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Calculation of crown formation time

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The crown formation time is calculated as the sum of the formation time of cuspal enamel and lateral enamel. Cuspal DSR is not constant during the whole cuspal enamel secretion, and it is often observed that the DSR increases when distance from EDJ increases, especially in thick-enameled taxa. It is also observed that, for different teeth of a single individual, the teeth having thinner enamel (such as anterior teeth) will exhibit cuspal DSR equivalent to the inner and middle values measured on the molars with thicker enamel, suggesting a general relationship between DSR and distance to the EDJ applying on the whole individual. Hence, instead of using a single value for DSR, we developed a method consisting of quantifying the gradient of DSR versus distance to the EDJ on M2 of this individual. From this gradient, it becomes then easy to derive an equation relating the cuspal thickness with the cuspal formation time, applicable on all the teeth of this individual, taking into account that average DSR of thinner-enameled teeth would be lower than that of thicker-enameled ones. DSR was measured three times in three different sections to quantify the inner, middle, and outer DSR on the M2 cuspal enamel of paracone (data file S1). For each measurement, a prism between two consecutive Retzius line was traced and its length was recorded in ImageJ. From these measurements, a simple regression was applied to relate the averaged measured DSR with their corresponding distance to the EDJ. It turned out that a simple linear regression was sufficient to efficiently characterize the DSR gradient in this individual (DSR = 0.00146xdisEDJ + 2.70; R2 = 0.812). From this gradient, the general equation relating cuspal enamel thickness and cuspal formation time was derived by simulating the complete secretion profile from EDJ to 1770 μm (thickest cuspal enamel observed for this individual), leading to the following polynomial equation: y = 1.20E−8x3 − 7.99E−5x2 + 0.363x + 0.556, where y is the cuspal enamel formation time and x is the cuspal enamel thickness (data file S1). Cuspal enamel thickness was measured from the dentine horn to the first perikymata on the outer enamel surface. The cuspal enamel thickness of the other teeth was then put into this equation, and the secretion time of their cuspal enamel was calculated (data file S1). Even if this approach is somehow experimental, it can be expected to be more relevant than using a single average value to estimate cuspal formation time over a complete dentition exhibiting very different cuspal enamel thicknesses. Lateral enamel formation times were calculated by multiplying the number of perikymata by the individual’s periodicity (10 days). The interobserver error of crown formation time varies from 3 to 52 days, depending on slight differences in the measurement of cuspal enamel thickness and perikymata counts between observers (Table 1 and table S1).

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