Fig 1.
Effect of simplification and smoothing on the largest (top) and smallest (bottom) teeth used in this study, where size is quantified by surface area (SA).
The cropping method shown here is EEC, and resolution is defined as triangles/mm2. At a resolution of 1, the Microcebus griseorufus tooth was composed of 4 triangles which, when smoothed, disappeared. Smoothing drastically changes tooth shape at low resolutions, but has a larger effect on smaller teeth than larger teeth. Corresponding triangle counts for the smoothed Varecia variegata surfaces are 247, 2471, 24712, and 247121, and for smoothed Microcebus griseorufus are 4, 45, 449, and 4489.
Fig 2.
Density plots showing the effect of smoothing on DNE, OPCR, RFI, PCV, surface area (SA), and tooth size.
A negative value indicates a decrease in the topographic value due to smoothing. Grey, solid lines are low triangle counts (< 210 triangles), dashed grey is medium-low triangle counts (210–1799 triangles), dashed black lines are medium-high triangle counts (1800–9999 triangles), and solid black lines are high triangle counts (10000+ triangles). For RFI, PCV, SA, and size, as triangle count increases, the effects of smoothing become more predictable, as is evidenced by the narrowing of the density distributions. DNE and OPCR are more sensitive to smoothing than the other metrics.
Table 1.
Descriptive statistics for density curves in Fig 1, showing the effects of smoothing.
Both mean and median are reported as the curves sometimes do not follow a normal distribution. Probabilities < 0.05 indicate a statistically significant result that smoothing decreases the topographic metric (p < 0.05), and probabilities > 0.95 indicate a statistically significant result that smoothing increases the topographic metric (p > 0.95). The 2.5% and 97.5% quantiles are given to represent the 95% confidence interval. Triangle counts of L = low (< 210), ML = medium-low (210–1799), MH = medium-high (1800–9999), and H = high (10000+). Bold p-values are significant for greater than zero, bold and italics for less than zero.
Table 2.
Statistics for density curves in Fig 2, showing the difference between the EEC and BCO cropping methods.
Both mean and median are reported as the curves sometimes do not follow a normal distribution. Probabilities < 0.05 indicate a statistically significant result that smoothing decreases the topographic metric (p < 0.05), and probabilities > 0.95 indicate a statistically significant result that smoothing increases the topographic metric (p > 0.95). The 2.5% and 97.5% quantiles are given to represent the 95% confidence interval. Triangle counts of L = low (< 210), ML = medium-low (210–1799), MH = medium-high (1800–9999), and H = high (10000+). Bold p-values are significant for greater than zero, bold and italics for less than zero.
Fig 3.
Density plots showing the effect of cropping method on DNE, OPCR, RFI, surface area (SA), and tooth size.
PCV was not calculated for surfaces cropped with the BCO method due to time constraints. A negative value indicates an increase in the topographic value going from EEC to BCO. Grey, solid lines are low triangle counts (< 210 triangles), dashed grey is medium-low triangle counts (210–1799 triangles), dashed black lines are medium-high triangle counts (1800–9999 triangles), and solid black lines are high triangle counts (10000+ triangles). In general, RFI, SA, and size values are smaller with BCO compared to EEC. DNE and OPCR are just as likely to increase or decrease. This is because, for a given triangle count, there are more triangles representing the occlusal surface using the BCO method, which can increase DNE and OPCR. But for a given resolution, fewer triangles represent the tooth with the BCO than the EEC, leading to a decrease in DNE and OPCR, which are summative metrics.
Table 3.
Five-way ANOVA testing the influence of diet, clade, smoothing, cropping, and triangle count on dental topographic values.
In the factor column, d = diet, g = group (clade), s = smoothing, cm = cropping method, tc = triangle count. F-values are given followed by p-values in parentheses. P-values of 0 are ≤0.0005. Bold and italics indicates p < 0.05.
Table 4.
Five-way ANOVA testing the influence of diet, clade, smoothing, cropping, and resolution on dental topographic values.
In the factor column, d = diet, g = group (clade), s = smoothing, cm = cropping method, r = resolution. F-values are given followed by p-values in parentheses. P-values of 0 are ≤0.0005. Bold and italics indicates p < 0.05.
Fig 4.
Boxplots showing prosimian (white) and platyrrhine (grey) DNE values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. Results at a triangle count of 10000 are comparable to those from [20]. Within prosimians, as triangle count increases, there appears to be more separation between dietary categories. At a triangle count of about 1000, the pattern of insectivores having the highest DNE, followed by folivores, omnivores, frugivores, and finally hard object feeders begins to emerge. This pattern generally holds true up until a triangle count of 100000. Within platyrrhines, there is no great distinction between folivores, omnivores, and frugivores up until a triangle count of 10000, but hard object feeders consistently have the dullest teeth (i.e. lowest DNE value). At higher resolutions, however, this changes, and at a triangle count of 100000 hard object feeders have the higher average DNE value, and folivores have the lowest. This pattern is better seen when the BCO cropping method is used, and/or surfaces are unsmoothed (see S1 Fig).
Fig 5.
Boxplots showing prosimian (white) and platyrrhine (grey) OPCR values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. Results at a triangle count of 10000 are comparable to those from [20]. As with DNE, the relationship between diet and OPCR changes with resolution. E.g. hard object feeding platyrrhines have the highest OPCR value at a triangle count of 100000, but the lowest at a count of 2000.
Fig 6.
Boxplots showing prosimian (white) and platyrrhine (grey) RFI values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. Results at a triangle count of 10000 are comparable to those from [20]. Once an adequate triangle count is reached (about 500), a pattern develops in both prosimians and platyrrhines where insectivores have the highest values, followed by folivores, frugivores, and hard object feeders.
Fig 7.
Boxplots showing prosimian (white) and platyrrhine (grey) PCV values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. Results at a triangle count of 10000 are comparable to those from [20]. As with RFI, once a sufficient triangle count is reached, a stable relationship develops between PCV and diet.
Fig 8.
Boxplots showing prosimian (white) and platyrrhine (grey) surface area (SA) values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. As surface area is a measure of tooth size, no expected relationship is expected to emerge, other than folivores having larger teeth and insectivores having smaller teeth.
Fig 9.
Boxplots showing prosimian (white) and platyrrhine (grey) tooth size (quantified through outline area, MorphoTester) values for each diet at different triangle counts (smoothed, EEC).
Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder. Results are almost identical to those in Fig 8 showing surface area (SA), as both size and SA are measures of size, not shape.
Table 5.
880 one-way ANOVAs were run to test for differences due to dietary category, one for each combination of topographic metric, smoothing, cropping method, and triangle count/resolution.
ANOVAs are divided between those run keeping triangle count constant (440) and those keeping resolution constant (440). Results here are the number of one-way ANOVAs with p-values less than 0.05, 0.01, and 0.0005, followed by the percent of the total ANOVAs in parentheses In general, all topographic metrics could successfully differentiate between dietary categories with a high level of accuracy, but DNE and OPCR seemed to perform slightly worse. Holding resolution constant yielded roughly the same results as holding triangle count constant.
Table 6.
Sum of number of Tukey HSD comparisons that yielded significant results (p < 0.05, 0.01, and 0.005) followed by percent of all Tukey HSD tests in parentheses for the triangle count dataset.
P-values adjusted for multiple comparisons using the TukeyHSD() function in R. ins = insectivore, fol = folivore, frug = frugivore, omn = omnivore, and hof = hard object feeder. Regardless of clade, smoothing, cropping method, or triangle count, tooth size never differed between hard object feeders and frugivores, and surface area and tooth size never differentiate between insectivores and hard object feeders, and nearly never differentiated between insectivores and omnivores.
Table 7.
Sum of number of Tukey HSD comparisons that yielded significant results (p < 0.05, 0.01, and 0.005) followed by percent of all Tukey HSD tests in parentheses for the resolution dataset.
P-values adjusted for multiple comparisons using the TukeyHSD() function in R. ins = insectivore, fol = folivore, frug = frugivore, omn = omnivore, and hof = hard object feeder.
Table 8.
Results of the linear discriminant function analyses when triangle count is held constant (Pros. = prosimian, Plat. = platyrrhine).
Values reported are the cross-validated success rate of correctly classifying diet. Classifications greater than 50% are in bold and colored tan. In general, topographic metrics correctly classify diet in platyrrhines more often than in prosimians.
Table 9.
Results of the linear discriminant function analyses when resolution is held constant (Pros. = prosimian, Plat. = platyrrhine).
Values reported are the cross-validated success rate of correctly classifying diet. Classifications greater than 50% are in bold and colored tan. In general, topographic metrics correctly classify diet in platyrrhines more often than in prosimians.
Table 10.
Percent of times significant correlations (Bonferroni corrected p-value of 0.05/15 = 0.0033) were found between variables.
More correlations were found between variables when resolution was held constant.
Fig 10.
Coefficients of correlations (R) plotted against the natural log of triangle count to show how correlations between topographic variables change with triangle count.
The grey area shows non-significant correlations between variables with a Bonferroni corrected p-value (0.05/15 = 0.00333). Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 11.
Coefficients of correlations (R) plotted against the natural log of resolution to show how correlations between topographic variables change with resolution.
The grey area shows non-significant correlations between variables with a Bonferroni corrected p-value (0.05/15 = 0.00333).
Fig 12.
Effect of resolution on DNE and OPCR in five primates.
The blue line is a folivorous prosimian (AMNH100503), black line is an insectivorous prosimian (AMNH207949), red line is a folivorous platyrrhine (AMNH211465), and green and grey lines are hard object feeding platyrrhines (MCZ30720 and USNM291128).
Fig 13.
Effect of triangle count on DNE and OPCR in five primates.
The blue line is a folivorous prosimian (AMNH100503), black line is an insectivorous prosimian (AMNH207949), red line is a folivorous platyrrhine (AMNH211465), and green and grey lines are hard object feeding platyrrhines (MCZ30720 and USNM291128).
Fig 14.
Effect of triangle count on topographic metrics (smoothed, EEC).
Averages for each topographic value are given with a 95% confidence interval. Blue = insectivore, green = folivore, grey = omnivore, red = frugivore, brown = hard object feeder. Thick solid line = insectivore, thin solid line = folivore, small dotted line = omnivore, thin dashed line = frugivore, thick dashed line = hard object feeder. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 15.
Effect of resolution on topographic metrics (smoothed, EEC).
Averages for each topographic value are given with a 95% confidence interval. Blue = insectivore, green = folivore, grey = omnivore, red = frugivore, brown = hard object feeder. Thick solid line = insectivore, thin solid line = folivore, small dotted line = omnivore, thin dashed line = frugivore, thick dashed line = hard object feeder.
Fig 16.
Absolute value of the percent difference between RFI and PCV values at the highest triangle count and lower triangle counts.
Dotted horizontal lines represent 5% difference. The confidence intervals are drawn at 80%, 95%, and 99%. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 17.
Absolute value of the percent difference between RFI and PCV values at the highest resolution and lower resolutions.
Dotted horizontal lines represent 5% difference. The confidence intervals are drawn at 80%, 95%, and 99%.
Fig 18.
Boxplots showing slope and intercept values for DNE and OPCR regressed against triangle count (smoothed, EEC).
Prosimians are in white and platyrrhines in grey. Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder.
Fig 19.
Boxplots showing slope and intercept values for DNE and OPCR regressed against resolution (smoothed, EEC).
Prosimians are in white and platyrrhines in grey. Diets are shown on the x-axis: ins = insectivore, fol = folivore, omn = omnivore, frug = frugivore, and hof = hard object feeder.
Fig 20.
Changes in p-values from Tukey HSD tests plotted against triangle count (prosimian, smoothed, EEC).
The grey shaded regions at the bottom of the graphs show p-values from 0–0.05. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 21.
Changes in p-values from Tukey HSD tests plotted against triangle count (platyrrhine, smoothed, EEC).
The grey shaded regions at the bottom of the graphs show p-values from 0–0.05. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 22.
Changes in p-values from Tukey HSD tests plotted against resolution (prosimian, smoothed, EEC).
The grey shaded regions at the bottom of the graphs show p-values from 0–0.05.
Fig 23.
Changes in p-values from Tukey HSD tests plotted against resolution (platyrrhine, smoothed, EEC).
The grey shaded regions at the bottom of the graphs show p-values from 0–0.05.
Fig 24.
Changes in p-values from linear DFAs plotted against triangle count (prosimians).
Horizontal lines represent p-values from linear DFAs constructed from the slopes/intercepts of DNE/OPCR being regressed against triangle count. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 25.
Changes in p-values from linear DFAs plotted against triangle count (platyrrhines).
Horizontal lines represent p-values from linear DFAs constructed from the slopes/intercepts of DNE/OPCR being regressed against triangle count. Vertical solid and dashed lines indicate triangle counts of 10000 and 20000, respectively.
Fig 26.
Changes in p-values from linear DFAs plotted against resolution (prosimians).
Horizontal lines represent p-values from linear DFAs constructed from the slopes/intercepts of DNE/OPCR being regressed against resolution.
Fig 27.
Changes in p-values from linear DFAs plotted against resolution (platyrrhines).
Horizontal lines represent p-values from linear DFAs constructed from the slopes/intercepts of DNE/OPCR being regressed against resolution.