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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

Abstract

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.

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Articles
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Canu, F. and Bassler, R. S. 1929. Bryozoa of the Philippine Region. U.S. Natl. Mus. Bull. 100:1685.Google Scholar
Cheetham, A. H., Hayek, L.-A. C., and Thomsen, E. 1980. Branching structure in arborescent animals: models of relative growth. J. Theor. Biol. 85:335369.Google Scholar
Cheetham, A. H., Hayek, L.-A. C., and Thomsen, E. 1981. Growth models in fossil arborescent cheilostome bryozoans. Paleobiology. 7:6886.Google Scholar
Cheetham, A. H. and Thomsen, E. 1981. Functional morphology of arborescent animals: strength and design of cheilostome bryozoan skeletons. Paleobiology. 7:355383.Google Scholar
Cohen, D. 1967. Computer simulation of biological pattern generation processes. Nature. 216:246248.Google Scholar
Condra, G. E. and Elias, M. K. 1944. Study and revision of Archimedes . Geol. Soc. Am. Sp. Papers. 53:1243.Google Scholar
Cook, P. L. 1977. Colony-wide water currents in living Bryozoa. Cah. Biol. Mar. 18:3147.Google Scholar
Gardiner, A. R. and Taylor, P. D. 1980. Computer modelling of colony growth in a uniserial bryozoan. J. Geol. Soc. London. 137:107.Google Scholar
Gould, S. J. and Katz, M. 1975. Disruption of ideal geometry in the growth of receptaculitids: a natural experiment in theoretical morphology. Paleobiology. 1:120.Google Scholar
Gould, S. J. and Lewontin, R. C. 1979. The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme. Proc. R. Soc. London B. 205:581598.Google Scholar
Harmer, S. F. 1931. Recent work on Polyzoa. Proc. Linnean Soc. London, sess. 143, 1930–31, pt. viii: 113–168.Google Scholar
Honda, H. 1971. Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the shape of the tree-like body. J. Theor. Biol. 31:331338.Google Scholar
Jackson, J. B. C. 1979. Morphological strategies of sessile animals. Pp. 499555. In: Larwood, G. and Rosen, B. R., eds. Biology and Systematics of Colonial Animals. Academic Press; London.Google Scholar
Jacobson, G. G. 1980. Computer modeling of morphogenesis. Am. Zool. 20:669677.Google Scholar
McGhee, G. R. Jr. 1978. Analysis of the shell torsion phenomenon in the Bivalvia. [Konstruktions-morphologie Nr. 91.] Lethaia. 11:315329.Google Scholar
McGhee, G. R. Jr. 1980a. Shell form in the biconvex articulate Brachiopoda: a geometric analysis. Paleobiology. 6:5776.Google Scholar
McGhee, G. R. Jr. 1980b. Shell geometry and stability strategies in the biconvex Brachiopoda. N. Jb. Geol. Paläont. Mh. 1980(3):155184.Google Scholar
McKinney, F. K. 1979. Some paleoenvironments of the coiled fenestrate bryozoan Archimedes . Pp. 321336. In: Larwood, G. P. and Abbott, M. B., eds. Advances in Bryozoology. Academic Press; London.Google Scholar
McKinney, F. K. 1980a. The Devonian fenestrate bryozoan Utropora Počta. J. Paleontol. 54:241252.Google Scholar
McKinney, F. K. 1980b. Erect spiral growth in some living and fossil bryozoans. J. Paleontol. 54:597613.Google Scholar
McKinney, F. K. 1981. Planar branch systems in colonial filter feeders. Paleobiology. 7:344354.Google Scholar
McKinney, F. K. and Gault, H. W. 1980. Paleoenvironment of Late Mississippian fenestrate bryozoans, eastern United States. Lethaia. 13:127146.Google Scholar
McKinney, F. K. and Stedman, T. G. 1981. Constancy of characters within helical portions of Archimedes . Pp. 151157. In: Larwood, G. P. and Nielsen, C., eds. Recent and Fossil Bryozoa. Olsen and Olsen; Fredenborg, Denmark.Google Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. J. Paleontol. 40:11781190.Google Scholar
Raup, D. M. 1968. Theoretical morphology of echinoid growth. J. Paleontol. 42:5063.Google Scholar
Raup, D. M. 1970. Modeling and simulation of morphology by computer. Proc. N. Am. Paleontol. Conv., Part B:7183.Google Scholar
Raup, D. M. and Michelson, A. 1965. Theoretical morphology of the coiled shell. Science. 147:12941295.Google Scholar
Seilacher, A. 1970. Arbeitskonzept zur Konstruktions-Morphologie. Lethaia. 3:393396.Google Scholar
Shulga-Nesterenko, M. I. 1955. Kamennougol'nye mshanki Russkoy platformy. Akad. Nauk SSSR Paleontol. Inst. Trudy. 57:1207.Google Scholar
Starcher, R. W. 1980. Computer simulation of bryozoan colony development. Geol. Soc. Am. Abstr. with Progr. 12:257.Google Scholar
Thompson, D'Arcy W. 1942. On Growth and Form. 2nd ed. 1116 pp. University Press; Cambridge.Google Scholar
Ward, P. 1980. Comparative shell shape distributions in Jurassic-Cretaceous ammonites and Jurassic-Tertiary nautilids. Paleobiology. 6:3243.Google Scholar
Winston, J. E. 1977. Feeding in marine bryozoans. Pp. 233271. In: Woolacott, R. M. and Zimmer, R. L., eds. Biology of Bryozoans. Academic Press; New York.Google Scholar