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A Turn in the Right Direction: Simulation of Erect Spiral Growth in the Bryozoans Archimedes and Bugula

Published online by Cambridge University Press:  14 July 2015


Colonies of the fossil bryozoan Archimedes and erect, spiralled species of the living bryozoan Bugula consist of wedge-shaped systems of radially diverging, bifurcated branches that extend from a helical axial margin. Morphology of these colonies may be simulated using few growth rules. These include 1) radius of the central helical margin (RAD), 2) rate of climb of central helical margin (ELEV), 3) radial angle between successive branches that originate from the central helical margin (ANG), 4) radial growth of all branches, 5) angle between branches and axis of central helical margin (BWANG), 6) distance between three adjacent, radially diverging branches at which the central branch bifurcates into two branches equally spaced between the two side branches (XMIN), and 7) placement of a spacing bar at base of newly bifurcated branches. In addition, size constraints on the simulations must be stipulated.

Simulations are begun at a proximal point along the central helix where a radial branch originates and are “grown” in repetitive steps by extending the central helical margin a distance distally, determined by ANG, then censusing established branches for XMIN in order to bifurcate appropriate branches and extend others in several short growth increments, etc. Growth of branches ceases at stipulated maximum width, and growth of the entire simulation ceases at stipulated maximum height.

The presence of a helical inner margin marked by uniformly spaced bifurcations generates the spiralled shape, i.e. ELEV must be a positive number. Values of RAD, ELEV (not zero), ANG and BWANG determine form of the spiral; the other growth rules apply to bifurcated unilaminate branch systems in general.

The range of observed colony forms and hypothetical morphospace of Archimedes may be simulated by varying BWANG, XMIN, and ELEV. RAD was kept constant, as its variation would be redundant with XMIN and ELEV. Variation in ANG affects near-helix morphology, but its influence is undetectable beyond this zone. Variability within colonies may be simulated by assigning to each variable a standard deviation with mean-centered randomly chosen values for each decision.

Copyright © The Paleontological Society 

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