Limits in the Evolution of Biological Form: a Theoretical Morphologic Perspective Rsfs.Royalsocietypublishing.Org George R

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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

Limits in the evolution of biological form can be empirically demonstrated by Research using theoretical morphospace analyses, and actual analytic examples are given for univalved ammonoid shell form, bivalved brachiopod shell form Cite this article: McGhee GR Jr. 2015 and helical bryozoan colony form. Limits in the evolution of form in these Limits in the evolution of biological form: animal groups can be shown to be due to functional and developmental a theoretical morphologic perspective. Interface constraints on possible evolutionary trajectories in morphospace. Future evol- Focus 5: 20150034. utionary-limit research is needed to analyse the possible existence of temporal http://dx.doi.org/10.1098/rsfs.2015.0034 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: 1. Limits in evolution: analytic examples astrobiology, computational biology, Actual analytic examples of limits in the evolution of biological form in synthetic biology theoretical morphospaces are given in figures 1–3, summarized in table 1, and are discussed in this section of the paper. Theoretical morphospaces are Keywords: ‘n-dimensional geometric hyperspaces produced by systematically varying evolutionary limits, evolutionary constraints, 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 simu- theoretical morphospaces, Ammonoidea, lations of both existent and non-existent biological form and hence contain the Brachiopoda, Bryozoa limit boundary between those two regions of the morphospace (for an overview of the technique of theoretical morphospace analysis, see [1,2]). Author for correspondence: In figure 1 is given a two-dimensional plane within a four-dimensional George R. McGhee Jr theoretical morphospace of computer-simulated planispiral univalved shell forms created by Raup [3] for the analysis of evolution in ancient nektonic e-mail: [email protected] 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 swimming- efficiency 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

4.5 rsfs.royalsocietypublishing.org

0.50 3.5

ELEV 0.20 W 2.5

0.05 nefc Focus Interface 10 30 50 70 90 1.5 BWANG Figure 3. A theoretical morphospace of computer-simulated helical bryozoan colony form, where the forms shown within the limits of the polygon bound-

0.1 0.3 0.5 0.7 5 D ary in the centre of the figure actually exist in helical bryozoans. Adapted 20150034 : from McGhee [1]. 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]. Table 1. Limits in the evolution of cephalopods, brachiopods and bryozoans.

13 swimming cephalopod shell forms 12 hydrodynamic limit: minimum SEC ¼ 40 for functional shell forms 11 10 biconvex brachiopod shell forms 9 internal volume limit: minimum volume-to-surface-area ratio ¼ 7 for 8 functional shell forms 7 whorl overlap limit: minimum dorsal log W ¼ 3, ventral log W ¼ 2, 6 5 for functional shell forms dorsal valve log W dorsal valve 4 helical bryozoan colony forms 3 ﬁltration efﬁciency limit: minimum colony SAI ¼ 0.5 and BDI ¼ 25 2 1 for functional colony forms 1 432 1312111098765 hydraulic resistance limit: maximum colony SAI ¼ 7 and BDI ¼ 60 ventral valve log W for functional colony forms 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]. 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 have W ¼ 3.4 and D ¼ 0.04 [3] and are very similar in appear- within the theoretical morphospace (table 1). The first is an ance to the shell form shown at coordinates W ¼ 3.5, D ¼ 0.1 internal volume limit: biconvex brachiopods use a tentacular within the polygon boundaries in figure 1. pumping and feeding organ, the lophophore, to partition the A second example of limits in evolution is given in interior of their shells into inhalent and exhalent filtration figure 2, which illustrates a plane within a seven-dimensional chambers for the purpose of filter-feeding seawater. The theoretical morphospace of planispiral bivalved shell forms lophophore is coiled in a variety of three-dimensional geome- created for the analysis of evolution in brachiopods [1]. The tries in living and fossil biconvex brachiopods, and all two dimensions of the space are logarithms of the whorl lophophore coil geometries require sufficient internal shell expansion rate, log W, for the dorsal and ventral valves of volume, V, to be contained within the external surface area, the brachiopod shell. This morphospace has been used in SA, of the shell—a proportion that is measured by a the analysis of 324 species of biconvex brachiopods (Brachio- volume-to-surface-area ratio, V/SA [1]. All shell forms poda: Rhynchonelliformes: Rhynchonellata) and has revealed evolved by the biconvex brachiopods have a minimum that those shell forms contained within the polygon bound- limit of V/SA ¼ 7; shell form geometries with V/SA ratios aries illustrated in the centre of figure 2 exist in biconvex below this limit are non-existent in biconvex brachiopods brachiopods. As with the ammonoid shell forms, simulated (for example, the non-existent biconvex brachiopod shell shell forms outside of the polygon are geometrically possible form shown at coordinates dorsal log W ¼ 13, ventral log but are non-existent in biconvex brachiopods. W ¼ 13 has V/SA ¼ 5.5). Downloaded from http://rsfs.royalsocietypublishing.org/ on November 16, 2015

Unlike univalved ammonoid shell forms (figure 1), the f:0 3 shell of a brachiopod consists of two separate univalves functional rsfs.royalsocietypublishing.org articulated together (figure 2). This bivalved shell geometry f:3 constraint boundary 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 f:1 a univalve occurs whenever W D 1 (for example, exam- ine the ammonoid shell at coordinates W ¼ 1.5, D ¼ 0.3 in developmental figure 1 in which the whorls of the shell overlap as W constraint boundary f:2 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 brachio- form hyperdimension Focus Interface pod is limited to values of W , 1/D in its valves because of whorl overlap. For example, the shell at coordinates dorsal Figure 4. Venn diagram of theoretically possible regions of form determined log W ¼ 3, ventral log W ¼ 2 in figure 2 has V/SA ¼ 11, and by the limits of functional and developmental constraint within theoretical

this V/SA value is the maximum possible in the morphospace morphospace. Forms f:0 are non-functional and developmentally impossible 5 20150034 : as all shells with lesser values of W have whorl overlap (as for life on Earth, forms f:1 are both functional and developmentally possible, illustrated by the rows of whorl-overlapped unarticulated forms f:2 are developmentally possible but non-functional and forms f:3 are valves in figure 2, and the two computer simulations in the functional but developmentally impossible for life on Earth. Adapted from lower left corner of the morphospace which illustrate imposs- McGhee [12]. ible 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 pos- maintain minimum limits of SAI ¼ 0.5 and BDI ¼ 25, and terior part of the shell). As biconvex brachiopods typically maximum limits of SAI ¼ 7 and BDI ¼ 60 [8–10]. have dorsal valves with D ¼ 0.01 and ventral valves with The minimum limits of SAI ¼ 0.5 and BDI ¼ 25 appear to D ¼ 0.1, they are limited to a minimum dorsal log W ¼ 3, be filtration efficiency limits (table 1) in that colonies with ventral log W ¼ 2 for functional shell forms (figure 2 and colony surface areas and branch densities less than those table 1). limits simply do not catch or intercept enough food across One last analytic example of limits in evolution is given in their filtration sheets to support the metabolic needs of the figure 3, which illustrates computer simulations in two dimen- colony (i.e. too much water escapes unfiltered through the sions of a three-dimensional theoretical morphospace of helical colony). The maximum limits of SAI ¼ 7 and BDI ¼ 60 bryozoan colony forms created for the analysis of their evol- appear to be hydraulic resistance limits (table 1) in that colonies ution by McKinney & Raup [6] and Raup et al. [7]. The two with colony surface areas and branch densities higher than dimensions of the space are ELEV, the rate of climb of the cen- those limits impede the flow of water through the colony [11] tral helix of the colony, and BWANG, the angle between the and dead zones of stagnant water develop within the colony helix axis and the filtration-sheet whorls of the colony. Helical centre (see discussion in [1]). For example, the non-existent colony forms have been convergently evolved by several clades colony geometry at coordinates ELEV ¼ 0.50, BWANG ¼ 90 of bryozoans, as seen in species of the genera Archimedes in figure 3 has SAI , 0.5 and, at the other extreme, the (Bryozoa: Stenolaemata: Fenestrata: Fenestellidae), Crisidmonea non-existent colony geometry at coordinates ELEV ¼ 0.20, (Bryozoa: Stenolaemata: Cyclostomata: Crisinidae), Bugula BWANG ¼ 10 has SAI ¼ 15. (Bryozoa: Gymnolaemata: Cheilostomata: Buguloidea: Buguli- dae) 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 2. Limits in evolution: theoretical possibilities those colonies contained within the polygon boundaries illus- The observed empirical limits in the evolution of actual animals trated in the centre of figure 3 exist in helical bryozoans even illustrated in figures 1–3 are abstracted to theoretical limits in a though, as for the ammonoids and brachiopods, computer theoretical morphospace in figure 4. Two types of limit in simulations reveal that other colony geometries are possible the evolution of biological form are graphically portrayed but have never been evolved by the bryozoans. within the morphospace of hypothetical forms: limits due to Why have the bryozoans convergently evolved some geo- functional constraint (the boundaries of the solid-line rectangle) metrically possible helical colony forms but not others? and limits due to developmental constraints (the boundaries of Unlike ammonoid and brachiopod individually shelled ani- the dotted-line rectangle). Empirical examples of actual func- mals, the helical bryozoans are colonies of thousands of tional constraint limits are illustrated in figures 1–3; these are tiny individual zooids arranged along the branches in the fil- the hydrodynamic, internal volume, filtration efficiency and tration-sheet whorls of the colony. Like the brachiopods, the hydraulic resistance limits (table 1) discussed in the previous bryozoans are also lophophorate filter feeders but now, section of the text. Biological forms shown within the limit instead of the geometric arrangement of one lophophore boundaries shown in figures 1–3 are functional for the animals within one brachiopod shell form, the geometric arrangement analysed, forms outside the limit boundaries are not. of thousands of tiny lophophores determines the form of the An empirical example of an actual developmental con- helical colony. Two aspects of the geometric arrangement of straint limit is seen in the brachiopod whorl overlap limit the zooids within the colony are measured by a colony sur- (figure 2 and table 1). The region of morphospace outside face area index (SAI) and a branch density index (BDI), and the whorl overlap limit does not contain non-functional analyses have revealed that helical bryozoan colonies forms; rather, this region contains geometrically impossible Downloaded from http://rsfs.royalsocietypublishing.org/ on November 16, 2015

forms. That is, it is impossible for a brachiopod to develop f:0 4 these forms at all—the question as to whether they are functional rsfs.royalsocietypublishing.org functional or non-functional is moot. f:3 constraint boundary The mapping of the functional and developmental limit boundaries in figure 4 allows us to discern a Venn diagram of f:1 four distinct sets of theoretical forms within the morphospace [12]:

f:4 (1) Form set ff:0g: these are the forms, f:0, that are non- developmental functional and cannot be developed by life on Earth. constraint boundary f:2 (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). form hyperdimension Focus Interface (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 Figure 5. Venn diagram of the actual Earth life forms subset f:4 region on Earth. within theoretical morphospace, illustrating the Gouldian ‘radical contingency

(4) Form set ff:3g: these are the forms, f:3, that are functional thesis’ that actualized biological forms are a small fraction of the set of func- 5 20150034 : but that cannot be developed by life on Earth. tional, Earth-possible morphologies f:1. Adapted from Powell & Mariscal [13].

Empirical examples of members of the form set ff:1g can be seen in all those forms located within the functional-limit natural selection theory, an obvious causal explanation for polygon boundaries illustrated in figures 1–3, and examples empty morphospace would be that the forms present in the of members of form set ff:2g can be seen in those simulated empty region of morphospace are non-functional; that is, forms located outside of the functional-limit polygon bound- they belong to form set ff:2g (figure 4). However, an alterna- aries. The morphospace region located outside the whorl tive point of view could just as easily maintain that such overlap developmental limit in figure 2 illustrates an empiri- hypothetical non-existent morphologies might function per- cal example of the morphospace coordinates for members of fectly well in nature but that the process of evolution the form set ff:0g. What is not illustrated in figures 1–3 are simply has not produced them yet. hypothetical members of theoretical form set ff:3g: forms The creation of Powell & Mariscal’s [13] new theoretical that are functional but that nevertheless cannot be developed subset ff:4g thus requires the existence of an additional by life on Earth. Does such a set of forms actually exist? new theoretical subset of ff:1g—there should exist members This is a question that will be considered in the next section of the functional and developmentally possible form set ff:1g of the paper. that are not members of the subset of actual forms ff:4g. A second question recently has been raised by Powell & These hypothetical forms belong to the following subset: Mariscal [13], who have argued for the subdivision of form set ff:1g to recognize a new subset of forms: (2) Form subset ff:5g: these are the forms, f:5, that are functional and developmentally possible but that nonetheless (1) Form subset ff:4g: these are the forms, f:4, that are func- have not yet been evolved by life on Earth. This subset is tional, developmentally possible, and that actually have here formally defined as ff:5g ¼ ff:1g\ff:4g ¼ ff j f [ been evolved by life on Earth. f:1, ff:4g.

The boundaries of the new subset of forms ff:4g within the The question is now not a question of whether Powell and theoretical morphospace is illustrated by Powell & Mariscal Mariscal’s subset ff:4g of actual functional forms exists—it [13] in figure 5. Note that they have drawn these boundaries does, as can be seen in figures 1–3 for ammonoids, brachio- such that the morphospace region occupied by the members pods and helical bryzoans—but rather whether subset ff:5g of this form subset is quite small. Powell & Mariscal [13] exists. If subset f f:5g does not exist, then neither does argued that Gould’s [14] ‘radical contingency thesis’ predicts subset ff:4g; that is, if set ff:5g ¼ Ø then ff:4g ¼ ff:1g. ‘smaller boundaries around the space of forms that are func- To rephrase the question: are there functional and devel- tional, developmentally possible, and actual’. Gould [14] opmentally possible forms that have not yet been evolved argued that all evolutionary trends are chains of historically by Earth life? That is, does ff:4g exist as a separate possible contingent events, and since the actual functional biological form subset? Or does ff:4g ¼ ff:1g; that is, have all func- forms that have been discovered by evolution are a function tional and developmentally possible forms for Earth life in of past contingent events there could exist numerous other fact been discovered by Earth life? 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 ‘his- torical constraint’ or ‘temporal constraint’ in the past (for 3. Questions for future research an extensive discussion of constraint concepts from a theoreti- An obvious question for future research concerns the exist- cal morphologic perspective, see [1]). The most striking ence or non-existence of form subset ff:5g. Is temporal feature of Raup’s [15] classic theoretical morphospace study constraint real—can we prove that perfectly functional, of computer-simulated mollusc shell form was that the over- developmentally possible biological forms exist that never- whelming majority of the morphospace was empty—that theless have not yet been evolved by life on Earth? In order there exist numerous geometrically possible shell forms that to answer that question, we must be able to create these no mollusc has ever evolved. From the point of view of non-existent forms and to analyse their functionality, and Downloaded from http://rsfs.royalsocietypublishing.org/ on November 16, 2015

the analytic techniques of theoretical morphology allow the dimensional geometry [27,28]. How many of the shell forms 5 researcher to do exactly that [2]. present in the morphospace region beyond the V/SA ¼ 7 rsfs.royalsocietypublishing.org Consider the case of the nektonic cephalopods in figure 1: limit in figure 2 were evolved by the strophomenate brachio- no active swimming cephalopods exist in the morphospace pods is currently not known but we do know that the region beyond the minimum limit of SEC ¼ 40. However, the region of space that contains non-functional forms, set ff:2g, for the of morphospace beyond the SEC ¼ 40 limit is not entirely biconvex rhynchonellate brachiopods contained functional empty of shelled cephalopods—this region was partially forms, set ff:1g, for the extinct strophomenate brachiopods. occupied early in the evolutionary history of the cephalopods At this point, a new morphospace containing non-biconvex but loosely coiled shell forms were rapidly, and convergen- concavo-convex and convexi-concave shell forms, in addition tly in multiple lineages, abandoned in favour of coiled to the biconvex spectrum of form shown in figure 2, has been forms with better streamlining and swimming efficiency created and the analysis of strophomenate shell form is [16–20]. Curiously, however, loosely coiled forms were also currently in progress. Focus Interface convergently re-evolved by cephalopods in the Mesozoic; Last, in the case of the filter-feeding helical bryozoans, for example, the Cretaceous ammonoid Crioceras and the there are no known bryozoan colonies that exist in the Ordovician nautiloid Aphetoceras had shells very similar to empty region of morphospace beyond the limits shown

the shell form seen at the morphospace coordinates W ¼ 2.5, in figure 3. This region of space appears to contain only 5 20150034 : D ¼ 0.5; shells in which the whorls do not touch. Even more non-functional forms for bryozoans—but are these forms extreme, the Jurassic ammonoid Spiroceras and the Devonian functional for some other evolutionary clade of organisms nautiloid Goldringia had shells very similar to that at coordi- with a different mode of feeding? Bryozoan-like fenestrated nates W ¼ 4.5, D ¼ 0.7, an odd geometry known as gyroconic colony forms have been convergently evolved by both the in nautiloids. cnidarians (e.g. the red octocoral Tubipora) and the hemichor- How could this be, as all of these shell forms have SEC , dates (e.g. the extinct graptolite Dictyonema), but the only 40? The answer is that these ammonoids and nautiloids did other helical colony forms known to me are the flexible not swim—they were either planktonic, passively floating skeletons of a few corals, such as the whip black coral up in the water column, or demersal, forms living on the Cirrhipathes [29]. These sessile predators have non-erect sea bottom [20–22]. Thus, the region of the morphospace colony forms that stretch horizontally in water currents, with non-functional forms, set ff:2g, for the nektonic shelled and possess a geometry unlike any of those shown in cephalopods contained functional forms, set ff:1g, for the figure 3 for the bryozoans. non-nektonic shelled cephalopods. How much of this A second question for future research concerns the exist- region of morphospace was occupied by non-nektonic cepha- ence or non-existence of form set ff:3g. This question is of lopods is currently not known—it is entirely possible that major importance to the study of convergent evolution as some of the shell forms in the morphospace beyond the these hypothetical forms imply that there exists somewhere SEC ¼ 40 limit boundary illustrated in figure 1 were possible in the universe an alien set of functional biological forms functional shell forms for non-nektonic cephalopods that that cannot be developed by Earth life, and thus these alien nevertheless were not evolved by any of the non-nektonic life forms would not be convergent on any of the forms of life cephalopods. We will not know until someone accepts the seen on Earth. Within our own Solar System (since, at pre- challenge to conduct theoretical morphospace analyses of sent, we can only dream of spacecraft that could take us to the non-nektonic shelled cephalopods—elegant computer other star systems) only the far-distant large planet-like simulations and morphospaces for these forms have been Titan, a moon of Saturn, and Triton, a moon of Neptune, created [23–25] and simply await data analyses [26]. offer physical conditions and chemistries radically different Consider next the case of the filter-feeding biconvex bra- from those found on Earth. It has already been hypothesized chiopods in figure 2: no biconvex brachiopods exist in the [30–32] that Titan might contain life forms that could metab- morphospace beyond the minimum limit V/SA ¼ 7, and there olize acetylene (C2H2), using atmospheric hydrogen (H2)to are good functional reasons why no brachiopods with complex produce methane (CH4), analogous to Earth life that metab- three-dimensionally coiled lophophores exist in this region of olizes glucose (C6H12O6) with atmospheric oxygen (O2)to the space. However, there existed other brachiopods—the produce carbon dioxide (CO2). non-biconvex brachiopods (Brachiopoda: Rhynchonelliformes: If life forms exist on Titan, they would belong to form set Strophomenata)—that did occupy some of this region of the ff:3g, and I predict they would look nothing like life on theoretical morphospace. Some of the extremely compressed, Earth. The challenge will be to design and send more space- flattish shell forms of the strophomenides in particular had craft to both Titan and Triton to search for life forms on their V/SA ratios as low as 0.5, approaching the absolute limit of surfaces with robot rovers. 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 Competing interests. I declare I have no competing interests. minimum internal volumes to maximum shell surface areas, Funding. Acknowledgement is made to the Donors of the Petroleum shell forms with the exact opposite geometry to those found Research Fund, administered by the American Chemical Society, in the biconvex brachiopods. for partial support of this research, and to the US National Science How could this be? Our best explanation is that the extinct Foundation. non-biconvex brachiopods used a radically different feeding Acknowledgements. I thank Simon Conway Morris for the invitation to system from that of the living biconvex ones, a feeding speak at the Cambridge conference on Limits in Evolution, and Vic- toria Ling for her assistance in the logistics of the conference system in which the entire mantle-tissue surface of the interior proceedings. I also thank Christian Klug and another anonymous of the shell was ciliated and gathered food in addition to that reviewer for their thoughtful comments and suggestions that gathered by a small, weak lophophore with a simple two- helped me improve the manuscript. Downloaded from http://rsfs.royalsocietypublishing.org/ on November 16, 2015

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