Sánchez Juan Armando, Lasker Howard R, Nepomuceno Erivelton G, Sánchez J Dario, Woldenberg Michael J
Department of Biological Sciences, University at Buffalo, State University of New York, Buffalo, New York 14260, USA.
Am Nat. 2004 Mar;163(3):E24-39. doi: 10.1086/382139. Epub 2004 Feb 17.
Despite the universality of branching patterns in marine modular colonial organisms, there is neither a clear explanation about the growth of their branching forms nor an understanding of how these organisms conserve their shape during development. This study develops a model of branching and colony growth using parameters and variables related to actual modular structures (e.g., branches) in Caribbean gorgonian corals (Cnidaria). Gorgonians exhibiting treelike networks branch subapically, creating hierarchical mother-daughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecological-physiological limit to growth or maximum number of mother branches (k). Shape is preserved by maintaining a constant ratio (c) between the total number of branches and the mother branches. The size frequency distribution of mother branches follows a scaling power law suggesting self-organized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with r<<c had a sigmoid logistic-like growth with a long asymptotic period before reaching k. Gorgonians exhibit c and r values in the range of the conditions for a stable equilibrium (c>r/2 or c>r>0). Ecological/physiological constraints limit growth without altering colony form or the interaction between r and c. The model described the branching dynamics giving the form to colonies and how colony growth declines over time without altering the branching pattern. This model provides a theoretical basis to study branching as a simple function of the number of branches independently of ordering- and bifurcation-based schemes.
尽管分支模式在海洋模块化群体生物中普遍存在，但对于它们分支形式的生长既没有清晰的解释，也不清楚这些生物在发育过程中是如何保持其形状的。本研究利用与加勒比柳珊瑚（刺胞动物门）实际模块化结构（如分支）相关的参数和变量，建立了一个分支和群体生长模型。呈现树状网络的柳珊瑚在亚顶端分支，在分支之间形成层次化的母女关系。我们对内在的亚顶端分支以及生长的生态生理极限或母分支的最大数量（k）进行了建模。通过保持分支总数与母分支之间的恒定比率（c）来保持形状。母分支的大小频率分布遵循标度幂律，表明存在自组织临界性。具有相同k值的物种之间分支的差异由r（分支率）和c决定。r<<c的物种具有类似S形逻辑斯蒂的生长，在达到k之前有一个很长的渐近期。柳珊瑚的c和r值处于稳定平衡条件的范围内（c>r/2或c>r>0）。生态/生理限制限制了生长，而不会改变群体形态或r与c之间的相互作用。该模型描述了赋予群体形状的分支动态以及群体生长如何随时间下降而不改变分支模式。该模型为研究分支作为分支数量的简单函数提供了理论基础，而与基于排序和分叉的方案无关。
