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首页> 外文期刊>Mathematical Biosciences: An International Journal >A growth-controlled model of the shape of a sunflower head
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A growth-controlled model of the shape of a sunflower head

机译：向日葵头形状的生长控制模型

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A mathematical model is presented which predicts the shape of a sunflower receptacle (or the compact receptacle of various other taxa) and the pattern of its floral parts (florets) from the time of their initiation to maturity. The model assumes that the expansion and curving of the receptacle surface is just sufficient to accommodate the development of the florets, thus minimizing the quantity of plant tissue involved. The model assumes a fixed angular separation (divergence) between successive florets, an S-shaped (sigmoidal) growth function followed by each florets, and a fixed time delay (period) between the initiation of successive florets. It is further assumes that the shape and relative position occupied by the florets on the receptacle surface are invariant in time. By this theory, the shape of the receptacle surface is fully determined once the mathematical form of the growth function is specified. Using the logistic growth function, the theory is tested against the measured shapes of plant receptacles from different taxa at various points in their development. The least-squares adjusted fits to the theory are, in most cases, very good indeed. (C) 2003 Elsevier Inc. All rights reserved. [References: 21]
机译：提出了一个数学模型，该数学模型预测了向日葵容器（或其他各种分类单元的紧凑容器）的形状以及从开花到成熟时其花部（小花）的图案。该模型假定容器表面的膨胀和弯曲刚好足以适应小花的发育，从而使所涉及的植物组织数量最少。该模型假设连续的小花之间具有固定的角度间隔（散度），每个小花后面都具有S形（S型）增长函数，并且在连续的小花起始之间具有固定的时间延迟（周期）。进一步假设小花在容器表面上占据的形状和相对位置在时间上是不变的。通过该理论，一旦指定了增长函数的数学形式，就可以完全确定容器表面的形状。使用逻辑增长函数，针对来自不同分类单元的植物容器在其发展的各个阶段所测量的形状，对该理论进行了测试。在大多数情况下，对理论进行最小二乘调整的拟合确实非常好。 （C）2003 Elsevier Inc.保留所有权利。 [参考：21]

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