A FUNDAMENTAL PROBLEM IN PLANT MORPHOGENESIS FROM THE STANDPOINT OF DIFFERENTIAL GROWTH

Abstract It is well known that the organization and functioning of the plant apex is profoundly influenced by differential growth, and allametry, represented by an equation of the type Y = aX b , is one of its expression. From the point of view of allometry, phyllotaxis, or the study of the arrangements of the primordia on the plant apex, received but very little mathematical consideration. The aim of this paper is to deliver allometric relations within the apex, between the radial primordial spacing, represented by r (the rise in the cylindrical representation of phyllotaxis) or by R (the plastochrone ratio in the centric representation), and any arrangement (m,n) of the primordia. These relations are r = klogR = p(β) (m+n) −2 , where p(β) is a constant, given the angle of intersection β of the opposed parastichies on which the primordia are distributed.