Comparison of techniques used in the prediction of yield in banana plants
Introduction
The banana cultivation is one of the main activities in the agribusiness world with plantations in more than 120 tropical and subtropical countries. In addition to being a vital food resource, the banana is the most popular fruit in the world, and its production occurs in virtually all developing countries. Brazil is the fourth largest producer of bananas, with an estimated production of 6972,408 t in 2007, covering 508,845 ha of harvested area (Silva et al., 2011).
In Brazil, the banana culture uses a wide diversity of cultivars with predominance of the popularly named ‘Prata’ (Silva et al., 2011), unlike the culture in other Latin American countries, targeting exportation, and using on cultivars from the Cavendish, Grande Naine, and Williams subgroups. However, no cultivar is resistant to all pests and diseases, present high yield, is premature, tasty, easy to handle, features longevity, and presents adequate market shelf life (Daniels, 2000). The program of genetic improvement of banana plants in Brazil has selected several promising genotypes and the cv. Tropical is one of them (Silva et al., 2011).
The genetic improvement process takes a key role in developing the ideotype variety, and in order to ensure the recommendation of superior genotypes, the final steps in the field evaluation experiments require precision. Thus, at this stage, the phenotypic characters that reflect growth, earliness and productivity are studied, because they are important for the identification and selection of superior individuals (Silva et al., 2011). These characters are usually quantitative, easy to measure, may be under polygenic control, susceptible to environmental influence and sustain economic importance (Ortiz, 1997). Genetic improvement of banana though laborious and time consuming has produced satisfactory results in the generation of disease resistant cultivars.
The knowledge of characteristics like plant height, perimeter of pseudostem, weight of the bunch, number of fruits per hand, and length and diameter of the fruit and their relationships with the final weight of the bunch can facilitate early decisions by the farmer or plant breeder or enable the producer to forecast financing aspects of the crop's harvest before the actual harvest of the bunches, because these characters are considered relevant for the selection of superior individuals, which may be recommended for incorporation in the farmer's production systems in the region (Heslop-Harrison and Schwarzacher, 2007).
Artificial neural networks (ANNs) modeling are designed to approximate mathematical functions, allowing quick and simple simulations to be performed. The ANNs are formed by simple processing interconnections between elements called neurons that have the ability to identify the relationships between entry and exit responses in given patterns, such as in the human neural activity (Gungula et al., 2003).
The number of hidden layers in the ANNs depends on the degree of complexity of the problem (Chen and Ramaswamy, 2002, Movagharnejad and Nikzad, 2007, Izadifar and Jahromi, 2007, Erzin et al., 2008) and the network application (Huang and Mujumdar, 1993). The selection of the number of neurons for each hidden layer is empirical. However, an inappropriate number of neurons to solve a problem can lead to unsatisfactory results. The difficulty lies precisely in determining the appropriate number of neurons in each layer. One or two hidden layers are extremely useful in most cases for most of the problems (Erzin et al., 2008). One hidden layer was used for this study according to results of preliminary tests. The use of a large number of hidden layers is not recommended. Each time the average error during training is used to update the weights of the synapses of the layer immediately above, it becomes less useful or accurate. The only layer that has a precise notion of error by the network is the output layer. The last hidden layer receives an estimate of the error. The penultimate hidden layer receives an estimate of the estimate, and so forth. Empirical tests with the MLP neural network backpropagation not demonstrate significant advantage in the use of two hidden layers instead of one to minor problems. Therefore, for the majority of problems use only one hidden layer and if necessary two and not more than that.
The study of these factors enables the producer to estimate projections for the harvest, because the prediction of the bunchs’ weight can lead to financial program initiatives. The current literature lacks recent studies on the prediction bunch's weight in banana plants; the latest studies in this subject were by Jaramillo (1982). Current studies have aimed to characterize and evaluate the behavior of genotypes (varieties and hybrids) with phenotypic descriptors relevant to the identification and selection of superior individuals. The simulation models are useful tools and can predict the yield according to the studied variables (Gungula et al., 2003). The present study compared the use of phenotypic descriptors in the multiple linear regression (MLR) and artificial neural networks (ANNs) analyses.
The theory of multiple regression has been widely disseminated and applied to several plant species, such as wheat (Le Bail et al., 2005), sugarcane (Scarpari and Beauclair, 2009), corn (Soler et al., 2007) with the purpose of estimating the yield and production. Many studies in agriculture have reported the use of artificial neural networks (Jiang et al., 2004, Bala et al., 2005, Diamantopoulou, 2005, Uno et al., 2005, Movagharnejad and Nikzad, 2007, Savin et al., 2007, Zhang et al., 2007). Most of these studies are dedicated to yielding predictions (Jaramillo, 1982, Stenzel et al., 2006, Ram et al., 2010). Although some studies report assessments of characters that are components of production in different banana genotypes (Jaramillo, 1982, Dadzie, 1998), the literature still lacks information that allow the use of some attributes measured at the stage of harvest to estimate the bunch’ weight.
The goal of this study was to establish a procedure based on studies with multiple linear regression and artificial neural networks to allow the prediction of the bunch's weight in banana plants cv. Tropical.
Section snippets
Culture implementation and maintenance
The experiment was performed in a Red–yellow Dystrophic Oxisol with a smooth, wavy landscape in the experimental area of the Antonio José Teixeira Federal Agrotechnical School, located in the district of Ceraima, municipality of Guanambi, in the Micro-Region of the Serra Geral, southwestern Bahia, with latitude of 14°13′30″ South and longitude of 42°46′53″ West of Greenwich, altitude of 525 m, average annual rainfall of 663.69 mm, and average temperature of 26 °C.
The experiment used
Results and discussion
The yielding variables total number of clusters per bunch, perimeter of the pseudo stem, diameter of the fruit, and diameter of the stalk were not included in the model adjusted by the multiple linear regression analysis because this method selects only the significant variables. This absence can be related to the little influence that these variables have on bunch's weight. According to the multiple linear equation, only the following variables were selected, number of live leaves at harvest,
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