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| Pointing out that the published experimental facts regarding development of sunflower capitulum can be understood better if the capitulum meristem is similar in size with the shoot apical meristem (SAM) of Arabidopsis, and then assuming that it functions also similarly as the Arabidopsis SAM, a model is proposed for the floral phyllotaxis of sunflower, which consists of the following three key points. The primordium initiation process of sunflower capitulum is interpreted as, in terms of mathematics, being equivalent to a series of hyperbolic rotations. To take advantage of the unique character of the hyperbolic-rotation transformation of a hyperbolic object, so to make the hundreds of primordia well organized on the capitulum, the meristem must be able to initiate primordia with a divergence angle of around 137.5°, so to form a quasi-hyperbolic object. This is why meristems possessing this capability are chosen by natural selection in evolution. Although random errors in divergence angles do make the floral patterns only quasi-hyperbolic, but do not block their development into a floral phyllotaxis with a Fibonacci ratio like 89:55, because the errors can be reduced step by step and spontaneously in the hyperbolic-rotation growth process. |
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| Keywords:sunflower capitulum;phyllotaxis;meristem;primordium initiation;hyperbolic rotation |
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