Historical , 2017 https://doi.org/10.1080/08912963.2017.1337760

Heritability: the link between development and the of molar tooth form

P. David Pollya and Orin B. Mockb

aDepartment of Earth and Atmospheric Sciences, Indiana University, Bloomington, IN, USA; bDepartment of , Kirksville College of Osteopathic Medicine, Kirksville, MO, USA

ABSTRACT ARTICLE HISTORY The developmental expression, , and variation in mammalian molar Received 29 May 2017 teeth has become increasingly well understood, providing a model system for synthesizing Accepted 30 May 2017 and developmental . In this study, we estimated additive genetic covariances in molar shape (G) KEYWORDS using parent-offspring regression in Cryptotis parva, the Least Shrew. We found that crown shape had an 2 Molars; evolution and overall h value of 0.34 (±0.08), with higher heritabilities in molar cusps than notches. We compared the development; heritability; genetic covariances to phenotypic (P) and environmental (E) covariances, and to the covariances in crown soricidae; geometric features expected from the enamel knot developmental cascade (D). We found that G and D were not morphometrics strongly correlated and that major axes of G (evolutionary lines of least resistance) are better predictors of evolutionary divergences in soricines than is D. We conclude that the enamel knot cascade does impose constraints on the evolution of molar shape, but that it is so permissive that the divergences among soricines (whose last common ancestor lived about 14 million years ago) do not fully explore its confines. Over tens of millions of years, G will be a better predictor of the major axes of evolution in molar shape than D.

Introduction adult molar crown and its many cusps, ridges, and basins. A Building on foundations laid by Butler (1941), (1956), (1995), dynamic system of interactions folds the inner enamel epithelium studies of mammalian molar teeth have begun to bridge the of the tooth germ and expands its mesenchymal base (Butler gap between evolutionary and quanti- 1956). Epithelial signaling centers called enamel knots influence tative genetics (Jernvall & Jung 2000; Tucker & Sharpe 2004; the growth of individual cusps, the formation of other knots, and Polly 2005, 2015; Kavanagh et al. 2007; Gómez-Robles & Polly proliferation in the epithelium and mesenchyme (Jernvall 2012; Jernvall & Thesleff 2012; Gomes Rodrigues et al. 2013; et al. 1994, 1998; Jernvall & Thesleff2000, 2012). This system Jheon et al. 2013; Harjunmaa et al. 2014; Ungar & Hlusko is shared, in its broad aspects, by with different tooth 2016). Interest in the connections between developmental gene morphologies. Species differences in gene expression patterns are expression and quantitative models of variation, selection, and associated with their differences in molar form (Keränen et al. evolution have brought attention to - maps 1998; Jernvall et al. 2000). Even though the experimental work that involve complex developmental interactions and how these from which the enamel knot cascade model was developed was processes constrain variation and influence the course of long- based on mice, histological observation (Butler 1956; Marshall & term evolution (Weiss 1993; Weiss & Fullerton 2000; Rice 2002, Butler 1966; Berkovitz 1967), empirical observations on patterns 2011; 2002; Klingenberg 2010; Salazar-Ciudad & Jernvall of variability in cusps positions (Polly 1998, 2005; Jernvall 2000), 2010; Goswami et al. 2014; Hlusko et al. 2016). In this paper, we and computer-assisted modeling of these developmental param- measure the genetic, phenotypic, and developmental covariance eters (Salazar-Ciudad & Jernvall 2002, 2010; Salazar-Ciudad structure in the tribosphenic lower molars of the Least shrew et al. 2003; Salazar-Ciudad & Marín-Riera 2013; Marin Riera (Cryptotis parva) and assess how these three population-level et al. 2015) all suggest that the enamel knot cascade model is components of variance are related to long-term phylogenetic generalizable to explain the phenotypic changes observed during divergence in molar shape. morphogenesis and evolution. These same models have empha- Mammalian teeth are a notable example of a system in which sized that development and evolution are not determined by gene the synthesis of molecular development, morphogenesis, adult expression alone, but that the changing three-dimensional topog- , and evolution is well underway. We now under- raphy of the tooth bud creates morphodynamic feedback systems stand how gene products interact in the context of growing epi- that regulate developmental interactions. The cascade of interac- thelial and mesenchymal tissues to create the topography of the tions between enamel knots are expected to induce a predictable

CONTACT P. David Polly [email protected] © 2017 Informa UK Limited, trading as Taylor & Francis Group 2 P. D. POLLY AND O. B. MOCK

morphological differences in other shrew species to see whether phylogenetic divergences in morphology were related to genetic variances and, by extension, to developmental interactions.

Materials and methods Molar shape data were collected from alcohol-preserved individuals of the Least Shrew, C. parva. These were from a long-term breeding colony at the Kirksville College of (A) Osteopathic Medicine (KCOM, Kirksville, Missouri, USA) that has been maintained for more than 40 years (Mock 1982). The original stocks were trapped in central Missouri in the mid 1960s buccal 3 and early 1970s. The animals included in this study were products mesial 7 of up to 30 generations of breeding, including some . 2 No selection was applied, but indirect selective effects on molar 6 4 width have been documented in Peromyscus when wild animals were bred in laboratory conditions (Leamy & Bader 1970). The 8 1 5 colony was not maintained with the intention of studying her- 9 itability, and our selection of offspring-parent pairs was limited by the number of carcasses that had been preserved and by the amount of wear on their teeth. In most cases only individuals (B) 05 mm with unworn teeth were used, but to increase the sample size a few individuals with moderately worn teeth were included when landmarks could be reliably identified. A total of 63 single off- Figure 1. A. Schematic diagram of developmental interactions superimposed spring- single parent pairs were available for this study. on a fully mineralized tooth in functional view (as in Figure 1(B)). Enamel knots (circles) are cellular signaling centers associated with each developing cusp. The Molar shape was measured with geometric morphometrics primary knot (1) influences the position of subsequent knots (2–5) by producing (Bookstein 1991; Dryden & Mardia 1998; Zelditch et al. 2012) of diffusable that inhibit knot formation in the immediate vicinity (thick nine two-dimensional Cartesian-coordinate landmarks to rep- black lines). Downstream knots have a similar effect on their own periphery. Each knot stimulates down-growth in epithelia between it and adjacent knots, resent the occlusal surface of the lower first molar (Figure 1). thus influencing the height and shape of cusps and the position of cingulae and Teeth were oriented in ‘functional view’ parallel to the angle of notches on the adult crown (thin black arrows). The knots also stimulate growth mandibular movement during phase one occlusion, an orienta- in the underlying mesenchyme, which further influences the spacing between knots (large grey arrows). Mesiodistal and buccolingual growth rates are partly tion achieved by aligning shear facets parallel to the line of sight independent. Change in any of these factors can alter placement of all the cusps. (Butler 1961). This position is the most replicable orientation B. Lower right first molar of Cryptotis parva in functional view showing the for a tribosphenic tooth, and it minimizes the effect of wear on nine landmarks used to represent crown shape. In order, they are the paraconid, preprotocristid notch, protoconid, postprotocristid notch, metaconid, cristid the apparent shape of the crown. To further minimize orienta- obliqua notch, hypoconid, entoconid, and talonid notch. The landmarks represent tion error, each specimen was photographed and landmarked those adult crown features that are directly associated with developmental factors. five and the replicates averaged (Polly 2001, 2003, 2007). By confining our analysis to two-dimensions we risk ignoring important components of the spatial patterning of the develop- pattern of covariance between cusps and notches (Figure 1(A)). mental cascade (see discussion below), but by focusing purely on The cascade predicts which parts of the tooth crown will be more the horizontal position of cusps we avoid conflating the effects variable, which will be gained and lost, and what the patterns of of tooth wear, which modifies the apical height of cusps, with variability in molar crown shape will be (Jernvall 1995, 2000; developmental or . Polly 1998, 2005; Salazar-Ciudad & Jernvall 2010). Shape variables were derived from the landmarks for further While we know how patterns of phenotypic shape variation analysis. The individual molar shapes were rescaled and superim- in mammalian molar crowns are associated with developmental posed using generalized least-squares Procrustes fit (Gower1975 ; processes, we neither know what aspects of that variation are Rohlf 1999). The consensus, or mean shape, was subtracted from heritable, nor how those aspects correspond to developmen- the superimposed shapes to yield Procrustes residuals, which tally channeled variation or whether the heritable components are approximate tangent space coordinates, or shape variables of variation correspond to evolutionary lines of divergence in (Dryden & Mardia 1998). The covariance matrix of Procrustes molar form. This study addresses these questions by examining residuals has fewer degrees of freedom than it does traits (2k-4 the shape of the first lower molar of C. parva, the Least shrew. for two-dimensional landmarks) from the loss of translation, We estimate the additive genetic variance of tooth shape with rotation, and scale (Dryden & Mardia 1998; Zelditch et al. 2012). offspring-parent regression, identify the major components of The loss of these degrees of freedom creates collinearities in the heritable shape variation, and compare those components to data that must be taken into account with statistical tests and the covariance structure expected from molar developmental which require pseudo-inverse methods for matrix operations. processes. We also compare the major axes of genetic variation, The dimensionality in this study was 2 × 9–4 = 14. which describe evolutionary lines of least resistance (Schluter Shape variables can also be constructed by rotating Procrustes 1996; Arnold et al. 2001; Renaud et al. 2006; Klingenberg 2010), to residuals to their principle components (eigenvectors). These HISTORICAL BIOLOGY 3

PC (principal components) scores have the advantage of being of the primary enamel knot in real tooth development (Jernvall uncorrelated with one another and inhabiting a shape morphos- et al. 1994, 1998). Paraconid and metaconid cusps (Landmarks pace with dimensionality equal to the degrees of freedom (Rohlf 1 and 5), which are formed by the next enamel knots in the cas- 1993; Dryden & Mardia 1998). If R is the matrix of Procrustes cade, are positioned with random vectors whose distributions of residuals and P is its covariance matrix (the phenotypic covar- angles and lengths were derived from the KCOM sample. The iance matrix), then UWV = SVD[P], where U is the matrix of positions of the entoconid and hypoconid (Landmarks 4 and 5), eigenvectors of P, W is a diagonal matrix of eigenvalues, and V which are controlled by enamel knots whose position is influ- is the conjugate transpose of U. PC scores are obtained by R.U. enced by the metaconid enamel knot, were similarly chosen by The PC score shape variables are equivalent to the Procrustes random vectors extending from the position of the metaconid. residuals in all respects except their coordinate system has been The notches between cusps (Landmarks 2, 4, 6, and 9) form from rotated, which means that virtually all comparisons described in down-growth of epithelium, so their positions were selected ran- this paper can be done on either the Procrustes or the PC shape domly based on the locations of their two adjacent cusps. The variables (Klingenberg & Leamy 2001). To make direct compari- result is a set of nine landmarks, the positions of which covary sons between the two coordinate systems – for example, to com- according to this hierarchy of development. To compare this the- pare a genetic covariance matrix estimated from the Procrustes oretical developmental covariance structure to real tooth shapes, coordinates with one estimated from PC scores – the U matrix the modeled teeth were Procrustes superimposed along with the must be used to rotate the data to the proper coordinate system. KCOM sample (see above). Superimposition redistributes the Quantitative genetic parameters were estimated using off- variance across landmarks, so the position of the protoconid spring-parent regression. The additive genetic covariance matrix appears to be variable in the superimposed sample even though G is it technically is not. The redistribution of variance does not affect comparisons of shape variation (Rohlf 1999; Klingenberg 2013; Cov , , (1) Bookstein 2016). The shape variation associated with P, G, E, and D were mod-

where RP is the matrix of parent Procrustes shape variables and eled as shape deformations. P and G were each decomposed RO is the matrix of corresponding offspring shape variables into orthogonal PC axes using singular-value decomposition (see (Lynch & Walsh 1998; Arnold & Phillips 1999). The traits were above). Each of the components in the U matrix represents a por- the eighteen Procrustes residuals. G can also be estimated from tion of the total additive or phenotypic variance and covariance PC shape variables (Klingenberg & Leamy 2001), which should that is uncorrelated with other axes, and the singular values W

be identical to the estimate based on Procrustes shape variables represent the variance associated with each component. Shapes except for rotation of the coordinate system described above. were modeled by multiplying the relevant column of U by the The phenotypic covariance matrix (P) is estimated from the position along the axis and adding the vector of consensus values Procrustes residuals of the parent sample and the environmental (Rohlf 1993; Dryden & Mardia 1998). Models were depicted as covariance matrix E is P-G (Lynch & Walsh 1998). thin-plate spline deformations from the consensus (Bookstein 2 2 An overall estimate of heritability (h ) is h = 2 VA/VP, where 1989; Rohlf 1993). Each component was modeled between the VA is the additive genetic variance and VP is the phenotypic values of −0.1 and 0.1, about two orders of magnitude greater variance, where the multiplier 2 is necessary because our esti- than the actual variance, so that shape patterns were clearly vis- mate was made from the covariances between one parent and ible in the plots. one offspring (Falconer & Mackay 1996; Lynch & Walsh 1998). Comparative shape data from other 12 shrew taxa were com- Thus h2 = 2 tr[G]/tr[P], where tr is the trace of the covariance pared to the shape variance associated with G, P, E, and D to matrix. Note that this h2 represents a sort of average heritability evaluate the contribution of genetic and developmental variance for shape variation that is inherently multivariate (Klingenberg & to phylogenetic divergence. Museum samples were obtained for Leamy 2001; Klingenberg 2003; Klingenberg & Monteiro 2005). Cryptotis goldmani from Oxaca, Mexico (n = 6); C. goodwini Heritability of individual components or crown features could from Guatamala (n = 9); C. gracilis from Costa Rica (n = 10); C. be either higher or lower than the overall h2. magna from Oxaca; Mexico (n = 8); C. mexicana from Oxaca, Standard errors (SE) for G and h2 were estimated by boot- Mexico (n = 8); Blarina brevicauda brevicauda from Ontario, strap (Manly 2007; Kowalewski & Novack-Gottshall 2010). One Canada (n = 14); B. b. manitobensis from Manitoba, Canada thousand random samples of offspring-parent pairs were selected (n = 8); Sorex antinorii from Haslital, Switzerland (n = 21); S. - with replacement, and the various recalculated. SE is neus from Alice Holt Forest, England (n = 33); S. coronatus from the standard deviation of the resulting values. Vercors, France (n = 9); S. granarius from Avila, Spain (n = 6); A developmental covariance matrix for molar shape (D) was and S. samniticus from Abruzzo, Italy (n = 11). The same data estimated using the modeling procedure described by Polly collection procedure was used and mean shapes estimated (2005), which is based on the enamel knot cascade and subse- as the consensus of each sample. S is the covariance matrix of the quent epithelial growth in teeth (Jernvall et al. 1994, species means, which contains the evolutionary covariances in 1998; Jernvall & Thesleff 2000, 2012). The model generates the shape. Some comparisons were made by projecting the C. parva nine molar landmarks (Figure 1) as a sequence of developmental specimens from which G and P were estimated and the shapes events, each with random noise of similar magnitude as found generated by the developmental model from which D was esti- in the KCOM sample of C. parva teeth. In the mode, the proto- mated into the PC morphospace of these 12 species (see above). conid cusp (Landmark 3) is treated as the fixed starting point of The statistical significance of matrix correlations between the developmental sequence because it represents the position covariance matrices was tested with Mantel test (Mantel 1967; 4 P. D. POLLY AND O. B. MOCK

Figure 2. Scree plots showing the proportion of variance explained by each of the PCs of the five covariance matrices (first column), along with shape models for the first two PCs (second and third columns). The landmarks on each model correspond to those in Figure 1. Notes: Thick light grey lines represent the shape at the negative end of the PC and thin black lines represent the shape at the positive end (see Figure 3(B)).

Cheverud et al. 1989) including the diagonal elements as recom- that P (phenotypic covariance) is the sum of G (genetic covari- mended for geometric morphometric datasets (Klingenberg & ance) and E (environmental covariance), all three of which were McIntyre 1998). Angles between eigevectors (PC axes) of covar- derived from the KCOM colony of C. parva. The other two matri- T iance matrices were calculated as arccos[abs[ua ub], where abs ces (S, species covariances; D, developmental covariances) were is the absolute value, ua and ub are eigenvectors of matrices a, b, derived independently. and T is transpose. The S matrix measures the evolutionary covariances among The amount of among-species variance explained by the first shrew species. Its first PC consists of mesiodistal elongation of two eigenvectors (PC axes) of G, P, E, and D (R2) was estimated the trigonid and buccolingual widening of the talonid. The sec- by projecting the scores of S onto the first two axes of each of the ond PC describes proportional changes length of the prevallid four covariance matrices, calculating the mean sum of squares blade between the paraconid (Landmark 1) and protoconid of the projected points and dividing by the mean sum of squares (Landmark 2) relative to the postvallid blade between protoco- of the full multivariate set of scores. nid and metaconid (Landmark 5), which is correlated with the width of the talonid basin. Both factors correspond to increased Results sectorial morphology toward the positive end of the PC (thin Evolutionary, genetic, environmental, and developmental black lines). shape variation The P matrix measures phenotypic covariances within C. parva (specifically among the individuals of the parent genera- The variation in shape associated with each of the five covariance tion of the KCOM sample). Its first axis consists of mesiodistal matrices have some parallels in their major axes (Figure 2). Note lengthening of the trigonid correlated with shortening of the HISTORICAL BIOLOGY 5

(A)

(B) (C)

Figure 3. A. Heritabilities (h2) of individual landmark coordinates. B. Diagrammatic rendering of the x and y coordinates of the nine landmarks for reference. C. Matrix showing in black those G matrix cells that have genetic variances or covariances that are significantly greater than zero. Notes: Diagonal elements are genetic variances and off-diagonal elements are genetic covariances. Note that genetic variance, like ordinary variance, is difficult to ascribe to particular landmarks in Procrustes superimposed data. Heritabilities should therefore be interpreted as the heritable relationship between that coordinate and all others. For example, one could argue that position of the protoconid (Landmark 3) is not heritable per se because it marks the beginning of the developmental cascade, but that its y-axis position relative to the rest of the tooth is highly heritable.

talonid basin in the same direction. The second P axis consists Table 1. Matrix correlations between S, P, G, E, and D. of buccolingual narrowing of the talonid basin and proportional P G E D shortening of the postvallid blade relative to the prevallid. 0.51 0.30 0.52 0.16 S The G matrix measures the additive genetic covariances 0.73 0.97 0.35 P between parents and offspring inC. parva. The firstG axis 0.53 0.16 G 0.37 D describes mesiodistal expansion of the trigonid relative to the talonid (similar in most respects to the first P axis). The sec- Note: All correlations are statistically greater than zero. ond axis describes shortening of the postvallid blade relative to the prevallid and reorientation of the talonid basin into a more The heritabilities of positions of the individual crown features mesiodistal direction. varied considerably. Cusp features had the highest h2 values, with The E matrix measures non-genetic (or at least non-addi- a mean of 0.40, whereas notches had a mean of 0.12 (Figure tive) covariances in C. parva. The first E axis, similar to P and 3(A)). Additive covariances among cusps were also higher with G, describes mesiodistal elongation of the trigonid relative to a mean of 0.000040 compared to 0.000020 among notch features the talonid. The second axis describes proportional shortening (Figure 3(C)). Mean additive covariance between cusp and notch of the postvallid blade and relative change in the angle of the features was intermediate at 0.000027. talonid basin. The D matrix describes the expected covariances that arise Correlations between S, G, P, E, and D and evolutionary from the developmental cascade of enamel knot formation and lines of least resistance epithelial growth. The first D axis describes the relative posi- tions of the notch landmarks relative to the cusps (which would, All five matrices were significantly correlated (Mantel test p-val- in principle, be driven primarily by changes in the epithelial ues <0.02 for all comparisons), but the magnitude of the corre- growth). The second developmental axis describes buccolingual lation varied substantially from 0.97 (P and E) to 0.16 (D with S widening of the tooth (which would be driven by the placements and G) (Table 1). Phenotypic covariances (P) were generally good of the second generation enamel knots relative to the protoco- predictors of genetic covariances (G; R = 0.73). Interestingly, nid knot). Developmental covariance patterns derived from our the genetic and developmental covariance structures had lower model are discussed in greater detail in Polly (2005). correlations with the evolutionary covariances (S) than did the phenotypic and environmental covariances. Genetic variance of molar shape Because matrix correlation is a blunt instrument that does not assess whether covariance matrices share any common patterns, The overall heritability (h2) of crown shape was 0.34 (±0.08), we also measured the relationships using vector angles between

with VA (tr[G]) = 0.0094 (±0.00023) and VP (tr[P]) = 0.0057 their major axes (Cheverud 1982; Klingenberg & McIntyre (±0.00041). Note that the units of variance in geometric shape 1998; Goswami & Polly 2010). The major axes of each covari- analysis are Procrustes units, which are arbitrarily determined ance matrix its principal components axes (eigenvectors), and by scaling all shapes to unit size and are thus comparable in the angle between eigenvectors from two covariance matrices magnitude to one another but not to other studies. measures the correlation between those particular factors. The 6 P. D. POLLY AND O. B. MOCK

Table 2. Vector angles between PC 1 of S, the major axis of interspecific evolution- in molar shape (Figure 4(C)). These first two PCs can be viewed ary divergence, and the first two PCs of the remaining covariance matrices. as the shape plane in which most evolutionary divergence has Matrix PC1 PC2 occurred. The shapes associated with this space are shown in P 68.9 52.8 the top row of Figure 2. Projecting the major axes of the other G 56.6 78.5 covariance matrices onto this plane shows the major directions E 75.8 71.7 D 81.7 70.3 that they channel evolution (direction of their vectors) and their relative contribution to change in this plane (lengths of their Notes: All angles are reported in degrees (°). Axes are more correlated when their angles are near 0° and less correlated as they approach 90°. vectors). The lines of least resistance ofP , G, and E (all of which were estimated from C. parva) in this space are closely aligned in roughly an axis that connects the B. brevicauda subspecies Table 3. Coefficient of determination (R2) describing the proportion of variance with Cryptotis goodwini and C. goldmani. The first axis of D is between species that is explained by the plane of least resistance of the P, G, E, roughly at right angles to the other matrices, parallel to the axis and D matrices. that separates the Cryptotis from the Sorex species. The second D Matrix R2 matrix axis is roughly aligned with the first axes of P, G, and E. S 0.82 P 0.37 G 0.26 Discussion E 0.22 D 0.12 Heritable variation in molar shape and developmental Notes: Each plane of least resistance is defined by the first two principal compo- patterns nents of the corresponding covariance matrix and represents the major direc- tions along which shape change would be channeled by each of the four factors. The heritability of cusp position was dramatically higher than notch position, a finding that makes sense from a developmental standpoint. Cusp tips are associated with enamel knot signaling first two PCs of the phenotypic covariances (P) and the first PC centers, which directly influence morphogenetic events in areas of the genetic covariances (G) were most closely aligned with topographically adjacent to them. The position, size, and shape the first PC of the species divergences (S), whereas the first axis of the adult cusp are partly realized through the effects of its of the developmental covariances (D) and the second axis of the associated knot, though they are also influenced by the activities genetic covariances were the most orthogonal to it (Table 2). of other developmental players, such as other knots, epithelial The major axes of each covariance matrix can also be viewed growth rates, and mesenchymal expansion. Notches have no such as ‘lines of least resistance’ (Schluter 1996; Arnold et al. 2001; centers and their positions are purely the product of morphody- Renaud et al. 2006; Klingenberg 2010). Regardless of the direc- namic interactions. Thus, we can expect cusps to be more tightly tion of selection, the covariance structure will channel pheno- regulated and, consequently, to have more variation explained typic variation toward its major axes, which should contribute to by heritable effects. long-term evolutionary divergence along those axes if the covar- Non-biological causes, such as systematically greater digi- iances are heritable (Arnold et al. 2001; Klingenberg & Leamy tizing error, could, in theory, explain the lower heritability of 2001). Of the four matrices considered here, the first axis of S notches, but they are more easily pinpointed as landmarks and is most closely aligned with the first axis of G, confirming that less obliterated by wear than are cusp tips. Consequently, any heritable line of least resistance contributes more to intraspecific systematic bias in error would be expected to favor notches. divergence than to the non-heritable (E) or developmental (D) Likewise, notch landmarks are less affected by orientation error lines of least resistance (Table 2). than cusps because they lie lower on the crown and are less prone One can also ask how much of between species divergence to parallax problems. is explained by the two-dimensional plane of least resistance, The first component of the genetic matrix is consistent with which is the plane defined by the first two PCs of each covari- previous studies on heritability in molar size, which found ance matrix (Klingenberg & Leamy 2001; Martínez-Abadías et al. high h2 values in buccolingual width, values that in many cases 2012). We used the coefficient of determinationR ( 2) to measure exceeded heritability in mesiodistal length (Bader 1965; Leamy how much of the variance in the species scores (i.e. the between & Bader 1968; Leamy & Touchberry 1974; Hlusko et al. 2002, species divergence) was explained by the first two axes of theP , 2006). The width of the molars has also been shown to be G, E, and D matrices (Table 3). A maximum proportion of 0.82 one of the best morphological discriminators of genotype in can be explained since this is the amount explained by the first mice (Leamy & Sustarsic 1978) and width has been shown to two PCs of S itself. P, which is composed of both genetic and be more genetically correlated with body size, unlike molar environmental components, explained the greatest amount of length, which has no significant with any factor (0.37), and G explained more (0.26) than D (0.12). body mass (Hlusko et al. 2006). These studies suggested that The relationship between evolutionary divergence and lines of the width parameter is more heritable than length (but see least resistance can also be visualized by projecting the major axes Townsend et al. 2003 who obtained a mix of heritabilities for of P, G, E, and D onto the first two axes of S (Figure 4). In this mesiodistal and buccolingual distances between cusp tips in figure, the phylogeny (Figure4 (A)) has been projected into the ), and thus more evolvable. Note, however, that the principal component space of the species (S, Figure 4(B)) using geometric morphometric methods employed in this study are Brownian motion reconstruction of ancestral shapes (Martins & relative and cannot distinguish an increase in width from a Hansen 1997; Rohlf 2002) to estimate evolutionary trajectories decrease in length. HISTORICAL BIOLOGY 7

(A) (B)

(C)

Figure 4. A. Phylogenetic relationships of the shrews in this study (after Repenning 1967; Woodman & Timm 1999, 2000; Fumagalli et al. 1996, 1999). B. First two principal components of molar morphospace for these species. These two axes define a plane of divergence among the shrew species.C . Projection of the first major axis (PC 1) of the P, G, and E matrices and the first two major axes of D onto the plane defined by the species. Note: The phylogenetic tree has also been projected onto this morphospace plane.

Some of the shape components of additive genetic covariance 2001) have been debated. The role of developmental processes in (Figure 2) correspond with developmental components. The first channeling evolutionary change in particular directions has also additive genetic component, which accounted for about 35% of been of continued interest (e.g. Cheverud 1984; Rice 2000, 2002, heritable variation in shape, describes buccolingual width of the 2011; Klingenberg 2010; Goswami et al. 2014; Laland et al. 2015). talonid relative to mesiodistal length trigonid, which is similar to One of our most interesting results is that the genetic covar- the second component of the developmental covariance matrix. iances of G are not closely aligned to the developmental covar- A change in the timing and duration of knot expression in the iances of D (R = 0.16), except insofar as described above, and metaconid and entoconid, combined with mesiodistal and buc- that neither of them are strongly aligned with the major axes of colingual growth of the papilla could produce correlated changes evolutionary divergence S (vector angles 56.6 and 81.7° respec- such as these. tively). G is a better predictor of evolutionary shape change in these shrews than D, whereas D is a good predictor of neither Additive genetic variance, development, and evolution the evolutionary change nor of the genetic covariances in molar shape. The relationship between additive genetic variance and long- That G and D are only loosely correlated may not be sur- term evolutionary change has been an important question for prising. If D is a good descriptor of the covariances imposed by evolutionary (Barton & Turelli 1989). Issues such as the enamel knot cascade, then G should be a subspace within which genetic parameters best predict response (Houle 1992; the one defined by D because it would be impossible for herit- Roff 1997), the extent to which genetic covariances may affect able variation outside the constraints imposed development. A response (Lande & Arnold 1983; Arnold et al. 2001; Marroig hypothetical example is illustrated in Figure 5. The constraints & Cheverud 2001); whether P matrices are an adequate substi- imposed by development are shown as a pair of correlated traits tute for G matrices (Cheverud 1988; Willis et al. 1991), and the (grey points and large ellipse) and the genetic covariances of a extent to which the G matrix remains constant over evolutionary single population are shown inside the developmental space (red (Atchley et al. 1981; Lofsvold 1986; Turelli 1988; Steppan points and small ellipse). Thus, we might expect a low matrix 1997; Arnold & Phillips 1999; Agrawal et al. 2001; Bégin & Roff correlation between G and D whenever variation in G is much 8 P. D. POLLY AND O. B. MOCK

will always contribute to the total distance between knots except in exceptional cases in which the knot/notch displacement is entirely parallel to the line of sight in occlusal view. The covar- iances imposed by the enamel knot cascade should therefore be detectable in 2D data, even though they will be dampened compared to 3D data. The competing advantage of using 2D landmarks is that the height of the cusps is more affected by wear than is the position of the cusps in the horizontal plane. Because this is a parent-­ offspring heritability study, the parent generation individuals frequently had teeth that were quite worn and would have to have been discarded from a 3D data-set.

Conclusion , in their contemporary guise of coding strands of DNA and their products, are the domain of molecular biologists, including developmental biologists. Studies of gene expression, Figure 5. Hypothetical example of a space described by developmental covariances particularly those driven by in situ hybridization techniques, (grey dots and large ellipse) with an uncorrelated genetic space located inside it have allowed the identification of those that are active during (red dots and small ellipses). development, and derivative research on the temporal and spatial interactions of gene products in the context of the developing smaller than that permitted by D. They might have individual phenotype has provided a basis for postulating how the actions of axes that align, depending on the situation. This may well be real genes are combined to produce heritable (or non-heritable) the situation with G and D in our study, where the first axis of covariances in the phenotype. The latter studies have brought G is partially aligned with the second axis of D but there is a into contact with and, very low matrix correlation between the two. But if so, then the it may be fair to say, bridged the gap between quantitative genet- evolutionary divergences in shrew molar shape represented by ics and genes, rather than between genetics and evolution. The S must also be comparatively small because of the equally low interface is now being explored by both quantitative geneticists correlation between S and D (R = 0.16). (Rice 2000, 2002; Johnson & Porter 2001; Porter & Johnson 2002; These results indicate that G is a more direct predictor of Wolf et al., 2001; Wolf 2002) and developmental biologists (Ahn long-term evolution in this of shrews than D. They also & Gibson 1999; Jernvall et al. 2000; Salazar-Ciudad & Jernvall suggest that the general covariance structure of G is conserved 2002; Rifkin et al. 2003). well enough for its major axis to be aligned with divergences This study was conceived as an empirical link at the bound- between Blarina and Cryptotis, which began about 12.1 million ary between quantitative genetics, developmental biology, and years ago (Dubey et al. 2007). A modeling study suggests that evolution. We found that additive genetic variances (G) were G will remain reasonably constant for long periods when corre- more closely aligned with evolutionary divergences than devel- lational selection is strong and effective population size is large opmental covariances (D). Furthermore, we found that genetic (Jones et al. 2003), a situation that is most likely the case for molar covariances were not predictable from developmental covari- shape and shrews even though P (and presumably G) are known ances, which is likely to be the case if development constrains the to change significantly over evolutionarily short timespans (Polly absolute bounds of variation and if the variation represented in 2005), even though the magnitude of changes in P is not always G is small compared to the permissible bounds of development. large even over periods as long as 20 million years (e.g. Grieco If this interpretation is correct, our analysis of shrews suggests et al. 2013). that the constraints imposed by the enamel knot cascade in molar development will be more detectable when comparing covari- Additive genetic variance, development, and evolution ances in taxa that diverged more than 12 million years ago. G may be a better predictor of major lines of divergence over periods Because our analysis of crown features is confined to two shorter than that. dimensions, we risk ignoring the vertical component of the developmental cascade. In tribosphenic molars like Cryptotis, Acknowledgements the difference in apical height between cusps is substantial. The Special thanks to Gregg Gunnell, Jerry Hooker, and Gareth Dyke for their diffusion-based morphodynamics of the enamel knot cascade efforts in organizing this volume, as well as to Percy Butler for insights are three-dimensional, meaning that the vertical component of he provided over the years about tooth development, , and evolu- cusp position is important (Jernvall 1995, 2000; Salazar-Ciudad tion. I thank S. Gilmour, J. Head, J. Jernvall, B. Khoruzhenko, N. MacLeod, & Jernvall 2010). In principle, the absolute distance between R.A. Nichols, I. Salazar-Ciudad, and two anonymous reviewers who enamel knots is the primary parameter of interest. In crowns with provided useful ideas and criticism that improved this study, and J. Eger (Royal Ontario Museum), T. Gorog (University of Michigan), J. Hausser high relief, the vertical component of that distance is probably (University of Lausanne), H. Price-Thomas (Queen Mary, University of larger than the horizontal component. However, as Pythagoras London), and N. Slade (University of Kansas), who provided access spec- theorem in trigonometry suggests, the horizontal component imens in their care. HISTORICAL BIOLOGY 9

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