To cite an example from one species (as a prototype for demonstrating the dominating relative influence that such constraints can exert in particular situations), one of the major covariance sets of Cerion's allometry — the “jigsaw
10-7. The three standard phases in the allometric growth of Cerion, responsible for major changes in adult form induced by small alterations early in development. From Gould, 1989a.
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constraint” of my terminology (Gould, 1989a) — may seem almost trivial in its obvious nature, but still exerts great influence in setting patterns of variation within Cerion at all levels, from intrapopulational variation, to geographic variation within a species, to chronoclines, to regional patterns of differentiation in species complexes (see Gould, 1989a, for details). If different shells reach virtually the same final size — and Cerion, as one of its major bio-metric advantages does, unlike most invertebrates, reach a final size marked by the secretion of a thickened lip in the third allometric phase — then shells with larger whorls must end their growth with fewer whorls. (In two jigsaw puzzles with frames of the same size, the one with smaller pieces must use more pieces to fill the common space — hence my name for the covariance set.)
The basic principle might be regarded as both obvious and entirely unprofound. Its operation would also impose scant effect upon any molluscan shell that grew in close conformity with the idealized logarithmic spiral — for two shells of the same size, one with few and the other with many whorls, would then display the same shape, and no substantial differences (beyond the number of whorls) would be apparent. But Cerion's extensive and distinctive allometry triggers a large and visually striking set of correlated changes, necessarily leading to obvious differences in form between few and many whorled shells of the same size. (Such distinctions can be readily characterized, and judged in relative strength, on factor or discriminant axes of multivariate biometric studies.) For example, large-whorled specimens grow fewer whorls and therefore undergo a later transition to the second allometric phase (which invariably occurs between the 5th and 6th whorl), thereby yielding a more triangular adult shell, as relatively less of the total growth occurs during the “barrel” of the second allometric phase.
This single constraint, with its complex sequelae, explains virtually all the interregional geographic variation in one of the most interesting, and certainly the most intensely studied, species of Cerion — the geographic and morphological outlier (also the holotype of the genus, and a species named by Linnaeus himself), Cerion uva from Aruba, Bonaire and Curasao. Moreover, recognition of the jigsaw constraint allowed me to resolve, in a manner congenial to all parties, the most substantial and longstanding debate in the history of Cerion studies.
In a large monograph, published in 1924, H. B. Baker, a great descriptive malacologist, claimed that he could distinguish four geographic domains of variation by subtle but entirely characteristic differences in shell form: Aruba, Bonaire, Eastern Curasao and Western Curasao. (The island of Curasao, shaped like a dumbbell with eastern and western portions joined by a much narrower neck of land, may be sensibly so divided; the two halves were probably separated by higher sea levels of former interglacial epochs.) Baker used the classical and subjective criterion of a taxonomist's “good eye,” and could therefore not defend his impressions in the face of extensive biometrical studies by Hummelinck (1940), then extended and confirmed by De Vries (1974). These Dutch researchers, unable to identify covariance sets with their univariate [Page 1048] and bivariate techniques, claimed that intrasample variation in mean shell size swamped all other factors. Moreover, they could locate no clear evidence at all for Baker's interregional distinctions.
By using multivariate methods to study the influence of covariance sets, particularly the jigsaw constraint, upon geographic variation, I was able to resolve this question (Gould, 1984b) in a way that honored (as partial) the findings of all these excellent researchers. The Dutch scientists correctly noted the strong influence of variation in mean shell size among samples. But I was able to show: (1) that this variation can be isolated on a single factor axis; (2) that size ranges among samples are effectively equal, and influence the shells in essentially the same way in each of the four regions; and (3) that these intraregional differences in size almost surely arise for ecophenotypic reasons (see argument and documentation in Gould, 1984b), based on more vigorous and continuous growth of shells in moist and well vegetated microhabitats.
But I also discovered that each of Baker's four regions could be clearly identified by the evolution of differences that may be small in a genetic sense (a common situation for geographic variation within species), but that produce substantial effects upon the adult phenotype by altering several key characters in tandem through constraints of ontogenetic channels identified by covariance sets. For example, shells from Bonaire (see Fig. 10-8) grow a distinctively jutting apertural lip, a consequence of conjoined modification in characters building the third allometric phase.
Effectively all other geographic variation could be ascribed to the jigsaw constraint. For reasons that I could not resolve, Cerion develops virtually no variation in average adult shell size (measured as height plus width) within local populations in each of Baker's four regions — with a range from 29.79 mm in Eastern Curasao to 30.69 mm for Aruba, giving a maximum interregional difference of only 1.6 percent. This contingently evolved (and not, obviously, geometrically necessary) invariance of size triggers a maximal effect for the jigsaw constraint — that is, so long as substantial variation exists in the sizes of whorls.
Cerion uva does, in fact, exhibit extensive and geographically distinctive variation in whorl sizes, with regional means spanning almost a full whorl, and ranging from 8.56 whorls in Western Curasao to 9.35 in Aruba. The maximal “play” thus accorded to the jigsaw constraint then establishes the interregional distinctions that Baker had correctly noted but could not adequately characterize. Figure 10-9 shows minimum convex polygons drawn around the multivariate means for samples in each region (in a study based on 135 samples of 19 measures on each of 20 snails). The corners of the triangular diagram represent the first three axes of a factor analysis for mean vectors of samples. The three axes hold nearly equal explanatory power (30.5, 34.2, and 32.6 percent respectively, for a total of 97.3 percent of all information in the 19 measures among samples).
The second axis absorbs the intersample differences in size that led Hummelinck and de Vries to miss the regional distinctions. The extensive variation on this dimension does not differentiate the four regions, as indicated by the [Page 1049] similar orientation of each polygon along this axis. (In an interesting exception, a few ancient samples (2000 to 3000 years old by radiocarbon) from Indian middens on Curacao (see Gould, 1971a), shown in the small polygon marked I on Fig. 10-9, include far larger shells with sample means well outside the range of modern variation — as shown by their localized and maximized values on this second axis.)
The first and third axes express different aspects of the jigsaw constraint. By these methods, we can isolate this interregional component (on truly independent, mathematically orthogonal axes) from the substantial intraregional variation in size that obscured the broader geographic pattern in the studies of Hummelinck and de Vries. We can also assess the relative strengths of these two sources in compositing the total amount of difference among sample means. Baker's interregional differences explain about % of the total variation among sample means. And, with the exception of Bonaire's distinction by a
10-8. Geographic variation in Cerion uva. Top row, Aruba; second row, Bonaire; third row, western Curacao; bottom row, Indian middens (3,000 years old) on Curasao. The Bonaire shells grow a jutting apertural lip arising from changes in the third allometric phase. All other major variation can be ascribed to the jigsaw constraint. The Aruba snails, with their small whorls, reach the same final size as modern Curacao specimens — with all major aspects
or their markedly different shape arising as consequences of different lengths of residence, based on whorl sizes, in the first two allomecric phases.
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different covariance set, expressed on the fourth axis of this analysis (as discussed previously), effectively all interregional difference arises from the operation of the jigsaw constraint — as generated by minor differences in whorl sizes promoted to substantial overall phenotypic effect through the allometric consequences of Cerion's ontogenetic channel, so long as average adult shells, as they do in this case, reach the same final size.
Note, in Figure 10-9, the separation of polygons for Aruba, Eastern Curasao and Western Curasao by the first and third axes that express the jigsaw constraint, while each polygon shows a similar extension along the second axis, representing the different and separable component of intraregional (and ecophenotypic) variation in mean shell size. Figure 10-8 shows characteristic shells for the regions. Note the jutting apertures from Bonaire (second row) and, especially, the contrast, built by the jigsaw constraint, between many-whorled specimens from Aruba in the top row (longer relative residence in the second allometric phrase which, distinctively in Cerion uva, induces an absolute narrowing in later whorls, leading to a “barrel” shape for the entire shell, fat in the middle and narrowing at both ends) — and the fewer whorled, but same sized, specimens from Western Curasao in the third row (which pass less of their ontogeny in the second “barrel” phase and therefore do not become constricted towards the end of growth, as in the Aruba specimens).
10-9. Minimum convex polygons drawn around the multivariate means for samples in each region. The ecophenotypic factor of size makes no distinctions as each polygon becomes elongated along this second axis, and as the truly larger fossil shells from Aruba occupy a separate position at the high size end of this spectrum. But the first and third axes express the jigsaw constraint, and the defining regional geographic variation within this type species of the genus achieves clear expression in the separation of polygons on these axes.
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If a constraint engendered by an allometric channel in ontogeny can so control the regional pattern of geographic variation in an important species of such a well-studied genus, then we cannot deny a major role to this positive mode of evolutionary change by developmental constraint.
THE APTIVE TRIANGLE AND THE SECOND POSITIVE MEANING: CONSTRAINT AS A THEORY-BOUND TERM FOR PATTERNS AND DIRECTIONS NOT BUILT EXCLUSIVELY (OR SOMETIMES EVEN AT ALL) BY NATURAL SELECTION
The model of the aptive triangle
In a classic line of contemporary American literature, W. P. Kinsella writes of a midwestern farmer so beguiled by the legend of the great baseball hero Shoeless Joe Jackson that he constructs a stadium in his wheatfield because he heard a voice saying to him: “if you build it, he will come.” I often feel that many modern evolutionary biologists unconsciously obey a similar mantra in their approach to the phenotypic features of organisms: “if it works well, then natural selection made it.”
In two historical discussion of this book's first part — my analysis of Darwin's fateful words at the end of chapter 6 of the Origin of Species (pp. 251-260), and my presentation of “Galton's Polyhedron” as the most effective formalist or structuralist metaphor for illustrating missing alternatives in schemes of evolutionary causality that consider natural selection as the only mechanism of change (pp. 342–351) — I presented triangular models of causal poles for the origin of phenotypic features: a representation well suited for portraying alternatives and complements to natural selection as the causal basis of organic form.
Let me now propose a slightly different triangular model with the same three poles, but now representing only organismal features that “work well” both in the classical sense of good biomechanical design, and the technical meaning of conferring fitness upon organisms in their interaction with environments — in other words, to the features that biological terminology, and ordinary vernacular usage, call “adaptations,” but that I would rather designate as “aptations” (see Gould and Vrba, 1982), a more general term that acknowledges their current utility while remaining agnostic about their source of origin. I will therefore designate this model (modified from Seilacher, 1970, and ultimately traceable to Galton's Polyhydron) as “the aptive triangle” (though I will submit to standard “loose” (or sensu lato) usage, and usually refer to the features plotted upon this diagram by the only term that current language recognizes — namely, adaptations).
The basic diagram (Fig. 10-10, presented before, in part, as Fig. 4-6) designates three vertices as idealized end members and also recognizes, of course, that almost any actual feature will plot either along an edge (influenced by two vertices), or, more frequently, in the triangle's interior (where all three end members contribute). This mode of ternary plotting has been used most frequently by petrologists for depicting the composition of actual rocks as [Page 1052] amalgamations of three idealized end-members, in full expectation that few, if any, real rocks will include only one end-member and plot right at one of the triangle's vertices.
In keeping with my previous discussion, and with Seilacher's original conception, we may call these idealized end-members “functional,” “historical,” and “structural.” In other words, any phenotypic feature now “working well” for an organism may have been constructed by a process that directly crafted the feature for its current function (the first corner), inherited from an ancestral form (the second corner), or built by some structural mechanism or process not directly related to, or engendered by, the functional needs of the organism.
As discussed in my previous analysis of Darwin's brilliant argument in Chapter 6 of the Origin (pp. 251-260), the argument for natural selection as the dominant cause of evolutionary change must be made in the following way under the aegis of this model (as Darwin did, but without constructing any formal picture like Fig. 10-10): At the functional vertex, natural selection stands alone as the only known and effective cause in this mode. If the Lamarckian mechanism operated in nature, then inheritance of acquired and adaptive characters would provide another functionalist option for explaining the origin of working design. But inheritance does not so operate, on this planet at least. (Darwin took the more generous view that Lamarckian inheritance might exist, but at a relative frequency distinctly subsidiary to natural selection.)
At the historical vertex, working features passively inherited from ancestors did not originate to meet current functional needs. But so long as these
10-10. Standard triangular diagrams for depicting basic causes of form as functional (immediate adaptation to current circumstances), historical (inherited by homology, whatever the basis of ancestral origin), and structural, or arising either as physical consequence of other features or directly from the nature of physical forces acting on biological materials. All vertices may yield aptive traits of great utility to the organism.
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features arose initially by natural selection in the ancestral line, then their ultimate origin remains functional — and natural selection, as previously noted, represents the only known (for Darwin, the only effective) cause of functional change. Finally, at the structural vertex, Darwin allowed that features not arising for functional reasons, but only coopted for current utility, must be admitted as genuine exceptions to the principle that adaptive features can only originate for functional reasons (with natural selection as the only known and sufficiently powerful functional mechanism). But he then demoted this class of real exceptions by the standard argument in studies of natural history: he claimed, invoking the classical justifications of “sequelae” and “nooks and crannies” (see p. 1249), that currently adaptive features with nonadaptive structural origins must, by their rarity, reach only an insignificant relative frequency among evolved traits of organisms.
The impeccable logic of this formulation can help critics by clarifying how any potenti
al argument against this hegemony of natural selection must proceed. At the functional vertex, one would have to identify other important mechanisms in addition to natural selection — and none have been proposed, at least to the satisfaction of this author (although the argument for “a little bit of bacterial Lamarckism” — as I like to characterize the controversial claims of Cairns et al. (1988) — may have some merit in a limited domain).
At the historical vertex, one would have to reject the contention that constraining homologies of inheritance, and the resulting heterogeneous clumping of species in organic morphospace, record the consequences of natural selection in constructing the novel traits of ancestral forms, followed by the continuing control of selection upon subsequent patterns of phyletic change in descendant lineages — an argument that I will advance in Section II of this chapter. Finally, at the structural vertex, one would have to counter Darwin's argument by asserting that he greatly underestimated the relative frequencies of these admitted exceptions to natural selection for the origin of currently functional features — a claim that I will advance in Chapter 11. Thus, the form of Chapters 10 and 11, and my argument for the importance of structural constraints at high relative frequency in the origin of currently adaptive organismal characters, will center upon recent arguments for a reconceptualization of the historical vertex, and for a reevaluation of relative frequency at the structural vertex of the aptive triangle.
The Structure of Evolutionary Theory Page 167