Agriculture implies high levels of production risks and many variables must be considered to take decisions. In order to define management strategies and development programmes, an adequate knowledge about variables most directly affecting production is essential. Understanding the behaviour of variables is difficult due to the complexity of relationships and to the amount of factors involved. Citrus production becomes a special challenge due to the significant spatial and temporal variability present in orchards.

In citrus orchards, production is primarily defined by the amount and size of fruits. Production can be affected by both endogenous and exogenous factors. Endogenous factors are, for instance, genetic characteristics of species or varieties, and physiological issues. Among the exogenous factors, environmental and crop conditions, especially irrigation and fertilisation, are highlighted ( Agustí, 2000 , 2003 ). Production is also determined by trees’ age, and their reaching a commercial production volume (> 50 kg/tree) at adult age (> 7 years after transplant) ( Orduz-Rodríguez et al ., 2007 ).

Citrus trees’ development is possible between 10°C and 40°C and optimised between 24°C and 32°C. Fruit size and final set depend, among other factors, on the availability of carbohydrates for developing flowers. Thermal influence is very limited in the range of 22°C to 30°C. However, if leaf temperature rises above 32°C, the CO ₂ assimilation rate decreases. Thermal influence on growth and competition between vegetative and reproductive developments, emphasise problems from a limitation in the CO ₂ fixation, such as the alternation of productivity between seasons, reducing fruits’ size, and final fruits set ( Agustí, 2003 ).

Maximum and average temperatures, reference evapotranspiration, wind speed, and relative humidity, are the meteorological variables with the greatest influence on fresh dough and equatorial diameter of fruits. In citrus orchards growing at temperate climates, autumn rains improve the fruits’ final size and juice content, and reduce the concentration of sugars and free acids. Total annual rainfall between 900 mm and 1200 mm is enough to ensure fruit development. On the other hand, drought periods (even if short) tend to reduce the fruit size. When lower values or dry seasons occur, complementary irrigation is needed ( Agustí, 2000 , 2003 ). Irrigation absence mainly affects the fruit size, although the effect of this absence also depends on the phenological state ( González-Altozano & Castel, 2003 ; García Petello & Castel, 2004 ; Gasque et al ., 2010 ).

Many variables must be considered prior to making decisions about planting the framework. Tree vigour and growth habitat, as influenced by variety and rootstock, are important, and site quality in terms of climate, soil characteristics, and water availability must be considered. In general, higher density plantings that rapidly develop into a hedgerow appear to be advantageous, especially at the beginning of trees’ production life. However, vigorous combinations with more spreading growth habits should be planted with wider spacing ( Tucker et al. , 1994 ; Medina-Urrutia et al. , 2004 ).

Machine Learning (ML) is a branch of artificial intelligence that provides methods with the ability to learn from or to make predictions on data. These methods build a model from example inputs in order to make predictions or to take decisions ( Mitchell, 1997 ). ML does not make any assumptions about the right structure of the data model, allowing the construction of complex non-linear models. There are many different paradigms in ML: lazy methods such as K-Nearest Neighbours (KNN) ( Altman, 1992 ) methods, based on tree construction, as, for instance, C4.5 ( Quinlan, 1993 ) or Neural or Bayesian networks ( Mitchell, 1997 ). All of them have been successfully used in many different domains. For instance, neural networks have been successfully used to predict maximum dry density and unconfined compressive strength of cement-stabilised soil ( Das et al ., 2011 ), or to detect structural damage ( Alavi et al. , 2016a , b ).

In particular, some of these methods have been applied for comprehensive agricultural planning in precision farming (PF) ( Arango et al. , 2015 ). PF techniques provide a complete knowledge about spatial variability and the different characteristics of a specific area, helping to define more efficient and rational crop management plans in relation to a more localised use of fertilisers and agrochemicals ( Yu et al ., 2010 ; Fernandez Quintanilla et al. , 2011 ).

Among the huge number of issues related to PF, pest prediction is a task where different ML techniques have been successfully applied. In particular, Bayesian techniques have been adopted ( Tripathy et al. , 2011 ; Pérez-Ariza et al ., 2012) . On the other hand, support vector machines are also extensively used ( Wang & Ma, 2011 ).

When the variable to predict is continuous, ML methods more commonly used are CART ( Breiman, 2001 ), M5 ( Quinlan, 1992 ), M5-Prime ( Wang & Witten, 1997 ), KNN ( Altman, 1992 ), or support vector regression (SVR, see Basak et al. , 2007 ).

The model tree technique (see, for example, Frank et al ., 1998 , or Samadi et al ., 2014 ) is based on combining decision trees with linear regression functions at the leaves. There are several techniques to predict numeric values instead of just a label. Standard regression imposes a linear relation on data; hence, it is not quite powerful. On the other hand, other paradigms not based on constructing a tree (such as Neural Networks, SVR or lazy classifiers) can be quite powerful, but their interpretability is low.

Regarding model tree techniques, the strategy to construct the tree is similar for all of them ( El Gibreeb & Aksoy, 2015 ). The main differences among the methods are the splitting criteria, the pruning rules, and the mechanism to estimate the leaf value. CART uses variance as the splitting criteria, while M5 uses standard deviation reduction (SDR). In addition, the estimated value for a leaf is constant in CART. In contrast, M5 approximates the leaf values by linear regression models. In addition, it is able to improve predictions by introducing a smoothing procedure ( Quinlan, 1992 ). Furthermore, trees generated with M5 are smaller than those generated with CART. Thus, M5 outperforms CART in accuracy and simplicity ( Uysal & Altay, 1999 ). M5-Prime is an improvement over M5 that can deal with missing values and enumerated attributes ( Wang & Witten, 1997 ) and has been used, for instance, to predict streamflow ( Onyari & Ilunga, 2013 ), to model sediment yield ( Goyal, 2014 ), to estimate the maximum scour depth at breakwaters ( Pourzangbar et al ., 2017 ) and to predict the compressive strength of high performance concrete ( Behnood et al ., 2017 ).

González-Sánchez et al . (2014) compared the predictive accuracy of ML and linear regression techniques for crop yield prediction in ten crop datasets. Multiple linear regression, M5-Prime model trees, Perceptron Multilayer Neural Networks, SVR, and KNN methods, were ranked. M5-Prime and KNN techniques obtained the lowest errors and the highest average correlation factors. M5-Prime, which achieves the largest number of crop yield models with the lowest errors, was considered a very suitable tool for massive crop yield prediction in agricultural planning. In addition, it is more interpretable than KNN. Other approaches combine partial least square models and spectral imaging technology ( Ye et al ., 2007 ).

As production-predictive tasks require the learned model to predict a numeric value associated with a variable rather than the class the example belongs to, model regression trees are proposed. Hence, this work checks the effectiveness of ML techniques in order to determine the affecting variables and classify citrus orchards according to production. In particular, the predictive mechanism established in this work to characterise the variables involved, and to identify the most important factors affecting citrus production, is based on the M5-Prime method.

The studies have been conducted during seasons 2013 and 2014, with field information from 964 Citrus orchards in the province of Corrientes, Argentina, located at latitudes 57°W to 59°W, and longitudes 27°S to 31°S. Orchard tree canopies belong to several varieties of three species: lemon ( Citrus limon Burman), mandarin ( Citrus reticulata Blanco), and sweet orange ( Citrus sinensis Osbeck), over diverse rootstocks.

Every orchard was characterised by the following variables: global position (latitude and longitude degrees, minutes and seconds); annual minimum and maximum average temperatures (ºC), annual total rainfall (mm) and annual total frost-free days defined from the corresponding isolines at orchards’ location; environment, species, variety, age of trees, planting framework (between rows’ distance, m; within rows’ distance, m), presence or absence of irrigation (binary) and production by tree (kg/tree).

Lemon was present in 94 orchards (9.6%), placed at 28°S to 30°S and 57°W to 59°W, in Mesopotamic Park and savanna environments, with annual average temperatures between 18°C and 21°C, total annual rainfall between 1000 mm and 1200 mm, and 320 to 340 frost free days in the year. Two varieties of lemon were found in the studied orchards: 'Eureka' (71% of orchards) and 'Genova' (26% of orchards). In addition, 3% of orchard varieties could not be identified (Unknown). Only 26.5% of the orchards were under irrigation, with similar percentages in all varieties. The characteristics of these orchards are presented in Table 1.

Mandarin was present in 364 orchards (37.6%), placed at 28°S to 30°S and 57°W to 59°W, with annual average temperatures between 18°C and 21°C, total annual rainfall between 1000 mm and 1200 mm and 320 to 360 frost free days in the year, in mesopotamic park and savanna environments (however, 'Clemenules', 'Murcott', 'Criolla', 'Nova', 'Dancy' and 'Okitsu' varieties appeared in all locations; W Murcott is present only at 59°W, 29°S in mesopotamic park environment and the others only at 57°W, 30°S in savanna environment). Twelve varieties of mandarin were found in the studied orchards: 'Murcott' (24% of orchards), 'Ellendale' (20%), 'Okitsu' (15%), 'Nova' (12%), 'Dancy' (8%), 'Clemenules' (6%), 'Criolla' (5%), 'Encore' (3%), 'Ortanique' (2%), 'Malvacio' (1%), 'Montenegrina' (1%) and 'W Murcott' (1%). In 1% of orchards, the variety could not be identified (Unknown). Irrigation was present in 45% of orchards, with higher percentages in 'Montenegrina', 'W Murcott', 'Clemenules', 'Nova' and 'Murcott'. Table 1 presents a description of these orchards.

Orange was present in 509 orchards (52.8%), placed at 28°S to 30°S and 57°W to 59°W, in mesopotamic park and savanna environments, with annual average temperatures between 18°C and 22°C, total annual rainfall between 1000 mm and 1400 mm, and 320 to 360 frost free days in the year. Fourteen varieties of orange were found in the studied orchards: Valencia late (50% of orchards), Salustiana (8%), Valencia seedless (7%), Washington navel (7%), Delta seedless (5%), Valencia frost (4%), Criolla (3%), Lane late (2%), Navel late (2%), Navelina (2%), Robertson navel (1%), Newhall (0.2%), Hamlin (0.2%) and Westin (0.2%). In 7% of the orchards, the variety could not be identified (Unknown). Irrigation was present in 42.4% of the orchards, with higher percentages in Salustiana, Midknight, Navelina, Robertson Navel, and Newhall. Description of these orchards is presented in Table 1 .

In this work, the factors affecting sweet orange, lemon, and mandarin production were studied using different techniques. In particular, statistical methods such as correlation coefficient, principal component analysis, and Biplot were employed, to identify such factors. In addition, in order to provide a more complete and interpretable point of view, a machine learning technique (known as M5-Prime) was applied.

M5-Prime is demonstrated appropriate to classify citrus orchards and allows for defining more informative, E ., more relevant, variables affecting tree production. For all the studied species, the most informative variable is tree age; in mandarin and orange orchards, age is followed by between and within rows distances; irrigation also affects mandarin production.

In all species studied, in younger orchards, higher productions are associated with stronger planting densities, mainly distance within rows.

Future studies would involve a more thorough investigation in the possibility of using ML techniques for the prediction of citrus yield, and comparing the effectiveness and efficiency of several different paradigms and learning methods, such as regression trees, SVR, neural networks… as well as combinations of them with techniques such as bagging, boosting or random forests.

New, complementary variables will also be incorporated, such as those obtained from hyperspectral satellite imagery, which have been already used successfully in Precision Farming problems ( Arango et al. , 2015 ). Finally, the possibility of extracting qualitative information from the data (for instance, with methods such as the self-organising maps proposed in Kohonen (1982) will be explored in this case.