Comparison of tree architecture using tree edit distances: application to 2-year-old apple hybrids

Abstract

In fruit trees, understanding genetic determinisms of architectural traits is considered as a promising manner to control vegetative development and yield regularity. In this context, our study aimed to classify 2-year-old apple hybrids on the basis of their architectural traits. From a fine phenotyping, trees were described as tree graphs, including topological and geometric information. To evaluate the similarity between trees, comparison methods based on edit operations (substitution, insertion and deletion) were carried out. Distance between two tree graphs was computed by minimising the sum of the costs of the edit operations applied to transform one tree into another. Two algorithms for the comparison of unordered and partially ordered tree graphs were applied to a sub-sample of the population, taking into account several geometric attributes. For each comparison, a dissimilarity matrix was computed, and subsequently trees were clustered. A local interpretation of the matched entities was proposed through schematic representations of the trees, and similarities between trees were analysed within and between clusters. The tree graphs, both unordered or partially ordered and whether the attributes were considered or not, were grouped, by clustering, according to the number of entities per tree. The robustness of the unordered comparison was demonstrated by its application to the whole population, since it provided results similar to those obtained on the sub-sample. Further developments towards a higher relative weight of geometric versus topological information are discussed in the perspective to define an architectural ideotype in apple.