44 research outputs found
Branching and SelfâOrganization in Marine Modular Colonial Organisms: A Model
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 motherâdaughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecologicalâphysiological 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 selfâorganized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with
râȘc
had a sigmoid logisticâlike 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 orderingâ and bifurcationâbased schemes
Branching and SelfâOrganization in Marine Modular Colonial Organisms: A Model
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 motherâdaughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecologicalâphysiological 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 selfâorganized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with
râȘc
had a sigmoid logisticâlike 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 orderingâ and bifurcationâbased schemes
Branching and SelfâOrganization in Marine Modular Colonial Organisms: A Model
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 motherâdaughter relationships among branches. We modeled both the intrinsic subapical branching along with an ecologicalâphysiological 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 selfâorganized criticality. Differences in branching among species with the same k values are determined by r (branching rate) and c. Species with
râȘc
had a sigmoid logisticâlike 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 orderingâ and bifurcationâbased schemes
BRCA and Beyond: Comprehensive Image-rich Review of Hereditary Breast and Gynecologic Cancer Syndromes
In addition to the well-characterize