Phyllotaxis: Leaf arrangement on a horizontal branch and crystallographic borders

Abstract

Phyllotaxis is an orderly arrangement of leaves on plant stems and branches. The natural reason of this arrangement is that each species based on the habitat conditions in the course of evolution in one way or another solved the problem of optimising the light flux reaching each leaf and providing photosynthesis. The found optimum was fixed in the genotype and became a species phenotypic trait. In a scientific study, it should be recorded with a reliability that allows for small fluctuations inherent in plant forms under the influence of the environment. Crystallography methods are used to describe the arrangement of leaves. In the course of the study, it has been proposed to describe the arrangement of leaves on a horizontal branch and a vertical stem using the theory of crystallographic borders in the first case, and helical axes – in the second. When describing the arrangement of leaves on a horizontal branch, seven types of crystallographic borders turned out to be theoretically consistent. The nomenclature of types according to the generating operations of symmetry is considered unambiguously fixing the orthogonal increment of a symmetrical sheet (PT, ST, RPT, PT*) and oblique – symmetrical and asymmetrical (T, T*, RT); their botanical prototypes have been established. The arrangement of leaves in many plants is not described by the proposed apparatus (they optimize the light flux differently), which guides scientists to search for deeper patterns and methods of mathematical description.