**Author details**

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).

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,

This paper shows that the specific numerical properties of compositional data require log ra‐ tio transformations before conducting statistical analyses of soil and plant compositional da‐ ta. Compared to raw concentration data, the orthonormal balances can be interpreted consistently and without numerical bias as isometric log ratio coordinates. The *ilr* approach can provide unbiased indices of nutrient balance in soils and plant tissues, biological stabili‐ ty of organic residues and soil quality. Well supported by techniques developed by compo‐ sitional data analysts, the balance paradigm and the elaboration of its SBP schemes prompt that many concepts inherited from the past centuries be debated and revisited in soil fertility

The balance paradigm was elaborated within the plant nutrition and soil carbon modules of the research project entitled 'Implementing means to increase potato ecosystem services' (CRDPJ 385199 – 09). We acknowledge the financial support of the Natural Sciences and En‐ gineering Research Council of Canada (NSERC), the Fundação de Amparo à Pesquisa do Es‐ tado de São Paulo (FAPESP), the Coordinação de Aperfeiçoamento de Pessoal de Nivel Superior (CAPES), as well as farm partners as follows: Cultures Dolbec Inc., St-Ubalde, Qué‐ bec, Canada; Groupe Gosselin FG Inc., Pont Rouge, Québec, Canada; Agriparmentier Inc. and Prochamps Inc., Notre-Dame-du-Bon-Conseil, Québec, Canada; Ferme Daniel Bolduc et

+0.0019 *SOL* <sup>|</sup> *HEM* , *CEL* - 0.1063 *HEM* <sup>|</sup>*CEL* (13)

*Clabile* =0.3065 - 0.1251 *SOL* .*HEM* , *CEL* , *LIG* | *N* + 0.0301 *SOL* , *HEM* , *CEL* | *LIG*

The equation was as follows:

108 Soil Fertility

**6. Conclusions**

and plant nutrition.

**Acknowledgements**

Fils Inc., Péribonka, Québec, Canada.

scale-invariant and free from spurious correlations.

S.É. Parent1 , L.E. Parent1 , D.E. Rozanne2 , A. Hernandes3 and W. Natale3

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

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

2 Departamento de Agronomia, Unesp, Universidade Estadual Paulista, Campus de Regis‐ tro, Registro, São Paulo, Brasil

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