Branching and Self‐Organization in Marine Modular Colonial Organisms: A Model

Abstract

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 tree- like networks branch subapically, creating hierarchical mother- daughter relationships among branches. We modeled both the in- trinsic 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 sug- gesting self-organized criticality. Differences in branching among spe- cies with the same k values are determined by r (branching rate) and c. Species with had a sigmoid logistic-like growth with a long r K c asymptotic period before reaching k. Gorgonians exhibit c and r values in the range of the conditions for a stable equilibrium (c 1 or ). Ecological/physiological constraints limit growth r/2 c 1 r 1 0