A Binary-Based Matrix Model for Malus Corolla Symmetry and Its Variational Significance

Floral symmetry (corolla symmetry) has important biological significance in plant genetics and evolution. However, it is often multi-dimensional and difficult to quantify. Here, we constructed a multi-dimensional data matrix [X Y Z] by extracting three qualitative variables with binary properties (X: corolla regularity of interval and coplanarity; Y: petal regularity of shape and size; Z: petal local regularity of curling and wrinkle) from different dimensions of petals (overall to individual, and then to the local): all petals (corolla), individual petals, and local areas of petals. To quantitatively express the degree of Malus corolla symmetry, these variables were then combined with weight assignments (X: 2(2) > Y: 2(1) > Z: 2(0)) based on their contributions to the corolla symmetry and the algorithm rule of converting binary to decimal values, which facilitated the unification of qualitative and quantitative analyses. Our results revealed significant reduction in degrees of Malus corolla symmetry along the direction of local to overall. Species showed higher degree of corolla symmetry than cultivars; however, taxa with stronger corolla symmetry might not necessarily be species. These findings provide new insights into the circumscription of Malus controversial species. The matrix model should be reference for future evaluation of angiosperm flower symmetry (lack of corolla fusion).