Morphogenesis of uniaxiate graptoloid colonies—a mathematical model

Abstract

Morphological gradients in graptoloid colonies are explained by the production and diffusion of a morphogen from the sicula distalwards. Size of the thecae is inversely related to the amount of morphogen present. The graduate decrease of morphogen is given by a set of algebraic equations, and its effect on zooid growth is described by a modified Michaelis-Menten relationship. Changes in size of thecae computed on the basis of these equations fit the changes observed in graptolite colonies. Sets of differential equations are also given to describe the rate of morphogen diffusion and some other processes possibly involved in the development of uniaxiate graptoloid colonies. The suggested basic model of these colonies can be completed by a number of additional assumptions; however, computer experiments reveal that such assumptions do not affect the main properties of the model, namely the appearance of graded series of thecae. New evidence for regeneration of the sicular portion of the broken rhabdosome is presented, providing arguments that morphogen was produced by the siculozooid as a single bolus of secretion. Some local exclusions from the regular size gradient are discussed, and tentative explanations are suggested.