CHAPTER 3 Landscapes, Surfaces, and Morphospaces: What Are They Good For?

Massimo Pigliucci

3.1 Introduction is precisely what in philosophy of science is meant by reduction; see Brigandt 2008). This time the non- Few metaphors in biology are more enduring fitness axes of the landscape were phenotypic traits, than the idea of Adaptive Landscapes, originally not genetic measures at all. Even more recently, proposed by (1932) as a way to Lande and Arnold (1983) proposed a mathematical visually present to an audience of typically non- formalism aimed at estimating actual (as opposed mathematically savvy his ideas about the to Simpson’s hypothetical) fitness surfaces, making relative role of and use of standard multiple regression analyses. But in the course of . The metaphor, how- while Simpson was talking about macroevolution- ever, was born troubled, not the least reason for ary change involving , Lande and Arnold which is the fact that Wright presented different were concerned with microevolutionary analyses diagrams in his original paper that simply can- within individual populations of a single . not refer to the same concept and are therefore In principle, it is relatively easy to see how hard to reconcile with each other (Pigliucci 2008). one can go from individual- landscapes For instance, in some usages, the landscape’s non- to genotypic-frequency landscapes (the two Wright fitness axes represent combinations of individual versions of the metaphor). However, the (implied) (which cannot sensibly be aligned on a further transition from either of these to pheno- linear axis, and accordingly were drawn by Wright types (either in the Lande–Arnold or in the Simpson as polyhedrons of increasing dimensionality). In version) is anything but straightforward because of other usages, however, the points on the diagram the notorious complexity and non-linearity of the represent allele or genotypic frequencies,andsoare so called genotype– mapping function actually populations, not individuals (and these can (Alberch 1991; Pigliucci 2010). This is a serious issue indeed be coherently represented along continuous if—as I assume is the case—we wish to use the land- axes). scape metaphor as a unified key to an integrated Things got even more confusing after the land- treatment of genotypic and phenotypic evolution scape metaphor began to play an extended role (as well as of micro- and macroevolution). Without within the Modern Synthesis in evolutionary biol- such unification would be left ogy and was appropriated by G. G. Simpson (1944) in the awkward position of having two separate to further his project of reconciling macro- and theories, one about genetic change, the other about , i.e. to reduce to pop- phenotypic change, and no bridge principles to con- ulation genetics (some may object to the characteri- nect them. zation of this program as a reductive one, but if the One more complication has arisen in more recent questions raised by one discipline can be reframed years, this one concerning Wright-style fitness land- within the conceptual framework of another, that scapes. Work by Gavrilets (2003; see also Chapter 17

26 LANDSCAPES, SURFACES, AND MORPHOSPACES: WHAT ARE THEY GOOD FOR? 27 this volume) and collaborators, made possible by context of the Modern Synthesis (Mayr and Provine the availability of computing power exceeding by 1980) as a theory essentially rooted in (though cer- several orders of magnitudes what was achievable tainly not limited to) , where throughout the twentieth century, has explored the evolution is often simply defined as change in features of truly highly dimensional landscapes—as allelic frequencies (Futuyma 2006). opposed to the standard two- or three-dimensional Despite some confusion due to the often inter- ones explicitly considered by Wright and by most changeable use of terms like “fitness” and “Adap- previous authors. As it turns out, evolution on tive” Landscape, I will use and build here on the so-called “holey” landscapes is characterized by more rigorous terminology followed by authors qualitatively different dynamics from those sug- such as McGhee (2007) and distinguish the follow- gested by the standard low-dimensional version ing four types of landscapes: of the metaphor—a conclusion that has led some landscapes. These are the sort of entities authors to suggest abandoning the metaphor alto- originally introduced by Wright and studied in a gether, in favor of embracing directly the results of high-dimensional context by Gavrilets and collabo- formal modeling (Kaplan 2008; though see Plutyn- rators. The non-fitness dimensions are measures of ski 2008 and Chapter 2 for a somewhat different genotypic diversity. The points on the landscape are take). population means, and the mathematical approach In this essay I wish to discuss the implications is rooted in population genetics. of four versions of the metaphor, often referred Adaptive Landscapes. These are the non- to as fitness landscapes, Adaptive Landscapes, fit- straightforward “generalizations” of fitness ness surfaces, and morphospaces. I will argue that landscapes introduced by Simpson, where the moving from one to any of the others is signifi- non-fitness dimensions now are phenotypic traits. cantly more difficult than might at first be surmised, The points on the landscape are populations and that work with morphospaces has been unduly speciating in response to ecological pressures or neglected by the research community. even above-species level lineages (i.e. this is about macroevolution). Fitness surfaces.ThesearetheLande–Arnoldtype 3.2 Four types of landscapes of landscapes, where phenotypic traits are plot- As I mentioned earlier, there are several versions of ted against a surrogate measure of fitness. They the “landscape” metaphor that have proliferated in are statistical estimates used in quantitative genetic the literature since Wright’s original paper. Indeed, modeling, and the points on the landscape can be Wright himself was referring—in that very same either individuals within a population or popu- paper—to at least two conceptions of landscapes, lation means, in both cases belonging to a single one with individual genotypes as the points on the species (i.e. this is about microevolution). (necessarily non-continuous) landscape, the other Morphospaces. These were arguably first intro- with populations identified by gene or genotype duced by Raup (1966), and differ dramatically from frequencies (in a continuous space). I will ignore the other types for two reasons: (a) they do not the distinction between the two types of Wright have a fitness axis; (b) their dimensions, while rep- landscapes for two reasons: first, they are con- resenting phenotypic (“morphological”) traits, are nected in a conceptually straightforward manner, generated via a priori geometrical or mathematical since it is obviously possible to go from individ- models, i.e. they are not the result of observa- ual genotypes to populations of genotypes with- tional measurements. They typically refer to across- out any theoretical difficulty. Second, most of the species (macroevolutionary) differences, though post-Wright literature, including the presentation they can be used for within-species work. of the metaphor in textbooks and the more recent work on “holey” landscapes, is framed in terms Let us take a look in a bit more detail at each type of gene/genotype frequencies, not individual geno- of landscape, to familiarize ourselves with their types. This is understandable within the broader respective similarities and differences. Throughout 28 PART I HISTORICAL BACKGROUND AND PHILOSOPHICAL PERSPECTIVES

Iwilluseboththeterminologyjustsummarized work of Cowperthwaite and Meyers (2007) on 30- and the names of the relevant authors, to reduce nucleotide long binary RNA molecules. This is confusion at the cost of some redundancy. The first arguably one of the simpler models of genotype– thing we notice from even a cursory examination phenotype–fitness relations, and it is computation- of the literature is that there are few actual biolog- ally tractable and empirically approachable. Still, ical examples of fitness landscapes (Wright-style) 30-nucleotide binary molecules correspond to a or Adaptive Landscapes (Simpson-style) available, bewildering one billion unique sequences! These while there is a good number of well understood in turn generate “only” about 220,000 unique fold- examples of morphospaces (Raup-style) and partic- ing shapes in a G/U landscape and a “mere” 1000 ularly of adaptive surfaces (Lande–Arnold style). shapes in the A/U landscape, both of which these These differences are highly significant for my dis- authors have tackled. In other words, a genotypic cussion of the metaphor. space of a billion sequences corresponds (obviously Beginning with Wright-type, fitness landscapes, in a many-to-many manner) to a phenotypic space many of the examples in the literature are entirely of thousands to hundreds of thousands of possibil- conceptual, i.e. presented by various authors only ities, each characterized by its own (environment- for heuristic purposes. It should be obvious why dependent, of course) fitness value. it is so: to actually draw a “real” fitness landscape Things get even more complex when we we need a reasonably complete description of the move from RNA to proteins: Wroe et al. (2007) genotype fitness mapping function, i.e. we need have explored evolution in protein structure- → data about the fitness value of each relevant combi- defined phenotypic space, focusing in particular nation of genotypes that we happen to be interested on so-called “promiscuity,” the ability of a given in. For most purposes this is next to impossible. protein to perform two functions because of the Dobzhansky (1970, p. 25) famously put it this way: alternation between multiple thermodynamically stable configurations. Proteins are, of course, much Suppose there are only 1000 kinds of genes in the more complicated biochemical objects than RNA world, each gene existing in 10 different variants or molecules. They are made of more types of build- alleles. Both figures are patent underestimates. Even ing blocks, and their three-dimensional structure is so, the number of gametes with different combina- more difficult to predict from their linear sequence. tions of genes potentially possible with these alleles Still, studies like those of Wroe et al. show some would be 101000. This is fantastic, since the number of subatomic particles in the universe is estimated as a interesting similarities between RNA and protein mere 1078. landscapes, perhaps one of the most significant being that—as predicted by the “holey” landscape Indeed, things are complicated even further by models studied by Gavrilets—large portions of phe- the fact that the genotype fitness function can be notypic hyperspace are actually neutral in terms of → thought of as the combination of two subfunctions: the fitness of the forms that define that space, which genotype phenotype and phenotype fitness. means that much of the time evolution is a matter → → The second function requires an understanding of of sliding around a fitness landscape via genetic fitness (Lande–Arnold) surfaces, which can then be drift, with occasional “punctuations” of selective translated into fitness landscapes through the first episodes. function. I know of very few instances in which Let us turn now to Adaptive (Simpson) Land- anything like that has even been attempted, given scapes. The original idea was to use the metaphor to the so far (and possibly in principle) enormous dif- show how macroevolutionary events like ecological ficulties, both empirical and computational. speciation can be understood in terms of the then The major class of exceptions to the paucity of nascent theory of population genetics, developed actual fitness (Wright) landscapes is in itself highly to directly address microevolutionary processes. illuminating of both the potential and limitations Simpson, for instance, presented a (hypothetical) of the metaphor: studies of the evolution of RNA analysis of speciation in the Equidae (horse) lin- and protein structures. Consider for instance the eage from the Cenozoic (Simpson 1953). The sub- LANDSCAPES, SURFACES, AND MORPHOSPACES: WHAT ARE THEY GOOD FOR? 29 family (i.e. significantly above species level) Hyra- (unlike the much more experimentally confined cotheriinae is represented as occupying an adap- cases of RNA and protein structures mentioned ear- tive peak characterized by their browsing-suited lier). Most crucially, of course, there is essentially teeth morphology during the Eocene. Simpson also no connection between fitness surfaces and either imagined a contemporary, empty, adaptive peak fitness (Wright) landscapes or adaptive (Simpson) for species whose teeth are suitable for grazing. landscapes. The reason for the former lack of con- The diagram then shows how gradually, during nection is that we do not have any idea of the the Oligocene, the subfamily Anchitheriinae evolved genotype phenotype mapping function under- → anagenetically (i.e. by replacement) from their Hyra- lying most traits studied in selection analyses, so cotheriinae ancestors. The new subfamily, as a result that we cannot articulate any transition at all from of evolving greater body size, also acquired a teeth Wright landscapes to Lande–Arnold surfaces. In morphology that corresponded to a gradual move- terms of a bridge from Lande–Arnold surfaces to ment of the peak itself closer to the empty grazing Simpson landscapes, this would seem to be easier zone. Finally, in the late Miocene, the Anchitheriinae because they are both expressed in terms of phe- gave origin, cladistically (i.e. by splitting) to two notypic measurements versus fitness estimates. But lineages, one of which definitely occupied the graz- there is where the similarity ends: Lande–Arnold ing peak and gave rise to the Equinae. Simpson’s selection coefficients cannot be compared across reconstruction of the events is, of course, compati- species, and they do not incorporate any of the func- ble with what we knew then of the phylogeny and tional ecological analyses of the type envisioned by functional ecology of the horse family, but the land- Simpson. Indeed, a major problem with the liter- scape’s contour and movements are by necessity ature on selection coefficients is that they simply entirely hypothetical. This is a truly heuristic device ignore functional ecology altogether: we can mea- to make a conceptual point, not the result of any sure selection vectors, but we usually have no idea quantitative analysis of what actually happened. of what causes them, and no such idea can come The situation is quite different for fitness (Lande– from multiple regression analyses (this is simply a Arnold) surfaces, which are supposed to be closely case of the general truth that correlation does not related to Simpson’s landscapes, but in fact work imply causation, let alone a specific type of causa- significantly differently in a variety of respects. tion). All of this means that—despite claims to the For one thing, the literature is full of Lande– contrary (Arnold et al. 2001; Estes and Arnold 2007; Arnold type selection analyses, because they are see also Chapter 13) adaptive surfaces are not awell relatively straightforward to carry out empirically worked out bridge between micro- and macroevo- and in terms of statistical treatment. As is well lution (see Kaplan 2009 for a detailed explanation known, phenotypic selection studies of this type are based on the specific claims made by Estes and based on the quantification of selection vectors by Arnold 2007). means of statistical regression of a number of mea- The situation is again different when we move to sured traits on a given fitness proxy, appropriate or morphospaces. Arguably the first example of these available for the particular organism under study. was proposed by Raup (1966), who generated a There are, however, several well-known problems theoretical space of all possible forms of bivalved of implementation (Mitchell-Olds and Shaw 1987). shells based on a simple growth equation, with Among other things, surveys of Lande–Arnold type the parameters of the equation defining the axes of studies show that many actual estimates of selec- the morphospace. As I have already noted, there tion coefficients are unreliable because they are is no fitness axis in morphospaces, though as we based on too small sample sizes (Kingsolver et al. shall see later, fitness/adaptive considerations do 2001; Siepielski et al. 2009). Moreover, they tend enter into how morphospaces are used. Moreover, to have very low replication either spatially (from morphospaces do not depend on any actual mea- one location to the other) or temporally (from one surement at all: they are not constructed empiri- season to another), thereby undermining any claim cally, by measuring gene frequencies or phenotypic to the generality or reproducibility of the results traits, they are drawn from a priori—geometrical 30 PART I HISTORICAL BACKGROUND AND PHILOSOPHICAL PERSPECTIVES or mathematical—considerations of what gener- one (Whitlock et al. 1995)—that do not actually exist ates biological forms. As documented in detail by as formulated, or that at the very least take a dra- McGhee (2007), morphospaces have been generated matically different form, in more realistic hyper- for a variety of organisms, from invertebrates to dimensional “landscapes.” Even when (relatively) plants, and they have been put to use by comparing low-dimensional scenarios actually apply, as in the actually existing forms with theoretically possible cases of RNA and protein functions briefly dis- ones that are either extinct or that for some reason cussed earlier, the work is done by intensive com- have never evolved. Which brings us to the ques- puter modeling, not by the metaphor, visual or tion of what biologists actually do with the various otherwise. types of landscapes. The peak shift problem started captivating researchers’ imagination soon after Wright’s origi- nal paper, and consists in explaining how natural 3.3 What are landscapes for? selection could move a population off a local fit- When it comes to asking what the metaphor of ness peak. The landscape metaphor seems to make landscapes in biology is for we need to begin by it obvious that there is a problem, and that it is distinguishing between the visual metaphor, which a significant one, because of course natural selec- is necessarily low-dimensional, and the general idea tion could not force a population down a peak to that evolution takes place in some sort of hyper- cross an adaptive valley in order to then climb up dimensional space. Remember that Wright intro- anearby(presumablyhigher)peak.Thatwould duced the metaphor because his advisor suggested amount to thinking of natural selection as a teleo- that a biological audience at a conference would logical process, something that would gratify cre- be more receptive toward diagrams than toward ationists of all stripes, but is clearly not a viable aseriesofequations.Butofcoursethediagrams solution within the naturalistic framework of sci- are simply not necessary for the equations to do ence (that said, there are situations described in their work. More to the point, the recent papers population genetics theory where natural selec- by Gavrilets and his collaborators, mentioned pre- tion does not always increase fitness, as in several viously, have shown in a rather dramatic fashion scenarios involving frequency dependent selection that the original (mathematical) models were too (Hartl and Clark 2006)). simple and that the accompanying visual metaphor Wright famously proposed his shifting balance is therefore not just incomplete, but highly mis- theory of interdemic selection as an alternative leading. Gavrilets keeps talking about landscapes mechanism to explain peak shifts (Wright 1982): of sorts, but nothing hinges on the choice of that genetic drift would move small populations off- particular metaphor as far as the results of his peak, and natural selection would then push some calculations are concerned—indeed, arguably we of them up a different peak. This particular solution should be using the more imagery-neutral concept to the problem has proven theoretically unlikely, of hyperdimensional spaces, so not to deceive our- and it is of course very difficult to test empiri- selves into conjuring up “peaks” and “valleys” that cally (Coyne et al. 1997). Several other answers to do not actually exist. the peak shift problem have been explored, includ- In a very important sense Wright’s metaphor of ing the (rather obvious) observation that peaks are what we have been calling fitness landscapes was not stable in time (i.e. they themselves move), or meant to have purely heuristic value, to aid biol- that and learning may help ogists to think in general terms about how evolu- populations make a local “jump” from one peak tion takes place, not to actually provide a rigorous to another. It is also interesting to observe that of analysis of or predictions about the evolutionary course there is no reason to think that natural selec- process (it was for the math to do that work). tion has to provide a way to shift between peaks, Seen from this perspective, fitness landscapes have since it is a satisficing, not an optimizing, pro- been problematic for decades, generating research cess. Getting stuck on a local peak and eventually aimed at solving problems—like the “peak shift” going extinct is the fate shared by an overwhelming LANDSCAPES, SURFACES, AND MORPHOSPACES: WHAT ARE THEY GOOD FOR? 31 majority of populations and species (van Valen sional fitness (but strictly speaking not adaptive) 1973). The current status of this particular prob- surfaces. Tellingly, though, what does the work is lem, as I said, is that Gavrilets’s work has shown not the occasional graph of a partial surface (or its that there simply aren’t any such things as peaks often hard to interpret multivariate rendition) but, and valleys in hyperdimensional genotypic spaces, instead, a tabular output from Lande–Arnold style but rather large areas of quasi-neutrality (where multiple regression analyses. What understanding therefore there is ample room for drift, in that we do have of fitness surfaces comes from the actual sense at least indirectly vindicating Wright’s origi- statistics and our ability to make sense of them (and nal intuition of the importance of stochastic events), of their limitations (Mitchell-Olds and Shaw 1987; punctuated by occasional fitness holes and “mul- Pigliucci 2006)), not from visualizations of biologi- tidimensional bypasses” (Gavrilets 1997), i.e. con- cally interpretable surfaces. nections between distant areas of the hyperspace The situation is significantly better, I suggest, in that can be exploited by natural selection to “jump,” the case of the fourth type of landscape: Raup- though the term now means nothing like what the style morphospaces. McGhee (2007) discusses sev- classical literature on peak shift refers to. eral fascinating examples, but I will focus here on Similar considerations to the ones made in work done by Raup himself, with crucial follow- the case of fitness landscapes apply to Adap- up by one of his graduate students, John Chamber- tive Landscapes, the phenotype-based version of lain. It is a study of potential ammonoid forms that the metaphor introduced by Simpson—albeit with puts the actual (i.e. not just heuristic) usefulness of some caveats. Again, the few actual visual examples morphospaces in stark contrast with the cases of fit- of such landscapes to be found in the literature have ness and Adaptive Landscapes/surfaces discussed heuristic value only, though at least they are poten- so far. tially less misleading than Wright-type fitness land- Raup (1967) explored a mathematical-geo- scapes simply because low dimensionality is a more metrical space of ammonoid forms defined by two realistic situation when we are considering specific variables: W, the rate of expansion of the whorl of aspects of the phenotype. (The phenotype tout court the shell; and D, the distance between the aperture of course is a high-dimensionality object, but biolo- of the shell and the coiling axis. As McGhee shows gists are rarely interested in that sort of phenotypic in his detailed discussion of this example, Raup analyses, focusing instead either on a small sam- arrived at two simple equations that can be used ple of characters, or on a particular aspect of the to generate pretty much any shell morphology phenotype—such as skull shape or leaf traits—that that could potentially count as “ammonoid-like,” can be studied via a small number of variables.) As including shells that—as far as we know—have we have seen, Simpson’s classic example concerned never actually evolved in any ammonoid lineage. the evolution of equids, the horse family, and the Raup then moved from theory to empirical data corresponding landscape first appeared in his The by plotting the frequency distribution of 405 actual Major Features of Evolution (Simpson 1953). That dia- ammonoid species in W/D space and immediately gram makes for a great story, which could even be discovered two interesting things: first, the true (and is certainly consistent with the paleonto- distribution had an obvious peak around 0.3

0 W = 1/D 0 3

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Figure 3.1 A frequency plot and functional analysis of the W/D morphospace of ammonoid shells, following work by Raup and Chamberlain. The upper graph is based on Raup’s (1967) original paper, and shows that of the 405 species of ammonoids known at that time all of them could be found below the W=1/Dhyperbole—inagreementwiththefactthatshellsfoundwithinthatparameterspacehavehigherswimmingefficiency.Noticetheonefrequency peak around the 0.3

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Figure 3.2 The same W/D morphospace originally studied by Raup and Chamberlain (Fig. 3.1), now augmented with an additional 597 newly discovered species of ammonoids. The frequency distribution of actual forms (top), showing two peaks, now nicely corresponds with the two predicted adaptive peaks based on drag coefficients (or its reverse, swimming efficiency, bottom). (Graphs from McGhee (2007), reproduced with permission from Cambridge University Press.) LANDSCAPES, SURFACES, AND MORPHOSPACES: WHAT ARE THEY GOOD FOR? 35

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0.8 2.5 Figure 3.3 Two more morphospaces defined by W/D: the top 0.7 graph shows the frequency distribution of Cretaceous ammonoids 0.6 0 (large area on the center-right) and nautilids (smaller area on the upper left). The bottom graph shows what happened after the 0.5 extinction of the ammonoids: the nautilids moved their main peak 0.4 down, but failed to expand toward the right of the morphospace. Possible reasons are discussed in the main text. (Graphs from McGhee (2007), reproduced with permission from Cambridge 0 0.1 0.2 0.3 0.4 0.5 0.6 University Press.) D 36 PART I HISTORICAL BACKGROUND AND PHILOSOPHICAL PERSPECTIVES and one fitness dimension), while recent work as problems with multicollinearity of different clearly shows that whatever intuitions one derives traits, the problem of the effect of “missing” (i.e. from low-dimensionality fitness landscapes they unmeasured) traits, the assumption of linearity of are likely to prove profoundly misleading. Indeed, the statistical models, the dearth of spatially and an argument can be made that entire research pro- temporally replicated studies with sufficient sam- grams, such as the search for mechanisms caus- ple sizes, etc. (Mitchell-Olds and Shaw 1987; King- ing “peak shifts,” have been informed by a faulty solver et al. 2001; Pigliucci 2006; Siepielski et al. assumption, since more realistic hyperdimensional 2009). None of this affects the conclusion that fit- genotypic spaces simply do not have anything that ness surfaces can be rigorously quantified, though resembles peaks and valleys. It seems like the ratio- their visualization must be left largely to ineffective nal thing to do in this case would in fact be to fol- multivariate compound variables. low Kaplan’s (2008) advice, abandon the metaphor Where both Simpson-type Adaptive Landscapes altogether and simply embrace directly the results and Lande–Arnold type fitness surfaces do not of formal modeling—as both the cases of Gavrilets’ deliver is when we assume that they are phe- “holey” spaces and the research on the evolution notypic versions of Wright-type landscapes, as of RNA and protein function elegantly illustrate. Simpson himself surely did. This simply cannot Wright may have needed to soften his math with be the case because of the high complexity and pictures in the 1930s, but surely modern biologists non-linearity of the genotype phenotype map- → ought to be able to take on the full force of the ping function, as argued elsewhere (Alberch 1991; mathematical theory of evolution. Pigliucci 2010). This is a problem insofar as we Simpson-style Adaptive Landscapes also aimed are interested in an evolutionary theory that pro- from the beginning at a heuristic value, as demon- vides us not just with an account of genetic strated by the fact that there are few examples change (as given by population and quantita- in the literature that are not hypothetical. How- tive genetics), but also with accounts of pheno- ever, it is arguable that these landscapes are in typic change and of how, precisely, the two are fact less misleading than fitness landscapes, since connected. their low dimensionality reflects the real fact that We finally get to Raup-style morphospaces, often biologists are interested in selected aspects which I think are not just heuristically useful (to of an organism’s phenotype, and rarely consider visualize the range of possible organismal forms simultaneously hundreds or thousands of charac- within particular aspects of the phenotype), but ters (again, unlike the genetic scenarios). Still, the actually have a nice if small record of generating point of Adaptive Landscapes is to study adap- new understanding, as well as testable hypotheses, tation and its macroevolutionary consequences in in biological research, despite still being somewhat terms of speciation and lineage divergence, which of a backwater topic in need of further attention. means that far more than Simpson-style suggestive As philosopher of science James Maclaurin (2003) pictures are necessary. Serious studies of Adaptive aptly put it: “Theoretical morphology might allow Landscapes need to integrate historical records (via us to sort life into the actual, the non-actual and paleontology and/or ), functional ecology, the impossible,” a research agenda splendidly illus- as well as morphology—a splendid area for fertile trated by the examples of ammonoids and nautilids interdisciplinary work, much of which remains to shell shapes discussed above and that can be traced be done. back to general attempts at theorizing about bio- Lande–Arnold style multiple regression analyses logical form that even predate an explicitly evo- of natural selection—and the graphical rendition lutionary approach (Thompson 1917). However, a of the underlying fitness surfaces—has been well survey of the literature on morphospaces (McGhee underway, and arguably represents the bulk of the 2007) shows that most of the available examples are empirical work inspired by landscape metaphors. restricted to a small range of animal taxa and lim- Yet Lande–Arnold selection analyses themselves ited aspects of their phenotype (with some excep- are characterized by many well-known issues, such tions concerning plants (Niklas 2004)). This could LANDSCAPES, SURFACES, AND MORPHOSPACES: WHAT ARE THEY GOOD FOR? 37 be due to the fact that comparatively few scien- Selection, Accident, Neutrality, and Function. Oxford tists (mostly drawn from paleontology) have even University Press, Oxford, pp. 135–162. thought about organizing their research using the Hartl, D.L. and Clark, A.G. (2006). Principles of Popula- framework of morphospaces, because until recently tion Genetics. 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