Geometric consequences of branching growth in adeoniform Bryozoa

Abstract

Many cheilostome bryozoans of diverse phylogenetic origin grow as erect, arborescent colonies with branches of modified planar form composed of two layers of zooids back to back. Regular branching enables a growing colony to expand in surface area, and hence in the number of zooids that feed, reproduce, and perform other vital functions, at an accelerating rate. During growth, branches first all diverge, then increasingly converge, and in late stages of growth begin to interfere with each other's growth and function. Interference can set limits to the width and thickness of branches and hence to the number and size of zooids.Simulation of growth using a 3–dimensional mathematical model shows that a narrow range of possible values of branching angles minimizes branch interference in late growth stages. These values are prevalent in fossil and modern species. Branch spacing at later growth stages is correlated with the distance between branches at first crossing, providing room for feeding organs of the two facing layers of zooids to protrude and function. Interbranch distances dwindle as branches increasingly converge, so emphasis on minimizing interference at a late stage sets a practical limit to growth beyond that stage. To gain this long-term benefit requires adhering to a regular pattern throughout growth. The considerable variation in branching properties in fossil and modern species, and a variability in spacing inherent in the growth pattern itself, limit the amount of usable interbranch space. Despite a higher intraspecific variability, branching properties are as distinctive interspecifically as zooidal properties, and variability is randomly distributed through the colony. A small reduction in variability between fossil and modern species suggests that increasing regularity may provide a selective advantage in the utilization of interbranch space.