Distribution of β-amylase I haplotypes among European cultivated barleys

The barley β-amylase I (Bmy1) locus encodes a starch breakdown enzyme whose kinetic properties and thermostability are critical during malt production. Studies of allelic variation at the Bmy1 locus have shown that the encoded enzyme can be commonly found in at least three distinct thermostability classes and demonstrated the nucleotide sequence variations responsible for such phenotypic differences. In order to explore the extent of sequence diversity at the Bmy1 locus in cultivated European barley, 464 varieties representing a cross-section of popular varieties grown in western Europe over the past 60 years, were genotyped for three single nucleotide polymorphisms chosen to tag the four common alleles found in the collection. One of these haplotypes, which has not been explicitly recognised in the literature as a distinct allele, was found in 95% of winter varieties in the sample. When release dates of the varieties were considered, the lowest thermostability allele (Bmy1-Sd2L) appeared to decrease in abundance over time, while the highest thermostability allele (Bmy1-Sd2H) was the rarest allele at 5.4% of the sample and was virtually confined to two-row spring varieties. Pedigree analysis was used to track transmission of particular alleles over time and highlighted issues of genetic stratification of the sample.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.