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. 2021 Jul 5;239(5):1170–1181. doi: 10.1111/joa.13500

Testing the inhibitory cascade model in a recent human sample

José María Bermúdez de Castro 1,2,✉, Mario Modesto‐Mata 3, Cecilia García‐Campos 1,4, Susana Sarmiento 4, Laura Martín‐Francés 1,2,4, Marina Martínez de Pinillos 1, María Martinón‐Torres 1,2
PMCID: PMC8546523  PMID: 34227109

Abstract

The Inhibitory Cascade Model was proposed by Kavanagh and colleagues (Nature, 449, 427–433 [2007]) after their experimental studies on the dental development of murine rodent species. These authors described an activator–inhibitor mechanism that has been employed to predict evolutionary size patterns of mammalian teeth, including hominins. In the present study, we measured the crown area of the three lower permanent molars (M1, M2, and M3) of a large recent modern human sample of male and female individuals from a collection preserved at the Institute of Anthropology of the University of Coimbra (Portugal). The main aim of the present study is to test if the size molar patterns observed in this human sample fits the Inhibitory Cascade Model. For this purpose, we first measured the crown area in those individuals preserving the complete molar series. Measurements were taken in photographs, using a planimeter and following well‐tested techniques used in previous works. We then plot the M3/M1 and M2/M1 size ratios. Our results show that the premise of the Inhibitory Cascade Model, according to which the average of the crown area of M2 is approximately one‐third of the sum of the crown area of the three molars, is fulfilled. However, our results also show that the individual values of a significant number of males and females are out of the 95% confidence interval predicted by the Inhibitory Cascade Model in rodents. As a result, the present analyses suggest that neither the sample of males, nor that of females, nor the pooled sample fits the Inhibitory Cascade Model. It is important to notice that, although this model has been successfully tested in a large number of current human populations, to the best of our knowledge this is the first study in which individual data have been obtained in a recent human population rather than using the average of the sample. Our results evince that, at the individual level, some factors not yet known could interfere with this model masking the modulation of the size on the molar series in modern humans. We suggest that the considerable delay in the onset of M3 formation in modern humans could be related to a weakening of the possible activation/inhibition process for this tooth. Finally, and in support of our conclusions, we have checked that the absolute and relative size of M1 and M2 is not related to the M3 agenesis in our sample. In line with other studies in primates, our results do not support the Inhibitory Cascade Model in a recent human sample. Further research is needed to better understand the genetic basis of this mechanism and its relationship to the phenotype. In this way, we may be able to find out which evolutionary changes may be responsible for the deviations observed in many species, including Homo sapiens.

Keywords: agenesis, Inhibitory Cascade Model, modern humans, molar size

In the present study, we measured the crown area of the three lower permanent molars (M1, M2, and M3) of a large recent modern human sample of male and female individuals from a collection preserved at the Institute of Anthropology of the University of Coimbra (Portugal). The main aim of the present study is to test if the size molar patterns observed in this human sample fits the Inhibitory Cascade Model. In line with other studies in primates, our results do not support this model.

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1. INTRODUCTION

Research carried out in recent decades has shown the existence of a molecular signal system that regulates dental development, as well as the congenital absence of particular teeth (e.g., Balic, 2019; Jernvall & Thesleff, 2000; Kwon et al., 2017; Lan et al., 2014; Tucker & Sharpe, 2004; Zhang et al., 2005; Zhou et al., 2011). Kavanagh et al. (2007) proposed the so‐called Inhibitory Cascade Model through in vitro experiments in mice. These authors suggest a developmental mechanism that determines the relative molar size through an activator (a)/inhibitor (i) ratio. According to this model, the molar a/i ratio is responsible for the size of subsequent developing molars (Kavanagh et al., 2007). Whereas the activation mechanism is principally considered to be of mesenchymal origin, the developing molars would produce signaling molecules that inhibit the development of subsequent buds. The genotypic–phenotypic relationship between molar position (first, second and third) and molar size was defined by the expression:

y=1+[(a‐i)/i](x‐1),

where y is the relative molar size estimated from the occlusal area, x is the place of the molar in the molar series, and a and i are the relative strength of the activation and inhibition, respectively. According to Kavanagh et al. (2007, p. 430), “...a balance between activation and inhibition results in equal‐sized molars (M1≈M2≈M3) and increasing inhibition has a cumulative effect on the posterior teeth giving a distinct M1>M2>M3 pattern”. One phenotypic consequence of this model is that the size of the central tooth of a triplet (like the three permanent molars) would be roughly equal to one‐third of the total triplet size; that is, (a/i)/[1 +  a/i + (2a/i‐1)] = 1/3 (Kavanagh et al., 2007).

The Inhibitory Cascade Model seems to explain a high proportion of the variation in relative molar size not only in murines but also in other mammals (Kavanagh et al., 2007; Polly, 2007). Polly (2007) observed that the sequence of the molar size of most of the analyzed species (except for three species of bear that do not fit the model) occupies a restricted area of the bivariate morphospace produced by two variables examined by Kavanagh and coworkers in their study: the ratio of the permanent lower second molar (M2) to permanent lower first molar (M1) area (M2/M1) and the ratio of permanent third molar (M3) to M1 area (M3/M1). Although the complex system of molecular signals that govern tooth development remain largely unknown (Balic, 2019), Polly's findings suggest that the regulation of the relative size of teeth could be highly channeled and that the molar size sequence should follow well‐defined patterns. However, some authors have tested the Inhibitory Cascade Model in extant and extinct mammals and the results have not always been convincing, particularly in primates (e.g., Bernal et al., 2013; Carter & Worthington, 2016; Roseman & Delezene, 2019).

In 2016, Evans and colleagues applied the Inhibitory Cascade Model to the lower deciduous and permanent molars of different hominin samples. They observed that early hominins, such as Ardipithecus, Australopithecus and Paranthropus, exhibit the M1 < M2 < M3 size relationship irrespective of overall dental size. These authors suggest that “near the origin of the genus Homo a change in the scaling relationship between the M1 size and the inhibitory cascade patterning occurs.” Evans and colleagues observed that in the genus Homo, including modern humans, there is a tight link between tooth proportions and absolute size so that a single developmental parameter can explain both the absolute and relative size of deciduous and permanent postcanine teeth. In subsequent years, other studies tested the Inhibitory Cascade Model in different hominin groups supporting Evans et al. (2016)’conclusions (Bermúdez de Castro et al., 2020; Schroer & Wood, 2015; see also comments in Gómez‐Robles, 2016).

To carry out their study, Evans et al. (2016) examined the average size of the three lower molars, M1, M2, and M3 in numerous modern populations from various regions of the planet. The data were obtained from the literature, as well as from dental casts housed at the Burlington Growth Center, (Toronto, Canada). These authors used the variable that results from multiplying the mesiodistal length by the maximum buccolingual width, which here we will call the computed crown area, following the terminology of Wood and Abbott (1983). The aim of this work is to test the Inhibitory Cascade Model in a large modern population, using the individual values of the measured crown area (Wood & Abbott, 1983) of the three molars. This is the first time in which individual values in a recent human sample are used to test this model, instead of the averages of current human populations (Evans et al., 2016).

2. MATERIALS AND METHODS

In this work, we have examined a sample of 458 human mandibles preserved at the Institute of Anthropology of the Universidade de Coimbra (Portugal). The mandibles belonged to Portuguese individuals who died between 1896 and 1936. Records of sex, age at death were available for each of these individuals. The collection includes individuals classified as: 1‐Identified Skeletal Collection (153 males and 126 females); 2‐Escolas Medicas Identified Skull Collection (89 males and 67 females); and 3‐International Exchange Collection (14 males and nine females). In this study, we have focused on obtaining the crown size of those individuals who preserved the complete molar series. We observed that individuals who died after reaching the age of 50 were frequently missing many of their teeth and when present, they were affected by severe occlusal wear so could not be included. Consequently, the present study was able to obtain data from a total of 116 individuals. These individuals present occlusal wear in their molars equal to or less than grade 4 of the Molnar (1971) classification.

Additionally, we identified a total of 34 individuals that preserve the first (M1) and second (M2) molars but were showing agenesis of the third molar (M3). Due to the absence of radiographic equipment, agenesis was determined based on careful visual examination, with particular attention to the lack of signs of alveolar absorption. Some authors consider that purely visual examination of dental agenesis leads to an overestimate of the true frequency of agenesis occurrence (Lavelle & Moore, 1973). However, other authors (Chagula, 1960; Goldstein, 1932) reported that this approach offers reliable results. Chagula (1960) corroborated his visual inspection through radiographic examination.

Here we obtained the measured crown area (crown area hereafter) of the lower molars of the Coimbra sample in occlusal photographs, following the protocol of Wood and Abbott (1983). Each specimen was oriented so that the occlusal plane was perpendicular to the optical axis of the camera fitted with an AF Micro‐Nikkor 105 mm, f/2.8D. To get a maximum depth of field, an aperture of f/32 was set. The magnification ratio was adjusted to 1:1, and a scale was included in each photograph and placed parallel to the occlusal plane. The scale was placed at approximately the same plane as the occlusal surface. To minimize the measurement error, the prints were made at X5 magnification, which proved to be a suitable augmentation for using a planimeter. The boundaries of the crown were marked with indelible ink following the Wood and Abbott (1983) protocol. Due to some interproximal wear, it was necessary in some cases to estimate the original mesial and/or distal borders of the crown by reference to the overall crown shape and the buccolingual extent of the wear facets. Before obtaining any measurement, the exact enlargement of each print was checked and the X = Y scale was entered into the planimeter. Using the appropriate scale, the planimeter returns the real value of the occlusal surface. Measurements were obtained in mm2. Each specimen was measured three times by two authors (JMBC and SS), and the mean value was used. One of the specimens was measured thirty times and the error standard of measurement was 0.067 (see Kieser, 1990). As mentioned above, this protocol was previously employed to assess the seventeen individuals who recovered from the Middle Pleistocene Sima de los Huesos site at the Sierra de Atapuerca (see Table 1 of Bermúdez de Castro et al., 2020).

TABLE 1.

Values for the RMA regression obtained in the Coimbra modern human sample for the variables M2/M1 vs. M3/M1. The values were obtained for males, females, and the pooled sample (see Methods and Figure 1)

n r r‐square Slope 95% confidence interval Intercept 95% confidence interval
Males 76 0.36 0.13 1.40 1.02–1.93 −0.46 −0.95 –0.10
Females 40 0.11 0.01 1.44 1.16–1.78 −0.46 −0.79–0.20
Pooled sex 116 0.28 0.07 1.47 1.23–1.75 −0.50 −0.76–0.27
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First, we tested whether the results obtained for the Coimbra sample conform to the Inhibitory Cascade Model. Using the R software, package lmodel2 (Legendre & Legendre, 1998; Queen et al., 2002), we applied the reduced major axis regression to explore the correlations between relative occlusal areas for the variables M2/M1 and M3/M1 in males, females, and the pooled sample. We applied the reduced major axis method instead of ordinary least squares because the variable represented on the X‐axis (M2/M1) is measured with error and also because this method is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which one is Y (Smith, 2009), like in the Inhibitory Cascade Model. The data were bootstrapped 1000 times and the resulting regression was compared with the Inhibitory Cascade Model described for murines. Confidence intervals of both the slope and the intercept were obtained from the RMA for the Coimbra sample. If the confidence intervals include the 2.0 slope and −1.0 intercept predicted by the murine Inhibitory Cascade Model, we considered the Coimbra regression as fitting that obtained for murines.

Besides, we also assessed if the observed value obtained from the M2 crown area in each individual is consistent with the one that would be obtained if the Inhibitory Cascade Model works. That is, if the expectations of this model are met, then the size of the crown area of the M2 should be one‐third of the total size of the triplet M1, M2, and M3 (Kavanagh et al., 2007). The percentage of deviation was obtained in each case.

Finally, we evaluated if the agenesis of M3 can alter the size relationship between M1 and M2. Using the t‐student test, we evaluated the differences between the sample of individuals with M3 and the sample of individuals with third molar agenesis.

3. RESULTS

When we plot the M3/M1 and M2/M1 size ratios (Figure 1), we observe that the values obtained from the Coimbra individuals do not fit the theoretical line that defines the Inhibitory Cascade Model predicted in rodents by Kavanagh et al. 2007, in which the slope is 2.0 and the intercept is −1.0. The scores of the RMA regression lines for the M2/M1 (x) and M3/M1 (y) variables obtained from males, females, and the pooled sample are given in Table 2. None of them conform to the Inhibitory Cascade Model. On the other hand and according to this model, the size of the central tooth of a triplet would be roughly equal to one‐third of the total triplet size (Kavanagh et al., 2007). When we compare the observed and the expected values of the M2 crown area in each one of the individuals of the pooled sample (Table 3), we observed that the premise is fulfilled with a very acceptable deviation of ≤±3% in 61 individuals (52.6%), with a deviation of between ±3.05% and ±≤5% in 24 individuals (20.7%), while that the deviation is >5.01% (up to 13.1%) in 31 individuals (26.7%) (Figure 2).

FIGURE 1.

FIGURE 1

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The plot of the values M2/M1 vs. M3/M1 in the Coimbra recent modern molar Dental sample in the developmental morphospace defined by these variables. From left to right: (a) males sample; (b) females sample; (c) pooled sample. The thick blue line plots the function y = 1 + [(a‐i)/] (x‐1) and it matches the prediction of Kavanagh et al. (2007) for rodents. The thin gray lines include the 95% confidence interval of this function. The dashed red line represents the RMA regression of the M2/M1 and M3/M1 variables in the Coimbra sample, and the red circles represent the Coimbra individuals. Note that most of the individuals have values M2/M1 and M3/M1 ratios that are lower than 1, which means that M1 > M2 and M1 > M3 However, few individuals have higher values for M2/M1 ratio, which indicates that M1 < M2. See Kavanagh et al. (2007), Polly (2007) and Schoer and Wood (2015) for further explanations

TABLE 2.

Raw data obtained in the Coimbra recent human sample for the MCA of the three lower permanent molars. Following the premise of the Inhibitory Cascade Model, the M2s should have a dimension equal to 1/3 of the sum of the MCA of the three molars

Individuals (males) Observed M1 (mm2) Observed M2 (mm2) Observed M3 (mm2) Expected M2 (mm2) Absolut difference (mm2) Relative difference, in percentage
3C 107.98 111.76 90.99 103.57 −8.19 7.89
4C 93.77 97.44 95.49 95.56 −1.87 1.95
6E 103.48 84.44 97.21 95.04 10.60 11.15
10E 112.68 105.58 108.68 108.98 3.40 3.11
13E 98.49 84.25 89.75 90.83 6.58 7.24
19C 96.04 89.99 81.08 89.03 −0.95 1.07
4 76.33 73.80 68.86 72.99 −0.80 1.09
28 87.86 89.24 87.91 88.33 −0.90 1.10
30C 93.45 90.57 86.25 90.09 −0.48 0.53
38 88.84 86.24 79.36 84.81 −1.42 1.67
47 96.73 86.05 91.34 91.37 5.32 5.82
50E 111.00 102.54 93.71 102.41 −0.13 0.12
51E 99.07 100.84 92.17 97.36 −3.48 3.57
59E 111.56 101.58 96.67 103.27 1.69 1.63
77 87.52 83.33 85.67 85.50 2.17 2.54
84 92.44 85.18 84.53 87.38 2.20 2.52
86 106.53 88.46 95.13 96.70 8.24 8.52
90 98.58 79.56 73.05 83.73 4.17 4.98
92 98.93 95.88 73.71 89.37 −6.51 7.28
96E 90.19 89.55 69.36 83.03 −6.52 7.85
97 97.56 97.01 90.35 94.97 −2.04 2.14
98 89.58 88.49 90.28 89.45 0.96 1.07
110E 97.09 86.07 60.25 81.13 −4.94 6.09
115E 95.68 90.96 96.27 94.34 3.38 3.58
131E 88.37 84.17 84.11 85.55 1.38 1.61
134 84.45 83.88 84.58 84.03 0.15 0.18
136E 88.47 89.09 85.00 87.51 −1.57 1.79
137E 108.20 92.53 107.43 102.72 10.19 9.92
139 88.85 84.90 79.95 84.56 −0.34 0.40
141 91.76 84.41 89.93 88.70 4.29 4.83
156 101.32 93.16 84.75 93.07 −0.09 0.09
157 95.46 89.62 91.31 92.13 2.51 2.72
162 96.28 89.40 92.72 92.80 3.40 0.36
163b 105.60 102.28 77.65 95.17 −7.51 7.89
172E 94.61 78.33 76.68 83.20 4.87 5.85
194E 103.19 90.12 78.20 90.50 0.38 0.42
199 96.45 94.62 94.36 95.14 0.52 0.54
203 100.64 100.21 90.34 97.06 −3.15 3.24
205 91.84 84.50 80.81 85.71 1.21 1.41
214 98.19 83.65 83.35 88.39 4.74 5.36
219 89.92 87.39 81.97 86.42 −0.97 1.12
231 105.44 106.87 102.59 104.96 1.91 1.82
236E 96.69 82.66 91.73 90.36 7.70 8.52
240 94.08 76.17 69.49 79.91 3.74 4.68
241 114.52 99.74 80.16 98.14 −1.60 1.63
246 92.12 86.28 85.72 88.04 1.76 2.00
255 M 82.28 74.03 68.26 74.85 0.82 1.09
260 92.42 87.52 69.23 83.72 −3.80 4.53
270 109.82 94.71 102.97 102.50 7.79 7.60
276 93.63 77.65 71.38 80.88 3.23 3.99
277 94.12 82.53 74.26 83.63 1.10 1.31
282 99.95 95.15 92.03 95.71 0.56 0.58
284 M 105.49 105.40 99.09 103.32 −2.08 2.01
297 98.84 92.31 98.19 96.44 4.13 4.28
308 100.39 105.41 95.48 100.42 −4.99 4.97
310 80.64 73.62 79.36 77.87 4.25 5.45
319S 92.68 86.64 79.74 86.35 −0.29 0.33
340 99.81 103.27 94.43 99.17 −4.10 4.13
343 95.19 94.55 87.09 92.27 −2.28 2.29
347 85.88 84.59 67.06 79.07 −5.52 6.98
353 93.63 92.85 81.53 89.33 −3.52 3.94
375 90.99 89.36 74.32 84.89 −4.47 5.26
381 99.19 87.46 79.47 88.70 1.24 1.39
390 95.66 91.81 94.91 94.12 2.31 2.45
397 105.66 95.62 96.68 99.32 3.70 3.72
M1 99.35 97.64 99.11 98.70 1.06 1.07
401 84.45 84.32 67.26 78.67 −5.65 7.18
416 94.05 91.27 90.72 92.01 0.74 0.80
428 96.90 86.39 80.23 87.84 1.45 1.65
459 81.93 82.63 76.36 80.30 −2.33 2.90
469 89.00 79.63 71.07 79.90 0.27 0.34
471 99.96 98.25 89.93 96.04 −2.21 2.30
473 106.28 98.57 97.98 100.94 2.37 2.34
469 85.89 77.49 74.14 79.07 1.58 1.99
424L 92.69 92.56 82.28 89.17 −3.48 3.90
417 88.25 80.26 83.97 84.36 4.10 4.87
Individuals (females) Observed M1 (mm2) Observed M2 (mm2) Observed M3 (mm2) Expected M2 (mm2) Absolute difference (mm2) Relative difference, in percentage
2 92.55 87.49 84.89 88.14 0.65 0.73
10 96.38 85.15 95.23 92.25 7.10 7.69
30 98.57 86.60 87.28 90.81 4.21 4.63
52 96.79 94.51 85.26 92.18 −2.33 2.52
58C 84.22 79.29 74.22 79.24 −0.05 0.06
59 93.23 76.40 79.20 82.94 6.54 7.88
67 79.56 73.09 55.36 69.33 −3.76 5.42
75 97.10 87.87 84.91 89.96 2.09 2.32
81 82.37 78.72 64.28 75.12 −3.60 4.79
99 96.28 80.37 61.86 79.50 −0.87 1.09
101E 94.78 83.72 80.58 86.36 2.64 3.05
105 85.03 75.87 83.80 81.56 5.69 6.97
107 81.04 77.93 71.92 77.08 0.85 1.10
117 89.68 88.73 85.33 87.91 −0.82 0.93
118E 86.56 89.33 60.90 78.93 −10.40 13.17
121E 94.90 89.13 83.08 89.03 −0.10 0.11
142 86.86 79.65 76.45 80.98 1.33 1.64
144 86.28 82.61 68.32 79.07 −3.54 4.47
148E 91.29 88.38 68.27 82.64 −5.74 6.94
149E 92.41 79.65 65.43 74.91 −4.74 6.32
153 90.28 88.47 65.43 81.39 −7.08 8.69
160 94.08 84.72 85.31 88.17 3.34 3.78
163 85.53 75.01 69.53 76.69 1.68 2.19
175E 90.51 90.51 71.38 84.13 −6.38 7.58
200 84.20 75.11 77.96 79.09 3.98 5.03
219E 97.06 100.15 84.45 93.88 −6.27 6.68
222 81.41 76.99 69.86 76.08 −0.91 1.19
234 85.87 76.65 71.47 77.89 1.24 1.59
247 81.54 78.28 71.48 77.10 −1.18 1.53
268 M 86.04 76.23 66.66 76.31 0.08 0.10
298 89.91 81.88 77.37 83.05 1.17 1.40
313 90.79 90.03 76.14 85.65 −4.38 5.11
328 90.68 99.30 78.88 89.62 −9.68 10.80
341S 93.32 89.37 89.45 90.71 1.34 1.47
349 85.22 81.94 71.37 79.51 −2.43 3.05
380S 92.76 79.35 73.80 81.97 2.62 3.19
343 88.96 83.94 77.77 83.65 −0.29 0.34
445 81.36 71.15 68.36 73.62 2.47 3.35
426 86.34 72.67 72.37 77.12 −0.15 0.19
454 91.11 90.04 93.10 91.41 1.37 1.50
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TABLE 3.

Descriptive statistics for the measured crown area (MCA) in the M1, M2, and M3 of the Coimbra recent human sample (pooled sex)

Tooth N Mean value Standard deviation Variance
M1 116 93.66 7.72 59.59
M2 116 87.61 8.57 73.44
M3 116 82.56 11.02 121.44
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FIGURE 2.

FIGURE 2

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Frequency histogram showing the deviation (in percentage) from the expected values for the crown area of M2, according to the Inhibitory Cascade Model. Pooled sex

These results suggest the need to examine the variability of the raw crown area data for M1, M2, and M3. In order to explore this variability we have used different statistical tests. Thus, we estimate the homoskedasticity of the variances through Levene´s test for the three variables: crown area of M1, M2, and M3 (package lmodel2). To do that, we test before that the samples fit a normal distribution employing a Kolmogorov–Smirnov analysis.

Table 1 shows the descriptive statistics for the raw data of the crown area in M1, M2, and M3 (pooled sex). The mean values indicates that M1 > M2 > M3, and that the variance of the M3 is greater than that of the M1 and the M2. The Kolmogorov–Smirnov test yielded the following results: M1 (0.06), M2 (0.07), and M3 (0.06). All the p‐values were higher than 0.05 meaning that the crown area of these teeth does not differ significantly from a normal distribution. When we estimate the homoskedasticity of the variances of M1, M2, and M3 through Levene’s test, we obtained that F = 10.3 (2 d.f.), being p < 0.05. Therefore, we checked that there is heteroskedasticity in the variances of the raw data of the crown area of the three molars. Figures 3 and 4 show the boxplot for the raw data of the crown area of M1, M2, and M3, as well as the distribution of the three variables. According to the data included in Table 1, we can visualize the remarkable variability of the M3 in comparison with M1 and M2.

FIGURE 3.

FIGURE 3

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Boxplots representing the measured crown area (mm2) of the M1, M2, and M3 in the Coimbra recent modern sample

FIGURE 4.

FIGURE 4

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Empirical cumulative density functions for the distributions of the occlusal areas (mm2) of M1, M2, and M3 in the Coimbra recent modern sample

In addition, we calculated the Pearson correlation coefficient for the raw data of the crown area for M1, M2, and M3 and we have obtained the following results: M1 vs. M2 (r = 0.75), M1 vs. M3 (r = 0.66) and M2 vs. M3 (r = 0.64). In all cases, the null hypothesis (ρ = 0) was rejected. Consequently, despite the results obtained from the reduced major axis regression, it can be observed a positive and significant correlation between the crown areas of the three molars. However, while the relationship between M1 and M2 is strong, the relationship for the M1 vs M3 and for the M2 vs M3 is moderate.

Finally, we have checked if the size sequence between M1 and M2 is influenced by the agenesis of M3. To do this, we first obtained the descriptive statistics for the variable M2/M1 in both males and females of the Coimbra sample (Table 4). Using the t‐student test, we observe that the difference between the two sexes is not statistically significant (p < 0.95) for the M2/M1 ratio. Therefore, we pooled male and female individuals in a single sample. Next, we have compared the sample of individuals with M3 and the sample of individuals with third molar agenesis. Our results (Table 4) show that there are no significant differences between both samples (t = 0.32; p < 0.005; 140 d.f.). Therefore, it seems that in our sample the absolute and relative size of the M1 and the M2 is not related to the M3 agenesis.

TABLE 4.

Descriptive statistics for the M2/M1 variable in samples of males, females, pooled sex without agenesia and pooled sex presenting third molar agenesia

Sex N X SD Student‐t p
Males 76 0.934 0.06
0.61 p < 0.005
Females 40 0.929 0.06
Pooled sex (without agenesia) 116 0.934 0.06
0.32 p < 0.005
Pooled sex (with agenesia) 34 0.950 0.08
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4. DISCUSSION

Dental development is a multifactorial process regulated by the interaction of different genetic and epigenetic agents and occurs progressively over time (Brook, 2009; Brook et al., 2014). These interactions can occur at the molecular, cellular or even extracellular level, generating diverse macroscopic outcomes that are reflected in the external and internal anatomy of each group’s dentition. Dental development is also multidimensional, as it involves changes in the size and shape of the tooth germs that occur in the three dimensions of space. The fourth dimension would be time, as tooth development is a progressive process that occurs over periods of time of varying length. In summary, and as Brook indicated in 2009, the different interactions, gradients and spatial effects of multiple genes influence the development of individual teeth, groups of teeth and the dentition as a whole. This context is included in the inhibitory cascade model proposed by Kavanagh et al. (2007).

In 2007, Kavanagh et al. established that dental development governs the relative size of molar teeth in mice. These authors then proposed an Inhibitory Cascade Model based on an activator‐inhibitor logic of sequential tooth development. The Inhibitory Cascade Model predicts that the second molar will always be one‐third of the total molar area. In the present study, we have examined the size of the occlusal surface of the lower molar series from a recent modern sample from the University of Coimbra to test if they concur with the Inhibitory Cascade Model.

Our results showed that the observed values for the slope and intercept of the RMA regression (95% confidence intervals) of the males, females, and pooled samples differ significantly from those obtained by Kavanagh et al. (2007) for rodent species. Moreover, we observed that slightly more than the half of the individuals in the sample meet one of the premises of this model: M2 = 1/3 (M1 + M2 + M3), 20.7% present a “reasonable” deviation (5%) from this premise, whereas 26.7% of the sample (31 individuals) show a high deviation, which must be explained by additional mechanisms.

Most of the deviations seem to lie in the unpredictable behavior of the size of the M3 regarding M1 and M2. Thus, in 13 individuals the M3 is greater (11) or equal (2) than the M2, although always smaller than M1. About 14 individuals presented the M1 ≥ M2 size pattern, but they showed an M3 more reduced than expected by the Inhibitory Cascade Model. In four individuals there is a “primitive” pattern M1 < M2, but a normal reduction in M3. The variance of the crown area of the size of the M3 is remarkably higher than that of the M1 and the M2, reinforcing the observation that this tooth has a very variable size. Furthermore, it seems that this variation is moderately correlated with the variation of the M1 and the M2. In fact, when we compare the raw data for the crown area of the three molars, we obtain a high correlation for the M1 vs. M2 and a moderate correlation for the values of M1 vs. M3 and M2 vs. M3.

Evans et al. (2016) studied numerous modern recent samples, but they employed the average (computed crown area) of each molar class instead of the individual data. As we see in Table 1, the crown area mean size for M1 in the Coimbra sample is 93.66, for M2 the mean size is 87.61, and for M3 the mean size is 82.05 and, therefore and on average, the Coimbra size sequence is M1 > M2 > M3. This is the usual pattern observed in modern humans (e.g., Garn et al., 1963). Furthermore, the crown area mean value obtain for the M2 is very similar to the expected value under the premise of the Inhibitory Cascade Model, that is: (93.66 + 87.61 + 82.05)/3 = 87.77. The absolute difference between the observed and expected M2 averages is only 0.11 (0.12%). However, when we analyze the problem considering information obtained in each individual, we see rather disparate results. About 31 individuals (26.7%) show differences that exceed a 5% and can reach up to a 13%. The study of each particular case offers information that we cannot obtain if we use only the averages of the sample.

Permanent molars form sequentially from a distal extension of the primary dental lamina (Järvinen et al., 2009). Like in great apes, the initiation of the first permanent molar in modern humans occurs at about four months in utero, and the mineralization of this tooth commences at birth (e.g., Dean & Cole, 2013). The second and third molars of modern humans form in succession from the dental lamina at the distal aspect of the previous molar. In radiographs, it is possible to observe that at the time when the crown of the first permanent molar has been completed, the follicle for the second permanent molar is visible (Kreiborg & Jensen, 2018). This event occurs around the age of 2.5 years (e.g., AlQahtani et al., 2010; Dean & Cole, 2013). Likewise, at the time the crown of the second permanent molar has been completed, the follicle of the third molar becomes visible (Kreiborg & Jensen, 2018). In modern humans, this event occurs about 8.0–8.5 years (e.g., AlQahtani et al., 2010; Dean & Cole, 2013; Kreiborg & Jensen, 2018). In great apes, the onset of M2 mineralization begins in the first year of life, while the onset of M3 mineralization occurs approximately 1 year later (Dean & Cole, 2013). In contrast, the onset of M3 formation in modern humans is delayed approximately 6 years after the onset of M2.

One of the premises of the Inhibitory Cascade Model is that subsequent developing teeth experiment cumulative effects due to previous events and the ratcheted nature of the model (Kavanagh et al., 2007). If the M2 experiences inhibition by the development of M1, the M3 should also be reduced. The data observed in the Coimbra sample suggest that the size of the M1 and M2 possibly are regulated by the inhibitory cascade mechanism. However, in a significant number of individuals, the development of M3 seems to be less influenced from this activation/inhibition pattern. We suggest that the considerable delay in the initiation of M3 formation in modern humans could be related to a weakening of the activation/inhibition process, possibly due to interference with other unknown epigenetic or environmental processes. As Balic (2019, p. 26) writes “the regulation of the initial stages of tooth development, as well as the cellular mechanisms that govern tooth development remain largely unknown.” What happens in the long span of time between the start of M2 and the start of M3 is a complex process and basically unknown nowadays. Schroer and Wood (2015) also suggest that the late emergence of M1 in hominoids may delay posterior molar initiation and affect final molar size. In the same line of argument, Carter and Worthington (2016) consider that anthropoid molar size ratios may be influenced by a relaxation of the activation/inhibition constraints due to temporal distancing in the onset of the formation of these teeth. In our study of the 17 hominins from the Sima de los Huesos site, we observed that the size (crown area) of the three molars fits with the Inhibitory Cascade Model (Bermúdez de Castro et al., 2020). However, it is likely that in these hominins the onset of the M3 formation was not significantly delayed with regard to the rest (see Modesto‐Mata et al., 2020). Perhaps a considerable delay in M3 is unique to H. sapiens.

On the other hand, it seems clear that M3 agenesis has a genetic basis (Pereira et al., 2006). Some experiments in mice have shown that the expression of Bmp4 and Msx1 genes fails when animals are homozygous for Pax9 null mutations. In these cases, development arrest occurs at the early bud stage (Peters et al., 1998; Zhou et al., 2011). The Pax9 gene has been associated with selective tooth agenesis in humans and mice, mainly involving the posterior teeth (Pereira et al., 2006). The fossil record of the genus Homo shows some rare cases of M3 agenesis, which could respond to a process similar to that in recent populations. Thus, the Lantian (personal observation in the original), Penghu 1 (Chang et al., 2015), Xiahe (Chen et al., 2019), and KNM‐WT 15000 (Brown & Walker, 1993) mandibles, show agenesis of the M3. In these cases, the observed sequence is M1 < M2. In contrast, the mandible D 2735 from Dmanisi (unilateral agenesis, personal observation) shows the sequence M1 > M2. Although it is very difficult to prove, these rare cases of M3 agenesis in the genus Homo may have a genetic origin similar to that hypothesized for modern human populations. In the latter, it is also possible that there are selective pressures derived from the reduction of the facial mass, which favor a high prevalence in M3 agenesis (e.g., Oeschger et al., 2020). In any case, regardless of the regulatory process behind, the results obtained in the present study show that the absence of the M3 does not seem to influence the relative size of the remainder molar series. This reinforces the argument of the existence of certain disconnection in the activation/inhibition pattern between first molars and the M3 in modern populations.

It is important to consider that the Inhibitory Cascade Model was conducted by examining the data at the individual level (Kavanagh et al., 2007) and is therefore an intraspecific model. Some papers have applied this model at the interspecific level using the averages of the variables in each of the taxa examined (e.g., Asahara, 2013; Evans et al., 2016; Halliday & Goswami, 2013; Polly, 2007). Although both approaches are very interesting, the results obtained cannot be considered equivalent. A puzzling question is why the average values for a species fit the Inhibitory Cascade Model well, while many of the individual values deviate from the model's predictions, as it is observed in our analyses.

In recent years, the premises of the Inhibitory Cascade Model have been applied to different primate species. At the interspecific level, Bernal et al. (2013) have studied 38 species of platyrrhines (South American primates) and find limited support for the Inhibitory Cascade Model. According to these authors, the highly derived dentition of some Platyrrhine (Callithrichines) clades, which includes the loss of M3s in marmosets and tamarins and reduction of M3 in Cebinae, may be behind these results. Carter and Worthington (2016) investigated the dentition of 100 species of Simiiformes and found that 44% of these species did not fit the Inhibitory Cascade Model. In particular, hominoids and cercopithecines strongly diverge from the Inhibitory Cascade Model, while platyrrhines, colobines, and papionins are more consistent with this model. These authors consider that dietary adaptations may explain these differences, which affect in particular the relatively larger size of M2. This argument is also employed by Halliday and Goswami (2013) to explain deviations from the Inhibitory Cascade Model in a wide set of Mesozoic and Cenozoic mammalian species. In agreement with our results, Carter and Worthington (2016) also note that the third molar has greater variation in size than either the first or second molars. Inhibitory Cascade Model predicts that M3 agenesis occurs when M2 size is less than half the size of M1. Therefore, in line with what we explained in the previous paragraph, M3 agenesis occurs in different primate species despite the fact that this premise is not fulfilled (Bernal et al., 2013; Carter & Worthington, 2016). Schroer and Wood (2015) examined individual data for 29 Old World primate species, including some extinct hominin species. For most species, the data fit the Inhibitory Cascade Model, except for the two Cercopithecus species, Papio anubis and Paranthropus boisei. In general, the samples analyzed by these authors are small, which may be influencing the results. Roseman and Delezene (2019) have used a considerable number of individual data from eight species of Catarrhini primates of known sex. These authors only found results consistent with the Inhibitory Cascade Model for Macaca fascicularis, while Gorilla gorilla meet none of the predictions of this model. In light of evidence from this and previous work, Roseman and Delezene (2019) believe that the Inhibitory Cascade Model should be rejected as the only mechanism capable of explaining the evolution and integration of relative molar size.

Hlusko et al. (2016) have questioned the direct application of the Inhibitory Cascade Model results obtained in murines to primates. They argues that we share with these mammals a last common ancestor, which lived approximately 70 million years ago (Eizirik et al., 2001). Although Hlusko et al. (2016) recognize that the developmental mechanisms underlying tooth organogenesis are evolutionarily conserved across mammals, the dentition of mice is highly derived and the characters of their peculiar life history pattern are very different from those of primates. These authors suggest the integration of quantitative genetics, paleontology and neontology to understand the genetic mechanisms underlying the evolution of primate dentition, and have proposed a substantial modification of the features that can be used in the analyses of tooth size covariation in this group.

Although the premises of the Inhibitory Cascade Model are fulfilled in certain mammal species (Halliday & Goswami, 2013; Kavanagh et al., 2007; Polly, 2007) and some aspects of the molecular regulation are already known (Balic, 2019), it is evident that there are many aspects of this regulatory process and its relation to dental development that we do not know. The phenotypic variability of the relative size of the molars seems reasonably well channeled and we can identify specific patterns. Nevertheless, we still have to understand the regulatory mechanisms behind this variability in many mammal species and especially in modern humans. Furthermore, judging by the variability in the size relationship between M1 and M2 (e.g., Bermúdez de Castro et al., 2020; Wolpoff, 1971; Wood & Collard, 1999), it seems that the regulation of the activation/inhibition model may be controlled by a genetic polymorphism in both modern humans and other species of the genus Homo.

5. CONCLUSIONS

In order to test the Inhibitory Cascade Model we have approached for the first time the individual study of the size of the crown area of the three lower permanent molars in a recent modern population. Further, we have used the direct measurement of the crown area instead of computed crown area (obtained by multiplying the mesiodistal and buccolingual dimensions). Our results suggest that there is a strong relationship between the size of the M1 and the M2, but more moderate when the size of the M3 is compared with those of the M1 and M2. When we applied the Inhibitory Cascade Model (Kavanagh et al., 2007) obtained in murines to the Coimbra recent modern sample, we observed that neither the sample of males, nor that of females, nor the pooled sample fits this model. Our results differ from those obtained by Evans et al. (2016), when he applied the model of Kavanagh et al. (2007) to hominins, including a considerable number of recent modern populations. One possible explanation for these differences is that we have used individual values, instead of averages. But there could be other interpretations for the present results, which we do not yet know.

Our results are in addition to those of other authors, who have also found limited support for the Inhibitory Cascade Model in primates (Bernal et al., 2013; Carter & Worthington, 2016, Roseman and Delezene, 2019). Although this model may still be an interesting reference, we need to consider other factors and bring new insights to understand the phenotype of mammalian dentition. According to Halliday and Goswami (2013), the Inhibitory Cascade Model could be the plesiomorphic mechanism for Mammalia, which would have been retained by murines. However, natural selection would have shaped this model of molar size covariation in numerous species as an adaptation to diet or biomechanical needs.

If the activation/inhibition mechanism is at work in the dentition of our species, we suggest that the considerable delay in the initiation of M3 lowers the effect of a possible activation/inhibition process in this tooth and that other external and/or internal environmental factors can interfere in its development.

DATA AVAILABILITY STATEMENT

The data used in this research are available in Table 2 of this article.

ACKNOWLEDGMENTS

This work has been mainly supported by the Dirección General de Investigación of the Spanish Ministry of “Ciencia, Innovación y Universidades”, grant number PGC2018‐093925‐B.C31, and the Consejería de Cultura y Turismo of the Junta de Castilla y León, We also acknowledge The Leakey Foundation through the personal support of Gordon Getty (2013) and Dub Crook (2014–2020) to one of the authors (M.M.‐T.), and to the Atapuerca Foundation for its continuous support in both field seasons and research. We thank the University of Coimbra for access to the collections of the Institute of Anthropology. In particular, our thanks to Eugénia Cunha.

Bermúdez de Castro, J.M. , Modesto‐Mata, M. , García‐Campos, C. , Sarmiento, S. , Martín‐Francés, L. , Martínez de Pinillos, M. , et al (2021) Testing the inhibitory cascade model in a recent human sample. Journal of Anatomy, 239, 1170–1181. 10.1111/joa.13500

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data used in this research are available in Table 2 of this article.

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