evaluate intercorrelations between clr variates, Badra et al. (2006) used the measure of sampling adequacy (MSA), allowing to compute a chi-square (χ 2) variable across “independent” (low MSA value) clr variates, as follows: χ2 ¼
XD i¼1
Iclri
2
¼ ðclrXi clrYi ÞVAR1 ðclrXi clrYi Þ
where VAR is the variance matrix.
4.2 Isometric log ratios Because there are D clr variates computable from a D-part composition, one clr variate must be discarded (generally Fv that is barely interpretable) to avoid computing a singular matrix when running multivariate analysis. Indeed, there are D 1 degrees of freedom available to run multivariate analysis of compositions (Aitchison and Greenacre, 2002). To reduce dimensionality, a useful case of linear independence is orthogonality whereby vectors are at perfectly right angles to each other (Rodgers et al., 1984). Egozcue et al. (2003) had the idea to partition D components into D 1 orthonormal balances hierarchically arranged among the D components of the system under study to compute isometric log ratios (ilr), as follows: 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 Qr k rk rffiffiffiffiffiffiffiffiffiffiffiffi i¼1 xi C rk sk B ln@ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ilrk ¼ A Q sk sk rk + sk x j¼1 j
where rk and sk are numbers of components in subsets at numerator and denominator, respectively;
qffiffiffiffiffiffiffiffiffi rk sk rk + sk
is a norqffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q k xi and malization coefficient; i and j refer to components at numerator and denominator, respectively; and rk ri¼1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q s sk k j¼1 xj are geometric means of component concentrations at numerator and denominator, respectively.
The balance design is an illustration allowing the researcher to describe how components and their related functions are connected in a closed system under study. Subsets of components are arranged into balances following a sequential binary partition (SBP). There are D!(D 1)!/2D1 possible balance designs in a D-part composition (Pawlowsky-Glahn et al., 2011). Multivariate distances remain the same whatever the SBP because switching from a balance design to another just rotates orthogonal axes. Concentration values in buckets do not change, but ilr values at fulcrum change where the balance design has been changed. The SBP can be supported by theory, biplot analysis, or management objectives such as fertilizer source and balance, expected synergistic effect, or selection of liming material based on Ca and Mg contents (Parent, 2011; Hernandes et al., 2012; Parent et al., 2012a,b; Montes et al., 2016). The dual ratios most relevant to the study are assigned first. Examples of balance design are presented in Table 12.2 and Fig. 12.2. Computations can be performed using freeware such as CoDaPack (Comas-Cufí and Thió-Henestrosa, 2011) and R (van den Boogaart et al., 2014). Log ratio means including that of the filling value can be back-transformed to familiar concentration values using the clrinv or ilrinv procedures in R. Several R codes are available to handle compositional data and run statistical analyses. TABLE 12.2
Sequential binary partition and balance formulation.
ilr
r
s
1
2
3
2
1
1
3
1
1
4
2
1
5
5
1
a
ilr formula pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6=5 ln N P= 3 K Mg CaÞ pffiffiffiffiffiffiffiffi 1=2 lnðN=PÞ pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 ln K=Mg pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=3 ln 2 K Mg=CaÞ pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5=6 ln 5 N P K Mg Ca=Fv Þa
Fv ¼ filling value between sum of analyzed nutrients and measurement unit.
Balance arrangement Anions versus cations Protein synthesis versus energy K-Mg antagonism Cationic antagonisms Nutrient dilution in biomass
5 Data partitioning
151
FIG. 12.2 Example of balance design for macronutrients. The ilrs are computed at fulcrums using concentration values located in buckets.
FIG. 12.3
Partitioning of 156 Brazilian mango (Mangifera indica) specimens returning an accuracy of 92% and critical Mahalanobis distance of 4.08. FN, false negative; FP, false positive; NPV, negative predictive value; PPV, positive predictive value; TN, true negative; TP, true positive; accuracy ¼ 92%. Parent, L.E., Rozane, D.E., Reproduced with permission from Parent, S.-E., Natale, W., 2013. Plant ionome diagnosis using sound balances: case study with mango (Mangifera indica). Front. Plant Sci. 4, 449. https://doi.org/10.3389/fpls. 2013.00449.
5 Data partitioning Based on research in soil fertility (Nelson and Anderson, 1984) and clinical biology (Swets, 1988), Parent et al. (2013b) proposed to partition data into four categories: true negative (TN), false negative (FN), true positive (TP), and false positive (FP). Crude data are first transformed into ilr variates. Mahalanobis distance (covariance matrix) is iterated across ilr values of healthy crops (true-negative specimens) as reference ilr variates (Fig. 12.3), starting with the compositions of preselected high-yielding crops. Accuracy, computed as the sum of TN and TP specimens over total, is generally >80% (Parent et al., 2012a, 2013a; Rozane et al., 2015; Souza et al., 2016). Lower accuracy is due to a high number of false-negative (Marchand et al., 2013) or true-positive (Deus et al., 2018) specimens. Imbalanced specimens are those showing Mahalanobis distance exceeding the critical multivariate distance. The clr values of TN specimens are computed as standards (means and standard deviations). The Mahalanobis distance squared is assumed to be distributed like a chi-square variable.
152
12. Diagnosis of nutrient composition in fruit crops: Major developments
To guide fertilizer recommendations, specimens are diagnosed using indices and nutrient ranking in the order of nutrient limitations to yield. Steps to diagnose nutrients are as follows: 1. Compute the Mahalanobis distance using ilr mean and covariance matrix of TN specimens as reference values at fulcrum (Fig. 12.2). The ilr means of TN specimens are back-transformed into reference concentration centroids (ilrinv) assigned to buckets that equilibrate at fulcrum (circles in Fig. 12.2) equilibrating at fulcrum. Compare specimen’s composition to the reference composition in buckets. 2. If the specimen is imbalanced (Mahalanobis distance larger than the critical distance), compute clr indices using mean and standard deviation of TN specimens as reference values (e.g., Table 12.2), and then order clr indices from the most negative to the most positive or provide a histogram of clr indices. 3. Make a recommendation to reestablish nutrient balance.
6 New lines of research Compositional data analysis provides sound modern tools to address old issues and face challenges related to plant tissue diagnosis. New knowledge could be developed on the following topics: 1. Based on literature and experimentation, develop and animate customized nutrient balance schemes picturing nutrient relationships specific to the problem under study. 2. Look beyond total elemental analysis to improve diagnostic accuracy. 3. Test coefficient (exponent) assignment to concentration values to normalize log ratios or account for nutrient mobility. 4. Validate numerical order of nutrient limitations against the order of plant responses to nutrient stress. 5. Calibrate nutrient indices against crop response. 6. Relate ionomics to fruit quality, nutrient management, and biofortification to enhance the contribution of fruit crops to human nutrition and health. 7. Acquire and store big data to support artificial intelligence models and optimize nutrient management in fruit agroecosystems worldwide.
6.1 Customized nutrient balance designs A customized balance (e.g., Fig. 12.2) is a comprehensive representation of the system designed managerially, phenomenologically, or heuristically to facilitate its interpretation. A catalog of customized balance designs could be elaborated to visualize and animate nutrient relationships relevant to a study or a diagnosis and monitor specific imbalances driven by treatments. For example, K fertilization, liming, and lime composition could be managed based on the interactive cationic subsystem (K, Ca, and Mg) operating in both soils and plant tissues (Parent and Parent, 2017). The N P synergism (protein synthesis vs energy supply) could be contrasted with subsystems of other macronutrients or cationic micronutrients to assess the impact of NP fertilization on other subsystems. The Cu, Zn, and Mn subsystem could be balanced with other subsystems to conduct global nutrient diagnosis. In some situations, fungicide applications can lead to excessive accumulations of Cu, Zn, and Mn on leaves that impact positively on yield by controlling foliar diseases. Nutrients contained in fungicides could be set apart as a specific subsystem of microcationic balances to assess fungicide capacity to sustain plant health with useful “contaminants” (Yamane, 2018).
6.2 Total analysis versus extracted forms Tissue diagnosis is commonly conducted using total elemental analysis, disregarding the fact that just a portion of total concentration may be available to accomplish biological functions. If some extraction methods allow partitioning total elemental concentration into more or less available or unavailable forms, total concentration can be split into several contrasts. If the new partition impacts on yield, diagnostic accuracy could be increased.
6.3 Box-Cox coefficients It is generally assumed that ilr variates are normally distributed, but this is not always the case. Non normal distribution can be recovered where appropriate after discarding outliers or by assigning Box-Cox coefficients varying
6 New lines of research
TABLE 12.3
153
Relative phloem mobility of essential elements (Epstein and Bloom, 2005).
Mobile
Intermediate
Immobile
Potassium
Sodium
Calcium
Nitrogen
Iron
Silicon
Magnesium
Manganese
Borona
Phosphorus
Zinc
a
Boron
Copper
Sulfur
Molybdenum
Chlorine a
Immobile except for phloem-mobile boron-sorbitol complexes in fruit trees of genera Pyrus, Malus, and Prunus (Brown and Hu, 1996).
between 0 and 1 to raw concentration values (Box and Cox, 1964). On the other hand, nutrients move differently from leaf to fruit through phloem transport, while xylem transport to low-transpiring organs may be limited. Assigning coefficients close to zero to the most immobile nutrients, coefficients close to one to most mobile ones, and intermediate coefficient values to partially mobile nutrients before ilr transformations may account for nutrient mobility (Table 12.3). While skewness of ilr values decreased using Box-Cox coefficients in a Brazilian banana (Musa spp.) data set, diagnostic accuracy was not improved (Deus et al., 2018). Nevertheless, the Box-Cox transformation may be an option for other crops.
6.4 How physiologically meaningful is nutrient numerical ordering? It is a truism that growers are more concerned about negative than positive nutrient indices. While nutrient needs are prioritized according to the order of nutrient limitations to crop yield and quality, such ordering should bear some physiological significance. For the diagnosis to be reliable and reproducible, the addition of the most limiting nutrients in the order of their limitation should influence tissue composition and crop yield in the same order. This could only be validated by local fertilizer trials.
6.5 What is the minimum nutrient dosage to recover from nutrient imbalance? By how much should present fertilization regimes be increased or decreased through soil or leaf applications in the case of nutrient imbalance? Plant response to applied nutrients must depend on whether and to what extent nutrient status is impacted by nutrient dilution in tissue mass, antagonism, synergism, luxury consumption, or contamination. As for soil testing where compositional models were also applied (Parent et al., 2012a,b; Parent and Parent, 2017), field calibration of tissue tests are needed to guide site-specific dosage of soil- and foliar-applied nutrients.
6.6 Ionomics, biofortification, and fruit quality The ionome is the mineral nutrient composition of living organisms (Huang and Salt, 2016). Ionomics is a tool to target healthier food through genetics and biofortification (Welch, 2002; Zuo and Zhang, 2008; Gang et al., 2018). Baxter (2015) raised the problem of how to solve myriads of known and unknown interconnections between nutrients in ionomics and viewed a possible solution in the nutrient balance concept proposed by SE Parent et al. (2013b). Understanding nutrient interactions involving Zn and Fe absorption by plant and human might support plant breeding programs aimed at improving food quality and human health. Fruit quality depends on genetics, management, and the environment. Fruit quality is often measured as Brix index, phenolics, and total anthocyanins (TAcy), as well as fruit acidity, firmness, and supply of minerals and vitamins essential to human health. Because organic acids and their salts (e.g., ascorbic acid, fumarate, malate, and citrate) can increase Zn and Fe bioavailability in fresh fruits (Bouis and Welch, 2010), such components could be balanced against each other (human nutrition forms also a compositional simplex). Some undesirable minerals could also be addressed.
154
12. Diagnosis of nutrient composition in fruit crops: Major developments
The leaf ionome at high fruit yield may differ from that at high fruit quality, and this may impact on nutrient management. Compositional data analysis provides a means (1) to optimize leaf ionomes at high fruit quality level and (2) to balance fruit concentrations of sugars, antioxidants, acids, and minerals to reach high fruit yield and quality. Such models should be developed.
6.7 Big data, machine learning, and artificial intelligence Plant nutrient diagnosis developed over the past centuries relied on overoptimistic assumptions. It was not until the theory of compositional data analysis was established on strong theoretical basis in 1986 using log ratios as data transformation techniques that plant tissue diagnosis gained a new momentum. Nutrient interactions, deficiency, luxury consumption, and contamination were viewed as numerical interplays between nutrient concentrations within the closed space of diagnostic tissues. Centered log ratios adjust every nutrient to the levels of other components. Isometric log ratios arrange selected nutrient interactions hierarchically. Data classification methods borrowed from soil fertility and clinical biology allowed delineating a hyperellipsoid within a critical Mahalanobis distance. There is no reason to believe that the healthy state of ionomes has regular geometry such as hyperellipsoidal. Data distribution could be of any shape (blob) as impacted by several factors (Fig. 12.1). The many interacting growth factors such as genetics (e.g., cultivar), soil (pH, texture, genesis, etc.), and weather documented in big data sets can be handled using a wide spectrum of machine learning methods. Nutrient imbalance can be defined as the shortest distance between an observation and the nearest centroids of a hyperblob portion or blob islands delineating highly performing crops (Yamane, 2018). The k-nearest neighbor technique assumes that an observation will respond in line with its closest highly performing neighbors. An international initiative to acquire and store big data from different fruit agroecosystems worldwide is required to develop models of artificial intelligence. In future research, machine learning methods and other tools of artificial intelligence will process higher-level models including an array of growth-impacting factors and metadata collected in big data sets. International collaboration will be needed to build such large data sets across fruit agroecosystems. Progress in compositional data analysis and artificial intelligence will undoubtedly foster the development of progressively more robust diagnostic tools to support high agronomic and environmental performance of fruit crops worldwide at lowest cost of inputs.
References Aitchison, J., 1986. The Statistical Analysis of Compositional Data. Chapman and Hall, London. Aitchison, J., Greenacre, M., 2002. Biplots of compositional data. J. R. Stat. Soc. Ser. C Appl. Stat. 51, 375–392. https://doi.org/10.1111/14679876.00275. Badra, A., Parent, L.E., Allard, G., Tremblay, N., Desjardins, Y., Morin, N., 2006. Effect of leaf nitrogen concentration versus CND nutritional balance on shoot density and foliage colour of an established Kentucky bluegrass (Poa pratensis L.) turf. Can. J. Plant Sci. 86, 1107–1118. https://doi.org/ 10.4141/p05-242. Baxter, I., 2015. Should we treat the ionome as a combination of individual elements, or should we be deriving novel combined traits? J. Exp. Bot. 66, 2127–2131. https://doi.org/10.1093/jxb/erv040. Benton Jones, J., Wolf, B., Mills, H.A., 1991. Plant Analysis Handbook: A Practical Sampling, Preparation, Analysis, and Interpretation Guide. Micro Macro Intl., Athens, GA. Bergmann, W., 1988. Ern€ahrungs-st€ orungen bei Kulturpflanzen. In: Auflage 2. Gustav Fischer Verlag, Stuttgart, New York. Beverly, R.B., 1987a. Comparison of DRIS and alternative nutrient diagnostic methods for soybean. J. Plant Nutr. 10, 901–920. Beverly, R.B., 1987b. Modified DRIS method for simplified nutrient diagnosis of “Valencia” oranges. J. Plant Nutr. 10, 1401–1408. Bouis, H.E., Welch, R.M., 2010. Biofortification—a sustainable agricultural strategy for reducing micronutrient malnutrition in the Global South. Crop Sci. 50, S-20–S-32. https://doi.org/10.2135/cropsci2009.09.0531. Bould, C., Bradfield, E.G., Clarke, G.M., 1960. Leaf analysis as a guide to the nutrition of fruit crops. I. General principles, sampling techniques and analytical methods. J. Sci. Food Agric. 11, 229–242. https://doi.org/10.1002/jsfa.2740110501. Box, G.E.P., Cox, D.R., 1964. An analysis of transformations. J. R. Stat. Soc. Ser. B 26 (2), 211–252. Brown, P.H., Hu, H., 1996. Phloem mobility of boron is species dependent: evidence for phloem mobility in sorbitol-rich species. Ann. Bot. 77, 497–505. Budhu, M., 2010. Soil Mechanics and Foundations. University of Arizona, Tucson, AR. https://doi.org/10.1017/CBO9781107415324.004. Clements, H.F., 1957. Crop-logging of sugar cane: the standard nitrogen index and the normal nitrogen index. In: Hawaïi Agric. Exp. Sta. Tech. Bull. 35. University of Hawaïi, Honolulu, HI. Das, D.K., Mandal, M., 2015. Advanced technology of fertilizer uses for crop production. In: Shishir, S., Pant, K.K., Bajpai, S. (Eds.), Fertilizer Technology I: Synthesis. Studium Press LLC, Mumbai, pp. 18–68. De Wit, C.T., 1992. Resource use efficiency in agriculture. Agric. Syst. 40, 125–151. https://doi.org/10.1016/0308-521x(92)90018-j. Natale, W., Parent, L.E., 2018. Balance design for robust foliar nutrient diagnosis superDeus, J.A.L.d., Neves, J.C.L., Correa, M.C.M., Parent, S.-E., vising the fertigation of banana “Prata” (Musa spp.). Nat. Sci. Rep. https://doi.org/10.1038/s41598-018-32328-y. Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barceló-Vidal, C., 2003. Isometric logratio transformations for compositional data analysis. Math. Geol. 35, 279–300. https://doi.org/10.1023/A:1023818214614. Epstein, E., Bloom, A.J., 2005. Mineral Nutrition of Plants: Principles and Perspectives. Sinauer Associates Inc., Sunderland, MA.
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Fleming, P.J., Wallace, J.J., 1986. How not to lie with statistics: the correct way to summarize benchmark results. Commun. ACM 29, 218–221. https:// doi.org/10.1145/5666.5673. Gang, M., Sharma, N., Sharma, S., Kapoor, P., Kumar, A., Chunduri, V., Arora, P., 2018. Biofortified crops generated by breeding, agronomy, and transgenic approaches are improving lives of millions of people around the world. Front. Nutr. https://doi.org/10.3389/fnut.2018.00012. Natale, W., Parent, L.E., 2012. Balancing guava nutrition with liming and fertilization. Rev. Bras. Frutic. 34, 1224–1234. Hernandes, A., Parent, S.-E., https://doi.org/10.1590/S0100-29452012000400032. Howarth, R.J., 1996. Sources for a history of the ternary diagram. Br. Soc. Hist. Sci. 29 (3), 337–356. Huang, X.Y., Salt, D.E., 2016. Plant ionomics: from elemental profiling to environmental adaptation. Mol. Plant 9, 787–797. Ingestad, T., 1987. New concepts on soil fertility and plant nutrition as illustrated by research on forest trees and stands. Geoderma 40, 237–252. https://doi.org/10.1016/0016-7061(87)90035-8. Kenworthy, A.L., 1967. Plant analysis and interpretation of analysis for horticultural crops. In: Stelly, M., Hamilton, H. (Eds.), Soil Testing and Plant Analysis, Part II. Soil Science Society of America, Madison, WI, pp. 59–75. Natl. Agron. Montp. 22, 50–158 (in French). Lagatu, H., Maume, L., 1934. Le diagnostic foliaire de la pomme de terre. Ann. Ec. Macy, P., 1936. The quantitative mineral nutrient requirements of plants. Plant Physiol. 11, 749–764. https://doi.org/10.1104/pp.11.4.749. Marschner, H., 1986. Mineral Nutrition of Higher Plants. Academic Press, London/Orlando, FL. https://doi.org/10.1146/annurev. es.11.110180.001313. Deland, J.P., Parent, L.E., 2013. Nutrient signature of Quebec (Canada) cranberry (Vaccinium macrocarpon Ait.). Rev. Bras. Marchand, S., Parent, S.-E., Frutic. 35 (1), 199–209. Natale, W., Modesto, V.C., 2016. Nitrogen and potassium fertilization in a Montes, R.M., Parent, L.E., de Amorim, D.A., Rozane, D.E., Parent, S.-E., guava orchard evaluated for five cycles: effects on the plant and production. Rev. Bras. Ci^enc. Solo. https://doi.org/ 10.1590/18069657rbcs20140532. Munson, R.D., Nelson, W.L., 1990. Principles and practices in plant analysis. In: Westerman, R.L. (Ed.), Soil Testing and Plant Analysis. Soil Science Society of America, Madison, WI, pp. 359–387. Nelson, L.A., Anderson, R.L., 1984. Partitioning of soil test-crop response probability. In: Stelly, M. (Ed.), Soil Testing: Correlating and Interpreting the Analytical Results. American Society of Agronomy, Madison, WI, pp. 19–28. Cecilio Filho, A.B., Rozane, D.E., Meneses, N.B., da Silva, J.A.D.S., Natale, W., Parent, L.E., 2017. Phosphorus overNowaki, R.H.D., Parent, S.-E., fertilization and nutrient misbalance of irrigated tomato crops in Brazil. Front. Plant Sci. https://doi.org/10.3389/fpls.2017.00825. Parent, L.E., 2011. Diagnosis of the nutrient compositional space of fruit crops. Rev. Bras. Frutic. 33, 321–334. https://doi.org/10.1590/S010029452011000100041. Parent, L.E., Dafir, M., 1992. A theoretical concept of compositional nutrient diagnosis. J. Am. Soc. Hortic. Sci. 117, 239–242. Parent, L.E., 2017. Balance designs revisit indices commonly used in agricultural science and eco-engineering. In: Hron, K., TolosanaParent, S.-E., Delgado, R. (Eds.), CodaWork 2017. The 7th International Workshop on Compositional Data Analysis. Abbadia San Salvatore, Italy, June 5-9, pp. 195–227. Proceedings book, http://www.compositionaldata.com/codawork2017/proceedings/ProceedingsBook2017_May30.pdf. Hebert-Gentile, V., Naess, K., Lapointe, L., 2013a. Mineral balance plasticity of cloudberry (Rubus chamaemorus) in QuebecParent, L.E., Parent, S.-E., Labrador. Am. J. Plant Sci. 4, 1509–1520. Parent, L.E., Egozcue, J.J., Rozane, D.E., Hernandes, A., Lapointe, L., Hebert-Gentile, V., Naess, K., Marchand, S., Lafond, J., Parent, S.-E., Mattos Jr., D., Barlow, P., Natale, W., 2013b. The plant ionome revisited by the nutrient balance concept. Front. Plant Sci. 4, 1–10. https:// doi.org/10.3389/fpls.2013.00039. Rozane, D.E., Amorim, D.A., Hernandes, A., Natale, W., 2012a. Unbiased approach to diagnose the nutrient status of red Parent, L.E., Parent, S.-E., guava (Psidium guajava). In: Santos, C.A.F. (Ed.), 3rd International Symposium on Guava and Other Myrtaceae, Petrolina, Brazil, April 23–25, 2012, pp. 145–159. https://doi.org/10.17660/ActaHortic.2012.959.18 ISHS Acta Horticulturae, Paper #959. Parent, L.E., Rozane, D.E., Hernandes, A., Natale, W., 2012b. Nutrient balance as paradigm of soil and plant chemometrics. In: Issaka, R. Parent, S.-E., N. (Ed.), Soil Fertility. IntechOpen Ltd., London, pp. 83–114. https://doi.org/10.5772/53343 Prado, R.M., Caione, G., 2012. Plant analysis. In: Issaka, R.N. (Ed.), Soil Fertility. IntechOpen Ltd., London, pp. 115–134. Rodgers, J.L., Nicewander, W.A., Toothaker, L., 1984. Linearly independent, orthogonal, and uncorrelated variables. Am. Stat. 38, 133. https://doi. org/10.2307/2683250. Rozane, D.E., Parent, L.E., Natale, W., 2015. Evolution of the predictive criteria for the tropical fruit tree nutritional status. Cientifica 44, 102–112. https://doi.org/10.15361/1984-5529.2016v44n1p102-112. Smith, G., Asher, G.J., Clark, C.J., 1997. Kiwifruit Nutrition Diagnosis of Nutritional Disorders. AG Press Communications Ltd, Wellington. Rozane, D.E., Amorim, D.A., Modesto, V.C., Natale, W., Parent, L.E., 2016. Guava waste to sustain guava (Psidium guajava) Souza, H.A., Parent, S.-E., agroecosystem: nutrient “balance” concepts. Front. Plant Sci. 7, 1–13. https://doi.org/10.3389/fpls.2016.01252. Swets, J.A., 1988. Measuring the accuracy of diagnostic systems. Science 240, 1285–1293. Ulrich, A., 1952. Physiological bases for assessing the nutritional requirements of plants. Annu. Rev. Plant Physiol. 3, 207–228. https://doi.org/ 10.1146/annurev.pp.03.060152.001231. Ulrich, A., Hills, F.J., 1967. Principles and practices of plant analysis. In: Stelly, M., Hamilton, H. (Eds.), Soil Testing and Plant Analysis. Part II. Soil Science Society of America, Madison, WI, pp. 11–24. Vitosh, M.L., Silva, G.H., 1994. A rapid petiole sap nitrate-nitrogen test for potatoes. Commun. Soil Sci. Plant Anal. 25 (3–4), 183–190. Walworth, J.L., Sumner, M.E., 1987. The diagnosis and recommendation integrated system (DRIS). Adv. Soil Sci. 6, 149–188. https://doi.org/ 10.1007/978-1-4612-4682-4. Welch, R.M., 2002. The impact of mineral nutrients in food crops on global human health. Plant Soil 247, 83–90. Wilkinson, S.R., 2000. Nutrient interactions in soil and plant nutrition. In: Sumner, M.E. (Ed.), Handbook of Soil Science. CRC Press, Boca Raton, FL, pp. D89–D112. Yamane, D.R., 2018. Nutrient Diagnosis of Orange Crops Applying Compositional Data Analysis and Machine Learning Methods. (Ph.D. thesis). Universidade Estadual Paulista (UNESP), Jaboticabal. Zuo, Y., Zhang, F., 2008. Iron and zinc biofortification strategies in dicot plants by intercropping with gramineous species. Agron. Sustain. Dev. 29, 63–71.
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Web references Beaufils, E.R., 1973. Diagnosis and recommendation integrated system (DRIS). Soil Sci. Bull., 1–132. Available from: http://www.worldcat.org/ title/diagnosis-and-recommendation-integrated-system-dris/oclc/637964264?ht¼edition&referer¼di. (Accessed 2 May 2013). Comas-Cufí, M., Thió-Henestrosa, S., 2011. CoDaPack 2.0. Universitat de Girona. Available from: http://ima.udg.edu/codapack/. (Accessed 10 December 2018). Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado, R., 2011. Principal balances. In: Egozcue, J.J., Tolosana-Delgado, R., Ortego, M.I. (Eds.), 4th International Workshop on Compositional Data Analysis (Codawork 2011). San Feliu de Guixols, Spain. Available from: http://congress.cimne. com/codawork11/Admin/Files/FilePaper/p55.pdf. (Accessed 10 December 2018). Santos, E.M.H., 2013. Programa de computador: Instituto Nacional da Propiedade Industrial— Rozane, D.E., Natale, W., Parent, L.E., Parent, S.-E., INPI: BR5120130003806. Universidade Estadual Paulista “Júlio de Mesquita Filho”; Universite Laval. http://www.registro.unesp.br/#!/sites/ cnd/. (Accessed 10 December 2018) (in Portuguese, Spanish, English and French). van den Boogaart, K.G., Tolosana-Delgado, R., Bren, M., 2014. “Compositions”: Compositional Data Analysis in R Package. Available from: http:// cran.r-project.org/package¼compositions. (Accessed 10 December 2018).
Further reading Barlow, P., Parent, L.E., 2015. Nutrient balances of New Zealand kiwifruit (Actinidia deliciosa cv. Hayward) at high yield level. Commun. Parent, S.-E., Soil Sci. Plant Anal. 46, 256–271. https://doi.org/10.1080/00103624.2014.989031. Parent, L.E., Rozane, D.E., Natale, W., 2013c. Plant ionome diagnosis using sound balances: case study with mango (Mangifera indica). Parent, S.-E., Front. Plant Sci. 4, 449. https://doi.org/10.3389/fpls.2013.00449.
12 Diagnosis of nutrient composition in fruit crops: Major developments Leon Etienne Parenta,*, Danilo Eduardo Rozaneb, Jose Aridiano Lima de Deusc, William Nataled a
Department of Soil and Agri-food Engineering, Universite Laval, Quebec, QC, Canada b Sa˜o Paulo State University, UNESP, Registro, Brazil c Institute of Technical Assistance and Rural Extension of Parana´ (EMATER-PR), Curitiba, Brazil d Federal University of Ceara´, Fortaleza, Brazil *Corresponding author. E-mail: [email protected] O U T L I N E 1 Introduction
145
2 Diagnostic methods 2.1 Early evidence of physiological balances between nutrients 2.2 Critical nutrient concentrations and concentration ranges 2.3 Weighted nutrient diagnosis
146 146 146 147
3 Nutrient balances as dual or stoichiometric ratios 147 3.1 Nutrient ratios 147 3.2 Diagnosis and recommendation integrated system 147 4 Compositional nutrient diagnosis 4.1 Centered log ratios 4.2 Isometric log ratios
148 148 150
5 Data partitioning
151
6 New lines of research 6.1 Customized nutrient balance designs 6.2 Total analysis versus extracted forms 6.3 Box-Cox coefficients 6.4 How physiologically meaningful is nutrient numerical ordering? 6.5 What is the minimum nutrient dosage to recover from nutrient imbalance? 6.6 Ionomics, biofortification, and fruit quality 6.7 Big data, machine learning, and artificial intelligence
152 152 152 152
References
154
Web reference
156
Further reading
156
153 153 153 154
1 Introduction Because the roots of fruit trees can explore soil layers well below the sampled layers, plant tissue analysis is a useful means to diagnose the nutrient status of fruit crops (Smith et al., 1997). Tissue nutrient concentrations are thought to integrate growth factors under the prevailing ecological conditions affecting crop response to fertilization (Munson and Nelson, 1990). Where one nutrient is supplied in insufficient amounts or in inappropriate combination with other nutrients to support plant growth, agroecosystems cannot be sustainable. At the other extreme, the overuse of fertilizers and inefficient nutrient uptake leads to luxury consumption (Nowaki et al., 2017; Deus et al., 2018), biochemical and physiological disorders, yield losses (Prado and Caione, 2012), wastage of fertilizers, and environmental damage (Das and Mandal, 2015). A.K. Srivastava, Chengxiao Hu (eds.) Fruit Crops: Diagnosis and Management of Nutrient Constraints https://doi.org/10.1016/B978-0-12-818732-6.00012-5
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© 2020 Elsevier Inc. All rights reserved.
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K
FIG. 12.1
Representation of the change in NPK balance in the potato diagnostic leaf in response to P fertilization, projected into a Lagatu and Maume (1934) center-scaled ternary diagram (N + P + K ¼ 100%). Nutrients move along the line as P dosage increased with spot size. The gray blob encloses the NPK composition of high-yielding crops, and Parent, L.E., the central spot is blob centroid. Reproduced with permission from Parent, S.-E., Rozane, D.E., Hernandes, A., Natale, W., 2012. Nutrient balance as paradigm of soil and plant chemometrics. In: Issaka, R.N. (Ed.), Soil Fertility. IntechOpen Ltd., London, pp. 83–114. https:// doi.org/10.5772/53343.
N
P
To diagnose plant nutrient status, total, soluble, or extractable nutrients are quantified in a selected tissue collected at a specific developmental stage (Bould et al., 1960). Cost-effective sampling procedures have been developed for each species (Benton Jones et al., 1991). Tissue analysis includes sample preparation, digestion, and quantification. The basis for nutrient expression is generally tissue dry matter but could be also fresh matter (Clements, 1957), petiole sap (Vitosh and Silva, 1994), or nitrogen (Ingestad, 1987). Quantified plant nutrients and undetermined tissue components are intrinsically multivariate and interrelated parts. Tissue compositions should thus be diagnosed holistically as nutrient combinations rather than as collections of nutrients addressed separately (Deus et al., 2018). In this chapter, we examine the science behind plant nutrient diagnosis from earlier methods that diagnosed nutrients separately under the laws of the minimum and the optimum to modern tools of compositional nutrient diagnosis that address nutrient combinations impacting fruit yield and quality.
2 Diagnostic methods 2.1 Early evidence of physiological balances between nutrients In the 1830s, Jean-Baptiste Boussingault advanced the idea that nutrient balances were more important for plant growth than nutrients examined separately (Epstein and Bloom, 2005). Lagatu and Maume (1934) represented Boussingault’s inkling as a blob or domain delineating optimum NPK combinations in potato leaves. To validate their theory, they used a ternary diagram, an old concept dating 1704 but widely used in many fields of science to synthesize three variables adding up to 100% (Howarth, 1996). Lagatu and Maume (1934) showed (Fig. 12.1) that Carl Sprengel’s Law of the Minimum popularized by Justus von Liebig (Epstein and Bloom, 2005) was based on overoptimistic assumptions for not accounting for nutrient interactions. Their brilliant demonstration of nutrient interactions remained unattended for nearly 50 years.
2.2 Critical nutrient concentrations and concentration ranges Macy (1936) was the first to define adequate concentration ranges in line with Georg Liebscher’s Law of the optimum stating that a growth-limiting factor contributes more to production the closer other production factors are to their optimum (De Wit, 1992). Ulrich (1952) set critical concentration values at 90%–95% maximum yield. Percentage of maximum yield was designed to remove the location-to-location variability due to factors other than the nutrient being studied, but this has serious agronomic (absolute profitability vs nutrient dosage) and statistical (variance heterogeneity and negligible interactions assumed) limitations (Nelson and Anderson, 1984). There is luxury consumption, accumulation, or contamination without yield loss above sufficiency range (Ulrich, 1952). At the far end of the response curve, a slow yield decrease indicates nutrient excess due to nutrient antagonism or toxicity. To establish nutrient concentration ranges, a gradient of nutrient doses must be planned in controlled experiments where the effect of target nutrient on yield is not altered by any harmful effect of another factor (Ulrich and Hills, 1967). Nutrient concentration ranges can also be computed from crop surveys as confidence intervals of nutrient
3 Nutrient balances as dual or stoichiometric ratios
147
concentrations at high-yield level. However, the assumptions behind the law of the optimum are rarely met under field conditions where factor levels vary widely. Critical concentration ranges are easy to interpret (Benton Jones et al., 1991). However, confidence intervals diagnose nutrients in one dimension and two nutrients in 2-D rectangles or squares delineated by the intervals (Nowaki et al., 2017). The 2-D scheme expands to hyperrectangles or hypercubes as more nutrients are added. Assuming normal (ellipsoidal) data distribution at high-yield level, the success across nutrient-by-nutrient diagnosis is conceptually low (Nowaki et al., 2017). Indeed, the volume of a hypersphere is small compared with that of a hypercube across several intervals.
2.3 Weighted nutrient diagnosis Running fertilizer experiments to delineate nutrient concentration ranges is expensive. Using both crop surveys and experimental data, Kenworthy (1967) suggested to standardize nutrient concentrations as percentages of mean values for “normal” crops and then to weight the result by the coefficient of variation V to account for variation in the data. A balance index B relative was computed as follows: If X < Std, ðX=StdÞ 100 ¼ P;ð100 PÞ ðV=100Þ ¼ I;P + I ¼ B If X > Std, ðX=StdÞ 100 ¼ P;ðP 100Þ ðV=100Þ ¼ I;P I ¼ B where X is tissue concentration of nutrient X, Std is standard nutrient concentration for “normal” crops, P is percentage of standard value, and I reflects the variation in standard values. Because Kenworthy’s equations were set symmetrical about 100, they allowed assessing relative shortage (<100) or excess (>100) of nutrients. However, the Kenworthy model did not address nutrient interactions.
3 Nutrient balances as dual or stoichiometric ratios 3.1 Nutrient ratios Interactions are important where one nutrient competes with or dilutes another one close to its deficiency threshold (Marschner, 1986). Nutrient interactions are reported as dual (Bergmann, 1988; Walworth and Sumner, 1987; Wilkinson, 2000) or stoichiometric (Ingestad, 1987) ratios. Selected ratios must reflect physiological functions such as protein synthesis (N and S) and plant-available energy (P) (Epstein and Bloom, 2005) or guide nutrient applications relative to nitrogen (Ingestad, 1987). Nutrient ratios assume sometimes erroneously that pairs of elements are linearly related (Kenworthy, 1967). Ratios can return similar values within deficiency, sufficiency, or toxicity ranges, confusing the interpretation of dual ratios if concentration values are not examined concomitantly (Marschner, 1986).
3.2 Diagnosis and recommendation integrated system The DRIS is an appealing diagnostic method that integrates dual ratios and functions into nutrient indices and arranges nutrients in the order of their limitation to yield (Beaufils, 1973). Dual ratios used to compute DRIS functions are as follows (Walworth and Sumner, 1987): ðA=BÞ κ 1 , if ðA=BÞ > ða=bÞÞ, f ðA=BÞ ¼ ða=bÞ cv ða=bÞ κ f ðA=BÞ ¼ 1 , if ðA=BÞ < ða=bÞÞ, ðA=BÞ cv f ðA=BÞ ¼ 0, if ðA=BÞ ¼ ða=bÞÞ, where A/B and a/b are dual nutrient ratios in diagnosed and reference compositions, respectively, and cv is coefficient of variation (standard deviation divided by mean) of the reference dual ratio. Factor κ accounts for differential measurement units. The ratio expressions (X/Y or Y/X) are selected from the highest variance ratio between the low- and high-yielding subpopulations. However, such selection procedure is questionable because false-positive specimens (high yield despite nutrient imbalance) may result from luxury consumption or contamination.
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The DRIS indices IA, IB, and IC are computed across nutrients A, B, and C by averaging DRIS functions after multiplying DRIS functions by (+1) if the nutrient is at numerator or (1) otherwise, as follows (Walworth and Sumner, 1987): IA ¼
f ðA=BÞ + f ðA=CÞ f ðA=BÞ f ðC=BÞ f ðA=CÞ + f ðC=BÞ ; IB ¼ ; IC ¼ 2 2 2 IA + IB + IC ¼ 0 jIA j + jIB j + jIC j ¼ NII
where NII is nutrient imbalance index. Because DRIS indices are symmetrical, their sum is constrained to zero (Beaufils, 1973). The DRIS was claimed wrongly to diagnose nutrient status irrespective of plant age and location (Walworth and Sumner, 1987; Epstein and Bloom, 2005). The DRIS has been modified empirically at several occasions, including nutrient products to account for nutrients accumulating in opposite directions with time and a dry matter index to delineate nutrient shortage from excess (Walworth and Sumner, 1987). The symmetry of DRIS indices was lost using nutrient products. The dry matter basis was viewed erroneously as a component rather than a scale of measurement. Beverly (1987a,b) suggested to log transform nutrient ratios to facilitate deriving DRIS norms. Indeed, the advantages of log transformations are as follows: • It is common to use a logarithmic scale where ratios are greater than 104 (Budhu, 2010). • ln(A/B) and log(B/A) are reflective because ln(A/B) ¼ ln(B/A); therefore, the variance is the same between both expressions. • The geometric mean is the most appropriate centroid to conduct statistical analyses on ratios (Fleming and Wallace, 1986). DRIS was a major step forward combining nutrients for diagnostic purposes. Nonetheless, the assumed additivity of DRIS functions and indices led to conceptual errors compared with the unbiased compositional data analysis methods (Parent and Dafir, 1992; Parent et al., 2012b).
4 Compositional nutrient diagnosis 4.1 Centered log ratios Aitchison (1986) used a ternary diagram to illustrate the closure problem of three-part geochemical compositions, where any change in the proportion of one part must resonate on others. The negative covariance inherent to resonance distorts the results of linear multivariate analysis and may lead to wrong conclusions. Nutrient interactions (synergism and antagonism), luxury consumption, nutrient excess or toxicity, and contamination are sources of resonance specific to the closed space of the tissue measurement unit (e.g., 1000 g/kg on a dry mass basis). To control resonance, Aitchison (1986) derived log-ratio transformations from the multinomial Dirichlet distribu p tion function across proportions and the logistic function ln 1p closed to one for probability p, (1 p) being the filling value to one. Because ln(A/B) ¼ ln (A) ln (B), a log ratio is a log contrast between two quantities. To close system space to 1000 g/kg in tissue dry matter, the filling value Fv in a D-part composition is computed by difference between measurement unit and the sum of proportions or concentrations as follows: XD1 Xi Fv ¼ 1000 i¼1 where Xi is the ith proportion or concentration. A compositional simplex comprising 12 components of which 11 are nutrients is described as follows on dry matter basis: 9 8 N, S, P, K, Mg, Ca, B, Fe, Mn, Zn, Cu, F ; v > > > > = < N > 0; S > 0; P > 0; K > 0; Mg > 0; Ca > 0; ; S12 ¼ B > 0; Fe > 0; Mn > 0; Zn > 0; Cu > 0; Fv > 0 > > > > ; : N + S + P + K + Mg + Ca + B + Fe + Mn + Zn + Cu + Fv ¼ 1000 g kg1 Aitchison (1986) proposed to express relationships among components as centered log ratios scaled on the geometric mean, as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðci Þ ¼ 12 N S P K Mg Ca B Fe Mn Zn Cu Fv
149
4 Compositional nutrient diagnosis
TABLE 12.1
clr
Centered log-ratio (clr) standards (mean and standard deviation (SD)) of Brazilian fruit crops. Guava
Mango
Grape
Atemoia
Psidium guajava
Mangifera indica
Vitis vinifera
Annona squamosa
Mean
SD
Mean
SD
Mean
SD
Mean
SD
N
2.831
0.190
2.541
0.129
2.761
0.160
3.294
0.164
P
0.435
0.236
0.075
0.227
0.652
0.164
0.070
0.616
K
2.689
0.186
2.175
0.198
1.981
0.208
2.606
0.117
Ca
2.074
0.164
2.978
0.203
2.085
0.178
2.497
0.232
Mg
0.744
0.182
0.620
0.178
0.531
0.147
0.947
0.285
S
0.870
0.174
0.253
0.145
0.718
0.111
0.452
0.220
B
3.499
0.330
3.718
0.273
3.953
0.257
2.934
0.215
Cu
3.310
0.911
4.072
0.650
4.956
0.152
4.795
0.463
Fe
2.827
0.386
2.807
0.287
2.719
0.228
2.549
0.342
Mn
2.790
0.259
0.782
0.344
1.263
0.246
2.596
0.540
Zn
3.972
0.188
3.950
0.336
2.148
0.322
3.677
0.624
Santos, E.M.H., 2013. Programa de computador: Instituto Nacional da Propiedade Industrial—INPI: Courtesy from Rozane, D.E., Natale, W., Parent, L.E., Parent, S.-E., BR5120130003806. Universidade Estadual Paulista “Júlio de Mesquita Filho”; Universite Laval. 2013. http://www.registro.unesp.br/%23!/sites/cnd/ (Accessed 10 December 2018). (in Portuguese, Spanish, English and French).
The clr is much easier to compute than DRIS indices, as follows:
Xi ¼ lnðXi Þ lnðGÞ clrXi ¼ ln G where Xi is the ith nutrient concentration, G is geometric mean, and clr is a log contrast between Xi and G. The clr is a linear combination of dual ratios as follows:
1 N N 12 12 clrN ¼ ln ¼ ln N P K Mg Ca B Fe Mn Zn Cu Fv G
1 N N N N N N N N N N N 12 ¼ ln N P K Mg Ca B Fe Mn Zn Cu Fv ¼ ln
N N N N N N N N N N + ln + ln + ln + ln + ln + ln + ln + ln + ln P K Mg Ca B Fe Mn Zn Cu Fv
As a result, each component is adjusted to every other, avoiding optimistic assumptions on optimum levels of other nutrients under the law of the optimum or equal levels of other nutrients under the law of the minimum. Parent and Dafir (1992) proposed to compute clr indices as follows: Iclri ¼
clri clr∗i , s∗clri
where clri is clr value of the ith component of the composition being diagnosed, clr∗i is clr mean of the ith component of the reference composition, and s∗clri is standard deviation of the ith component of the reference composition. Positive and negative Iclri values can be ranked on a histogram to illustrate nutrient limitations as shortage or excess. The clr standards (clr∗i and s∗clri) of some Brazilian fruit crops are presented in Table 12.1. The difference between any two compositions X and Y can be computed as Euclidean distance 2 as follows (Aitchison, 1986): XD ðclrXi clrYi Þ2 ¼ ðclrXi clrYi ÞI 1 ðclrXi clrYi Þ 2¼ i¼1 where I is the identity matrix and X and Y refer to compositions X and Y, respectively. The clr and the ordinary log transformation return identical Euclidean distances if and only if geometric means are identical.
150
12. Diagnosis of nutrient composition in fruit crops: Major developments
As a means to evaluate intercorrelations between clr variates, Badra et al. (2006) used the measure of sampling adequacy (MSA), allowing to compute a chi-square (χ 2) variable across “independent” (low MSA value) clr variates, as follows: χ2 ¼
XD i¼1
Iclri
2
¼ ðclrXi clrYi ÞVAR1 ðclrXi clrYi Þ
where VAR is the variance matrix.
4.2 Isometric log ratios Because there are D clr variates computable from a D-part composition, one clr variate must be discarded (generally Fv that is barely interpretable) to avoid computing a singular matrix when running multivariate analysis. Indeed, there are D 1 degrees of freedom available to run multivariate analysis of compositions (Aitchison and Greenacre, 2002). To reduce dimensionality, a useful case of linear independence is orthogonality whereby vectors are at perfectly right angles to each other (Rodgers et al., 1984). Egozcue et al. (2003) had the idea to partition D components into D 1 orthonormal balances hierarchically arranged among the D components of the system under study to compute isometric log ratios (ilr), as follows: 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 Qr k rk rffiffiffiffiffiffiffiffiffiffiffiffi i¼1 xi C rk sk B ln@ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi ilrk ¼ A Q sk sk rk + sk x j¼1 j
where rk and sk are numbers of components in subsets at numerator and denominator, respectively;
qffiffiffiffiffiffiffiffiffi rk sk rk + sk
is a norqffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q k xi and malization coefficient; i and j refer to components at numerator and denominator, respectively; and rk ri¼1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q s sk k j¼1 xj are geometric means of component concentrations at numerator and denominator, respectively.
The balance design is an illustration allowing the researcher to describe how components and their related functions are connected in a closed system under study. Subsets of components are arranged into balances following a sequential binary partition (SBP). There are D!(D 1)!/2D1 possible balance designs in a D-part composition (Pawlowsky-Glahn et al., 2011). Multivariate distances remain the same whatever the SBP because switching from a balance design to another just rotates orthogonal axes. Concentration values in buckets do not change, but ilr values at fulcrum change where the balance design has been changed. The SBP can be supported by theory, biplot analysis, or management objectives such as fertilizer source and balance, expected synergistic effect, or selection of liming material based on Ca and Mg contents (Parent, 2011; Hernandes et al., 2012; Parent et al., 2012a,b; Montes et al., 2016). The dual ratios most relevant to the study are assigned first. Examples of balance design are presented in Table 12.2 and Fig. 12.2. Computations can be performed using freeware such as CoDaPack (Comas-Cufí and Thió-Henestrosa, 2011) and R (van den Boogaart et al., 2014). Log ratio means including that of the filling value can be back-transformed to familiar concentration values using the clrinv or ilrinv procedures in R. Several R codes are available to handle compositional data and run statistical analyses. TABLE 12.2
Sequential binary partition and balance formulation.
ilr
r
s
1
2
3
2
1
1
3
1
1
4
2
1
5
5
1
a
ilr formula pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 6=5 ln N P= 3 K Mg CaÞ pffiffiffiffiffiffiffiffi 1=2 lnðN=PÞ pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi 1=2 ln K=Mg pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=3 ln 2 K Mg=CaÞ pffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 5=6 ln 5 N P K Mg Ca=Fv Þa
Fv ¼ filling value between sum of analyzed nutrients and measurement unit.
Balance arrangement Anions versus cations Protein synthesis versus energy K-Mg antagonism Cationic antagonisms Nutrient dilution in biomass
5 Data partitioning
151
FIG. 12.2 Example of balance design for macronutrients. The ilrs are computed at fulcrums using concentration values located in buckets.
FIG. 12.3
Partitioning of 156 Brazilian mango (Mangifera indica) specimens returning an accuracy of 92% and critical Mahalanobis distance of 4.08. FN, false negative; FP, false positive; NPV, negative predictive value; PPV, positive predictive value; TN, true negative; TP, true positive; accuracy ¼ 92%. Parent, L.E., Rozane, D.E., Reproduced with permission from Parent, S.-E., Natale, W., 2013. Plant ionome diagnosis using sound balances: case study with mango (Mangifera indica). Front. Plant Sci. 4, 449. https://doi.org/10.3389/fpls. 2013.00449.
5 Data partitioning Based on research in soil fertility (Nelson and Anderson, 1984) and clinical biology (Swets, 1988), Parent et al. (2013b) proposed to partition data into four categories: true negative (TN), false negative (FN), true positive (TP), and false positive (FP). Crude data are first transformed into ilr variates. Mahalanobis distance (covariance matrix) is iterated across ilr values of healthy crops (true-negative specimens) as reference ilr variates (Fig. 12.3), starting with the compositions of preselected high-yielding crops. Accuracy, computed as the sum of TN and TP specimens over total, is generally >80% (Parent et al., 2012a, 2013a; Rozane et al., 2015; Souza et al., 2016). Lower accuracy is due to a high number of false-negative (Marchand et al., 2013) or true-positive (Deus et al., 2018) specimens. Imbalanced specimens are those showing Mahalanobis distance exceeding the critical multivariate distance. The clr values of TN specimens are computed as standards (means and standard deviations). The Mahalanobis distance squared is assumed to be distributed like a chi-square variable.
152
12. Diagnosis of nutrient composition in fruit crops: Major developments
To guide fertilizer recommendations, specimens are diagnosed using indices and nutrient ranking in the order of nutrient limitations to yield. Steps to diagnose nutrients are as follows: 1. Compute the Mahalanobis distance using ilr mean and covariance matrix of TN specimens as reference values at fulcrum (Fig. 12.2). The ilr means of TN specimens are back-transformed into reference concentration centroids (ilrinv) assigned to buckets that equilibrate at fulcrum (circles in Fig. 12.2) equilibrating at fulcrum. Compare specimen’s composition to the reference composition in buckets. 2. If the specimen is imbalanced (Mahalanobis distance larger than the critical distance), compute clr indices using mean and standard deviation of TN specimens as reference values (e.g., Table 12.2), and then order clr indices from the most negative to the most positive or provide a histogram of clr indices. 3. Make a recommendation to reestablish nutrient balance.
6 New lines of research Compositional data analysis provides sound modern tools to address old issues and face challenges related to plant tissue diagnosis. New knowledge could be developed on the following topics: 1. Based on literature and experimentation, develop and animate customized nutrient balance schemes picturing nutrient relationships specific to the problem under study. 2. Look beyond total elemental analysis to improve diagnostic accuracy. 3. Test coefficient (exponent) assignment to concentration values to normalize log ratios or account for nutrient mobility. 4. Validate numerical order of nutrient limitations against the order of plant responses to nutrient stress. 5. Calibrate nutrient indices against crop response. 6. Relate ionomics to fruit quality, nutrient management, and biofortification to enhance the contribution of fruit crops to human nutrition and health. 7. Acquire and store big data to support artificial intelligence models and optimize nutrient management in fruit agroecosystems worldwide.
6.1 Customized nutrient balance designs A customized balance (e.g., Fig. 12.2) is a comprehensive representation of the system designed managerially, phenomenologically, or heuristically to facilitate its interpretation. A catalog of customized balance designs could be elaborated to visualize and animate nutrient relationships relevant to a study or a diagnosis and monitor specific imbalances driven by treatments. For example, K fertilization, liming, and lime composition could be managed based on the interactive cationic subsystem (K, Ca, and Mg) operating in both soils and plant tissues (Parent and Parent, 2017). The N P synergism (protein synthesis vs energy supply) could be contrasted with subsystems of other macronutrients or cationic micronutrients to assess the impact of NP fertilization on other subsystems. The Cu, Zn, and Mn subsystem could be balanced with other subsystems to conduct global nutrient diagnosis. In some situations, fungicide applications can lead to excessive accumulations of Cu, Zn, and Mn on leaves that impact positively on yield by controlling foliar diseases. Nutrients contained in fungicides could be set apart as a specific subsystem of microcationic balances to assess fungicide capacity to sustain plant health with useful “contaminants” (Yamane, 2018).
6.2 Total analysis versus extracted forms Tissue diagnosis is commonly conducted using total elemental analysis, disregarding the fact that just a portion of total concentration may be available to accomplish biological functions. If some extraction methods allow partitioning total elemental concentration into more or less available or unavailable forms, total concentration can be split into several contrasts. If the new partition impacts on yield, diagnostic accuracy could be increased.
6.3 Box-Cox coefficients It is generally assumed that ilr variates are normally distributed, but this is not always the case. Non normal distribution can be recovered where appropriate after discarding outliers or by assigning Box-Cox coefficients varying
6 New lines of research
TABLE 12.3
153
Relative phloem mobility of essential elements (Epstein and Bloom, 2005).
Mobile
Intermediate
Immobile
Potassium
Sodium
Calcium
Nitrogen
Iron
Silicon
Magnesium
Manganese
Borona
Phosphorus
Zinc
a
Boron
Copper
Sulfur
Molybdenum
Chlorine a
Immobile except for phloem-mobile boron-sorbitol complexes in fruit trees of genera Pyrus, Malus, and Prunus (Brown and Hu, 1996).
between 0 and 1 to raw concentration values (Box and Cox, 1964). On the other hand, nutrients move differently from leaf to fruit through phloem transport, while xylem transport to low-transpiring organs may be limited. Assigning coefficients close to zero to the most immobile nutrients, coefficients close to one to most mobile ones, and intermediate coefficient values to partially mobile nutrients before ilr transformations may account for nutrient mobility (Table 12.3). While skewness of ilr values decreased using Box-Cox coefficients in a Brazilian banana (Musa spp.) data set, diagnostic accuracy was not improved (Deus et al., 2018). Nevertheless, the Box-Cox transformation may be an option for other crops.
6.4 How physiologically meaningful is nutrient numerical ordering? It is a truism that growers are more concerned about negative than positive nutrient indices. While nutrient needs are prioritized according to the order of nutrient limitations to crop yield and quality, such ordering should bear some physiological significance. For the diagnosis to be reliable and reproducible, the addition of the most limiting nutrients in the order of their limitation should influence tissue composition and crop yield in the same order. This could only be validated by local fertilizer trials.
6.5 What is the minimum nutrient dosage to recover from nutrient imbalance? By how much should present fertilization regimes be increased or decreased through soil or leaf applications in the case of nutrient imbalance? Plant response to applied nutrients must depend on whether and to what extent nutrient status is impacted by nutrient dilution in tissue mass, antagonism, synergism, luxury consumption, or contamination. As for soil testing where compositional models were also applied (Parent et al., 2012a,b; Parent and Parent, 2017), field calibration of tissue tests are needed to guide site-specific dosage of soil- and foliar-applied nutrients.
6.6 Ionomics, biofortification, and fruit quality The ionome is the mineral nutrient composition of living organisms (Huang and Salt, 2016). Ionomics is a tool to target healthier food through genetics and biofortification (Welch, 2002; Zuo and Zhang, 2008; Gang et al., 2018). Baxter (2015) raised the problem of how to solve myriads of known and unknown interconnections between nutrients in ionomics and viewed a possible solution in the nutrient balance concept proposed by SE Parent et al. (2013b). Understanding nutrient interactions involving Zn and Fe absorption by plant and human might support plant breeding programs aimed at improving food quality and human health. Fruit quality depends on genetics, management, and the environment. Fruit quality is often measured as Brix index, phenolics, and total anthocyanins (TAcy), as well as fruit acidity, firmness, and supply of minerals and vitamins essential to human health. Because organic acids and their salts (e.g., ascorbic acid, fumarate, malate, and citrate) can increase Zn and Fe bioavailability in fresh fruits (Bouis and Welch, 2010), such components could be balanced against each other (human nutrition forms also a compositional simplex). Some undesirable minerals could also be addressed.
154
12. Diagnosis of nutrient composition in fruit crops: Major developments
The leaf ionome at high fruit yield may differ from that at high fruit quality, and this may impact on nutrient management. Compositional data analysis provides a means (1) to optimize leaf ionomes at high fruit quality level and (2) to balance fruit concentrations of sugars, antioxidants, acids, and minerals to reach high fruit yield and quality. Such models should be developed.
6.7 Big data, machine learning, and artificial intelligence Plant nutrient diagnosis developed over the past centuries relied on overoptimistic assumptions. It was not until the theory of compositional data analysis was established on strong theoretical basis in 1986 using log ratios as data transformation techniques that plant tissue diagnosis gained a new momentum. Nutrient interactions, deficiency, luxury consumption, and contamination were viewed as numerical interplays between nutrient concentrations within the closed space of diagnostic tissues. Centered log ratios adjust every nutrient to the levels of other components. Isometric log ratios arrange selected nutrient interactions hierarchically. Data classification methods borrowed from soil fertility and clinical biology allowed delineating a hyperellipsoid within a critical Mahalanobis distance. There is no reason to believe that the healthy state of ionomes has regular geometry such as hyperellipsoidal. Data distribution could be of any shape (blob) as impacted by several factors (Fig. 12.1). The many interacting growth factors such as genetics (e.g., cultivar), soil (pH, texture, genesis, etc.), and weather documented in big data sets can be handled using a wide spectrum of machine learning methods. Nutrient imbalance can be defined as the shortest distance between an observation and the nearest centroids of a hyperblob portion or blob islands delineating highly performing crops (Yamane, 2018). The k-nearest neighbor technique assumes that an observation will respond in line with its closest highly performing neighbors. An international initiative to acquire and store big data from different fruit agroecosystems worldwide is required to develop models of artificial intelligence. In future research, machine learning methods and other tools of artificial intelligence will process higher-level models including an array of growth-impacting factors and metadata collected in big data sets. International collaboration will be needed to build such large data sets across fruit agroecosystems. Progress in compositional data analysis and artificial intelligence will undoubtedly foster the development of progressively more robust diagnostic tools to support high agronomic and environmental performance of fruit crops worldwide at lowest cost of inputs.
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Web references Beaufils, E.R., 1973. Diagnosis and recommendation integrated system (DRIS). Soil Sci. Bull., 1–132. Available from: http://www.worldcat.org/ title/diagnosis-and-recommendation-integrated-system-dris/oclc/637964264?ht¼edition&referer¼di. (Accessed 2 May 2013). Comas-Cufí, M., Thió-Henestrosa, S., 2011. CoDaPack 2.0. Universitat de Girona. Available from: http://ima.udg.edu/codapack/. (Accessed 10 December 2018). Pawlowsky-Glahn, V., Egozcue, J.J., Tolosana-Delgado, R., 2011. Principal balances. In: Egozcue, J.J., Tolosana-Delgado, R., Ortego, M.I. (Eds.), 4th International Workshop on Compositional Data Analysis (Codawork 2011). San Feliu de Guixols, Spain. Available from: http://congress.cimne. com/codawork11/Admin/Files/FilePaper/p55.pdf. (Accessed 10 December 2018). Santos, E.M.H., 2013. Programa de computador: Instituto Nacional da Propiedade Industrial— Rozane, D.E., Natale, W., Parent, L.E., Parent, S.-E., INPI: BR5120130003806. Universidade Estadual Paulista “Júlio de Mesquita Filho”; Universite Laval. http://www.registro.unesp.br/#!/sites/ cnd/. (Accessed 10 December 2018) (in Portuguese, Spanish, English and French). van den Boogaart, K.G., Tolosana-Delgado, R., Bren, M., 2014. “Compositions”: Compositional Data Analysis in R Package. Available from: http:// cran.r-project.org/package¼compositions. (Accessed 10 December 2018).
Further reading Barlow, P., Parent, L.E., 2015. Nutrient balances of New Zealand kiwifruit (Actinidia deliciosa cv. Hayward) at high yield level. Commun. Parent, S.-E., Soil Sci. Plant Anal. 46, 256–271. https://doi.org/10.1080/00103624.2014.989031. Parent, L.E., Rozane, D.E., Natale, W., 2013c. Plant ionome diagnosis using sound balances: case study with mango (Mangifera indica). Parent, S.-E., Front. Plant Sci. 4, 449. https://doi.org/10.3389/fpls.2013.00449.