**1. Introduction**

With the world population expected to reach more than 9 <sup>10</sup><sup>9</sup> people by 2050, the food demand must increase by 70% in a situation where yield average of several staple crops is expected to decline [1]. More than 95% of our food is produced on soil [2]. Despite the general perception that soil is an abundant resource, the reality is that the soil resource is degrading at fast rate as a result of salinization, erosion, compaction, contamination, structure collapse, acidification, loss of organic matter and biological activities, as well as land allocation to urban and industrial development. Gains in technology alone will not suffice to compensate the harmful agricultural practices thought heroically to maintain soil productivity and farm viability on the long run. Understanding comprehensively how agroecosystems build and function worries more. Two centuries ago, German scientist Alexander von Humboldt warned that

management of living systems must be based on the rigorous collection of contextual facts and local knowledge [3]. His thoughts translate today into data acquisition from diverse sources, data mining and data processing methods to assist making wise decisions on how to manage soils properly at local scale.

The land is the basic resource for food production. There is a need to develop soil quality criteria and implement them where it matters most. Keppel and Kreft [4] attributed large disparities in decision-making thought naively to manage soils properly to unequal, insufficient or inadequate collection of information, widespread ignorance on how agroecosystems function, lack of understanding on how factors interact, and the wrong perception that buisiness-oriented economic and social values outweigh environmental damages or beneficial ecosystem services. Indeed, high crop productivity relies on positive interactions between climatic, managerial and edaphic factors [5]. Data must be integrated into comprehensive decision-making models to manage complex systems sustainably. High-quality and diversified information reduces the risk of making wrong decisions based on regional averages rather than at the right interaction level at field scale [6, 7]. Judicious decisions on locally acceptable actions should rely on well-documented facts and sound knowledge of environmental conditions. Besides traditional means to diagnose soil–plant systems, progress on data acquisition tools includes proximate and remote sensing, high-throughput laboratory technologies or on-the-go data acquisition kits of precision agriculture.

Several diagnostic models support decisions on soil and nutrient management. While soil properties and plant compositions have been addressed as separate variables in reductionist models [8], empirical-mechanistic models were developed to synthesize more data, balancing untestable and testable concepts [9–11]. This required not only sufficient data input, but also calibrating empirical coefficients and validating the results in a wide variety of environments. More recently, modern tools of artificial intelligence allowed to process large and diversified datasets in relation with ecosystem performance based on Alexander von Humboldt's principles of biogeography [3].

On the other hand, soil and plant analytical data are inherently multivariate compositional data constrained to the measurement unit, posing a serious numerical problem of "resonance" within the constrained space of compositions, such as 100% or the unit of measurement [12]. Ternary diagrams were the first representations of the closed space of three interrelated variables [13]. Lagatu and Maume [14] related tissue N, P and K concentrations in a ternary NPK diagram to delineate the space of successful tissue compositions. It was not until [12] that ternary diagrams formed the basis of an emerging and appealing field of mathematics called "Compositional Data Analysis" (CoDa). CoDa rely on log ratio transformations. Egozcue et al. [15] developed means to project compositions as coordinates in the Euclidean space. The CoDa concepts corrected computational errors and fallacies in earlier plant and soil diagnostic models [16, 17].

On the other hand, the fractal theory has been useful to address the geometry of soil aggregation [18] and the kinetics of carbon decomposition in soils [19]. Fractal kinetics assigned to time a coefficient between 0 and 1 to explain the reduction in decomposition rate due to reduced contact between organic matter particles and their immediate environment resulting from aggregate buildup with time [19]. Fractal coefficients also provided a description of aggregate fragmentation patterns upon mechanical stress and avoided computational errors reported in classical synthetic measures of aggretation [20].

Machine learning, compositional and fractal modeling tools can process large and diversified soil–plant datasets that allow conducting side-by-side comparisons between failure and success. We hypothesized that well-informed models can assist *Machine Learning, Compositional and Fractal Models to Diagnose Soil Quality and Plant… DOI: http://dx.doi.org/10.5772/intechopen.98896*

making wise decisions on soil and nutrient management at local scale. In this chapter, we address carbon sequestration and factor-specific fertilization to sustain soil productivity and support resource conservation actions.
