The landscape of tooth shape: Over 20 years of dental topography in primates

Abstract Diet plays an incontrovertible role in primate evolution, affecting anatomy, growth and development, behavior, and social structure. It should come as no surprise that a myriad of methods for reconstructing diet have developed, mostly utilizing the element that is not only most common in the fossil record but also most pertinent to diet: teeth. Twenty years ago, the union of traditional, anatomical analyses with emerging scanning and imaging technologies led to the development of a new method for quantifying tooth shape and reconstructing the diets of extinct primates. This method became known as dental topography.

Occasionally, the two categories are combined, often to investigate the adaptations of hard object feeding (i.e., durophagy). 6,12

| Dental form and function
Primate teeth are multifunctional tools and play an important role in food item breakdown. During feeding, incisors and (sometimes) canines are used to ingest foods, dividing foods into pieces small enough to fit in the oral cavity. 13,14 Premolars and molars are used to masticate foods by shearing, crushing, and grinding them in the oral cavity. 9,15 Exceptions include strepsirrhines with toothcombs, which do not use their lower incisors/canines to parse foods or their caniniform premolars (P 3 ) to chew foods, and some hominoids, which can wear their canines to the level of the postcanine tooth row, making them "masticatory teeth" (  This weakens the correlation between incisor/canine form and diet. However, the monofunctional role of postcanine teeth (food breakdown) has created a strong relationship between molar form and diet.
Kay and colleagues developed one of the first metrics for quantifying primate occlusal molar shape (herein, tooth shape) in a dietary context, correlating M 2 shearing capability to chewing efficiency (the ability to break down foods [16][17][18][19] ). 4,17,19 In their experiments, insectivores, with relatively longer shearing crests, had higher chewing efficiencies than frugivores, with relatively shorter shearing crests ( Figure 3). 4,17,19 They hypothesized that primates with diets difficult to digest (e.g., chitin in insects, fiber in leaves) evolved relatively longer shearing crests, allowing them to digest food more efficiently. Their measure for shearing capability evolved into the shearing quotient (SQ: Box 2). [20][21][22] The SQ is determined by regressing shearing crest length, the sum of a set of linear distances between discrete, homologous, and anatomical landmarks on the occlusal surface, against tooth length. Primates with positive residuals have relatively longer shearing crests and negative residuals have relatively shorter crests. In this respect, SQ analyzed tooth shape while accounting for allometric differences in tooth size.
Later, researchers used the SQ, and derivatives thereof, such as the shearing ratio (SR) and shearing ratio based on body mass (SRM), 6,23,24 to show that folivores also have relatively long shearing crests, presumably because of their high-fiber diets. 22,[25][26][27] Although primates that are primarily insectivorous and folivorous have similar relative shearing crest lengths, it is possible to differentiate between them using body size: insectivorous primates are ≤250 g and folivorous primates are ≥700 g. 28 Together, this research showed that insectivores and folivores have relatively longer shearing crests than frugivores and hard-object feeders (i.e., durophages). This may be because the selective pressure acting on chewing efficiency is stronger in insectivores and folivores than the selective pressure acting on fruit smashing/juicing 11,15 and dissipating high bite forces, [29][30][31][32] and the opposite is true for frugivores and hard-object feeders.
Despite successes, these metrics were limited by their reliance on occlusal landmarks that could only be measured on relatively unworn teeth with prominent shearing crests. This prevented the inclusion of molars that were worn and taxon with poorly developed molar shearing crests (e.g., Daubentonia, Figure 4) from topographic analyses. 6 Importantly, complex ecological questions related to dental wear could not be addressed. For example, what are the effects of climate change on primate dietary ecology? 33 As global warming changes the environment and thereby food availability, what is the likelihood different species will survive, or go extinct? 33 How does climate/climate change and consumption of invasive species affect dental wear, evolutionary fitness, and primate evolution? 27,34,35 How does tooth shape change throughout an animal's life, and how does this affect its ability to survive? And finally, how is tooth shape affected by factors such as primary/fallback foods and foods with different physical properties, and how does that correlate with an animal's ability to survive? 8,9 To address more complicated questions about dental ecology, 36 a new method needed to be developed. But first, barriers related to data acquisition and quantification had to be overcome.

| The development of dental topography
The first barrier was how to digitally capture whole tooth shape. Previously, whole tooth shape did not need to be captured, as shearing

BOX 1 Choice of tooth
The first topographic studies used M 2 s, and many subsequent analyses followed suit. But, why M 2 s and not the entire postcanine tooth row, as in Evans and colleagues? 50 The use of M 2 s can be traced to two studies, which use the second to last tooth in the dental row, as it was the most "average"shaped molar. 19,20 Some studies maintain this protocol, using M 1 s when M 3 is absent, while others use M 2 for homology. Lower molars are used because, under the mortar and pestle hypothesis, lower molars act as a pestle, breaking foods, while upper molars act as a mortar, stabilizing them. 11,15,83 Therefore, lower molar shape should reflect food item breakdown, while upper molar shape should reflect food item stabilization. A study comparing RFI, OR, and SQ in platyrrhine upper and lower M 1 s supports the preferential use of lower molars for dietary reconstruction, while pointing toward the usefulness of upper molars. 62 Third molars are more variable in shape, but Glowacka and colleagues found M 3 s gave similar results as M 1 s and M 2 s in known age mountain gorillas.
Using the entire tooth row can be problematic. First, not all specimens have the entire tooth row preserved. Second, dental topography is sensitive to tooth wear, 40,42,47,63,[65][66][67] and differences in timing of dental eruption cause variable levels of wear between teeth within a chewing row (e.g., M 1 vs. M 3 , Figure 2). This can be exacerbated by differences in dental wear rates due to diet. In these cases, it is not possible to hold wear stage. Finally, there is sometimes a problem in deciding which teeth should be considered part of the chewing tooth row, and how to hold that constant between species. In some strepsirrhines, the caniform LP 3 is not part of the chewing row, and some primates incorporate their canines into their chewing row ( Figure 2). Further, what if third molars are not present in only some of the sample (e.g., callitrichids-marmosets, tamarins), or when supernumerary teeth are present, like fourth molars? 109 While tooth rows present a more comprehensive picture, they can be much more problematic. That being said, more information is needed to investigate variation in dental topography along the tooth row. In particular, information on premolar tooth shape is needed, as this could reveal novel aspects of primate dental adaptations. 54,110 crest length was measured using linear distances and a microscope reticle. 22 But for whole tooth shape to be quantified, it needed to be captured.
The first attempt used a low-resolution electromagnetic 3D scanner to produce a rough digital approximation of the occlusal surface. 37 A later attempt used laser confocal microscopy: 38 this produced more accurate scans, but did not gain traction in primate dental studies. Eventually, laser and micro-computed tomography (microCT) scanners were chosen as effective ways of creating digitized representations of teeth. 10,39 The second barrier was how to quantify tooth shape without landmarks. 40 Most studies came to the same conclusion: if cusps were treated as mountains and basins as valleys, geographic information systems (GIS) software, developed to quantify landscape topography, could be used to quantify tooth shape. 37,38,39 The idea of using GIS software to quantify tooth shape was a novel, 1 clever way of excluding landmarks, allowing for the quantification of worn tooth shape. 40 This new method for quantifying tooth shape was dubbed dental topography.

| DENTAL TOPOGRAPHY DEFINITIONS
The term "dental topography" gained its present meaning in 2000, where it was defined as "a method for modeling the shapes of the biting surfaces of teeth as topographic surfaces for analysis using geographic information systems technology." 39 Since 2000, studies have incorporated more aspects of the tooth than just the biting surface (e.g., enamel walls) and used non-GIS software and techniques. 10,[41][42][43] As such, Berthaume 44 suggested defining dental topography as, "a [landmark free] method of quantifying and representing 2.5 or 3D whole tooth shape with a single metric." 44 Importantly, both The main topographic metrics used today and their mathematical and biological meanings are presented in Table 1 and briefly discussed in the following.
2.1 | Ambient occlusion (portion de ciel visible: translated to "portion of visible sky") Ambient occlusion is a computer graphics technique used to make surfaces appear 3D by approximating the proportion of ambient light shining on the surface. The specific method for ambient occlusion being discussed here is portion de ciel visible ("portion of visible sky," PCV). If a tooth is oriented as if it were positioned in situ within a maxilla/mandible and light is shone from the occlusal direction, points on the tooth that interact more with the bolus/occluding tooth during a masticatory cycle (e.g., cusps, crests) tend to have higher ambient occlusion values, and points that interact less with the bolus/occluding tooth during a masticatory cycle (e.g., basins, enamel walls) tend to have lower ambient occlusion values ( Figure 6). As PCV values are normalized between zero and one, they can be thought of as probabilities that portions of the tooth will interact with the bolus/occluding tooth during a given masticatory cycle. This provides location-specific information about which parts of the tooth are more/less likely to contact the bolus/ occluding tooth, and thereby experience wear. Average PCV has, therefore, been suggested a measure of morphological wear resistance (i.e., how effective the shape of the tooth is at resisting wear).

BOX 2 Glossary of abbreviations
Ambient occlusion (portion de ciel visible, PCV: translated to "portion of visible sky"): A dental topographic metric that utilizes a computer graphics technique to make surfaces appear 3D by approximating the proportion of ambient light shining on a surface to quantify a tooth's morphological wear resistance (i.e., how effective the shape of the tooth is at resisting wear).
Basin cutoff (BCO): Method for cropping digital representations of a tooth, where only the portion of the tooth superior to the inferiormost point in the occlusal basin is considered.
Dental topography (DT) or dental topographic analysis (DTA): A landmark free method of quantifying and representing 2.5 or 3D whole tooth shape with a single metric.
Dirichlet normal energy (DNE): A dental topographic metric that quantifies the curvature of a surface using Dirichlet energy. Within primates, teeth with curvy surfaces are generally sharper: as such, DNE is often used to quantify tooth sharpness.
Entire enamel cap (EEC): Method for cropping digital representations of a tooth, where the entire outer surface of the enamel cap is considered.
Enamel-dentin junction (EDJ): The boundary between the enamel and the underlying dentin in a tooth.
Finite element analysis (FEA): Method for solving engineering and mathematical models using a meshed area of interest, constitutive equations, boundary conditions, and material properties.
Geographic information systems (GIS): Conceptual framework that provides the user with the ability to capture and analyze spatial and geographic data.
Micro-computed tomography (microCT): An imaging technique where X-rays are used to take slice-by-slice images of an object, and computer algorithms are used to reconstruct the 3D object.
Outer enamel surface (OES): The portion of the enamel cap that is exposed to the external environment.
Orientation patch count (OPC): A dental topographic metric that quantifies the orientation of each polygon on a digitized tooth's surface and counts the number of "patches" that form on the tooth, where a patch is defined as a predetermined number (often 3 or 5) of adjacent polygons with the same orientation. It is used to estimate dental complexity.
Orientation patch count rotated (OPCR): A derivative of OPC that normalizes for initial error in tooth orientation by rotating an occlusally aligned tooth clockwise or counter-clockwise (usually 8 times), calculating OPC at each new orientation, and averaging all the OPC values together.
Occlusal relief (OR): A dental topographic metric that quantifies the relative height of the occlusal portion by first cropping a tooth using the basin cutoff (BCO) method, and then taking the ratio of the tooth's outer enamel surface (OES) area to its cross-sectional area.
Relief index (RFI): A dental topographic metric that quantifies the relative height of a tooth by taking the ratio of a tooth's outer enamel surface (OES) area to its cross-sectional area. It differs from occlusal relief (OR) in that RFI utilizes the entire enamel cap (EEC).
Shearing ratio (SR): A derivative of the shearing quotient, which calculates the relative length of a shearing crest in a manner independent of the sample being analyzed.
Shearing quotient (SQ): A dental topographic metric that quantifies the relative length of a shearing crest on a tooth's surface. As it utilizes residuals, SQ metrics are dependent on the sample being analyzed.
A study testing the relationship between PCV and diet in platyrrhines and prosimians has shown primates with lower crowned teeth and/or teeth with bulbous cusps, like those found in frugivores and hard-object feeders, have higher average PCV, and primates with higher crowned teeth and/or teeth with taller cusps, like those found in folivores and insectivores, have lower average PCV. 52 This was supported by another study on South African hominins, which showed a strong relationship between relative crown height and PCV in Homo naledi, Paranthropus robustus, and Australopithecus africanus. 42 Interestingly, PCV appears efficient at predicting what F I G U R E 4 Daubentonia madagascariensis M2 (AMNH-41334, morphosource.org). Scale = 3 mm F I G U R E 5 Alouatta palliata tooth (USNM 171063, morphosource.org) cropped using the BCO (left) and EEC (right). Scale = 6 mm. BCO, basin cutoff; EEC, entire enamel cap spots of a tooth will experience wear once wear facets have formed. 52 As dental wear occurs from dietary and environmental sources, it is possible PCV could be used to address questions concerning dietary and environmental shifts.

| Angularity and curvature
These metrics quantify the sharpness of a tooth's surface. Mathematically, angularity is the second derivative of elevation (i.e., the change in slope across the surface), and the inverse of the second derivative of elevation is sharpness, so lower angularity values correspond to sharper teeth. 40,53 Curvature is similar, but calculated by taking the mean of the two principal curvatures for each polygon used to digitally represent the surface of the tooth. 43 Essentially, it measures how much the tooth's surface bends at different points on the surfaceareas that bend more are sharper.
Teeth with sharper occlusal surfaces, like those found in species with relatively long shearing crests, tend to have higher angularity and curvature than species with relatively shorter shearing crests.

| Dirichlet normal energy
The variability in any mathematical function can be quantified using Dirichlet energy. Functions that are more curvilinear tend to be more

BOX 3 Performing dental topographic analyses
The following steps are consistent across all topographic studies: 1. Obtain specimens or molds of teeth from collections.
2. Take 2.5D or 3D scans of the teeth.
3. Edit scans to isolate portions of the tooth for quantification.
4. Quantify tooth shape using one or more parameters.
Scanning original material is preferential, but not always possible. If scanning original material with laser or light scanners, enamel may need to be coated with a mat substance (e.g., Magnaflux Spotcheck SKD-S2 Developer) to reduce the reflectivity of the enamel. 54,67 Topographic analyses use 2.5D and 3D scans. 2.5D scans are projections of a 2D plane into the third dimension, meaning one height coordinate exists for each pair of length and width coordinates. This generally represents the occlusal surface well, but portions of the tooth remain hidden, 39,40,63 preventing the calculation of some topographic metrics (e.g., RFI). Tactile, laser, and light scanners typically generate 2.5D scans. 3D scanners (e.g., microCT, 10 X-ray synchrotron microtomography) 111 are generally more expensive, but capture all aspects of tooth shape. 6,10 Scans are either output as point clouds or surface (polygon) files.
Tooth orientation is important, particularly when taking 2.5D scans or when using orientation-sensitive metrics (e.g., OPC, RFI). 74 Teeth are generally oriented in anatomical position (i.e., how it would be in the mouth), 10,40,42,54,63 maximal occlusal view, 27,50 or using the tips of dentin horns. 43 The first two methods suffer from human error, and the last suffers the use of landmarks and internal geometry. The last method also risks orienting the tooth in a physiologically unrealistic manner, particularly if there is high variation in cusp height, as such, the authors recommend not using this method.
After scanning, surfaces are edited, cropped, and smoothed using a variety of programs (e.g., ArcMap, 112 Avizo, 10,43,55 Geomagic, 42,43,55 Meshlab, 41 and CloudCompare 54 ). The two most popular cropping methods are the basin cutoff (BCO) and the EEC. 42 BCO isolates the portion of the tooth superior to the inferiormost point in the occlusal basin ( Figure 5). A drawback to this method is some molars have deep basins and mesially-inclined cervical margins, so the BCO results in the inclusion of portions of the tooth root. 10 Further, variable percentages of the enamel cap are deleted, particularly when teeth are worn and have deep dentin pools. 27 The EEC method analyzes portion of the entire tooth, and not just portions responsible for food item breakdown. Teeth cropped using these two methods cannot be directly compared. 42 Studies have investigated the sensitivity of EEC to cropping around the cervical margin 10,41,74 have revealed topographic parameters are insensitive to intra-and inter-observer error. However, larger samples size need be considered.
During editing, scans are normalized by resolution or triangle count, as some topographic metrics are sensitive to triangle count (e.g., curvature, DNE, OPCR). 33,49,76 There appears to be no ideal triangle count for dental topographic analyses, 33,41,54,55,73,76 but resolution/triangle count must be high enough to represent the surface.
As with editing and cropping, there is no ideal smoothing method. Some topographic metrics, such as RFI, are relatively insensitive to smoothing, while others, like DNE, are sensitive to smoothing and smoothing protocol. 42,49,54 There are many acceptable methodologies for performing dental topographic analyses, and none are perfect; but if methodologies are consistent, measures are comparable.
variable and have higher energy. Dirichlet normal energy (DNE) measures surface variability, meaning teeth with higher DNE have curvier, or more variable, surfaces. Within primates, teeth with curvy surfaces (e.g., those with lots of cusps and crests or crenulations) are generally sharper. 41 Primates with relatively taller cusps and crenulated surfaces have higher DNE than those with relatively shorter cusps. 6,42,54,55 DNE is conceptually and geometrically similar to angularity, 45 curvature, and SQ. However, a recent study showed DNE and angularity are poorly correlated 56 and the correlation between SQ and DNE is weak (Figure 7), meaning that, although these metrics are similar, they are not interchangeable or directly comparable. It is therefore possible for studies that use DNE, angularity, and SQ to reach different conclusions, even though they quantify similar aspects of dental function.
When calculating DNE, a percent of the data can be discarded to account for geometrical singularities (e.g., sharp points/edges) that artificially inflate the score, 46 usually 0.1% area × energy. A larger percentage (1-5%) may be discarded when many geometrical singularities are present (e.g., due to taphonomic erosion, scanning artifacts). 42 Contour DNE plots on the tooth's surface can help determine if this is needed. 49 Different DNE programs (e.g., the R package molaR 57 and morphotester) 46 have different protocols for excluding triangles at the edge of the surface. Excluding a variable number of triangles can be problematic, as DNE is sensitive to triangle count (see Box 3). 49,52 A newly introduced metric, ariaDNE, appears to be less sensitive to these factors compared to DNE. 58

| Elevation
Elevation is a height map of the tooth: it has yet to be correlated to diet. 43,50 It is useful in quantifying absolute tooth and/or cusp height.

| Slope and inclination
Slope is the derivative of, or change in, elevation over the surface of the tooth. 40 Inclination is similar to slope, but measured differently.
Assuming a tooth is oriented/aligned during scanning so the occlusal surface is pointed in the +z direction, inclination is the angle between the vector normal to the triangle in the −z direction and the horizontal, xy plane. 43 Slope and inclination are not measures of sharpness, and relate to diet in the same manner as angularity and curvature.
Teeth with taller cusps will have steeper slopes/inclinations. As such, slope/inclination values appear to relate to diet similarly to RFI/OR, but have not been extensively used in dietary reconstructions. 43 were calculated to investigate the influence of EDJ shape on OES shape. It can also be used to address questions about certain portions of the tooth (e.g., shape of the mesial vs. distal half). 64

| Comparability of topographic metrics
Several of the topographic metrics are conceptually/geometrically similar and compute similar aspects of dental form. For example, DNE, 41 angularity, 40 and curvature 43 all measure tooth curviness/sharpness, but differences in the mathematics behind these metrics mean that values cannot be interchanged, with the correlation between variable being potentially extremely weak (e.g., in platyrrhines, DNE and angularity are weakly linearly correlated, p = .018, r 2 = 0.043). 56 While several methods exist for measuring the same aspect of dental morphology, it is difficult to pick the "best" metric for quantifying a distinct aspect of dental morphology, as the relationship between dental shape quantified through dental topography and diet can vary between clades. 6 For example, DNE is effective at differentiating molars of folivorous from frugivorous platyrrhines, 6 but angularity is not. 45 Conversely, DNE is ineffective at predicting diet in hominoids-unless sympatric species are being compared, as character displacement has occurred in hominoid diet and tooth morphology 54 -but angularity is potentially effective. 40,47 It is further difficult to pick the "best" metric as no studies use all metrics, and not all studies use the same molar, making it difficult to compare results across studies.
Dental topographic metrics that quantify conceptually/geometrically dissimilar aspects of dental form are also often correlated, but the strength and significance of the correlations vary. 41 Despite these and other problems, some mathematical relationships exist, making the following generalities possible.
1. Average slope/inclination and OR are strongly correlated. For a given cross-sectional area, teeth with increased surface area will be relatively taller, and cusps will require steeper slopes to reach the bottom of the basins.
2. Orientation, OPCR, and OPC are correlated, but values are not interchangeable.
3. DNE, angularity, and curvature may be correlated in some situations, but highly uncorrelated in others. 43

| Effects of wear and age
Being a landmark free method, dental topography is often used to investigate the effects of wear on tooth shape 40,42,47,63,65-68 ; when created, this was one of the stated advantages of dental topography. 40 Dental wear changes tooth shape, but the magnitude and direction of that change depends on the taxa and metric. As molars wear, wear facets begin to form, potentially altering complexity and curvature.
Cusps begin to decrease in height, becoming flatter/rounder, and eventually dentine becomes exposed, producing an enamel ridge around the dentin pool that acts as a compensatory crest. Dentin pools increase in size and the enamel ridge increases in length with age up until a point, when the dentin pools converge and there is a drastic decrease in enamel ridge length. In Propithecus edwardsi, this corresponds with a decrease in chewing efficiency and infant survival rate. 27 Dental topography can be used to analyze assemblages/collections of worn teeth, but teeth of different wear stages cannot be directly compared. Table 1 in a study by Glowacka and colleagues 47 summarized the relationship between dental wear and topographic metrics in studies published prior to 2016. In general, molars either maintain or lose sharpness, complexity, and relative height with wear.

| Sensitivity to data acquisition and processing
Most topographic metrics are sensitive to data acquisition and processing 41 Summative metrics and metrics that analyze triangles in (near) isolation, such as DNE and OPCR, are sensitive to triangle count and smoothing. 33,42,54,76 At high triangle counts, both RFI and OR are relatively insensitive to triangle count and smoothing. 10,73 Average angularity, curvature, and shearing crest length are likely sensitive to smoothing, as smoothing erases sharp edges, and average slope and inclination are likely less affected, as smoothing will not decrease tooth height. One newly introduced metric, ariaDNE, has the ability to robustly quantify surface curviness, and appears insensitive to all processing assumptions, except for cropping. 58 All metrics will be affected by cropping, as cropping changes the shape of the surface being analyzed.

| What metrics should be used?
Not all metrics are appropriate for all studies. If dental variation in a small group of closely related primates is being compared, OPCR is often not informative due to low variation in dental complexity. 6,42 PCV, DNE, angularity, curvature, slope, inclination, RFI, and OR would be more appropriate, given their ability to pick up subtle, subspecies, and population level differences in diet. 40 78 Natural selection is likely acting on tooth shape through one or more of these functions, and the relative importance of these functions depends on diet. For example, trapping and stabilizing foods (herein trapability) 78 is likely more important for animals with diets requiring high bite forces as they need to transfer large forces to the food without it slipping, while food breakdown efficiency is more important for diets consisting of foods difficult to digest.
The first publications on dental topography suggested basin volume and drainage could be used to quantify trapability and food clearance, but these metrics were later dismissed. 37,39 No subsequent topographic metrics have quantified trapability or food clearance, and it is therefore unknown how these factors relate to dental function and diet in primates.
The majority of aspects of dental morphology related to longevity (tooth size, enamel thickness, enamel microstructure, and fracture risk) 79,80 are related to internal dental structure/geometry and not quantified by dental topography. As PCV can quantify morphological wear resistance, it could potentially be used to quantify morphological dental longevity. Another metric, RFI, may also be able to predict the maximum lifetime, and therefore longevity, of a tooth, as it quantifies relative tooth height. While primates with abrasive diets have increased relief and morphological wear resistance (e.g., folivores), primates with nonabrasive diets can have higher and lower relief and morphological wear resistance (e.g., insectivores and frugivores), making it possible, but unlikely, that selection is acting on tooth shape to increase morphological longevity. 6,51 Selection is likely working on other topographic metrics through food breakdown. Tooth shape is correlated to chewing efficiency, 4,17,19 which is positively correlated to both digestive efficiency and caloric intake 19,27,81,82 : this provides an evolutionary pathway through which selection can act on tooth shape, and thereby dental topography, in animals that require high chewing efficiencies (i.e., insectivores and folivores). 4 For primates with relatively lower chewing efficiencies (e.g., frugivores, hard-object eaters), selection is not acting strongly in favor of chewing efficiency, and selection is likely acting strongly on an aspect of food breakdown independent of chewing efficiency.
What is being selected for in these groups? Researchers have suggested frugivores need to juice foods, and the most effective way to do this is through dull cusps and large basins (i.e., the mortar and pestle hypothesis). 9,15,83,84 However, no experiments have compared the benefits of juicing foods versus cutting foods into small enough pieces to be swallowed, and how this would result in an increased evolutionary fitness.
A range of hypotheses exist governing the relationship between cusp/tooth shape and hard-object feeding. For complete descriptions of these hypotheses, and references supporting their formation, please see papers by Berthaume and colleagues. 85,86 Briefly, the Blunt Cusp Hypothesis comes from comparative anatomy and predicts dull cusps are better for hard-object feeding, potentially because they reduce masticatory force and/or energy. 11,26,67,85 The Strong Cusp Hypothesis comes from contact mechanics, and similarly predicts dull cusps are better for hard-object feeding, but because it reduces enamel stresses, decreasing risk of enamel fracture. Conversely, the Pointed Cusp Hypothesis, also from contact mechanics, predicts sharp cusps are better because they increase stresses in the food item. 85,[87][88][89] Cusp sharpness is certainly correlated for food item breakdown in single cusped teeth [87][88][89] and symmetrical molars, 86 but physical experimentations and finite element models failed to find support for these hypotheses in multicusped, asymmetrical molars. 85,86,90 From these studies, the Complex Cusps Hypothesis emerged, which states hard-object feeders should maximize the stresses in the food item while minimizing stresses in the enamel. As a result, multicusped, asymmetrical teeth should have a combination of sharp and dull cusps where one dull cusp transfers the majority of forces to the food item while the others act to stabilize the food, promoting food item failure while preventing enamel fracture. Looking at the ratio of stresses in the food item to stresses in the enamel, a hemispherical food item and a set of four cusped hypothetical molars, the authors found support for this hypothesis 86 across a range of food item sizes. 90 A later study tested the relationship between dental topography and energy, stresses in the food, stresses in the enamel, and the ratio of these stresses using the hypothetical molars, but found no relationship between shape and function. 44 The mechanical reason why hard-object feeding primates tend to have low crowned, bulbous molars remains unknown, possibly because (a) natural selection is acting on tooth shape in a way not encompassed by those hypotheses or experiments, or (b) selection is not acting on tooth shape at all in hard-object feeders, but another factor (e.g., enamel thickness) 55 that covaries with tooth shape (e.g., see Biological sources of variation in tooth shape).
Much more research is needed to unveil the complex relationship between tooth shape and function in primates, particularly to understand how selection is working on molar shape in frugivores and hardobject feeders.

| Heritability
Despite understanding the heritability of some aspects of dental morphology, 91,92 we have no understanding of the heritability of biomechanically relevant aspects of molar occlusal morphology and how it relates to EDJ shape and/or enamel secretion patterns in primates. 93 This is necessary to construct evolutionary models to (a) understand how selection is acting on dental topography and (b) perform more accurate dietary reconstructions, by understanding how long it takes teeth to become adapted to diet. Here, the biggest challenge lies in gaining a pedigreed collection of unworn dental molds: worn teeth cannot be used for these purposes, as their shape is a product of genetic and environmental factors. 94

| Developmental sources of variation in occlusal topography
Unlike bone, dental enamel does not remodel, meaning changes in unworn occlusal topography occur because of changes in dental growth and development. During growth and dental development, enamel is deposited by ameloblasts traveling from the EDJ toward the OES, 79 making the shapes of the EDJ and OES correlated. 48,92,95 Therefore, it is possible that variation in EDJ shape and/or enamel deposition may be responsible for the variation in occlusal topography.
Three studies investigated the relationship between dental growth and development and dental topography. The first study discovered the following three relationships between EDJ and OES complexity (a) OPC in the EDJ and OES are similar, (b) OES OPC is moderately higher than EDJ OPC, and (c) OES OPC is much higher than EDJ OPC. 95 Skinner and colleagues 95 concluded that OES complexity is controlled primarily by the EDJ in first and second relationships, but enamel deposition in third relationship, and EDJ complexity can provide a lower limit for OES complexity (i.e., OES OPC ≥ EDJ OPC).
The second study investigated relationship between EDJ shape, OES shape, and enamel thickness, and concluded that the inclination, orientation, and curvature of the EDJ and OES were highly correlated, and OES mean curvature was affected by enamel thickness. 55 The correlation between enamel thickness and OES shape requires further investigation. Finally, the third study combined their results with Guy and colleagues 55 and found a stronger correlation between EDJ and OES in DNE, RFI, and OPCR within nonprimate Euarchonta compared with primates, 96 implying that primate OES is determined more by enamel deposition than EDJ morphology. However, Selig and colleagues 96 directly compared DNE and curvature to come to this conclusion, and as previously stated, these values are not directly comparable.

| Dietary mechanical properties
Mechanical properties are the intensive (size independent) properties of a material that describe how the foods behave under a load. 8 Dietary mechanical properties are the cumulative set of mechanical properties for a diet. They are often measured by following an animal/ set of animals in the field, and testing the mechanical properties of the foods they consume. 8,9 Collection of dietary mechanical properties is challenging, requiring researchers to follow primates in the field, collect foods that are being consumed from the exact site/plant they are being foraged, properly store foods for transport, and test the properties of those foods within 24 hours using a (portable) universal tester. Ideally, foods that the primates are actively consuming, and not those nearby, are tested, as there may be differences in mechanical properties between these foods. In the field, foods must be tested relatively quickly, or their mechanical properties will begin to change. 8,9 Presumably Within hominins, an increase in tooth sharpness, as was observed in South African hominins relative to extant great apes, 42  6 | THE NEXT 20 YEARS

| Ground-truthing
The largest barrier facing dental topographic studies is the lack of a relationship between dental form and masticatory performance. The first studies to investigate the relationship between dental form and masticatory performance by Kay and Sheine found a tooth's shearing capability was an efficient predictor of chewing efficiency in two primate, and one non-primate, mammal species. 4,17,19 One more recent study investigated the relationship between four dental topographic metrics and biomechanics using a computational modeling approach.
Berthaume 44 constructed a parametric model of a four cusped molar and used finite element analysis (FEA) to investigate the relationship between DNE, OPCR, RFI, and PCV and stresses in the food item, stresses in the enamel, the ratio of these two metrics, and energy absorbed by the food item during hard food item biting. However, no correlation was found between the dental topographic and functional parameters. Laird and colleagues 82 investigated the relationship between chewing efficiency, one dental topographic metric (slope), and metrics for tooth size in modern humans using an in vivo experimental set up. They found chewing efficiency was not correlated to slope, but was positively correlated to tooth size, indicating larger teeth chewing more efficiently.
Barring these studies, little has been done to investigate the relationship between these dental topographic metrics and masticatory performance, begging the question: all else being equal, do dental topographic metrics actually correlate to food breakdown during mastication? This question goes beyond dental topography, and cuts to the heart of dental functional morphology. For this field to move forward efficiently, we require a ground-truth relationship between these shape metrics and masticatory performance.
Some additional issues that are often ignored must also be addressed for the field to move forward and are discussed briefly later.

| Standardization of metrics
One of the challenges of dental topography is the numerous methodologies for quantifying tooth shape. New metrics may not be needed, unless they can quantify other aspects of dental form currently being ignored, or aspects of dental form directly related to masticatory performance. An increased understanding of metric comparability, particularly of metrics that quantify similar aspects of dental form, is needed for study comparability. 56 Ideally, a standardized methodology for performing analyses, complete with a standardized set of metrics that are functionally significant, will also be developed and adapted.

| Population level variation
Similarly, little is known about population level variation in dental topography. One study showed population level differences in Lemur catta, 77 and another on atelids showed population differences in tooth wear, but not shape. 104 Population level studies, especially those that include genetic, genomic, and/or proteomic data, will help explain how quickly diet can act on tooth shape through natural selection and provide valuable insights into the possible effects of gene flow, genetic drift, and other evolutionary mechanisms on tooth shape. This will further aid clarifying the use of dental topographic metrics in detecting new species in the fossil record.

| Sexual dimorphism
Sexually dimorphic differences in dental characters sometimes exist independent of size. 105 In dental topographic studies, sexual dimorphism is often ignored, and differences between species are assumed to be greater than differences between sexes. This may or may not a valid assumption, particularly when considering primates with large levels of body mass sexual dimorphism, such as Theropithecus, Pongo, and Gorilla, and there is evidence to suggest primates with large levels of body mass sexual dimorphism have dimorphic diets. 106 6.6 | Does body mass matter?
Small primates are more limited in their ability to forage over long distances and produce high bite forces, meaning they need to be more efficient to survive. Larger primates have the luxury of being less efficient, as they may already possess tools that are "good enough" for their function due to allometry. The shorter intergenerational times of smaller primates also implies the cumulative effects of selection acting on tooth shape may become apparent over a shorter period of time, potentially making the correlation between tooth shape and diet stronger in smaller primates.
Since dental topography quantifies shape, it should be independent of tooth size, implying topographic metrics do not need to be normalized by size. This is supported by dental topographic studies which find a correlation between tooth shape and diet across a broad range of body sizes. 6,10,12,45,51 But larger teeth have the potential to hold more features, and more triangles may be needed to capture their shape digitally. 54,97 Together, this means size may be important to dental topographic studies for both biological and methodological reasons.
6.7 | What role does grit and dust play in molar shape?
Both RFI and PCV are well suited to investigate the effects of environment on molar shape. It is possible teeth with higher RFI are better adapted to more abrasive diets, and if other topographical parameters, such as DNE and OPCR, are constant, differences in RFI may reflect differences in grit/dust consumption. 42 Similarly, as PCV measures morphological wear resistance, it may also be useful in investigating environmental factors, such as grit/dust, related to dental wear.

| Are crenulations important?
Most studies investigating tooth sharpness simplify teeth to the point where crenulations begin to disappear 5,6,54 (c.f. 55 ). However, crenulations have biomechanical consequences, as a smooth surface will transmit forces to an object differently from a "bumpy" surface. In primates, they are hypothesized to "grip" foods, 7 which is why they are believed to be present in hard-object feeders. Functionally, it is possible that crenulations could also cut fibers: after all, crenulations increase tooth sharpness and complexity. 6,54 If crenulations do act as a cutting surface, they play an important, unrecognized biomechanical function that should be considered in dental topographic analyses. This could explain how species with low SQ and crenulated cusps could be efficient folivores. 107,108 The absence of crenulations from the most highly folivorous primates, for which cutting is important, could challenge the hypothesis that crenulations are acting as a cutting surface. However, these species generally possess molars with high OR, and it is possible either crenulations or high OR, and not both, are needed to create an efficient cutting surface. The degree of molar crenulation will also likely be important in testing this hypothesis, as it is possible that crenulated molars do not become efficient at cutting until a certain degree of crenulations is reached. Biomechanical studies are needed to address this question.
6.9 | Does molar shape matter in modern humans?
After the advent of stone tools, cooking may have greatly relaxed the selective pressures working on tooth shape in modern humans. (Note: in Berthaume and colleagues' study, 42 the lack of lithics or evidence of controlled fire use for H. naledi led the authors to hypothesize that selection was still acting on tooth shape in H. naledi the same way it was in other primates.) However, dental morphology may still reflect diet in certain situations. For example, the advent of agriculture led to an increase in carbohydrate consumption and dental caries. It is possible that more complex teeth have more places for cavity-causing bacteria to hide, and therefore selection may have acted against complex teeth. To date, no studies have investigated modern human variation in dental topography.

| CONCLUDING REMARKS
The amount we have learned about primate teeth and function is astounding. We have a better idea of how tooth shape relates to diet than ever before. But, at the same time, the question of why the variation in primate molars exists is far from being answered. Diet is a major factor in determining molar shape, but many mysteries still surround the evolutionary pathways that relate tooth shape and diet. In some clades, chewing efficiency and energy are important, while in others these factors matter less.
The complex relationship between dental development, molar shape, and how EDJ shape and ameloblasts affect dental function is only beginning to be understood. Other questions require much more experimental/simulated data which, together, can address some of the big questions surrounding primate evolution. With time, dental topography could be used to predict future trend in extant primate evolution. And in the hand of conservationists, these data could help predict the extinction risk of some primates and help establish protocols to prevent their demise. 33 What an exciting time it is to be studying primate dental topography!