Physical Phenomenology of Phyllotaxis

We propose an evolutionary mechanism of phyllotaxis, regular arrangement of leaves on a plant stem. It is shown that the phyllotactic pattern with the Fibonacci sequence has a selective advantage, for it involves the least number of phyllotactic transitions during plant growth

Rhombic Tilings and Primordia Fronts of Phyllotaxis

We introduce and study properties of phyllotactic and rhombic tilings on the cylin- der. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, and thus multi-jugate config- urations. We provide partial results toward proving that the attractor for S is entirely composed of rhombic tilings and is a strongly normally attracting branched manifold and conjecture that this attractor persists topologically in nearby systems. A key tool in understanding the geometry of tilings and the dynamics of S is the concept of pri- mordia front, which is a closed ring of tangent disks around the cylinder. We show how fronts determine the dynamics, including transitions of parastichy numbers, and might explain the Fibonacci number of petals often encountered in compositae.Comment: 33 pages, 10 picture

Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport

Morphogenesis during multicellular development is regulated by intercellular signaling molecules as well as by the mechanical properties of individual cells. In particular, normal patterns of organogenesis in plants require coordination between growth direction and growth magnitude. How this is achieved remains unclear. Here we show that in Arabidopsis thaliana, auxin patterning and cellular growth are linked through a correlated pattern of auxin efflux carrier localization and cortical microtubule orientation. Our experiments reveal that both PIN1 localization and microtubule array orientation are likely to respond to a shared upstream regulator that appears to be biomechanical in nature. Lastly, through mathematical modeling we show that such a biophysical coupling could mediate the feedback loop between auxin and its transport that underlies plant phyllotaxis

Analysis and Definition of the close-to-crop Area in Relation to Robotic Weeding

The objective of this paper is to analyse and define the field conditions close to the crop plants of sugar beet (Beta vulgaris L.). The aim is to use this study for the choice and development of new physical weeding methods to target weeds at individual plant scale level. It was found that the close to crop area is like a ring structure, comprising an area between an inner- and outer-circle around the sugar beet seedling. Physical weeding should not be applied to the area within the inner circle. The radius of the inner circle increases with the appearance of young beet leaves during the growth season. It was also found, that no weeds were germinating within 1 cm around individual sugar beet seedlings. Therefore this distance should be added to the radius of the inner circle. The space between the inner and outer circle is termed the close to crop area where physical weeding should be applied. The size of this area is defined by the developmental stage of the sugar beet fibrous root system and foliage. Thus, the determination of the growth stage of individual crop plants is necessary before any physical weeding can take place in the close to crop area. Uprooting, cutting between stem and root or damage of main shoot can do the physical control of most weed species located in the close to crop area. However, the targeting of weeds from above and from different angels above ground is limited in the close to crop area. This is caused by the fact that sugar beet leaves do not leave much space between leaves and ground and that our own study indicate that 26.4% of sugar beet plants at the 4-6 leaf stage are covering the main shoot of weeds. The most problematic weeds are the species, which have their main shoot and leaves located close to ground level. These species can either be controlled by damage of the main shoot or with a combination of shallow surface cutting and burial. Discrimination between weed species is beneficial under certain circumstances. First, the efficiency of the physical control of individual weed species is depending on the timing. Secondly some weeds species do not have significant negative impact on the yield, but instead leaving these species uncontrolled could benefit to an increased bio-diversity and reduced time and energy input for a physical weeding process. This paper is contributing to the ongoing Danish research project Robotic Weeding