Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
Limits in the evolution of biological form: a theoretical morphologic perspective rsfs.royalsocietypublishing.org
George R. McGhee Jr Department of Earth and Planetary Sciences, Wright-Rieman Laboratories, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854, USA
Research Cite this article: McGhee GR Jr. 2015 Limits in the evolution of biological form: a theoretical morphologic perspective. Interface Focus 5: 20150034. http://dx.doi.org/10.1098/rsfs.2015.0034
Limits in the evolution of biological form can be empirically demonstrated by using theoretical morphospace analyses, and actual analytic examples are given for univalved ammonoid shell form, bivalved brachiopod shell form and helical bryozoan colony form. Limits in the evolution of form in these animal groups can be shown to be due to functional and developmental constraints on possible evolutionary trajectories in morphospace. Future evolutionary-limit research is needed to analyse the possible existence of temporal constraint in the evolution of biological form on Earth, and in the search for the possible existence of functional alien life forms on Titan and Triton that are developmentally impossible for Earth life.
One contribution of 12 to a theme issue ‘Are there limits to evolution?’ Subject Areas: astrobiology, computational biology, synthetic biology Keywords: evolutionary limits, evolutionary constraints, theoretical morphospaces, Ammonoidea, Brachiopoda, Bryozoa Author for correspondence: George R. McGhee Jr e-mail: [email protected]
1. Limits in evolution: analytic examples Actual analytic examples of limits in the evolution of biological form in theoretical morphospaces are given in figures 1–3, summarized in table 1, and are discussed in this section of the paper. Theoretical morphospaces are ‘n-dimensional geometric hyperspaces produced by systematically varying the parameter values of a geometric model of form’ [2] and are particularly useful in the analysis of limits in evolution in that they contain computer simulations of both existent and non-existent biological form and hence contain the limit boundary between those two regions of the morphospace (for an overview of the technique of theoretical morphospace analysis, see [1,2]). In figure 1 is given a two-dimensional plane within a four-dimensional theoretical morphospace of computer-simulated planispiral univalved shell forms created by Raup [3] for the analysis of evolution in ancient nektonic cephalopods. The two dimensions of the space are W, the whorl expansion rate of the shell, and D, the distance from the coiling axis to the aperture of the shell (for a detailed discussion of the morphospace, see [1]). This morphospace was used by Raup [3] in the analysis of 405 species of ammonoids (Mollusca: Cephalopoda: Ammonoidea), and by Saunders et al. [4] in the analysis of an additional 597 species. Their combined analyses revealed that those shell geometries contained within the polygon boundaries illustrated in the lower left corner of figure 1 exist in actual ammonoids—all other simulated shell forms are geometrically possible but are non-existent in these ancient nektonic cephalopods. Why did the ammonoids evolve some geometrically possible shell forms but not others? The polygonal boundary line shown in figure 1 maps a hydrodynamic limit to the evolution of shell forms by the nektonic cephalopods within the theoretical morphospace (table 1). Chamberlain [5] measured drag coefficients in flume experiments with model shell forms that have been used to calculate a swimmingefficiency coefficient (SEC) for all of the shell geometries shown in figure 1. All shell forms evolved by the ammonoids have a minimum limit of SEC ¼ 40; all shell geometries outside of the polygon in figure 1 have SEC values less than this limit (for example, the non-existent ammonoid shell form shown at the coordinates W ¼ 3.5, D ¼ 0.5 has SEC ¼ 8). Not surprisingly, this same hydrodynamic limit holds for shell forms of the other major clade of nektonic cephalopods, the nautiloids (Mollusca: Cephalopoda: Nautiloidea). For example, the convolute shells of the living Nautilus
& 2015 The Author(s) Published by the Royal Society. All rights reserved.
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
2
rsfs.royalsocietypublishing.org
4.5 0.50 ELEV
3.5
W
0.20
2.5 0.05 70
50
90
BWANG
0.1
0.3
0.5
0.7
D
Figure 1. A theoretical morphospace of computer-simulated ammonoid shell form, where the forms shown within the limits of the polygon boundary in the lower left corner of the figure actually exist in ammonoid cephalopods. Adapted from McGhee [1].
dorsal valve log W
30
13 12 11 10 9 8 7 6 5 4 3 2 1
Figure 3. A theoretical morphospace of computer-simulated helical bryozoan colony form, where the forms shown within the limits of the polygon boundary in the centre of the figure actually exist in helical bryozoans. Adapted from McGhee [1].
Table 1. Limits in the evolution of cephalopods, brachiopods and bryozoans. swimming cephalopod shell forms hydrodynamic limit: minimum SEC ¼ 40 for functional shell forms biconvex brachiopod shell forms internal volume limit: minimum volume-to-surface-area ratio ¼ 7 for functional shell forms whorl overlap limit: minimum dorsal log W ¼ 3, ventral log W ¼ 2, for functional shell forms helical bryozoan colony forms filtration efficiency limit: minimum colony SAI ¼ 0.5 and BDI ¼ 25
1
2
3
4
5 6 7 8 9 10 11 12 13 ventral valve log W
Figure 2. A theoretical morphospace of computer-simulated brachiopod shell form, where the forms shown within the limits of the polygon boundary in the centre of the figure actually exist in biconvex brachiopods. Adapted from McGhee [1].
have W ¼ 3.4 and D ¼ 0.04 [3] and are very similar in appearance to the shell form shown at coordinates W ¼ 3.5, D ¼ 0.1 within the polygon boundaries in figure 1. A second example of limits in evolution is given in figure 2, which illustrates a plane within a seven-dimensional theoretical morphospace of planispiral bivalved shell forms created for the analysis of evolution in brachiopods [1]. The two dimensions of the space are logarithms of the whorl expansion rate, log W, for the dorsal and ventral valves of the brachiopod shell. This morphospace has been used in the analysis of 324 species of biconvex brachiopods (Brachiopoda: Rhynchonelliformes: Rhynchonellata) and has revealed that those shell forms contained within the polygon boundaries illustrated in the centre of figure 2 exist in biconvex brachiopods. As with the ammonoid shell forms, simulated shell forms outside of the polygon are geometrically possible but are non-existent in biconvex brachiopods.
for functional colony forms hydraulic resistance limit: maximum colony SAI ¼ 7 and BDI ¼ 60 for functional colony forms
Why do the biconvex brachiopods evolve some geometrically possible shell forms but not others? The polygonal boundary line shown in figure 2 actually maps two separate limits to the evolution of shell forms by biconvex brachiopods within the theoretical morphospace (table 1). The first is an internal volume limit: biconvex brachiopods use a tentacular pumping and feeding organ, the lophophore, to partition the interior of their shells into inhalent and exhalent filtration chambers for the purpose of filter-feeding seawater. The lophophore is coiled in a variety of three-dimensional geometries in living and fossil biconvex brachiopods, and all lophophore coil geometries require sufficient internal shell volume, V, to be contained within the external surface area, SA, of the shell—a proportion that is measured by a volume-to-surface-area ratio, V/SA [1]. All shell forms evolved by the biconvex brachiopods have a minimum limit of V/SA ¼ 7; shell form geometries with V/SA ratios below this limit are non-existent in biconvex brachiopods (for example, the non-existent biconvex brachiopod shell form shown at coordinates dorsal log W ¼ 13, ventral log W ¼ 13 has V/SA ¼ 5.5).
Interface Focus 5: 20150034
10
1.5
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
f:0
3 functional constraint boundary
f:3
f :1 developmental constraint boundary
f :2
Figure 4. Venn diagram of theoretically possible regions of form determined by the limits of functional and developmental constraint within theoretical morphospace. Forms f:0 are non-functional and developmentally impossible for life on Earth, forms f:1 are both functional and developmentally possible, forms f:2 are developmentally possible but non-functional and forms f:3 are functional but developmentally impossible for life on Earth. Adapted from McGhee [12].
maintain minimum limits of SAI ¼ 0.5 and BDI ¼ 25, and maximum limits of SAI ¼ 7 and BDI ¼ 60 [8 –10]. The minimum limits of SAI ¼ 0.5 and BDI ¼ 25 appear to be filtration efficiency limits (table 1) in that colonies with colony surface areas and branch densities less than those limits simply do not catch or intercept enough food across their filtration sheets to support the metabolic needs of the colony (i.e. too much water escapes unfiltered through the colony). The maximum limits of SAI ¼ 7 and BDI ¼ 60 appear to be hydraulic resistance limits (table 1) in that colonies with colony surface areas and branch densities higher than those limits impede the flow of water through the colony [11] and dead zones of stagnant water develop within the colony centre (see discussion in [1]). For example, the non-existent colony geometry at coordinates ELEV ¼ 0.50, BWANG ¼ 90 in figure 3 has SAI , 0.5 and, at the other extreme, the non-existent colony geometry at coordinates ELEV ¼ 0.20, BWANG ¼ 10 has SAI ¼ 15.
2. Limits in evolution: theoretical possibilities The observed empirical limits in the evolution of actual animals illustrated in figures 1–3 are abstracted to theoretical limits in a theoretical morphospace in figure 4. Two types of limit in the evolution of biological form are graphically portrayed within the morphospace of hypothetical forms: limits due to functional constraint (the boundaries of the solid-line rectangle) and limits due to developmental constraints (the boundaries of the dotted-line rectangle). Empirical examples of actual functional constraint limits are illustrated in figures 1–3; these are the hydrodynamic, internal volume, filtration efficiency and hydraulic resistance limits (table 1) discussed in the previous section of the text. Biological forms shown within the limit boundaries shown in figures 1–3 are functional for the animals analysed, forms outside the limit boundaries are not. An empirical example of an actual developmental constraint limit is seen in the brachiopod whorl overlap limit (figure 2 and table 1). The region of morphospace outside the whorl overlap limit does not contain non-functional forms; rather, this region contains geometrically impossible
Interface Focus 5: 20150034
form hyperdimension
rsfs.royalsocietypublishing.org
Unlike univalved ammonoid shell forms (figure 1), the shell of a brachiopod consists of two separate univalves articulated together (figure 2). This bivalved shell geometry brings us to the second limit in brachiopod evolution: whorl overlap must be absent in both valves of the shell in order for them to be articulated together. Whorl overlap in a univalve occurs whenever W D 1 (for example, examine the ammonoid shell at coordinates W ¼ 1.5, D ¼ 0.3 in figure 1 in which the whorls of the shell overlap as W D ¼ 0.45). It is advantageous for the brachiopod to have low values of W in both valves of the shell as this produces a shell geometry with high values of V/SA, yet the brachiopod is limited to values of W , 1/D in its valves because of whorl overlap. For example, the shell at coordinates dorsal log W ¼ 3, ventral log W ¼ 2 in figure 2 has V/SA ¼ 11, and this V/SA value is the maximum possible in the morphospace as all shells with lesser values of W have whorl overlap (as illustrated by the rows of whorl-overlapped unarticulated valves in figure 2, and the two computer simulations in the lower left corner of the morphospace which illustrate impossible geometries in which the whorls of each valve of the shell interpenetrate one another, with the shell material of each valve occupying the same space at the same time in the posterior part of the shell). As biconvex brachiopods typically have dorsal valves with D ¼ 0.01 and ventral valves with D ¼ 0.1, they are limited to a minimum dorsal log W ¼ 3, ventral log W ¼ 2 for functional shell forms (figure 2 and table 1). One last analytic example of limits in evolution is given in figure 3, which illustrates computer simulations in two dimensions of a three-dimensional theoretical morphospace of helical bryozoan colony forms created for the analysis of their evolution by McKinney & Raup [6] and Raup et al. [7]. The two dimensions of the space are ELEV, the rate of climb of the central helix of the colony, and BWANG, the angle between the helix axis and the filtration-sheet whorls of the colony. Helical colony forms have been convergently evolved by several clades of bryozoans, as seen in species of the genera Archimedes (Bryozoa: Stenolaemata: Fenestrata: Fenestellidae), Crisidmonea (Bryozoa: Stenolaemata: Cyclostomata: Crisinidae), Bugula (Bryozoa: Gymnolaemata: Cheilostomata: Buguloidea: Bugulidae) and Retiflustra (Bryozoa: Gymnolaemata: Cheilostomata: Flustoidea: Flustridae). The analysis of 207 colonies of 26 species of these convergent bryozoan colonies [8–10] has revealed that those colonies contained within the polygon boundaries illustrated in the centre of figure 3 exist in helical bryozoans even though, as for the ammonoids and brachiopods, computer simulations reveal that other colony geometries are possible but have never been evolved by the bryozoans. Why have the bryozoans convergently evolved some geometrically possible helical colony forms but not others? Unlike ammonoid and brachiopod individually shelled animals, the helical bryozoans are colonies of thousands of tiny individual zooids arranged along the branches in the filtration-sheet whorls of the colony. Like the brachiopods, the bryozoans are also lophophorate filter feeders but now, instead of the geometric arrangement of one lophophore within one brachiopod shell form, the geometric arrangement of thousands of tiny lophophores determines the form of the helical colony. Two aspects of the geometric arrangement of the zooids within the colony are measured by a colony surface area index (SAI) and a branch density index (BDI), and analyses have revealed that helical bryozoan colonies
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
Empirical examples of members of the form set ff :1g can be seen in all those forms located within the functional-limit polygon boundaries illustrated in figures 1 –3, and examples of members of form set ff :2g can be seen in those simulated forms located outside of the functional-limit polygon boundaries. The morphospace region located outside the whorl overlap developmental limit in figure 2 illustrates an empirical example of the morphospace coordinates for members of the form set ff :0g. What is not illustrated in figures 1 –3 are hypothetical members of theoretical form set ff :3g: forms that are functional but that nevertheless cannot be developed by life on Earth. Does such a set of forms actually exist? This is a question that will be considered in the next section of the paper. A second question recently has been raised by Powell & Mariscal [13], who have argued for the subdivision of form set ff :1g to recognize a new subset of forms: (1) Form subset ff :4g: these are the forms, f :4, that are functional, developmentally possible, and that actually have been evolved by life on Earth. The boundaries of the new subset of forms ff :4g within the theoretical morphospace is illustrated by Powell & Mariscal [13] in figure 5. Note that they have drawn these boundaries such that the morphospace region occupied by the members of this form subset is quite small. Powell & Mariscal [13] argued that Gould’s [14] ‘radical contingency thesis’ predicts ‘smaller boundaries around the space of forms that are functional, developmentally possible, and actual’. Gould [14] argued that all evolutionary trends are chains of historically contingent events, and since the actual functional biological forms that have been discovered by evolution are a function of past contingent events there could exist numerous other functional forms that have not yet been discovered purely as a function of history. This concept is older than Gould’s [14] contingency thesis and has been variously called a ‘historical constraint’ or ‘temporal constraint’ in the past (for an extensive discussion of constraint concepts from a theoretical morphologic perspective, see [1]). The most striking feature of Raup’s [15] classic theoretical morphospace study of computer-simulated mollusc shell form was that the overwhelming majority of the morphospace was empty—that there exist numerous geometrically possible shell forms that no mollusc has ever evolved. From the point of view of
4 functional constraint boundary
f:3 f:1 f:4
developmental constraint boundary
f:2
form hyperdimension
Figure 5. Venn diagram of the actual Earth life forms subset f :4 region within theoretical morphospace, illustrating the Gouldian ‘radical contingency thesis’ that actualized biological forms are a small fraction of the set of functional, Earth-possible morphologies f:1. Adapted from Powell & Mariscal [13].
natural selection theory, an obvious causal explanation for empty morphospace would be that the forms present in the empty region of morphospace are non-functional; that is, they belong to form set f f:2g (figure 4). However, an alternative point of view could just as easily maintain that such hypothetical non-existent morphologies might function perfectly well in nature but that the process of evolution simply has not produced them yet. The creation of Powell & Mariscal’s [13] new theoretical subset ff :4g thus requires the existence of an additional new theoretical subset of ff :1g—there should exist members of the functional and developmentally possible form set ff :1g that are not members of the subset of actual forms ff :4g. These hypothetical forms belong to the following subset: (2) Form subset f f:5g: these are the forms, f :5, that are functional and developmentally possible but that nonetheless have not yet been evolved by life on Earth. This subset is here formally defined as ff :5g ¼ ff :1g\f f:4g ¼ ff j f [ f :1, ff :4g. The question is now not a question of whether Powell and Mariscal’s subset ff :4g of actual functional forms exists—it does, as can be seen in figures 1–3 for ammonoids, brachiopods and helical bryzoans—but rather whether subset f f:5g exists. If subset ff :5g does not exist, then neither does subset f f:4g; that is, if set ff :5g ¼ Ø then ff :4g ¼ ff :1g. To rephrase the question: are there functional and developmentally possible forms that have not yet been evolved by Earth life? That is, does ff :4g exist as a separate possible form subset? Or does ff :4g ¼ ff :1g; that is, have all functional and developmentally possible forms for Earth life in fact been discovered by Earth life?
3. Questions for future research An obvious question for future research concerns the existence or non-existence of form subset ff :5g. Is temporal constraint real—can we prove that perfectly functional, developmentally possible biological forms exist that nevertheless have not yet been evolved by life on Earth? In order to answer that question, we must be able to create these non-existent forms and to analyse their functionality, and
Interface Focus 5: 20150034
(1) Form set ff :0g: these are the forms, f:0, that are nonfunctional and cannot be developed by life on Earth. (2) Form set ff :1g: these are the forms, f :1, that are both functional and that can be developed by life on Earth (the shaded region in figure 4). (3) Form set ff :2g: these are the forms, f :2, that can be developed but that are non-functional and thus lethal for life on Earth. (4) Form set f f:3g: these are the forms, f :3, that are functional but that cannot be developed by life on Earth.
f:0
rsfs.royalsocietypublishing.org
forms. That is, it is impossible for a brachiopod to develop these forms at all—the question as to whether they are functional or non-functional is moot. The mapping of the functional and developmental limit boundaries in figure 4 allows us to discern a Venn diagram of four distinct sets of theoretical forms within the morphospace [12]:
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
Competing interests. I declare I have no competing interests. Funding. Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research, and to the US National Science Foundation. Acknowledgements. I thank Simon Conway Morris for the invitation to speak at the Cambridge conference on Limits in Evolution, and Victoria Ling for her assistance in the logistics of the conference proceedings. I also thank Christian Klug and another anonymous reviewer for their thoughtful comments and suggestions that helped me improve the manuscript.
5
Interface Focus 5: 20150034
dimensional geometry [27,28]. How many of the shell forms present in the morphospace region beyond the V/SA ¼ 7 limit in figure 2 were evolved by the strophomenate brachiopods is currently not known but we do know that the region of space that contains non-functional forms, set f f:2g, for the biconvex rhynchonellate brachiopods contained functional forms, set ff:1g, for the extinct strophomenate brachiopods. At this point, a new morphospace containing non-biconvex concavo-convex and convexi-concave shell forms, in addition to the biconvex spectrum of form shown in figure 2, has been created and the analysis of strophomenate shell form is currently in progress. Last, in the case of the filter-feeding helical bryozoans, there are no known bryozoan colonies that exist in the empty region of morphospace beyond the limits shown in figure 3. This region of space appears to contain only non-functional forms for bryozoans—but are these forms functional for some other evolutionary clade of organisms with a different mode of feeding? Bryozoan-like fenestrated colony forms have been convergently evolved by both the cnidarians (e.g. the red octocoral Tubipora) and the hemichordates (e.g. the extinct graptolite Dictyonema), but the only other helical colony forms known to me are the flexible skeletons of a few corals, such as the whip black coral Cirrhipathes [29]. These sessile predators have non-erect colony forms that stretch horizontally in water currents, and possess a geometry unlike any of those shown in figure 3 for the bryozoans. A second question for future research concerns the existence or non-existence of form set ff :3g. This question is of major importance to the study of convergent evolution as these hypothetical forms imply that there exists somewhere in the universe an alien set of functional biological forms that cannot be developed by Earth life, and thus these alien life forms would not be convergent on any of the forms of life seen on Earth. Within our own Solar System (since, at present, we can only dream of spacecraft that could take us to other star systems) only the far-distant large planet-like Titan, a moon of Saturn, and Triton, a moon of Neptune, offer physical conditions and chemistries radically different from those found on Earth. It has already been hypothesized [30 –32] that Titan might contain life forms that could metabolize acetylene (C2H2), using atmospheric hydrogen (H2) to produce methane (CH4), analogous to Earth life that metabolizes glucose (C6H12O6) with atmospheric oxygen (O2) to produce carbon dioxide (CO2). If life forms exist on Titan, they would belong to form set ff :3g, and I predict they would look nothing like life on Earth. The challenge will be to design and send more spacecraft to both Titan and Triton to search for life forms on their surfaces with robot rovers.
rsfs.royalsocietypublishing.org
the analytic techniques of theoretical morphology allow the researcher to do exactly that [2]. Consider the case of the nektonic cephalopods in figure 1: no active swimming cephalopods exist in the morphospace beyond the minimum limit of SEC ¼ 40. However, the region of morphospace beyond the SEC ¼ 40 limit is not entirely empty of shelled cephalopods—this region was partially occupied early in the evolutionary history of the cephalopods but loosely coiled shell forms were rapidly, and convergently in multiple lineages, abandoned in favour of coiled forms with better streamlining and swimming efficiency [16–20]. Curiously, however, loosely coiled forms were also convergently re-evolved by cephalopods in the Mesozoic; for example, the Cretaceous ammonoid Crioceras and the Ordovician nautiloid Aphetoceras had shells very similar to the shell form seen at the morphospace coordinates W ¼ 2.5, D ¼ 0.5; shells in which the whorls do not touch. Even more extreme, the Jurassic ammonoid Spiroceras and the Devonian nautiloid Goldringia had shells very similar to that at coordinates W ¼ 4.5, D ¼ 0.7, an odd geometry known as gyroconic in nautiloids. How could this be, as all of these shell forms have SEC , 40? The answer is that these ammonoids and nautiloids did not swim—they were either planktonic, passively floating up in the water column, or demersal, forms living on the sea bottom [20–22]. Thus, the region of the morphospace with non-functional forms, set ff :2g, for the nektonic shelled cephalopods contained functional forms, set ff :1g, for the non-nektonic shelled cephalopods. How much of this region of morphospace was occupied by non-nektonic cephalopods is currently not known—it is entirely possible that some of the shell forms in the morphospace beyond the SEC ¼ 40 limit boundary illustrated in figure 1 were possible functional shell forms for non-nektonic cephalopods that nevertheless were not evolved by any of the non-nektonic cephalopods. We will not know until someone accepts the challenge to conduct theoretical morphospace analyses of the non-nektonic shelled cephalopods—elegant computer simulations and morphospaces for these forms have been created [23 –25] and simply await data analyses [26]. Consider next the case of the filter-feeding biconvex brachiopods in figure 2: no biconvex brachiopods exist in the morphospace beyond the minimum limit V/SA ¼ 7, and there are good functional reasons why no brachiopods with complex three-dimensionally coiled lophophores exist in this region of the space. However, there existed other brachiopods—the non-biconvex brachiopods (Brachiopoda: Rhynchonelliformes: Strophomenata)—that did occupy some of this region of the theoretical morphospace. Some of the extremely compressed, flattish shell forms of the strophomenides in particular had V/SA ratios as low as 0.5, approaching the absolute limit of V/SA ¼ 0 in which the two valves of the shell fit perfectly together and there is no internal volume space at all between them. These ancient brachiopods developed shell forms with minimum internal volumes to maximum shell surface areas, shell forms with the exact opposite geometry to those found in the biconvex brachiopods. How could this be? Our best explanation is that the extinct non-biconvex brachiopods used a radically different feeding system from that of the living biconvex ones, a feeding system in which the entire mantle-tissue surface of the interior of the shell was ciliated and gathered food in addition to that gathered by a small, weak lophophore with a simple two-
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
References 1.
12.
13.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
(ed. E Savazzi), pp. 263–298. Chichester, UK: John Wiley. Okamoto T. 1996 Theoretical modeling of ammonoid morphology. In Ammonoid paleobiology (eds NH Landman, K Tanabe, RA Davis), pp. 225–251. New York, NY: Plenum Press. Parent H, Greco AF, Bejas M. 2010 Size-shape relationships in the Mesozoic planispiral ammonites. Acta Palaeontol. Pol. 55, 85– 98. (doi:10.4202/app. 2009.0066) Parent H, Bejas M, Greco A, Hammer Ø. 2012 Relationships between dimensionless models of ammonoid shell morphology. Acta Palaeontol. Pol. 57, 445 –447. (doi:10.4202/app.2010.0118) Tendler A, Mayo A, Alon U. 2015 Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells. BMC Syst. Biol. 9, 12. (doi:10. 1186/s12918-015-0149-z) Westbroeck P, Yanagida J, Isa Y. 1980 Functional morphology of brachiopod and coral skeletal structures supporting ciliated epithelia. Paleobiology 6, 313 –330. Hoel OA. 2007 Cementing strophomenide brachiopods from the Silurian of Gotland (Sweden): morphology and life habits. Geobios 40, 589 –608. (doi:10.1016/j.geobios.2006.08.003) Bavestrello G, Cattaneo-Vietti R, Di Camillo CG, Bo M. 2012 Helicospiral growth in the whip black coral Cirrhipathes sp. (Antipatharia, Antipathidae). Biol. Bull. 222, 17 –25. McKay CP, Smith HD. 2005 Possibilities for methanogenic life in liquid methane on the surface of Titan. Icarus 178, 274–276. (doi:10.1016/j. icarus.2005.05.018) Strobel DF. 2010 Molecular hydrogen in Titan’s atmosphere: implications of the measured tropospheric and thermospheric mole fractions. Icarus 208, 878–886. (doi:10.1016/j.icarus.2010.03. 003) Clark RN et al. 2010 Detection and mapping of hydrocarbon deposits on Titan. J. Geophys. Res. Planets 115, E10005. (doi:10.1029/2009JE003369)
Interface Focus 5: 20150034
14.
constraints and minimum fenestrule widths. Hist. Biol. 25, 201 –222. (doi:10.1080/08912963.2012. 713948) McGhee GR. 2011 Convergent evolution: limited forms most beautiful. Cambridge, MA: Massachusetts Institute of Technology Press. Powell R, Mariscal C. 2014 There is grandeur in this view of life: the bio-philosophical implications of convergent evolution. Acta Biotheor. 62, 115–121. (doi:10.1007/s10441-014-9211-2) Gould SJ. 1989 Wonderful life: the Burgess Shale and the nature of history. New York, NY: W. W. Norton. Raup DM. 1966 Geometric analysis of shell coiling: general problems. J. Paleontol. 40, 1178 –1190. Korn D, Klug C. 2003 Morphological pathways in the evolution of Early and Middle Devonian ammonoids. Paleobiology 29, 329–348. (doi:10.1666/00948373(2003)029,0329:MPITEO.2.0.CO;2) Klug C, Korn D. 2004 The origin of ammonoid locomotion. Acta Palaeontol. Pol. 49, 235 –242. (http://app.pan.pl/article/item/app49-235.html) Monnet C, De Baets K, Klug C. 2011 Parallel evolution controlled by adaptation and covariation in ammonoid cephalopods. BMC Evol. Biol. 11, 15. (doi:10.1186/1471-2148-11-115) De Baets K, Klug C, Korn D, Landman NH. 2012 Early evolutionary trends in ammonoid embryonic development. Evolution 66, 1788 –1806. (doi:10. 1111/j.1558- 5646.2011.01567.x) Ritterbush KA, Hoffmann R, Lukeneder A, De Baets K. 2014 Pelagic palaeoecology: the importance of constraints on ammonoid palaeobiology and life history. J. Zool. 292, 229–241. (doi:10.111/jzo. 12118) Westermann GEG. 1996 Ammonoid life habitat. In Ammonoid paleobiology (eds NH Landman, K Tanabe, RA Davis), pp. 607–707. New York, NY: Plenum Press. Westermann GEG. 1998 Life habits of nautiloids. In Functional morphology of the invertebrate skeleton
rsfs.royalsocietypublishing.org
McGhee GR. 2012 The geometry of evolution: adaptive landscapes and theoretical morphospaces. Cambridge, UK: Cambridge University Press. 2. McGhee GR. 1999 Theoretical morphology: the concept and its applications. New York, NY: Columbia University Press. 3. Raup DM. 1967 Geometric analysis of shell coiling: coiling in ammonoids. J. Paleontol. 41, 43 –65. 4. Saunders WB, Work DM, Nikolaeva SV. 2004 The evolutionary history of shell geometry in Paleozoic ammonoids. Paleobiology 30, 19– 43. (doi:10.1666/ 0094- 8373(2004)030,0019:TEHOSG.2.0.CO;2) 5. Chamberlain JA. 1981 Hydromechanical design of fossil cephalopods. Syst. Assoc. Special Vol. 18, 289–336. 6. McKinney FK, Raup DM. 1982 A turn in the right direction: simulation of erect spiral growth in the bryozoans Archimedes and Bugula. Paleobiology 8, 101–112. 7. Raup DM, McGhee GR, McKinney FK. 2006 Source code for theoretical morphologic simulation of helical colony form in the Bryozoa. Palaeontol. Electron. 9, 7. (http://palaeo-electronica.org/paleo/ 2006_2/helical/index.html) 8. McGhee GR, McKinney FK. 2000 A theoretical morphologic analysis of convergently evolved erect helical colony form in the Bryozoa. Paleobiology 26, 556–577. (doi:10.1666/0094-8373(2000) 026,0556:ATMAOC.2.0.CO;2) 9. McGhee GR, McKinney FK. 2002 A theoretical morphologic analysis of ecomorphologic variation in Archimedes helical colony form. Palaios 17, 556–570. (doi:10.1669/0883-1351(2002) 017,0556:ATMAOE.2.0.CO;2) 10. McKinney FK, McGhee GR. 2003 Evolution of erect helical colony form in the Bryozoa: phylogenetic, functional, and ecological factors. Biol. J. Linn. Soc. 80, 235–260. (doi:10.1046/j.1095-8312.2003. 00227.x) 11. Starcher RW, McGhee GR. 2013 Theoretical morphology of colonial meshworks in the Fenestrata (Bryozoa): modelling hydraulic-resistance
6
Limits in the evolution of biological form: a theoretical morphologic perspective rsfs.royalsocietypublishing.org
George R. McGhee Jr Department of Earth and Planetary Sciences, Wright-Rieman Laboratories, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854, USA
Research Cite this article: McGhee GR Jr. 2015 Limits in the evolution of biological form: a theoretical morphologic perspective. Interface Focus 5: 20150034. http://dx.doi.org/10.1098/rsfs.2015.0034
Limits in the evolution of biological form can be empirically demonstrated by using theoretical morphospace analyses, and actual analytic examples are given for univalved ammonoid shell form, bivalved brachiopod shell form and helical bryozoan colony form. Limits in the evolution of form in these animal groups can be shown to be due to functional and developmental constraints on possible evolutionary trajectories in morphospace. Future evolutionary-limit research is needed to analyse the possible existence of temporal constraint in the evolution of biological form on Earth, and in the search for the possible existence of functional alien life forms on Titan and Triton that are developmentally impossible for Earth life.
One contribution of 12 to a theme issue ‘Are there limits to evolution?’ Subject Areas: astrobiology, computational biology, synthetic biology Keywords: evolutionary limits, evolutionary constraints, theoretical morphospaces, Ammonoidea, Brachiopoda, Bryozoa Author for correspondence: George R. McGhee Jr e-mail: [email protected]
1. Limits in evolution: analytic examples Actual analytic examples of limits in the evolution of biological form in theoretical morphospaces are given in figures 1–3, summarized in table 1, and are discussed in this section of the paper. Theoretical morphospaces are ‘n-dimensional geometric hyperspaces produced by systematically varying the parameter values of a geometric model of form’ [2] and are particularly useful in the analysis of limits in evolution in that they contain computer simulations of both existent and non-existent biological form and hence contain the limit boundary between those two regions of the morphospace (for an overview of the technique of theoretical morphospace analysis, see [1,2]). In figure 1 is given a two-dimensional plane within a four-dimensional theoretical morphospace of computer-simulated planispiral univalved shell forms created by Raup [3] for the analysis of evolution in ancient nektonic cephalopods. The two dimensions of the space are W, the whorl expansion rate of the shell, and D, the distance from the coiling axis to the aperture of the shell (for a detailed discussion of the morphospace, see [1]). This morphospace was used by Raup [3] in the analysis of 405 species of ammonoids (Mollusca: Cephalopoda: Ammonoidea), and by Saunders et al. [4] in the analysis of an additional 597 species. Their combined analyses revealed that those shell geometries contained within the polygon boundaries illustrated in the lower left corner of figure 1 exist in actual ammonoids—all other simulated shell forms are geometrically possible but are non-existent in these ancient nektonic cephalopods. Why did the ammonoids evolve some geometrically possible shell forms but not others? The polygonal boundary line shown in figure 1 maps a hydrodynamic limit to the evolution of shell forms by the nektonic cephalopods within the theoretical morphospace (table 1). Chamberlain [5] measured drag coefficients in flume experiments with model shell forms that have been used to calculate a swimmingefficiency coefficient (SEC) for all of the shell geometries shown in figure 1. All shell forms evolved by the ammonoids have a minimum limit of SEC ¼ 40; all shell geometries outside of the polygon in figure 1 have SEC values less than this limit (for example, the non-existent ammonoid shell form shown at the coordinates W ¼ 3.5, D ¼ 0.5 has SEC ¼ 8). Not surprisingly, this same hydrodynamic limit holds for shell forms of the other major clade of nektonic cephalopods, the nautiloids (Mollusca: Cephalopoda: Nautiloidea). For example, the convolute shells of the living Nautilus
& 2015 The Author(s) Published by the Royal Society. All rights reserved.
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
2
rsfs.royalsocietypublishing.org
4.5 0.50 ELEV
3.5
W
0.20
2.5 0.05 70
50
90
BWANG
0.1
0.3
0.5
0.7
D
Figure 1. A theoretical morphospace of computer-simulated ammonoid shell form, where the forms shown within the limits of the polygon boundary in the lower left corner of the figure actually exist in ammonoid cephalopods. Adapted from McGhee [1].
dorsal valve log W
30
13 12 11 10 9 8 7 6 5 4 3 2 1
Figure 3. A theoretical morphospace of computer-simulated helical bryozoan colony form, where the forms shown within the limits of the polygon boundary in the centre of the figure actually exist in helical bryozoans. Adapted from McGhee [1].
Table 1. Limits in the evolution of cephalopods, brachiopods and bryozoans. swimming cephalopod shell forms hydrodynamic limit: minimum SEC ¼ 40 for functional shell forms biconvex brachiopod shell forms internal volume limit: minimum volume-to-surface-area ratio ¼ 7 for functional shell forms whorl overlap limit: minimum dorsal log W ¼ 3, ventral log W ¼ 2, for functional shell forms helical bryozoan colony forms filtration efficiency limit: minimum colony SAI ¼ 0.5 and BDI ¼ 25
1
2
3
4
5 6 7 8 9 10 11 12 13 ventral valve log W
Figure 2. A theoretical morphospace of computer-simulated brachiopod shell form, where the forms shown within the limits of the polygon boundary in the centre of the figure actually exist in biconvex brachiopods. Adapted from McGhee [1].
have W ¼ 3.4 and D ¼ 0.04 [3] and are very similar in appearance to the shell form shown at coordinates W ¼ 3.5, D ¼ 0.1 within the polygon boundaries in figure 1. A second example of limits in evolution is given in figure 2, which illustrates a plane within a seven-dimensional theoretical morphospace of planispiral bivalved shell forms created for the analysis of evolution in brachiopods [1]. The two dimensions of the space are logarithms of the whorl expansion rate, log W, for the dorsal and ventral valves of the brachiopod shell. This morphospace has been used in the analysis of 324 species of biconvex brachiopods (Brachiopoda: Rhynchonelliformes: Rhynchonellata) and has revealed that those shell forms contained within the polygon boundaries illustrated in the centre of figure 2 exist in biconvex brachiopods. As with the ammonoid shell forms, simulated shell forms outside of the polygon are geometrically possible but are non-existent in biconvex brachiopods.
for functional colony forms hydraulic resistance limit: maximum colony SAI ¼ 7 and BDI ¼ 60 for functional colony forms
Why do the biconvex brachiopods evolve some geometrically possible shell forms but not others? The polygonal boundary line shown in figure 2 actually maps two separate limits to the evolution of shell forms by biconvex brachiopods within the theoretical morphospace (table 1). The first is an internal volume limit: biconvex brachiopods use a tentacular pumping and feeding organ, the lophophore, to partition the interior of their shells into inhalent and exhalent filtration chambers for the purpose of filter-feeding seawater. The lophophore is coiled in a variety of three-dimensional geometries in living and fossil biconvex brachiopods, and all lophophore coil geometries require sufficient internal shell volume, V, to be contained within the external surface area, SA, of the shell—a proportion that is measured by a volume-to-surface-area ratio, V/SA [1]. All shell forms evolved by the biconvex brachiopods have a minimum limit of V/SA ¼ 7; shell form geometries with V/SA ratios below this limit are non-existent in biconvex brachiopods (for example, the non-existent biconvex brachiopod shell form shown at coordinates dorsal log W ¼ 13, ventral log W ¼ 13 has V/SA ¼ 5.5).
Interface Focus 5: 20150034
10
1.5
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
f:0
3 functional constraint boundary
f:3
f :1 developmental constraint boundary
f :2
Figure 4. Venn diagram of theoretically possible regions of form determined by the limits of functional and developmental constraint within theoretical morphospace. Forms f:0 are non-functional and developmentally impossible for life on Earth, forms f:1 are both functional and developmentally possible, forms f:2 are developmentally possible but non-functional and forms f:3 are functional but developmentally impossible for life on Earth. Adapted from McGhee [12].
maintain minimum limits of SAI ¼ 0.5 and BDI ¼ 25, and maximum limits of SAI ¼ 7 and BDI ¼ 60 [8 –10]. The minimum limits of SAI ¼ 0.5 and BDI ¼ 25 appear to be filtration efficiency limits (table 1) in that colonies with colony surface areas and branch densities less than those limits simply do not catch or intercept enough food across their filtration sheets to support the metabolic needs of the colony (i.e. too much water escapes unfiltered through the colony). The maximum limits of SAI ¼ 7 and BDI ¼ 60 appear to be hydraulic resistance limits (table 1) in that colonies with colony surface areas and branch densities higher than those limits impede the flow of water through the colony [11] and dead zones of stagnant water develop within the colony centre (see discussion in [1]). For example, the non-existent colony geometry at coordinates ELEV ¼ 0.50, BWANG ¼ 90 in figure 3 has SAI , 0.5 and, at the other extreme, the non-existent colony geometry at coordinates ELEV ¼ 0.20, BWANG ¼ 10 has SAI ¼ 15.
2. Limits in evolution: theoretical possibilities The observed empirical limits in the evolution of actual animals illustrated in figures 1–3 are abstracted to theoretical limits in a theoretical morphospace in figure 4. Two types of limit in the evolution of biological form are graphically portrayed within the morphospace of hypothetical forms: limits due to functional constraint (the boundaries of the solid-line rectangle) and limits due to developmental constraints (the boundaries of the dotted-line rectangle). Empirical examples of actual functional constraint limits are illustrated in figures 1–3; these are the hydrodynamic, internal volume, filtration efficiency and hydraulic resistance limits (table 1) discussed in the previous section of the text. Biological forms shown within the limit boundaries shown in figures 1–3 are functional for the animals analysed, forms outside the limit boundaries are not. An empirical example of an actual developmental constraint limit is seen in the brachiopod whorl overlap limit (figure 2 and table 1). The region of morphospace outside the whorl overlap limit does not contain non-functional forms; rather, this region contains geometrically impossible
Interface Focus 5: 20150034
form hyperdimension
rsfs.royalsocietypublishing.org
Unlike univalved ammonoid shell forms (figure 1), the shell of a brachiopod consists of two separate univalves articulated together (figure 2). This bivalved shell geometry brings us to the second limit in brachiopod evolution: whorl overlap must be absent in both valves of the shell in order for them to be articulated together. Whorl overlap in a univalve occurs whenever W D 1 (for example, examine the ammonoid shell at coordinates W ¼ 1.5, D ¼ 0.3 in figure 1 in which the whorls of the shell overlap as W D ¼ 0.45). It is advantageous for the brachiopod to have low values of W in both valves of the shell as this produces a shell geometry with high values of V/SA, yet the brachiopod is limited to values of W , 1/D in its valves because of whorl overlap. For example, the shell at coordinates dorsal log W ¼ 3, ventral log W ¼ 2 in figure 2 has V/SA ¼ 11, and this V/SA value is the maximum possible in the morphospace as all shells with lesser values of W have whorl overlap (as illustrated by the rows of whorl-overlapped unarticulated valves in figure 2, and the two computer simulations in the lower left corner of the morphospace which illustrate impossible geometries in which the whorls of each valve of the shell interpenetrate one another, with the shell material of each valve occupying the same space at the same time in the posterior part of the shell). As biconvex brachiopods typically have dorsal valves with D ¼ 0.01 and ventral valves with D ¼ 0.1, they are limited to a minimum dorsal log W ¼ 3, ventral log W ¼ 2 for functional shell forms (figure 2 and table 1). One last analytic example of limits in evolution is given in figure 3, which illustrates computer simulations in two dimensions of a three-dimensional theoretical morphospace of helical bryozoan colony forms created for the analysis of their evolution by McKinney & Raup [6] and Raup et al. [7]. The two dimensions of the space are ELEV, the rate of climb of the central helix of the colony, and BWANG, the angle between the helix axis and the filtration-sheet whorls of the colony. Helical colony forms have been convergently evolved by several clades of bryozoans, as seen in species of the genera Archimedes (Bryozoa: Stenolaemata: Fenestrata: Fenestellidae), Crisidmonea (Bryozoa: Stenolaemata: Cyclostomata: Crisinidae), Bugula (Bryozoa: Gymnolaemata: Cheilostomata: Buguloidea: Bugulidae) and Retiflustra (Bryozoa: Gymnolaemata: Cheilostomata: Flustoidea: Flustridae). The analysis of 207 colonies of 26 species of these convergent bryozoan colonies [8–10] has revealed that those colonies contained within the polygon boundaries illustrated in the centre of figure 3 exist in helical bryozoans even though, as for the ammonoids and brachiopods, computer simulations reveal that other colony geometries are possible but have never been evolved by the bryozoans. Why have the bryozoans convergently evolved some geometrically possible helical colony forms but not others? Unlike ammonoid and brachiopod individually shelled animals, the helical bryozoans are colonies of thousands of tiny individual zooids arranged along the branches in the filtration-sheet whorls of the colony. Like the brachiopods, the bryozoans are also lophophorate filter feeders but now, instead of the geometric arrangement of one lophophore within one brachiopod shell form, the geometric arrangement of thousands of tiny lophophores determines the form of the helical colony. Two aspects of the geometric arrangement of the zooids within the colony are measured by a colony surface area index (SAI) and a branch density index (BDI), and analyses have revealed that helical bryozoan colonies
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
Empirical examples of members of the form set ff :1g can be seen in all those forms located within the functional-limit polygon boundaries illustrated in figures 1 –3, and examples of members of form set ff :2g can be seen in those simulated forms located outside of the functional-limit polygon boundaries. The morphospace region located outside the whorl overlap developmental limit in figure 2 illustrates an empirical example of the morphospace coordinates for members of the form set ff :0g. What is not illustrated in figures 1 –3 are hypothetical members of theoretical form set ff :3g: forms that are functional but that nevertheless cannot be developed by life on Earth. Does such a set of forms actually exist? This is a question that will be considered in the next section of the paper. A second question recently has been raised by Powell & Mariscal [13], who have argued for the subdivision of form set ff :1g to recognize a new subset of forms: (1) Form subset ff :4g: these are the forms, f :4, that are functional, developmentally possible, and that actually have been evolved by life on Earth. The boundaries of the new subset of forms ff :4g within the theoretical morphospace is illustrated by Powell & Mariscal [13] in figure 5. Note that they have drawn these boundaries such that the morphospace region occupied by the members of this form subset is quite small. Powell & Mariscal [13] argued that Gould’s [14] ‘radical contingency thesis’ predicts ‘smaller boundaries around the space of forms that are functional, developmentally possible, and actual’. Gould [14] argued that all evolutionary trends are chains of historically contingent events, and since the actual functional biological forms that have been discovered by evolution are a function of past contingent events there could exist numerous other functional forms that have not yet been discovered purely as a function of history. This concept is older than Gould’s [14] contingency thesis and has been variously called a ‘historical constraint’ or ‘temporal constraint’ in the past (for an extensive discussion of constraint concepts from a theoretical morphologic perspective, see [1]). The most striking feature of Raup’s [15] classic theoretical morphospace study of computer-simulated mollusc shell form was that the overwhelming majority of the morphospace was empty—that there exist numerous geometrically possible shell forms that no mollusc has ever evolved. From the point of view of
4 functional constraint boundary
f:3 f:1 f:4
developmental constraint boundary
f:2
form hyperdimension
Figure 5. Venn diagram of the actual Earth life forms subset f :4 region within theoretical morphospace, illustrating the Gouldian ‘radical contingency thesis’ that actualized biological forms are a small fraction of the set of functional, Earth-possible morphologies f:1. Adapted from Powell & Mariscal [13].
natural selection theory, an obvious causal explanation for empty morphospace would be that the forms present in the empty region of morphospace are non-functional; that is, they belong to form set f f:2g (figure 4). However, an alternative point of view could just as easily maintain that such hypothetical non-existent morphologies might function perfectly well in nature but that the process of evolution simply has not produced them yet. The creation of Powell & Mariscal’s [13] new theoretical subset ff :4g thus requires the existence of an additional new theoretical subset of ff :1g—there should exist members of the functional and developmentally possible form set ff :1g that are not members of the subset of actual forms ff :4g. These hypothetical forms belong to the following subset: (2) Form subset f f:5g: these are the forms, f :5, that are functional and developmentally possible but that nonetheless have not yet been evolved by life on Earth. This subset is here formally defined as ff :5g ¼ ff :1g\f f:4g ¼ ff j f [ f :1, ff :4g. The question is now not a question of whether Powell and Mariscal’s subset ff :4g of actual functional forms exists—it does, as can be seen in figures 1–3 for ammonoids, brachiopods and helical bryzoans—but rather whether subset f f:5g exists. If subset ff :5g does not exist, then neither does subset f f:4g; that is, if set ff :5g ¼ Ø then ff :4g ¼ ff :1g. To rephrase the question: are there functional and developmentally possible forms that have not yet been evolved by Earth life? That is, does ff :4g exist as a separate possible form subset? Or does ff :4g ¼ ff :1g; that is, have all functional and developmentally possible forms for Earth life in fact been discovered by Earth life?
3. Questions for future research An obvious question for future research concerns the existence or non-existence of form subset ff :5g. Is temporal constraint real—can we prove that perfectly functional, developmentally possible biological forms exist that nevertheless have not yet been evolved by life on Earth? In order to answer that question, we must be able to create these non-existent forms and to analyse their functionality, and
Interface Focus 5: 20150034
(1) Form set ff :0g: these are the forms, f:0, that are nonfunctional and cannot be developed by life on Earth. (2) Form set ff :1g: these are the forms, f :1, that are both functional and that can be developed by life on Earth (the shaded region in figure 4). (3) Form set ff :2g: these are the forms, f :2, that can be developed but that are non-functional and thus lethal for life on Earth. (4) Form set f f:3g: these are the forms, f :3, that are functional but that cannot be developed by life on Earth.
f:0
rsfs.royalsocietypublishing.org
forms. That is, it is impossible for a brachiopod to develop these forms at all—the question as to whether they are functional or non-functional is moot. The mapping of the functional and developmental limit boundaries in figure 4 allows us to discern a Venn diagram of four distinct sets of theoretical forms within the morphospace [12]:
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
Competing interests. I declare I have no competing interests. Funding. Acknowledgement is made to the Donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research, and to the US National Science Foundation. Acknowledgements. I thank Simon Conway Morris for the invitation to speak at the Cambridge conference on Limits in Evolution, and Victoria Ling for her assistance in the logistics of the conference proceedings. I also thank Christian Klug and another anonymous reviewer for their thoughtful comments and suggestions that helped me improve the manuscript.
5
Interface Focus 5: 20150034
dimensional geometry [27,28]. How many of the shell forms present in the morphospace region beyond the V/SA ¼ 7 limit in figure 2 were evolved by the strophomenate brachiopods is currently not known but we do know that the region of space that contains non-functional forms, set f f:2g, for the biconvex rhynchonellate brachiopods contained functional forms, set ff:1g, for the extinct strophomenate brachiopods. At this point, a new morphospace containing non-biconvex concavo-convex and convexi-concave shell forms, in addition to the biconvex spectrum of form shown in figure 2, has been created and the analysis of strophomenate shell form is currently in progress. Last, in the case of the filter-feeding helical bryozoans, there are no known bryozoan colonies that exist in the empty region of morphospace beyond the limits shown in figure 3. This region of space appears to contain only non-functional forms for bryozoans—but are these forms functional for some other evolutionary clade of organisms with a different mode of feeding? Bryozoan-like fenestrated colony forms have been convergently evolved by both the cnidarians (e.g. the red octocoral Tubipora) and the hemichordates (e.g. the extinct graptolite Dictyonema), but the only other helical colony forms known to me are the flexible skeletons of a few corals, such as the whip black coral Cirrhipathes [29]. These sessile predators have non-erect colony forms that stretch horizontally in water currents, and possess a geometry unlike any of those shown in figure 3 for the bryozoans. A second question for future research concerns the existence or non-existence of form set ff :3g. This question is of major importance to the study of convergent evolution as these hypothetical forms imply that there exists somewhere in the universe an alien set of functional biological forms that cannot be developed by Earth life, and thus these alien life forms would not be convergent on any of the forms of life seen on Earth. Within our own Solar System (since, at present, we can only dream of spacecraft that could take us to other star systems) only the far-distant large planet-like Titan, a moon of Saturn, and Triton, a moon of Neptune, offer physical conditions and chemistries radically different from those found on Earth. It has already been hypothesized [30 –32] that Titan might contain life forms that could metabolize acetylene (C2H2), using atmospheric hydrogen (H2) to produce methane (CH4), analogous to Earth life that metabolizes glucose (C6H12O6) with atmospheric oxygen (O2) to produce carbon dioxide (CO2). If life forms exist on Titan, they would belong to form set ff :3g, and I predict they would look nothing like life on Earth. The challenge will be to design and send more spacecraft to both Titan and Triton to search for life forms on their surfaces with robot rovers.
rsfs.royalsocietypublishing.org
the analytic techniques of theoretical morphology allow the researcher to do exactly that [2]. Consider the case of the nektonic cephalopods in figure 1: no active swimming cephalopods exist in the morphospace beyond the minimum limit of SEC ¼ 40. However, the region of morphospace beyond the SEC ¼ 40 limit is not entirely empty of shelled cephalopods—this region was partially occupied early in the evolutionary history of the cephalopods but loosely coiled shell forms were rapidly, and convergently in multiple lineages, abandoned in favour of coiled forms with better streamlining and swimming efficiency [16–20]. Curiously, however, loosely coiled forms were also convergently re-evolved by cephalopods in the Mesozoic; for example, the Cretaceous ammonoid Crioceras and the Ordovician nautiloid Aphetoceras had shells very similar to the shell form seen at the morphospace coordinates W ¼ 2.5, D ¼ 0.5; shells in which the whorls do not touch. Even more extreme, the Jurassic ammonoid Spiroceras and the Devonian nautiloid Goldringia had shells very similar to that at coordinates W ¼ 4.5, D ¼ 0.7, an odd geometry known as gyroconic in nautiloids. How could this be, as all of these shell forms have SEC , 40? The answer is that these ammonoids and nautiloids did not swim—they were either planktonic, passively floating up in the water column, or demersal, forms living on the sea bottom [20–22]. Thus, the region of the morphospace with non-functional forms, set ff :2g, for the nektonic shelled cephalopods contained functional forms, set ff :1g, for the non-nektonic shelled cephalopods. How much of this region of morphospace was occupied by non-nektonic cephalopods is currently not known—it is entirely possible that some of the shell forms in the morphospace beyond the SEC ¼ 40 limit boundary illustrated in figure 1 were possible functional shell forms for non-nektonic cephalopods that nevertheless were not evolved by any of the non-nektonic cephalopods. We will not know until someone accepts the challenge to conduct theoretical morphospace analyses of the non-nektonic shelled cephalopods—elegant computer simulations and morphospaces for these forms have been created [23 –25] and simply await data analyses [26]. Consider next the case of the filter-feeding biconvex brachiopods in figure 2: no biconvex brachiopods exist in the morphospace beyond the minimum limit V/SA ¼ 7, and there are good functional reasons why no brachiopods with complex three-dimensionally coiled lophophores exist in this region of the space. However, there existed other brachiopods—the non-biconvex brachiopods (Brachiopoda: Rhynchonelliformes: Strophomenata)—that did occupy some of this region of the theoretical morphospace. Some of the extremely compressed, flattish shell forms of the strophomenides in particular had V/SA ratios as low as 0.5, approaching the absolute limit of V/SA ¼ 0 in which the two valves of the shell fit perfectly together and there is no internal volume space at all between them. These ancient brachiopods developed shell forms with minimum internal volumes to maximum shell surface areas, shell forms with the exact opposite geometry to those found in the biconvex brachiopods. How could this be? Our best explanation is that the extinct non-biconvex brachiopods used a radically different feeding system from that of the living biconvex ones, a feeding system in which the entire mantle-tissue surface of the interior of the shell was ciliated and gathered food in addition to that gathered by a small, weak lophophore with a simple two-
Downloaded from http://rsfs.royalsocietypublishing.org/ on February 12, 2016
References 1.
12.
13.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
(ed. E Savazzi), pp. 263–298. Chichester, UK: John Wiley. Okamoto T. 1996 Theoretical modeling of ammonoid morphology. In Ammonoid paleobiology (eds NH Landman, K Tanabe, RA Davis), pp. 225–251. New York, NY: Plenum Press. Parent H, Greco AF, Bejas M. 2010 Size-shape relationships in the Mesozoic planispiral ammonites. Acta Palaeontol. Pol. 55, 85– 98. (doi:10.4202/app. 2009.0066) Parent H, Bejas M, Greco A, Hammer Ø. 2012 Relationships between dimensionless models of ammonoid shell morphology. Acta Palaeontol. Pol. 57, 445 –447. (doi:10.4202/app.2010.0118) Tendler A, Mayo A, Alon U. 2015 Evolutionary tradeoffs, Pareto optimality and the morphology of ammonite shells. BMC Syst. Biol. 9, 12. (doi:10. 1186/s12918-015-0149-z) Westbroeck P, Yanagida J, Isa Y. 1980 Functional morphology of brachiopod and coral skeletal structures supporting ciliated epithelia. Paleobiology 6, 313 –330. Hoel OA. 2007 Cementing strophomenide brachiopods from the Silurian of Gotland (Sweden): morphology and life habits. Geobios 40, 589 –608. (doi:10.1016/j.geobios.2006.08.003) Bavestrello G, Cattaneo-Vietti R, Di Camillo CG, Bo M. 2012 Helicospiral growth in the whip black coral Cirrhipathes sp. (Antipatharia, Antipathidae). Biol. Bull. 222, 17 –25. McKay CP, Smith HD. 2005 Possibilities for methanogenic life in liquid methane on the surface of Titan. Icarus 178, 274–276. (doi:10.1016/j. icarus.2005.05.018) Strobel DF. 2010 Molecular hydrogen in Titan’s atmosphere: implications of the measured tropospheric and thermospheric mole fractions. Icarus 208, 878–886. (doi:10.1016/j.icarus.2010.03. 003) Clark RN et al. 2010 Detection and mapping of hydrocarbon deposits on Titan. J. Geophys. Res. Planets 115, E10005. (doi:10.1029/2009JE003369)
Interface Focus 5: 20150034
14.
constraints and minimum fenestrule widths. Hist. Biol. 25, 201 –222. (doi:10.1080/08912963.2012. 713948) McGhee GR. 2011 Convergent evolution: limited forms most beautiful. Cambridge, MA: Massachusetts Institute of Technology Press. Powell R, Mariscal C. 2014 There is grandeur in this view of life: the bio-philosophical implications of convergent evolution. Acta Biotheor. 62, 115–121. (doi:10.1007/s10441-014-9211-2) Gould SJ. 1989 Wonderful life: the Burgess Shale and the nature of history. New York, NY: W. W. Norton. Raup DM. 1966 Geometric analysis of shell coiling: general problems. J. Paleontol. 40, 1178 –1190. Korn D, Klug C. 2003 Morphological pathways in the evolution of Early and Middle Devonian ammonoids. Paleobiology 29, 329–348. (doi:10.1666/00948373(2003)029,0329:MPITEO.2.0.CO;2) Klug C, Korn D. 2004 The origin of ammonoid locomotion. Acta Palaeontol. Pol. 49, 235 –242. (http://app.pan.pl/article/item/app49-235.html) Monnet C, De Baets K, Klug C. 2011 Parallel evolution controlled by adaptation and covariation in ammonoid cephalopods. BMC Evol. Biol. 11, 15. (doi:10.1186/1471-2148-11-115) De Baets K, Klug C, Korn D, Landman NH. 2012 Early evolutionary trends in ammonoid embryonic development. Evolution 66, 1788 –1806. (doi:10. 1111/j.1558- 5646.2011.01567.x) Ritterbush KA, Hoffmann R, Lukeneder A, De Baets K. 2014 Pelagic palaeoecology: the importance of constraints on ammonoid palaeobiology and life history. J. Zool. 292, 229–241. (doi:10.111/jzo. 12118) Westermann GEG. 1996 Ammonoid life habitat. In Ammonoid paleobiology (eds NH Landman, K Tanabe, RA Davis), pp. 607–707. New York, NY: Plenum Press. Westermann GEG. 1998 Life habits of nautiloids. In Functional morphology of the invertebrate skeleton
rsfs.royalsocietypublishing.org
McGhee GR. 2012 The geometry of evolution: adaptive landscapes and theoretical morphospaces. Cambridge, UK: Cambridge University Press. 2. McGhee GR. 1999 Theoretical morphology: the concept and its applications. New York, NY: Columbia University Press. 3. Raup DM. 1967 Geometric analysis of shell coiling: coiling in ammonoids. J. Paleontol. 41, 43 –65. 4. Saunders WB, Work DM, Nikolaeva SV. 2004 The evolutionary history of shell geometry in Paleozoic ammonoids. Paleobiology 30, 19– 43. (doi:10.1666/ 0094- 8373(2004)030,0019:TEHOSG.2.0.CO;2) 5. Chamberlain JA. 1981 Hydromechanical design of fossil cephalopods. Syst. Assoc. Special Vol. 18, 289–336. 6. McKinney FK, Raup DM. 1982 A turn in the right direction: simulation of erect spiral growth in the bryozoans Archimedes and Bugula. Paleobiology 8, 101–112. 7. Raup DM, McGhee GR, McKinney FK. 2006 Source code for theoretical morphologic simulation of helical colony form in the Bryozoa. Palaeontol. Electron. 9, 7. (http://palaeo-electronica.org/paleo/ 2006_2/helical/index.html) 8. McGhee GR, McKinney FK. 2000 A theoretical morphologic analysis of convergently evolved erect helical colony form in the Bryozoa. Paleobiology 26, 556–577. (doi:10.1666/0094-8373(2000) 026,0556:ATMAOC.2.0.CO;2) 9. McGhee GR, McKinney FK. 2002 A theoretical morphologic analysis of ecomorphologic variation in Archimedes helical colony form. Palaios 17, 556–570. (doi:10.1669/0883-1351(2002) 017,0556:ATMAOE.2.0.CO;2) 10. McKinney FK, McGhee GR. 2003 Evolution of erect helical colony form in the Bryozoa: phylogenetic, functional, and ecological factors. Biol. J. Linn. Soc. 80, 235–260. (doi:10.1046/j.1095-8312.2003. 00227.x) 11. Starcher RW, McGhee GR. 2013 Theoretical morphology of colonial meshworks in the Fenestrata (Bryozoa): modelling hydraulic-resistance
6
