Variations of growth in shoot apical domes of spruce seedlings: A study using the growth tensor

Abstract

Variations of the relative elemental rate of growth within apical domes, for the case when dome geometry changes during development, were modeled. It was ascertained that: 1) the domes of spruce seedlings have a paraboloidal shape; 2) the shape is maintained during growth, but the domes become higher and wider; 3) the relative elemental rate of growth in area on dome surface is isotropic, as indicated by analysis of cell packets in the surface layer. These data were used in modeling by means of the growth tensor and natural coordinate system. Growth of the dome was considered a superposition: 1) of relatively fast steady shape growth, where the isotropy of growth in area on the surface of the dome, was determined, and 2) of relatively slow isogonic growth, which does not disturb the isotropy. The convergent parabolic system was selected as the natural coordinate system. Distributions of the growth rates in the form of computer-made maps for three domes differing in age, were obtained. It appears that the growth rates within the dome are relatively high in the distal part and smaller in the central and peripheral regions. This variation decreases progressively with seedling age when the dome becomes wider. The relative elemental rate of growth in volume, averaged for the whole dome, also decreases.