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 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.

Branch to colony trajectory in a modular organism: Pattern formation in the Indo‐Pacific coral Stylophora pistillata

“…1b (Rinkevich and Loya, 1985a). As in other colonial organisms Sá nchez and Lasker, 2003;Sá nchez et al, 2004), these developmental patterns may reveal evolutionary fixed robustness of morphological integration. This study focuses on identification of such a suite of architectural rules for colony pattern formation and branch morphometric forms among colonies of Stylophora pistillata from the Red Sea.…”

“…The literature (Bell, 1986;Rosen, 1986;Dauget, 1991b;Abraham, 2001;Kaandorp and Kubler, 2001;Merks, 2003;Sá nchez et al, 2004) considers the development of modular organisms, including coral colonies, as an iterative process. In this process, a colony is being constructed by adding identical modules through the same pathway of development (Jackson, 1979;Dauget, 1991b;Lasker et al, 2003;Sá nchez and Lasker, 2003;Sá nchez et al, 2004).…”

“…In this process, a colony is being constructed by adding identical modules through the same pathway of development (Jackson, 1979;Dauget, 1991b;Lasker et al, 2003;Sá nchez and Lasker, 2003;Sá nchez et al, 2004). According to this tenet, the basic architectural rules remain the same during the entire development.…”

“…A fundamental requirement for understanding development is comprehension of the relationships between genes and morphologies (Nijhout et al, 1986;Sá nchez et al, 2004). Such relationships are elucidated, experimentally, by several methodologies.…”

Patterns of morphological integration in marine modular organisms: supra-module organization in branching octocoral colonies

“…B (2003) positional differences among them. Branching in holaxonian octocorals (which are gorgonian corals) is a subapical process where branches, 'mother branches', produce new branches, 'daughter branches', at roughly fixed distances or internodes (Sánchez et al 2003d ). The process of branching can be described by an array of colony-level traits such as the length of a daughter branch and the length of internodes (the distance between daughter branch points; figure 1).…”