Current progress in theoretical morphospace analyses

The discipline of theoretical morphology is still in its infancy (McGhee, 1999, 2001a). Even so, a considerable number of different forms of life have been the subject of theoretical morphospace analyses to the present date (Table 9.1). Much work has been done with organisms that possess shells, such as brachiopods, cephalopods, gastropods and bivalves. This is due to the fact that all of these organisms grow by simple accretion, and accretionary growth systems are some of the easiest to model mathematically (for a detailed example of such modelling, see McGhee 1999). Other organisms appear to be radically different but in fact can be modelled by geometries that are strikingly similar. These morphologies include those possessed by trees, which are land-dwelling plants, and bryozoans, which are ocean-dwelling animals! Both groups of organisms use branching growth systems, and models designed to produce hypothetical tree morphologies often can be used to model many bryozoan forms as well.

Other groups of organisms, such as arthropods and vertebrates, have very intricate skeletal morphologies and are much more difficult to model. Here theoretical morphologists have begun to analyse these organisms by simply modelling parts of arthropod or vertebrate morphology, rather than the much more complex total.

Most theoretical morphologic simulations these days are programmed in BASIC or C/C++ for the microcomputer, your standard PC. My first simulations of shell form in brachiopods, back in the 1970s, were written in FORTRAN for mainframe computers. Even further

Table 9.1. Selected groups of organisms that have been the subject of theoretical morphospace analyses. For a detailed review of many of these studies see McGhee (1999)


Silicoflagellates (delicate silica-lattice skeletal forms): McCartney and Loper (1989, 1992).

Foraminiferids (delicate calcareous-sphere skeletal forms): Berger (1969), Brasier (1980), Signes et al. (1993), Tyszka and Topa (2005), Tyszka (2006).


Stromatoporoids (ancient forms of calcareous sponges): Kershaw and Riding (1978), Swan and Kershaw (1994).

Bryozoans (delicate colony forms of moss animals): McKinney and Raup (1982), Cheetham and Hayek (1983), McGhee and McKinney (2000, 2002), Starcher and McGhee (2000, 2002), McKinney and McGhee (2003, 2004), McGhee and Starcher (2006).

Brachiopods (shell forms of the lampshell animals): Raup (1966), McGhee (1980a, 1980b, 1995, 1999), Okamoto (1988), Ackerly (1989).

Cephalopods (chambered shell forms of swimming molluscs): Raup (1966, 1967), Chamberlain (1981), Ward (1980), Bayer and McGhee (1984), Saunders and Swan (1984), Okamoto (1988), Ackerly (1989), Dommergues, Laurin, and Meister (1996), Korn (2000), Checa, Okamoto, and Keupp (2002), Wolfram (2002), Saunders, Work, and Nikolaeva (2004), McGowan (2004), Hammer and Bucher (2005).

Gastropods (spired shell forms of the snails): Raup and Michelson (1965), Raup (1966), Davoli and Russo (1974), Kohn and Riggs (1975), Rex and Boss (1976), Cain (1977), Williamson (1981), Okamoto (1988), Ackerly (1989), Schindel (1990), Stone (1996, 1998, 1999, 2002, 2004), Wolfram (2002).

Bivalves (bivalved shell forms of clams, scallops, and kin): Raup (1966), Savazzi (1987), Okamoto (1988), Ackerly (1989, 1992), Wolfram (2002), Ubukata (2000, 2001, 2003a, 2003b, 2005).

Echinoderms (plated skeleton forms of echinoids and kin): Waters (1977), Ellers (1993), Kendrick (2007).

Hemichordates (delicate colony forms of graptolites): Fortey (1983), Starcher and McGhee (2003), McGhee and Starcher (2006).

Urochordates (larval swimming morphologies): McHenry and Patek (2004).

Chondrichthyans (denticle scale skins of sharks): Reif (1980).


From primitive stem plants to bushes, shrubs, and trees: Honda and Fisher (1978), Niklas and Kerchner (1984), Ellison and Niklas (1988), Niklas (1986, 1997a, 1997b, 2004, 2006).

Leaf morphologies: Wolfram (2002), Zwieniecki, Boyce, and Holbrook (2004).


Reptiles (archosaur pelvic morphologies): Rasskin-Gutman and Buscalioni (2001 ).

Birds (scavenger guild morphologies): Hertel and Lehman (1998).

Mammals (predatory guild morphologies): Van Valkenburgh (1985, 1988).

Mammals (primate facial morphologies): Richtsmeier and Lele (1993).


All marine or terrestrial animals that possess skeletons, internal or external: Thomas and Reif (1993), Thomas et al. (2000), Thomas (2005).

back in time the founder of theoretical morphology, Dave Raup, used analogue computers to produce the simulation graphics on oscilloscope screens! At a conference on 'Computational Approaches to Theoretical Morphology', called by the Santa Fe Institute in November of 2000, the computer scientist Przemyslaw Prusinkiewicz noted that Dave Raup's early computer simulations of growth in molluscs (Raup, 1961) used computer graphics two years before 'computer graphics' had been established as a field (Przemyslaw Prusinkiewicz, quoted in McGhee, 2001a) in that Foley and Van Dam (1982, p. 18) state that the 'beginnings of modern interactive computer graphics are found in Ivan Sutherland's seminal Ph.D. work on the Sketchpad system (1963)'.

Several published sources of source code for computer programs used in theoretical morphological simulations of organic form are given in Table 9.2 (see also the 'problem-solving environment' approach to computer simulation of Merks et al., 2006). Unfortunately, many scientific journal editors are reluctant to publish computer source code, as the per-page costs for printing those journals is expensive, thus the list given in Table 9.2 is not as long as I would like it to be. Things are changing, however, and with the advent of electronic publishing and personal Websites on the Internet, much more information will become easily available in the future.

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