Development of a matrix model for evaluating tree architecture regularity and its phenotypic variation patterns in Malus spp

The precise quantitative evaluation of three-dimensional tree architecture remains a major challenge in plant phenotyping research. Regularity is the macroscopic manifestation of developmental homeostasis and genetic canalization shaped during long-term plant evolution. Using 206 Malus spp. germplasms (encompassing species, North American cultivars, and self-bred cultivars) preserved in the National Repository of Crabapple Germplasm of China as experimental materials, this study introduces a two-dimensional matrix model into the evaluation of macroscopic three-dimensional tree architecture for the first time. By setting a coefficient of variation (CV) threshold of < 0.1 for structural traits, a tree architecture regularity matrix model [X Y Z] was constructed across three dimensions: macroscopic (X), branch (Y), and local detail (Z), from which a quantified Regularity Index (RI) was calculated. The results demonstrated the following: (1) Significant differentiation in tree architecture regularity occurred among Malus populations of different origins; species exhibited the highest regularity level (RI = 6.74), followed by self-bred cultivars (RI = 6.05), whereas North American cultivars showed a significantly reduced regularity index with the largest variance (RI = 4.66). (2) During artificial domestication and breeding, the local detail dimension (Z) of Malus was more prone to variation than its macroscopic structure, indicating that the decline in regularity followed an evolutionary pattern from local details to the overall structure. (3) Pedigree analysis of parents and offspring revealed that the RI of 25 descendant cultivars failed to exceed the maximum RI value of their respective parent species. The regularity evaluation system established in this study not only provides an auxiliary reference for the systematic classification and delimitation of Malus germplasms based on phenotypic evolutionary patterns, but also offers an innovative quantitative methodology and theoretical support for the early precise screening and directional breeding of tree architectural traits in woody ornamental plants.