Branching structure in arborescent animals: Models of relative growth

Many invertebrate animals belonging to diverse phyla grow as regularly branching structures with the general appearance of miniature trees. If it is assumed that regularity of branching implies regularity in growth, models can be mathematically derived to depict growth of such a structure as a set of changing morphologic properties. Modes of growth, branching properties, and growth models can be expected to differ markedly from one major taxonomic group to another. Nevertheless, these properties can furnish a useful basis for comparing adaptive morphologies and underlying mechanical designs not only among arborescent animals, but with arborescent plants as well.Branching structures of some cheilostome bryozoans with rigidly erect, arborescent growth habits are inferred to result from continuous growth at steadily increasing numbers of growing tips through a process of repeated bifurcation and lengthening. In a model of continuous growth, the pattern by which the number of growing tips increases can be shown to be a generalized mathematical series, of which the Fibonacci series and a geometric series are two special cases. The quantities which determine the series can be calculated from measurable properties of the branching structure: lengths of paired branch portions ending in growing tips (relative growth ratio), lengths of paired branch portions between bifurcations (mean link length and link-length ratio), and numbers of branch portions belonging to different orders (branching ratio). Data for eight species of cheilostome bryozoans indicate, with high levels of confidence, that measurable branching properties and the models of relative growth inferred from them are species-specific. This specificity and a tendency to adhere to characteristic values of branching properties during growth are apparently direct expressions of internal control in these bryozoans.