Examining the lingual surface of the maxillary incisor crown, we often find more or less swollen lateral borders and a hollow in the center of the crown. The strong expression of such a configuration is called "shovelling." It is well known nowadays that this shovel ling frequently occurs in Mongoloids, but rarely in either Caucasoids or Negroids, The most common view regarding its function is that possibly it strengthens the structure of the incisor. However, the question of why the incidence of shovelling is higher in Mongoloids, or of why only Mongoloids must strengthen their incisors, has not been discussed fully. Most of the previous studies on shovelling either demonstrated how useful it is as a racial marker or only utilized it as a marker.

The present paper is comprised of three parts. In the first part, the interrelations are estimated between shovelling and some morphological component characters of the incisor crown, and the problem of what such interrelations imply is discussed. Second, the relations of shovelling to some other characters of the whole dentition are estimated. For instance, it is examined whether there is any difference between the relations of shovelling to the anterior and posterior tooth size if shovelling is required to strengthen the anterior teeth. Based on these analyses, the adaptive significance of shovelling is inferred. And, third, the associations between shovelling and climatic factors or ways of life are estimated by using the published data on the incidences of shovelling in modern populations worldwide. If any association is found between them, it will render a power ful aid in understanding the significance of the existence of shovelling.

In the following sections, a historical review of the studies on shovelling, the concept of non-metrical characters including shovelling and the reaaonability of the methods adopted here for analyzing non-metrical characters will be briefly given.

1.1. Historical Review

(1920) is considered the pioneer in the study of shovelling. Since then, a great many papers investigating shovelling have been published.

A historical sketch of the studies preceding 1920 was presented by (1920) in his paper, "Shovel-shaped teeth." According to him, the first author who used the term "shovel-shaped" teeth is unknown. Since the beginning of the latter half of the 19th century, however, Carabelli, Tomes, Mühlreiter, Zuckerkandl, Black, Wortman and others had noticed a hollow in the lingual surface of the incisor. The term "Schaufel" can be found in an anatomical book written by Muhlreiter dated 1870 (, 1920). It was in 1907 that himself for the first time used the term "shovel-shaped" in describing the maxillary incisors of American Indians (, 1920). In his 1920 paper, stated most of the currently accepted tenants regarding shovelling. That is to say, first, that shovelling frequently occurs in modern Mongoloids such as American Indians, Malayans, Mongolians, Chinese, Japanese, etc., but rarely in other modern populations. Secondly, the Krapina incisors described by -Kram berger (1906) definitely exhibit shovelling characteristic and well-developed lingual tubercles. Thirdly, shovelling may be functionally interpreted as strengthening the incisors. Fourthly, shovelling is observable not only in the maxillary permanent incisors but also in the mandibular permanent incisors and canines or the deciduous incisors. Fifthly, the combination of marginal ridges and a central hollow is easily recognizable on the lingual surfaces of the incisors not only in man but in other primates and animals as well. In addition, argued that this character was of ancient origin and must be present in an ancestor common to all living terrestrial mammals. Furthermore, he said that the reason why shovelling largely disappeared in such highly cultured popula tions as modern whites was the decreased use of the teeth, and that, if this were the case, a high frequency of shovelling could be expected in prehistoric populations. He considered, on the other hand, that the higher frequency of shovelling in modern Mongol oids could probably be explained not so much by the greater call upon the teeth as by a hereditary persistence from earlier times, possibly coupled with the play of selection (, 1920). Regarding the structure of shovelling, he believed that a marginal ridge surrounding the lingual fossa was a composite structure, not all being derived from the cingulum but only the basal part of it, probably homologous to the cingula of other teeth (, 1920).

Most of the studies following (1920) are confirmations or minor refutations of 's observations and/or opinions. Therefore, an outline only of new evidence and significant views will be presented below.

Adloff (1927) thought that the shape of the incisor was derived from a simple conical tooth as seen in the dentition of reptiles. According to him, the mesial and distal mar ginal ridges were derived from the cingulum, and the central ridge corresponds to the original cone. Further, he inferred that the basal lingual tubercle had been generated from the cingulum and was a feature common to mammals, i.e., a primitive character.

Through his investigation of the teeth of Peking man, Homo erectus pekinensis, Weiden reich (1937) suggested that Peking man was more closely related to modern Mongols than to any other living population mainly because well-developed shovelling was easily recognizable in the incisors. At the same time, he argued that the shovelling seen in the incisors of European Neanderthals had disappeared in the evolutionary process, and hence was not transmitted to modern Europeans. Further, Weidenreich pointed out, based on the observation of worn teeth, that not only the enamel but also the dentin of shovel-shaped incisors were lingually folded, though (1920) stated that the marginal ridges were folds of the enamel. Additionally, Weidenreich argued that the lingual fossa of the incisor clearly depended upon the presence of the marginal ridges, contrary to 's view that the ridges and the fossa were independent. Weidenreich (1937) also disputed an assertion by Adloff that shovelling was not present in the incisors of Peking man or of Neanderthals but exclusively in those of modern man, a common feature of all modern populations. Weidenreich claimed that the presence in Peking man of a character which was regarded as shovelling, according to 's definition, was not a matter of interpretation but a fact, as was held for Neanderthals. He emphasized the importance of shovelling occurring in special races up to nearly 100%, over occur rence to a certain extent in all races in a minor percentage.

Refuting the above opinion by Weidenreich, Adioff (1938) argued that, according to the definition of shovelling offered by before 1920, it was clear that thought the shovel-shaped incisor to have no or only a vestigial lingual tubercle, as well as a smooth and hollow lingual surface. He maintained that an incisor with a well-developed lingual tubercle must not be called "Schaufelform" (shovel-shape) but "Höcker form" (tubercle-shape), and that, because the lateral incisors of Peking man were cer tainly shovel-shaped but the central incisors were "Höckerform," it could not be said that Peking man had shovelling in general. Accordingly, Adloff did not accept Weidenreich's (1937) assertion that Peking man was a direct ancestor of Mongoloids. After all, Adloff (1938) concluded that the "Schaufelform" had been derived secondarily from the "Höckerform" through the reduction of the lingual tubercle, and that shovelling was not of phylogenetic importance, but rather a special character derived at a later evolutionary stage. Additionally, he disputed the view by Weidenreich that the lingual tubercle was a character common only to hominids and apes, not derived from lower primates.

McCown and Keith (1939) reported that the teeth possessed many Neander thalian (Palaeoanthropic) features, while the teeth manifested modern (Nean thropic) features. In their publication, McCown and Keith pointed out that the well developed lingual tubercle observable in the maxillary incisors and canines was a feature distinguishing Neanderthalian teeth from those of others, which they termed "pre molarism."

Lasker (1945) investigated the dental morphology and caries of modern Chinese. He quoted Morse's work of 1937 which stated that the frequency of shovelling was higher in Chinese females than in males, and that there was a cline of its frequency in China, i.e., a tendency of the incidence to be higher in the eastern, northern and central regions of China, while lower in the western and, especially, southern regions. Through his observations, Lasker confirmed this frequency cline to be higher in North China and lower in South China.

For the first time, in 1947 Dahlberg and Mikkelsen tried to quantify the degree of development of shovelling. For details of general quantification methods for non-metri cal characters, see the following section (1,4.).

Goldstein (1948) investigated the teeth of Texas Indians from pre- and proto-hiatoric ages, and found that the incidence of shovelling in the permanent incisors was com pletely different from that in the deciduous incisors, the latter being lower than the former. He also criticized a hypothesis by (1920) that the virtual elimination of shovelling in. various "cultured" groups of "white" men was due to the disuse of the incisors, and declared this hypothesis to be essentially Lamarduan.

In his morphological study of Indo-European and Mongoloid dentitions, Tratman (1950) histologically demonstrated that the marginal ridges of the shovel-shaped incisors had not only enamel but also dentin in their insides. Further, he pointed out that the Mongoloid incisors exhibited shovelling in the lingual surfaces whenever the labial marginal ridges were highly developed, that the Mongoloid maxillary incisors had a strong bend of the longitudinal axis at the dental neck and that the roots of the teeth were shorter in Mongoloids than in Indo-Europeans.

Lasker (1950) said that among American whites developed shovelling was more frequent in the lateral incisors than in the centrals, and that there was a tendency of the expressivities of shovelling to be similar between monozygotic twins.

Dahlberg (1951) also presented the view that shovelling was not a result of excessive growth of the enamel alone but a primary character consisting of both the enamel and dentin. He named the fossa which sometimes occurred in the labial surface of the shovel shaped incisor, "double-shovel" (Dahlberg and Mikkelsen, 1949; Dahlberg, 1951). In addition, Dahlberg (1951) found anomalous forms with the large lingual tubercle, which looked like premolars, among the maxillary lateral incisors of Pima Indians and called them "barrel shape." He thought the development of this cusp-like lingual tubercle was associated with shovelling. Regarding the evolutionary change of the incisors, Dahlberg (1951) inferred the following. At the stages of Homo erectus and Homo sapiens neanderthalensis, the incisors were large and their lingual marginal ridges were highly developed. In modern whites, however, the frequency of the simplified and non-shovel shaped incisors increased, while in American Indians, the marginal ridges became more specialized and more developed than in the earlier hominids. As a whole, however, the dentition of the Indians is, in most respects, no more specialized than that of other modern populations.

Kikuchi (1954) investigated the interrelation between shovelling and occlusion in modern Japanese. He classified three groups of individuals according to the conditions of occlusion: a normal occlusion group, a malocdusion group and a non-selected group. Among these three groups, the latter two were found to have almost the same incidence of shovelling, while the incidence for the normal occlusion group was only half as much as those for the latter two groups. Therefore, he concluded that shovelling might be asso ciated with the overjet of the maxillary teeth. Concerning this, Sakai (1954) confirmed that the more the shovelling of the maxillary incisors was developed the greater the "degree of incisor articulation," which is the shortest distance between the center of the incisal edge of the left maxillary central incisor and the labial surface of the crown of the corresponding mandibular tooth. It should be noted, however, that Sakai also said that shovelling was extremely developed in all cases of edge-to-edge bite (labidodon tia) where the degree of incisor articulation was zero. Furthermore, he suggested the possibility that the presence of shovelling might explain the incidence of stegodontia being generally higher in Mongoloid populations.

Shimizu (1955) reported that the similarity of shovelling of the maxillary anterior teeth was higher in monozygotic twins than in dizygotic ones in a Japanese sample.

Dahlberg et al. (1956) inferred, on the basis of a pedigree study, that shovelling was probably controlled by multiple alleles. They also stated that shovelling could not be represented only by a measurement of the depth of the lingual fossa, which was a partial function of tooth size (especially the mesiodistal dimension) and directly influenced by the central ridge. Additionally, they said that the variation of the cingulum was greater in shovel-shaped incisors.

Robinson (1956) intensively investigated the dentition of the australopithecines in South Africa. He reported that the morphology of their maxillary incisors was similar to that seen in modern man except for the roots of the australopithecines being more robust. Robinson(1956) claimed that Weidenreich's (1937) Peking man-Mongols hypoth esis was not necessarily correct, and argued that shovelling was apparently a character common to hominids because African australopithecines in general had moderately developed shovelling and Neanderthals and modern American Indians had highly-devel oped shovelling in addition to modern Mongols living in Asia. Further, Robinson disputed Adioff's view (1938) that teeth called shovel-shaped incisors must be restricted to the incisors with no or smaller lingual tubercles, and declared that such a view was unreasonable. He (Robinson, 1956) believed the lingual tubercle is neither a primitive feature nor a character derived directly from the ape-like lingual cingulum because the australopithecines who were chronologically older than Neanderthals or Homo erectus had poorly developed lingual tubercles in their incisors, though Adloff and Weidcnreich considered this trait to be primitive. Robinson (1956) supposed well-developed lingual tubercles were a characteristic peculiar to modern man, Neanderthals and the like.

Riesenfeld (1956) found a dine in the frequencies of shovelling and reduced lateral incisors from the west to the east in Oceania, i.e., from Indonesia through Micronesia to Polynesia. He considered this cline to be evidence supporting a hypothesis that Mongol oids had migrated from the west to the east, and, therefore, opposed Heyerdahl's claim of an American origin of the Polynesians.

Moorrees (1957) pointed out that the Aleut had both extremely developed shovelling and mandibular tori.

Remanc (1960) thought that the shape of the incisor originated secondarily from a single-cusped tooth, a haplodont, because, e.g., in gorillas and Oreopithecus, the central incisor had an incisal edge, while the lateral incisor remained in the shape of a conical tooth (Spitzzahn). He further stated that the lingual tubercle was morphologically not a homogeneous structure but a composite of which the major part was derived from the cingulum and the other from the basal part of the central ridge, though it might also originate from the cingulum alone, and that the marginal ridges, which might produce a shovel-shaped tooth by surrounding the lingual surface of the incisor, were derived from the cingulum. Remane moreover stated that the shovel-shaped incisors occurred not only in Hominidae but also in Hylobatidae, while in Cercopithecidae there was a vertical furrow in the lingual surface of the incisor.

Carbonell (1963) thoroughly investigated shovelling and documented that there was a significant positive correlation between the depths of lingual fossae in the central and lateral incisors. She also stated, through a literature survey on fossil hominids, that the structural patterns of the lingual surfaces of the maxillary incisors appeared to have continuously changed from australopithecines to modern man, though the origin of shovelling was unclear, and emphasized the necessity for searching for its phylogenetical meaning.

Quoting the work of 1962 by Kraus and Ooe, which showed that in the fetuses of American Indians and Japanese well-developed shovelling was observable even before the commencement of calcification of the incisors, Kraus and Jordan (1965) argued that shovelling had its origin, in an embryological sense, in the differential growth of the inner enamel epithelium or in the genetic control of mitotic activity of the epithelial cells.

Sakai et al. (1965) decalcified the enamel of the maxillary central incisors, and gave a detailed account of the various morphological features of the dentmoenamel junction. Through their study, it was confirmed that the labial and lingual surfaces of the dentino enamel junction were each fundamentally composed of five ridges, as on the enamel surface, i.e., the mesial and distal marginal ridges, the central ridge and the mesial and distal accessory ridges. They stated that the development of the two marginal ridges waso ften reciprocally proportional to that of the other ridges.

Suzuld and Sakai (1966) illustrated that various human populations could roughly be classified into four groups based on the frequencies of shovelling. The group with the highest incidence consisted of such Mongoloids as American Indians, Eskimos, Mon golians, part of the Japanese and part of the Chinese; the second group with a relatively high incidence was Hawaiian aborigines, most of the Japanese and most of the Chinese; the third group consisted of Indonesians, Polynesians, Micronesians and Sakhalin Ainu; and the fourth group with the lowest incidence was American Negroes, Bantu, Fijians, American whites and Finns. After Vallois' hypothesis that the Indonesians were closer to the common stock of man than other Mongoloid populations, Suzuki and Sakai argued that, if the increased frequency of shovelling was one of the characteristics indicating the differentiation of the Mongoloids, it seemed reasonable for the frequency in the Indonesians to be lower than that of other Mongoloid populations. Further, they reported the frequencies of shovelling in all the anterior teeth, maxillary and man dibular, of a Japanese group, and concluded, based on the results of χ²-tests for the interrelations between shovelling, the double-shovel, the labial and lingual ridges and the lingual tubercles, that shovelling was none other than a final phenotype caused by the differences or variation in the absolute and/or relative development of many mor phological features on the lingual surfaces, rather than an independent character. Suzuki and Sakai (1966) furthermore reported that the mesiodistal crown diameters of the well developed shovel-shaped incisors were significantly larger than those of the non-shovel shaped ones.

Hanihara (1966) introduced the concepts of "Mongoloid dental complex" and "Caucasoid dental complex" into dental anthropology on the basis of his morphological studies on deciduous teeth. These concepts were created under the belief that the prop erties of any population could not be properly represented by only one character, but might be better described by a complex of many characters. He included, minimally, shovelling, the protostylid, the deflecting wrinkle, the sixth cusp and the seventh cusp in the Mongoloid dental complex, in the case of deciduous teeth. For permanent teeth, however, Hanihara (1968) suggested the protostylid and seventh cusp be excluded from the Mongoloid dental complex mentioned above.

Turner (1967) hypothesized that shovelling was controlled by a pair of alleles, and tried to examine the goodness of fit of such a hypothesis to the Hardy-Weinberg theorem, in spite of acknowledging the shovelling indicated almost continuous variation, As a result, although no significant difference was found between the observed and the expected values for the maxillary central incisor nor for the lateral incisor in the case of Eskimos, Turner stated that a model with a greater number of genes would be better. After this study, however, Turner again attempted to examine such a two-allele model by using data from other populations (Turner, 1969). A similar attempt was also performed by Devoto et al. (1968).

Ooë (1968) observed the lingual tubercle and the marginal ridges of the incisor already existing on the enamel epithelium at the precalcification stage.

Pinto-Cisternas and Figueroa (1968) investigated the frequencies of shovelling and Carabelli's tubercle in Chileans, and examined the interrelation between them as well as the relations of such characters to nutrition, blood types, color blindness, occlusion types, socio-economic conditions, etc. They stated, on the basis of χ²-tests, that shovelling was found more frequently to a significant extent in individuals in conditions of poor nutrition and in those who had stegodontia or hyatodontia. They also suggested that there was no significant correlation between shovelling and Carabelli's tubercle.

Cohen et al, (1970) compared the tooth crown characters of trisomy G (or mongolism or Down's syndrome) patients with those of normal controls. They found that the frequency of shovelling was 26.5% for the mongolism patients but only 9.0% for the controls, and that there were also considerable differences between the patients and the controls in some other dental characters: e.g., the amount of reduction of the hypocone in the maxillary molars was much greater in the former than in the latter. To explain these phenomena, Cohen et al. suggested that some common factors might influence both the central nervous system and the tooth crowns simultaneously because both of these tissues were of ectodermal origin and, besides, began to differentiate at the fifth or sixth week of fetal life.

Brabant (1971) argued, on the basis of teeth excavated from various sites of ca. 2500-1000 B.C. in France, that the frequency of shovelling had decreased from the neolithic age to the present in Western Europe.

Lee and Goose (1972) observed the teeth of Chinese families living in Liverpool in order to examine the modes of inheritance for shovelling and other dental characters. They concluded that it was difficult for a simple model of Mendelian inheritance to be accepted for such characters as shovelling and Carabelli's tubercle, and that, instead, it seemed better to assume multifactorial inheritance because these characters in fact varied continuously.

Sofaer et al. (1972a) estimated parent-offspring, sib-sib and intercharacter correlations with respect to five tooth crown characters including shovelling, Carabelli's tubercle, etc. (probably using the four-fold point correlation coefficient), and argued that the additive genetic variance was generally apt to be smaller in late developing teeth than in early developing teeth within the same tooth classes.

Portin and Alvesalo (1974) examined several models of the mode of inheritance for shovelling in the maxillary central incisor. As a result, they could not reject at least three hypotheses of a single intermediate autosomal gene, of one locus with more than two alleles and of polygenes. They claimed, therefore, that a simple model of Mendelian inheritance as proposed by Turner (1967) was not supported, and conclusively stated that shovelling seemed to be basically controlled by polygenes.

Hanihara et al. (1975a) reported, based on the correlation coefficients between parents and offspring, and between siblings as well as between twins, that the depth of the lingual fossa of the maxillary central incisor exhibited extremely high heritability in the Japanese.

Scott (1975) investigated the associations between fifteen non-metrical tooth crown characters, and recognized strong associations between shovelling of the maxillary and mandibular incisors, between the lingual tubercles of the maxillary incisors and the canine, between the hypocone and Carabelli's tubercle, etc.

Mizoguchi (1976) estimated the tetrachoric correlation coefficients between shovelling and Carabelli's tubercle under the assumptions that they had a mode of polygenic inheri tance and were continuous variates, at least in the underlying condition. As a result, the estimates for three kinds of correlations, i.e., phenotypic, genetic and environmental were low.

Harris (1976), using 2×2 tables, estimated the φ coefficients of some tooth crown characters, including shovelling, between sibs. Based on the results, he aruged that the modes of inheritance for these characters could not be explained by a single gene model but by a multifactorial threshold model.

Mizoguchi (1977b) estimated the heritabilities of shovelling and the depth of the lingual fossa, in which the former was based on the tetrachoric correlation coefficients between twins and the latter based on the commonly used product-moment correlation coefficients. He suggested from this estimation that the heritabilities of shovelling and the depth of the lingual fossa in the maxillary central incisor were relatively low, while the heritability of shovelling in the lateral incisor was high.

Mizoguchi (1978) also investigated the relations of several small component characters of the lingual surface to shovelling and mesiodistal crown diameter in each of three maxillary anterior teeth by path analysis. He confirmed that the mesial and distal marginal ridges contributed highly to shovelling in the maxillary central incisor, as had been expected, and further suggested that, in the lateral incisor, the mesial and distal spines of the lingual tubercle also contributed to shovelling, especially in females.

Yamada et al. (1979) estimated Cramèr's coefficients of contingency between 28 tooth crown characters including shovelling and applied model IV of Hayashi's quantification theory to the above coefficients in order to investigate the whole intercharacter relations. They stated that four groups of mutually associated characters were recognizable, one of which was composed of such characters as shovelling of the maxillary central and lateral incisors and the size reduction of the lateral incisor.

Harris (1980), from the literature, collected data on the frequencies of shovelling in 38 samples from world populations and classified them into six groups, i.e., Caucasian, Asian, Polynesian, Melaneaian, American Indian and American Black, in which males and females were dealt with separately. Harris argued that the frequency of shovelling was significantly higher in females than in males in all the groups but the American Blacks. For this between-sex difference, he proposed the hypothesis that part of the genes controlling shovelling were on the X-chromosomes and both X-chromosomes infemales contributed to its expressivity, resulting in the degree of development being stronger in females.

Kirveskari and Alvesalo (1981) compared Finnish 47,XYY patients with their relatives in the first degree with respect to shovelling and the depth of the lingual fossa. They found that these characters had no significant between-sample differences in the maxillary central incisor but, in the lateral incisor, the incidence of shovelling was significantly higher and the depth of the lingual fossa was deeper in the 47,XYY patients than in their relatives. Further, they stated that the lingual fossae in the 47,XYY patients were deeper than those in the general Finnish population, while the lingual fossae in Turner's syndrome (45,X) patients, which they had previously investigated, were shallower. Based on these facts, Kirveskari and Alvesalo argued that, if their maturity was delayed, the prolongation of the period for morphological differentiation might cause more intensive expressionof shovelling in the taller 47,XYY patients.

The above is a historical sketch of the studies on shovelling by (1920) and subsequent researchers. In sum, the following points seem at present to be accepted as a consensus of opinion.

1. Shovelling or the like is widely observable in mammals.
2. Shovelling has an extensive range of variation in expressivity among modern men, and the frequency of well-developed expressivity is highest in Mongoloids.
3. Both Peking man and Krapina man have strong shovelling accompanied by well-developed lingual tubercles.
4. The expression of shovelling continuously varies, probably suggesting a poly genic inheritance mode.
5. The shape of shovelling is formed before the commencement of calcification of the incisor crown.
6. Shovelling is a composite character which is produced by differences in develop ment between the component characters on the lingual surface of the tooth crown. In particular, these component characters are the marginal ridges and the central ridge. They intensively, but inversely, influence the expression of shovelling.
7. The function of shovelling is presumably to strengthen the structure of the anterior teeth mechanically.

1.2. Definition of Shovelling and its Synonyms

Regarding the definition of shovelling, Weidenreich (1937) and Adloff (1938) held opposing views, as mentioned above. In the present study, the configuration which is composed of well-developed marginal ridges and a deep lingual fossa at least on the incisal half of the crown is regarded as shovelling, even though it has a form with the highly developed lingual tubercle which was termed "Höckerform" by Adloff (1938). That is to say, the present author adopted the description in lines 12 to 16 on page 429 of (1920) as the definition of shovelling, as Weidenreich (1937) did:

The character in question consists of a peculiar, pronounced hollow of the lingual surface of the teeth, bounded laterally or surrounded by a well-defined elevated enamel border. Such teeth resemble more or less an ordinary coal shovel, in consequence of which they were termed 'shovel-shaped' incisors.

Further, the present author used 's (1920) descriptions in lines25 to 28 on page 448 and in lines 17 to 2S on page 449 as the definition of the four grades in the development of shovelling:

The writer, as a matter of experience, has adopted the terms shovel (s) for all the better developed grades; semi-shovel (ss) for the less well developed; and trace-shovel (tr.) for slight but distinct indications.

Under the term 'shovel-shaped' are included all incisors whose lingual surfaces howed the enamel rim with the enclosed fossa well developed. The term 'semi-shovel' was applied to all teeth in which the enamel rim was distinct, but the enclosed fossa was shallow. The term 'trace' covers all those teeth in which there were distinct traces of the enamel rim, but which could not be classed as yet as 'semi-shovel.' Finally as 'no-shovel' were recorded all those incisors in which there was either no perceptible trace of rim and fossa, or in which traces of these were so faint or imperfect as not to deserve a special characterization.

Here, even if any relation might exist between the shovelling and the lingual tubercle, such characters were treated separately when observing them; that is, the presence or absence or the degree of development of the lingual tubercle was not involved in the definition of shovelling. Even in the case of the "barrel shape" (Dahlberg, 1951), if the marginal ridges and part of the lingual fossa could be observed, the presence or absence of shovelling was judged based only on them, regardless of the lingual tubercle.

The present author has hitherto used the terms "shovelling" and "shovel-shaped incisors" in this paper. However, many other synonyms have been used by previous authors in order to express the character denned above and the teeth showing such a character. Of those synonyms, the representatives are as follows.

For teeth with this character, the most commonly used in English is "shovel-shaped incisors (teeth)," which has been employed by a great number of authors, e.g., (1920), Gregory (1929), Montelius (1933), Nelson (1938), Dahlberg (1945), Goldstein (1948), Lasker (1950), Tratman (1950), Riesenfeld (1956), Robinson (1956), Moorrees (1957), Carbonell (1963), Barnes (1969), Mayhall (1979) and others. The terms "shovel incisors" (Gates, 1956), "shovel shape incisors" (Escobar et al., 1977), "shovelled shaped anterior teeth" (Bailit et al., 1968), "rimmed and hollowed incisors" (Hrdlicka, 1920), etc. are rarely used.

The corresponding terminology in German is "schaufelförmige Schneidezähne" (Adloff, 1938; Thoma, 1964; Remane, 1960) and in French, "incisives en pelle" (Patte, 1976; Ménard, 1978; Vallois and de Felice, 1979). In Japanese, the term "shaberu-gata sesshi (shiga)" has most often been used, e.g., by Kikuchi (1954), Sakai (1954), Suzuki and Sakai (1966), Fujita (1973) and others. "Shaberu-jo sesshi" (Hanihara, 1954; Take hisa, 1957) is also sometimes employed.

For the character itself, there are many more synonyms. The three terms most com monly used in English are "shovel shape (shovel-shape)," "shovelling" and "shoveling." "Shovel shape (shovel-shape)" has been employed by Weidenreich (1937), Moorrees (1957), Kraus and Jordan (1965), Hanihara (1966), Kirveskari (1978) and others. "Shov elling" has been. used by Koski and Hautala (1952), Carbonell (1963), Lee and Goose (1972), Berry (1976), Mizoguchi (1977b), Mayhall (1979) and others and "shoveling" by Nelson (1938), Moorrees (1957), Coon (1962), Turner (1969), Harris (1980) and others. In addition to these, "shovel-shaping" (Carbonell, 1963; Dahlberg, 1963b), "shovel-shaped form or character" (Nelson, 1938; Dahlberg, 1945; Weidenreich, 1945b; Riesenfeld, 1956), "shovel shape trait, form or character" (Lasker, 1950; Dahlberg et al., 1956; Mayhall, 1979), "shovel form, character or nature" (Goldstein, 1948; Carbonell, 1963; Dahlberg, 1963b), etc. are relatively often employed. Although another name, "keilo koilomorphy," proposed by (1920) means "keilodonty and koilomorphy" or "rim and hollow," it has not been frequently used. Furthermore, sometimes used are "shovel" (Weidenreich, 1937), "shovel-shapedness" (Robinson, 1956), "lingual mar ginal ridging" (Bailit et al., 1968; Harris, 1980), etc. The terms "shovelled" (Greene,1972; Berry, 1978) and "shoveled" (Greene et al., 1967; Turner and Hanihara, 1977) are occasionally used adjectivally. The terms "scoop-like concavity or trough-like depres sion" (, 1920) and "scoop-shaped" (Tratman, 1950) are rarely used.

In German, the term "Schaufelform" (Adloff, 1938) has been used in order to express this character. In French, "form en pelle" (Thoma and Vallois, 1977), "disposition en pelle" (Tillier, 1979), etc, are employed. In Japanese, "shaberu-kei" (Fujita, 1973; Mizoguchi, 1976), "shaberu-kei (kata)" (Sakai, 1963; Suzuki and Sakai, 1966; Hanihara, 1966), "shaberu-jo keitai" (Hanihara, 1954; Shimizu, 1955), etc. are usually employed.

In the following sections, the present author will use the term "shovelling" for the character and the term "shovel-shaped incisors or teeth" for teeth with this character.

1.3. Non-metrical Characters and Quasi-continuous Characters

In bones and teeth, some small extra tubercles or foramina may occasionally, though not always, occur. These morphological characters are usually called "non-metrical or discontinuous traits" (Brothwell, 1972), or, sometimes, "epigenetic variants" (Berry and Berry, 1967), "minor variants" (Berry, 1968; Berry, 1976), "all-or-none attributes" (Cavalli-Sforza and Bodmer, 1971) or "discrete traits" (Corruccini, 1976). However, it is rare that they are "discontinuous or discrete," even if "non-metrical." The human third molars, for example, have a certain range of variation in size, and frequently do not occur. Grüneberg (1952) termed such characters "quasi-continuous characters." He assumed that the genetic background of a quasi-continuous character was controlled by many genes, and was an underlying continuous variate which made such a character occur phenotypically only when its value exceeded a certain physiological threshold. Therefore, this may also be called a "threshold character" (Falconer, 1960; Cavalli Sforza and Bodmer, 1971).

The concept of quasi-continuous characters has to date been introduced to many anthropological studies. Berry and Berry (1967) and Berry (1968) regarded some non metrical cranial characters as such, and Sofaer et al. (1972b) and Scott (1974), as well as Mizoguchi (1976, 1977b, 1978a, b) treated some non-metrical dental traits as quasi continuous characters. From the same viewpoint as that of the above authors, all of the non-metrical tooth crown characters dealt with here were also assumed to be quasi continuous characters. Of those non-metrical characters, however, some, e.g., the size of the lingual cusps of the maxillary premolars and a few others, seem to be completely continuous characters, In these cases, it should be noted that they were treated as quasi continuous characters for the sake of convenience because of the technical difficulties in measuring them.

1.4. Quantification of Non-metrical Characters

A few trials of quantifying so-called non-metrical characters have already been done. For instance, Dahlberg and Mikkelsen (1947) measured the depth of the lingual fossae in the maxillary incisors to describe shovelling as objectively as possible. Since then, many researchers have performed similar measurements (see Table 44). Another example of quantification is the contour lines method (Wakamatsu, 1962) in which, first, a coat of white paint is applied to the surface of a tooth crown, and then soot is added to the surface and, finally, contour lines are drawn on the crown surface and counted. Further more, measurements of tooth crowns made on photographs have been. performed relatively often (Erdbrink, 1965; Biggerstaff, 1969, 1975; Hanihara et al., 1970a). Recently,Taverne et al. (1979) and Kanazawa et al. (1983) tried to measure various parts of a tooth crown surface by such an indirect three-dimensional measurement method as the so called moiré method or the like.

Although common usage of direct three-dimensional measurement methods will become technically possible in the near future, there are at present no methods other than those depending upon the classification of the degree of development of dental char acters based on visual observations, especially when a great number of subjects must be dealt with. With respect to the correlations between such characters that can only be analyzed non-metrically, in spite of being continuous characters, there is an appropriate estimation method, which is theoretically expected to present the same results as for measurable characters. This is the tetrachoric correlation method mentioned below.

1.5. Correlations between Underlying Continuous Variates

The concepts of underlying continuous variates and thresholds, which are contained in the idea of quasi-continuous characters mentioned above, in fact, did not begin with Grüneberg (1951, 1952) but appeared much earlier. The method for estimating the correlations between these underlying continuous variates had already been developed by Pearson in 1900. The correlation coefficients obtained by this method are called "tetrachoric correlation coefficients" (Pearson, 1900; Yasuda, 1969). Pearson (1900), using the stature data of relatives and other characters, demonstrated that tetrachoric correlation coefficients were virtually the same as product-moment correlation coeffi cients used in the case of continuous variates. The present author (Mizoguchi, 1977b) also confirmed this to be true using data on the depth of the lingual fossa in the maxil lary central incisor.

However, because the amount of calculation for obtaining an estimate of the tetra choric correlation coefficient is enormous, alternate approximation algorithms have been proposed. One is an approximation method by Falconer (1965) exclusively for estimating the correlation coefficients between relatives. But this method has already been criticized for contributing too high an error factor to the results (Edwards, 1969; Bulmer, 1970). Edwards (1960, 1969) invented a formula which more easily produced better approxima tions than Falconer's method. In this case, however, the application of the formula is restricted to cases where the incidence of a character in the relatives of propositi is of about 0.5% to 5%. Besides the above, there is another approximation method applicable to more general cases, i.e., Pearson's cosine method (Arkin and Colton, 1956; Yasuda, 1969). However, this may also result in estimates considerably different from those by the tetrachoric correlation method. Consequently, it seems best to use the original tetrachoric correlation method (Pearson, 1900) for estimating the correlations between underlying continuous variates, as was recommended by Bulmer (1970). Nevertheless, it cannot be said that the tetrachoric correlation method is problem free. For example, this method is not applicable to cases where thresholds for appearance of characters may vary due to some conditions (Edwards, 1969). In the present work, however, this tetra choric correlation method will be employed under the simple assumption that an under lying continuous character has only a constant threshold.

Apart from χ²-tests and Fisher's exact probability test for qualitatively testing the interrelationship between non-metrical characters, there are many different coefficients of association whose purpose is to quantitatively show the degree of association (Yasuda, 1969). In studies of dental anthropology, for instance, the four-fold point correlation coefficient (Sakai et al., 1965; Pinto-Cisternas and Figueroa, 1968; Berry, 1978) and Yule's coefficient of association (Sakai, 1954; Rosenzweig and Zilberman, 1969) have been widely used. Recently, Scott (1977a, b, c, 1978) often employed Kendall's rank correlation coefficient. Besides, the coefficient of mean-square contingency (Sakai, 1954), the φ coefficient (Harris, 1976; Scott, 1978), Cramèr's coefficient of contingency (Yamada et al., 1979), etc, have sometimes been applied to non-metrical data of teeth. In passing, the above è coefficient obtained in a 2 × 2 contingency table is equivalent to the four-fold point correlation coefficient, and, in turn, the latter corresponds to the prod uct-moment correlation coefficient formally calculated based on 0-1 data (Yasuda, 1969).

The coefficients of association referred to, however, have many problems compared with the product-moment correlation coefficient. For example, the results obtained may differ greatly from case to case owing to the different ways of classifying the degrees of development of the same characters in question. This is the case in all kinds of co efficients of association except the tetrachoric correlation coefficient (Yasuda, 1969). The tetrachoric correlation method is similarly applicable to the cases estimating cor relation coefficients not only between two arbitrary dichotomous attributes but also between a dichotomous attribute and a continuous variate. This is very advantageous. Another serious problem concerns the possibility of expansion into multivariate analyses. According to Yasuda (1969), there are extremely few coefficients of association which can lead to the analysis of partial association or multiple association in the same way as the product-moment correlation coefficient for continuous variates. A rare exception to this is again the tetrachoric correlation coefficient. However, other coefficients of asso ciation may possibly be used in multivariate analyses different from the case of the product-moment correlation coefficient (Yasuda, 1969). For instance, Yamada et al. (1979) estimated the associations between 28 non-metrical tooth crown characters by using Cramèr's coefficient of contingency, and then applied Model IV of Hayashi's quantification theory to the estimates of this association coefficient to check for any particular tendencies. In this case, however, it seems difficult to compare the results with those of other studies on the same level because all estimates are affected by the grading procedures.

As was stated above, the tetrachoric correlation coefficient is of great use if the assump tion of normality for underlying continuous variates is reasonable. Nonetheless, this coefficient has not been used frequently in the field of anthropology, probably because of the tedious calculations involved. As far as the present author knows, Schwidetzky (1959) employed this tetrachoric correlation method in her study on the cranial structure. However, some of the attributes she dealt with were ratios or indices, in which the application of the normality assumption was questionable. All other examples seem to be previous studies by this author, in which this method was employed to estimate the heritabilities of non-metrical tooth crown characters (Mizoguchi, 1977b) and to investigate the intercharacter correlations between non-metrical tooth crown characters (Mizoguchi, 1976, 1978a, b).