Yield stability analysis of maize hybrids using the self-organizing map of Kohonen

Abstract

The purpose of this study is to classify 32 commercial maize hybrids with regard to grain yield stability by using an artificial neural network procedure. The hybrids were evaluated at five locations, in two late growing seasons. Each replication (R1 and R2) of the response variable was used as a network input signal to trigger the network learning process. The underlying network model has a topology consisting of two neurons in the input layer and ten neurons arranged in a two-dimensional grid. The competitive process was induced by the random presentation of an input vector $$x = [x_{1} ,x_{2} , \ldots ,x_{n} ]^{{\text{T}}}$$ from the network training set, without specifying a desired output. A grid neuron y responded best to this stimulus. Thus, the neuron with the shortest Euclidean distance between the input vector and the respective weight vector $$w_{i} = [w_{i1} ,w_{i2} , \ldots ,w_{in} ]^{{\text{T}}}$$ , at moment t, was selected as the winner. The winning neuron indicates the center of a topological neighborhood of cooperative neurons. The adaptive process occurred via applying an adjustment Δwij to the synaptic weights wij during learning, until convergence of the network. The results showed that the classes of hybrids with the same performance pattern across environments were not altered by the network, confirming the high yield stability and satisfactory overall performance associated with higher grain yield means (above 6 t ha−1). The single-cross hybrid 10 (CD-387) stood out at all locations in both years, with unaltered data classification by the network. Therefore, it was considered to be stable in all environments, without performance variation over the years, as well as adaptable.