AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 78:37-59 (1989) Complex Segregation Analysis of Dental Morphological Variants CHRISTIAN R. NICHOL Department of Anthropology, Arizona State University, Tempe, Arizona 85287 KEY WORDS Dental anthropology, Genetics, Environmental effects, Mode of inheritance, Crown traits, Dental crown ABSTRACT A set of 20 morphological variants of the dental crowns and four characteristics of the jaws are tested for probable mode of inheritance using the complex segregration analysis method of Morton et al. (Am. J. Hum. Genet. 23:602-611, 1971). Models tested include three two-allele single-locus models (dominant, codominant, and recessive) and a model employing the polychotomized normal distribution of liability (an additive polygenic model), with transmissibility estimated via maximum likelihood. Most of the traits studied are observed using ordinal scales with several grades, and many are tested using more than one dichotomy of their scale. These multiple analyses allow for a n examination of such factors as trait incidence on the results of the statistical analysis. The results of the analysis yield propositions of major genes for 13 of the 24 traits examined. Two traits give good evidence of being polygenic in origin. The remaining nine characters present methodological problems that do not allow for a definite conclusion on their mode of inheritance at this time. The ability to test varying levels of transmissibility in the polygenic model allows for a n estimation of the percentage of trait variance determined by familial factors. Estimates of transmissibility for all characters examined range from 0 to 1,with a mean of 0.36. These findings may suggest a large environmental role in the development of dental crown morphology. However, the possibility exists that difficulties in the ability to classify the expression of certain traits consistently result in overestimates of the environmental influences on the development of those characters. Over the years, several investigations into the mode of inheritance for various characteristics of the human dentition have been performed. Of the attributes examined, those that have received the most attention are the tooth crown diameters and Carabelli’s trait. There is general agreement that the inheritance of crown dimensions is multifactorial (Goose, 1971; Townsend and Brown, 1978a). Divergent opinions do exist on the role of sexlinked genes in the formation of tooth size. Some studies have indicated that X-linked genes play a role in size development (Garn et al., 1965; Lewis and Grainger, 1967; Alvesalo, 1971); others have demonstrated that a sex-linkage model is not necessary to explain the observed sexual dimorphism (Goose, 1971; Townsend and Brown, 1978a; Potter et al., 1983). Most of the more recent studies of 0 1989 ALAN R. LISS, INC the genetics of crown dimensions have accepted polygenic inheritance and have concentrated on the analysis of the relative contributions of genetic and environmental factors to the development of tooth crown size (Potter et al., 1968, 1976, 1983; Goose, 1971; Alvesalo and Tigerstedt, 1974; Townsend and Brown, 197813; Corruccini and Potter, 1981). Of the morphological characteristics of the tooth crowns, the one that has provoked the most argument over its mode of inheritance is Carabelli’s trait. Several researchers (Kraus, 1951; Tsuji, 1958; Turner, 1967b; Kolakowski et al., 1980)have suggested the possibility of single or major gene involvement Received November 9, 1987; accepted August 31,1988. Address reprint requests to C.R. Nichol, 66 Grandview DriveLeft Side, N. Tonawanda, NY 14120. 38 C.R. NICHOL in the expression of this trait. Cadien (1970) has proposed a two-locus model to explain the inheritance of Carabelli’s trait. Also, analyses by Goose and Lee (1971) and Lee and Goose (1972) have indicated that the development of the trait is under the control of many genes. Various other dental variants have also been suggested to have single or major gene determination. Evidence of major gene influence on the development of winging of the upper central incisors has been found via segregation analysis (Escobar et al., 1976). Turner (1967b)suggests the possibility of major gene involvement in the development of both the hypocone and incisor shoveling based on correspondence of categories of expression to expected Hardy-Weinberg proportions in a population sample. However, Turner himself (1967a, 1969) has indicated the potential weakness of such a method for determining the mode of inheritance of a character, and Sofaer (1970) has pointed out that even obviously nongenetic events can sometimes fit Hardy-Weinberg expectations. Studies that have analyzed various sets of characters (Scott, 1973; Harris, 1977; Berry, 1978) indicate that morphological traits of the dentition tend to be inherited in a complex, probably polygenic, fashion. The methods employed in the above-mentioned studies include a variety of population and familial analyses of trait expression. Much of the methodology used in the past does not allow for discrimination between a complex, multifactorial model and a singlegene model. Usually, testing was done to find goodness-of-fitto a single-gene model. If single-gene determination was rejected, then polygenic inheritance was accepted. Recent developments in complex segregation analysis allow for simultaneous testing of polygenic (at least using a simple additive hypothesis) and single-locus models. These developments permit rejection of the additive polygenic model even when the data do not yield good fit to a single-gene model. Segregation analysis is generally the method of choice for a familial analysis of trait inheritance. Early methods of segregation analysis (Snyder, 1932; Smith, 1956) were designed to test statistically whether the distribution of expression of a character among the offspring produced by matings of individuals with certain combinations of trait expression corresponds to expected Mendelian proportions. Beginning in the late 1950s, work by Falconer (1960,1965) and others laid the groundwork for testing the goodness-offit of data to polygenic models compared to single-gene models. In the 1970s, methods developed by Morton and his colleagues (Morton et al., 1971; Morton and MacLean, 1974) out of this work began to allow for simultaneous testing of single-gene and polygenic models. In the present study, a series of morphological traits of the human dentition undergo a complex segregation analysis in a n attempt to find information concerning their mode of inheritance. Parameters of concern to the study are the degree of dominance of the allele for affection when the data yield best fit to a single-locus model and the transmissibility when the data correspond to a polygenic model. The results of the study are intended to give insight into the possibility of major gene influences on dental trait expression and the relative proportion of genetic and environmental influences on the development of multifactorially determined characters. MATERIALS AND METHODS Sample Between 1946 and 1972, A.A. Dahlberg directed the collection of casts of dental impressions taken from persons residing in the Gila River Indian and Salt River Pima-Maricopa Communities near Phoenix, Arizona. During this period, approximately 8,800 sets of dental casts were collected. Because many individuals had impressions taken on more than one occasion, the 8,800 casts actually represent 3,632 individuals. The number of people with casts in the collection is approximately one-third of the total population of these two reservations a t the termination of the collection period. Accompanying the collection are detailed records giving a range of information concerning each individual represented. Most important to the present study are records concerning known relatives. From this information, extensive pedigrees have been compiled. Because the familial information comes from several sources, including medical, educational, and tribal personnel, as well as the individuals themselves, it is reasonable to expect that the familial data are accurate. This magnificent research collection is now housed in the Department of Anthropology a t Arizona State University. A sample of casts representing 600 individuals from 83 nuclear families is selected from the collection for use in the present study. SEGREGATION ANALYSIS OF DENTAL TRAITS 39 TABLE 1. Distribution ofsibship sizes i n the sample’ Number of sibshios 2 3 4 5 13 11 14 11 Number of sibs 6 7 8 9 10 11 12 7 7 3 0 1 9 7 ‘Total number of sibships, 83; total number of sibs, 434; total number of males, 215; total number of females, 219; average sibship size, 5.22. These 83 nuclear families are all sibships identified in the collection for which casts of both parents and at least two sibs are available for observation. Information concerning the sample is given in Table 1. The sizes of the sibships range from 2 to 12, and the number of sibships with each number of sibs is presented. Because both parents from each sibship are included in the sample, the 600 individuals includes 166 parents and 434 sibs. The sex distribution among the 434 sibs in the sample is nearly equal, with a slight excess of females (50.5%).The sex distribution in the sample is fairly representative of that of the collection, in which 50.9% of the individuals are female. Although sex dimorphism does occur in tooth crown dimensions, most of the morphologic attributes of the crowns have not shown strong or consistent sex differences in occurrence or expression (Nichol, n.d.). One notable exception is the distal accessory ridge of the upper and lower canines. Scott (1973, 1977) first demonstrated strong sexual dimorphism in the expression of this trait, and his findings have since been borne out in several studies (Harris, 1977; Kieser and Preston, 1981; Kaul and Prakash, 1981). Sex differences have also been found for shoveling of the upper central incisor (Harris, 1980). However, these differences are so slight that it took a n analysis of 19, 137 individuak to achieve significance. Some significant differences in trait frequencies have been found in this sample. In that a sex-linkage model is not examined in this study, any sex dimorphism is not directly dealt with. However, significant findings of sex differences will be noted as possibly complicating factors to the stated goals of this study. The segregation analysis method selected requires neither of the aforementioned conditions, that both parents and at least two sibs be available, for inclusion in the sample. Therefore, there is no concern for missing data, except in those cases when none of the sibs in a family can be observed. When none of the sibs in a family can be observed for a trait, that sibship provides no information to the segregation analysis and is therefore eliminated from the analysis of that character. The column in Table 2 labeled ‘‘ > 0 Sibs observed” gives the number of sibships used for each trait, on each tooth the trait is observed on, and a t each of the dichotomies of the observation scale submitted to a run of the segregation analysis. The numbers of sibships used in any run range from 83 €or several traits to 72 for UI2 interruption grooves. The condition that casts of both parents be available is implemented because a n assumption concerning equal fertility among phenotypes need not be made when the status of both parents is known. However, for each of the traits examined, one or both parents of some sibships are not observable; therefore, the assumption of equal fertility must be retained for these families. The column in Table 2 labeled “Both parents observed’’ gives the number of sibships in which both parents could be observed for each data run. Because of attrition and caries some traits are difficult to observe in adults (parents). For six characters; distal accessory ridge UC and LC, groove pattern LM1 and LM2, cusp 5 LMl, and the maxillary torus (the latter because of casting methodology early in the collection period rather than wear and caries); more than half of the sibships used in the analysis have one or both parents unobserved. The worst case is distal accessory ridge LC, for which only 14 of the 80 (17.5%) sibships used have both parents observed. Also contained in Table 2 is a breakdown of the number of sibships with both parents observed by the number of parents affected. Two traits have been tested to determine whether using the sibships in which the status of both parents is not known had any effect on the results. The traits selected are 40 C.R. NICHOL maxillary incisors: winging, procumbency, and insetting; four characteristics of the jaws: the maxillary and mandibular tori and the forms of each of the two arches; and 17 morphological attributes of the tooth crowns. Several of the 17 crown variants are observed on more than one tooth, bringing the total number of attributes examined in the study to 38. All traits are observed using either the Arizona State University standard reference plaques or standards developed by the author (Nichol, n.d.1. The names of the traits and the teeth for which they are observed are given in the first columns of Tables 2-4. Because the segregation analysis method selected is designed for use with dichotomous characteristics, and the traits are generally observed using ranked scales with several classes, decisions must be made on where to dichotomize the distribution of expression for each trait into the normal and affected categories. For all but four characters, a dichotomy is made at what is considered to be the presence/absence level. In the four cases when a trait is not analyzed at the presence/ absence breakpoint (shoveling of both the central and lateral maxillary incisors and hypocones of the maxillary first molar and the hypoconulid of the mandibular first molar), a dichotomy a t this level places 100% of the observed sib (or, in the case of the hypoconulid, all but one observed sib) in the affected category, making analysis a t this level of expression pointless. Furthermore, all traits that could be analyzed a t more than one scale breakpoint underwent more than one analysis. The determination of whether the analysis is to be done at a certain breakpoint is made on the basis of the frequency of individuals demonstrating expression at or beyond the breakpoint. Frequencies below 5% or above 95% are considered to be too extreme to be informative. In two cases, this guideline is violated. For labial convexity of the lateral incisor, a n analysis is done a t the presence/ absence level even though the frequency of individuals in the affected class (trait present) is 95.4%. For the protostylid of the lower second molar a t the 112 breakpoint, a run is made even though the frequency is only 3.3% for reasons to be discussed. When the trait frequency changes less than 5% when the breakpoint is moved up one grade, the inforCharacters examined mation is considered to be redundant (test Twenty-four traits are analyzed for proba- runs indicated this to be true), and a run is ble mode of inheritance in this study. In- not made a t the higher of the two breakcluded are three positional variants of the points. The reasons for performing multiple those showing the greatest raw (transverse ridge LP2 at the 011 breakpoint) and ratio (protostylid LM2 at the 112 breakpoint) differences in frequency among sibs between those sibships with both parents observed and those with one or both parents not observed. The results of these tests show some slight changes in the calculated likelihood ratios, but no changes in what model is selected as the best fit, for both traits. These findings suggest that a concern over the assumption of equal fertility among phenotypes is unwarranted. The condition that casts of at least two sibs be observable is employed because the amount of information obtained per sibship increases with the size of the sibship. Furthermore, the same sample is used in a path analysis of the inherited and random factors involved in the development of dental crown diameters (Nichol, n.d.). The path analysis requires sib correlations, making the availability of at least two siblings per family a n important consideration. The column in Table 3 labeled “Sibs observed under total sample” gives the number of sibs who could be observed for each trait in each run and is the number used as N in calculating the trait incidence. The number of sibs observed ranges from 423 for Carabelli’s trait to 205 for UI2 interruption grooves. Careful examination of this column reveals that there are two different numbers of sibs observed for cusp 5 on the lower second molar. The difference is due to there being 13 individuals for whom it is possible to see that cusp 5 is present but for whom it is not possible to estimate the size of the cusp because of the presence of cusp 6. Table 3 also gives the trait incidence used in each run of the segregation analysis. The incidence in any run is the total number of offspring considered affected, a t the scale breakpoint being analyzed in that run, divided by the total number of offspring observed. The incidence given under the heading “Total sample” is that used to estimate certain parameters of the models tested in the segregation analysis. These parameters are mentioned in the discussion of the statistical method. Also presented in this table are the number of sibs in families, with each number of affected parents and the incidence among the sibs in each category. SEGREGATION ANALYSIS OF DENTAL TRAITS analyses of certain traits are 1)to determine if the analysis produces consistent results if the trait incidence is changed and 2) to get a n idea whether the genetics of trait presence and trait expression are the same. In all, 76 separate runs of the complex segregation analysis are done. The scale breakpoints for each of the runs are presented in the second columns of Tables 2-4. A description of the scales and breakpoints thereof follows. Winging. Rotation of the upper central incisors is classified according to the categories of Enoki and Dahlberg (1958). The classifications have been assigned grade numbers as follows: grade 1 is bilateral winging; grade 2 is unilateral winging; grade 3 is the “normal” position; and grade 4 is counterwinging (either unilateral or bilateral). Because of the understanding that counterwinging and unilateral winging are the result of tooth crowding and that bilateral winging is not, it was decided to analyze only bilateral winging in this study. The dichotomy of the trait is made with bilateral winging placed in the affected class and all other conditions in the normal category. Central incisor procumbency. The degree of procumbency of the upper central incisor is scored using a standard developed by the author (Nichol, n.d.1. This standard presents a range from nonprocumbent incisors, those oriented perpendicularly to the occlusal plane, in grade 0 to pronounced labial inchnation of the teeth in grade 3. It is possible to analyze procumbency at two breakpoints of the scale under the conditions set out. These include absence/presence (0/1) and slightlmoderate expression (1/2) dichotomies. The higher degree of expression in both cases is placed in the affected category. Lateral incisor insetting. The degree of insetting of the upper lateral incisor is rated according to a standard developed by the author (Nichol, n.d.1. This scale assesses the alignment in the arch of the lateral incisor in relation to the central. The “normal” relationship between the two incisors, when the alignment is good, is scored as grade 1. Grade 0 is the opposite of insetting, when the lateral incisor is out of alignment in a labial direction, and grades 2-6 demonstrate varying degrees of lingual placement of the lateral incisor from slight insetting (grade 2) to where the lateral incisor is so far out of alignment with the central that the teeth are no longer in contact (grade 6). Three dichotomies of the insetting scale are tested. These are the 1/2 (absencelpresence), 2/3, and 3/4 breakpoints. For all three breakpoints, the 41 higher grades are considered as affected in the analysis. Incisor labial convexity. The standard of Nichol et al. (1984) is used to score the degree of convexity of the labial surface of the upper incisors. For both the central and lateral incisors, dichotomies are made between grades 0 and 1(the absencehrace presence level) and between grades 1 and 2 (the tracelmoderate expression level). In both cases, the greater degree of convexity is treated as affected. Interruption grooves. The presence of interruption grooves of the upper lateral incisors is assessed using the procedure of Turner (1967a). The trait is dichotomized with the absence of any grooves considered a s normal and the presence of a groove crossing the cingulum in any location classified as affected. Shoveling. Scott’s (1973) standards are used to classify the degree of expression of lingual marginal ridges (shoveling) on the upper central and lateral incisors. The high frequency of absence and the weaker degrees of expression of shoveling on the central incisor in this sample mean that testing cannot be done at any breakpoint lower than that between grades 2 and 3. This division is equivalent to a tracehemishovel dichotomy using the Hrdlicka (1920) scale. Additionally, it is possible to test the 314 breakpoint on this tooth. For the lateral incisor, a somewhat greater spread of individuals across the classes allows for analysis a t the 1/2, 2/3, 3/4, and 415 breakpoints. The latter is the equivalent of a semishovellshovel dichotomy on the Hrdlicka scale. In all cases, the higher degrees of trait expression at the breakpoint are treated as affected. Double-shoveling. The degree of expression of lingual marginal ridges (double-shoveling) of the upper incisors, canine, and first premolar is scored using the standard of Turner and Dowda (1979). For all four teeth, a dichotomy is made at the absencelpresence (01 1)breakpoint. Low frequency of expression beyond the trace level on the canine and premolar indicates that analysis be done only a t this point for these two teeth. However, further analyses are possible for the two incisors. For the central incisor, three other breakpoints-1/2, 213, and 314-are examined. On the lateral incisor, the 1/2 breakpoint is also analyzed. The higher set of grades is placed in the affected class in each data run. Canine distal accessory ridge. The size of the distal accessory ridge on both the upper and lower canines is rated according to 42 C.R. NICHOL Scott’s (1977) standards. On the upper canine, all possible breakpoints are analyzed, from the absenceltrace presence (011) level to the point at which only the largest form of the ridge (grade 5) is considered affected. On the lower canine, the low frequency of grade 5 ridges means that analysis cannot be done at the 415 breakpoint. All other breakpoints can be and are studied. The affected category contains the higher set of grades at each dichotomy. Premolar mesial and distal accessory cusps. The presence of mesial and distal accessory cusps on the maxillary first and second premolars is assessed using the procedures of Turner (1967a). The trait is dichotomized, with the absence of any accessory cusp treated as normal and the appearance of an accessory cusp on either the mesial or distal margin classified as affected. Hypocone (Cusp 4). The standard of Larson et al. (1975)is employed to classify size variation for the hypocone of the upper molars. The complete lack of absent and the rarity of greatly reduced (grades 1 and 2) hypocones on the first molar prohibits analysis at any level lower than the 314 breakpoint. The 415 breakpoint, which is the equivalent of a 4-1 4 division of the Dahlberg (1956) scale is also examined. For the second molar, all possible breakpoints up to and including the 314 dichotomy are studied. The set of grades at a particular breakpoint that exhibit the greatest degree of reduction (lower-numbered grades) are placed in the normal category, and the higher grades (larger hypocones) are consigned to the affected class. Metaconule (Cusp 5). The size of the metaconule (cusp 5 ) of the upper first molar is rated using the standard of Turner and Warner (1977a). The standard presents a range from a small to a large cusp. Because of the low frequency of any degree of expression of the trait in this sample, the only practical dichotomy to be made is at the absence (grade Ofipresence(grades 1-5) level. Absence is considered as normal, and presence is classed as affected. Carabelli’s trait. Dahlberg’s (1956) standard is used to score variation in the expression of Carabelli’s trait on the upper first molar. Two breakpoints are examined in the study. One is at the absenceipresence (011) level, and the second (the 112 breakpoint) includes the pit form of the trait (grade 1)with absence (grade 0). It would be highly desirable to analyze this trait at the noncusp (grades 0-3)lcusp (grades 4 and higher) level to obtain an idea whether the cusp and seemingly incipient forms (pits and grooves) have the same genetics. However, the low freconquency of the cusp in this sample ( - 1%) traindicates analysis of this question. In both cases studied, the higher grades are treated as affected. Premolar lingual cusp number. Variations in the number and relative sizes of the lingual cusps of the mandibular premolars are categorized according to slight variations of Scott’s (1973) standards. For both plaques, absence of any lingual cusp is scored as grade 0, a single cusp is scored as grade 1, two lingual cusps are assigned grades 2-7 depending on the relative sizes of the mesial and distal cusps, and three or more cusps are placed in grade 8. The rarity of absence of any cusp dictates that the no cusp/cusp(s)(01 1)breakpoint cannot be examined. For both teeth, the onelmore than one cusp (112) breakpoint is tested. Sufficient frequencies of two lingual cusps occur on the second premolar for the 213 and 314 breakpoints (considering increases in size of the distolingual cusp) to be studied as well. In all cases, the higher grades are relegated to the affected category. Transverse ridge. The transverse ridge of the lower premolar is scored using a standard developed by the author (Nichol, n.d.1, following a description given by Kraus et al. (1969). This standard is nearly identical to Scott’s (1973) standard for the uninterrupted sagittal sulcus. Grade 0 exhibits no expression of the transverse ridge (the uninterrupted sagittal sulcus), grade 1shows a ridge with some interruption along its course by the sagittal sulcus, and grade 2 is a transverse ridge that completely interrupts the sulcus. Both possible dichotomies are analyzed for both teeth, with the affected class containing the higher grade(s). Molar groove pattern. Jorgensen’s (1955) classifications are used to categorize the groove pattern of the lower molars. The dichotomy has the Y-pattern treated as normal and any other cusp contact pattern (i.e., + or X) considered as affected for both teeth. Hypoconulid (cusp 5). The size of the hypoconulid (cusp 5) of the lower molars is scored using the standard of Turner and Warner (1977b). Because absence of the cusp and occurrence of the smaller forms of the cusp (grades 1 and 2) are relatively rare on the first molar, analysis for this character is not SEGREGATION ANALYSIS OF DENTAL TRAITS possible a t levels lower than the 314 breakpoint on this tooth. On the second molar, absence is much more frequent ( 36%). Therefore, the absencelpresence (011) dichotomy can be analyzed for this tooth. The low frequencies of tiny (grade 1)and large (grade 5) cusps meant that the 112 and 415 breakpoints cannot be examined. However, the 213 and 314 levels are studied. The presence of the cusp or the larger forms of the cusp are placed in the affected category. Entoconulid (cusp 6). Turner’s (1970) standard is employed to classify the size variation for the entoconulid (cusp 6) of the lower molars. The first three possible breakpoints-01 1, 112, and 213-are examined for the first molar, and only the absencelpresence level is considered on the second because of the low frequency of the sixth cusp on this tooth. The presence of the cusp (or the larger cusp in the cases of the 112 and 213 dichotomies for M1) is considered as affected. Metaconulid (cusp 7). The size of the metaconulid (cusp 7) of the lower first molar is rated according to Turner’s (1970) standard. Because of the relative rarity of this trait, analysis was performed only a t the presence1 absence level. Absence of cusp 7 (grade 0) is treated as normal, and the presence of any degree of expression of the cusp (grades 1-4) is considered as affected. Deflecting wrinkle. The degree of expression of the deflecting wrinkle of the lower first molar is scored using the standard of Seybert and Turner (1975). All possible breakpoints of this scale can be tested. The 011 breakpoint has complete absence of the deflecting wrinkle (grade 0) in one category and any form of the trait in the other. The 11 2 breakpoint adds a ridge without a deflection to the absent class. The 213 breakpoint combines a deflecting wrinkle that does not extend into the molar grooves with grades 0 and 1. In each case, the higher grade(s) is placed in the affected class. Protostylid. Dahlberg’s (1956) standard is used to rate the degree of expression of the protostylid of the lower molars. The class frequencies allow the scale to be divided at the 011 (absencelpresence) and 112 (combining the buccal pit with absence) breakpoints for both the first and second molars. (Actually, the trait frequency of grade 2 and higher on the second molar is, as mentioned, lower than the stated guideline, but analysis at this breakpoint was retained in the study because of the results obtained, as will be - 43 shown.) Furthermore, for the first molar, it was also possible to perform analysis a t the 213 (adding the distal deflection of the buccal groove to absence) and 314 (further adding the minimal expression of a secondary groove to absence) breakpoints. The affected category contains the higher set of grades a t each breakpoint used. Maxillary and mandibular tori. The standards of N.T. Morris (1970) are used to score the size of the maxillary and mandibular tori. Low frequency of occurrence of the torus in either jaw dictates that only a n absence (grade 0) as normal and presence (grades 13) as affected scheme be used in both cases. Maxillary and mandibular arch form. Variation in the form of the maxillary and mandibular arches is categorized according to classifications developed by the author (Nichol, n.d.). Each of these standards has two narrow (parabolic) and two wide (U-shaped) categories. For both jaws, the dichotomy is made between grades 1 and 2, placing the wide forms into the normal class and the narrow forms in to the affected category. Low frequencies in both the extreme grades (0 and 3) contraindicate analysis a t any other breakpoint for either arch. Scoring procedure Each tooth in the normal human dentition exists in two copies. However, only one observation per individual for each character is desired in order not to inflate the sample size falsely. A procedure often used to surmount this problem is to score only one side of the dentition in each individual. This method would seem to restrict the sample size unnecessarily, although some authors (i.e., Zubov and Khaldeyeva, 1979)have surmounted that difficulty by observing the antimere if the tooth on the selected side is missing. Turner and Scott (1977) recommend a procedure in which the teeth on both sides of the mouth are observed, and then the maximum of the two scores for a trait is used as the observation for that individual. This method assumes that the member of a pair of asymmetric antimeres that exhibits the greatest degree of trait expression best represents the genetic potential for that character in that individual. Turner and Scott’s procedure is followed in the present study for all traits except winging. As mentioned, unilateral and bilateral winging are thought to be the result of different factors. Therefore, 44 C.R. NICHOL the expression of the trait on both teeth is of interest for this trait. Statistical methods The statistical method selected to accomplish a complex segregation analysis is the 1971 method of Morton, Yee, and Lew. Although Morton himself (Morton and Rao, 1978) has stated that this particular method has less power to discriminate between complex hypotheses than does the 1974 method of Morton and MacLean, the method was selected for two reasons. The overriding concern is that, with the number of traits analyzed, a considerable amount of computer CPU time and memory is required for parameter estimation. Because the 1971 method involves the estimation of fewer parameters than does the 1974 method, the 1971 method is more realistic when a large number of characteristics are examined, as in the present study. Second, the 1974 method is designed for use with characters that are continuous, or a t least may have their range of expression trichotomized. Whereas the majority of traits in the present study are observed using ordinal scales, making trichotomization possible, two traits, interruption grooves and maxillary premolar accessory cusps, are observed on a dichotomous basis. To date, no acceptable ranked scoring scheme has been found for these two traits, which makes trichotomization into normal, intermediate, and affected categories impossible at this time. Furthermore, some of the traits studied occur in this sample at such high or low frequencies that trichotomization would strain even further the limited available information. Three different general models for the mode of inheritance can be tested using this method. These are the generalized two-allele single-locus model, the beta distribution of risk (which is not considered in this study), and the polychotomized normal distribution of liability. Under the two-allele single-locus model, three main parameters may be estimated. The first of these is the degree of dominance (d) of the allele for affection (GI. Following Morton’s suggestion of the most important special cases of d, three levels of d have been tested. These are: when G is recessive (d = 0), G is dominant (d = l), and a model that Morton calls additive in which d = 112. The single-gene additive model, which is not to be confused with the additive poly- genic model described below, is the equivalent of a codominant two-allele system in which the heterozygote has a 50% chance of being affected. The two other parameters to estimate are the penetrance (t)of G and the frequency (z) of nonheritable (or sporadic) cases. In the present study, G is estimated to be completely penetrant, and the frequency of sporadic cases is estimated to be 0. The frequency G is estimated from trait incidence and Hardy-Weinberg assumptions given the chosen values of d, t, and z. The model for the polychotomized normal distribution of liability is a n application of Falconer’s (1965) proposition of a n additive polygenic liability scale that has a sharp threshold for affection. Falconer’s model is a mathematical consideration of Gruneberg’s (1952) model of quasicontinuous inheritance. Under this model, two parameters need to be estimated. These are the standardized normal deviate of the threshold for affection (Z), which is estimated from trait incidence, and the transmissibility (TI, which is estimated via maximum likelihood. For each model, the probability of observing r affected out of s sibs, given the probability of parental matings of each combination of genotypes and the risk of affection in children resulting from such matings, can be estimated for each sibship. The expected number of affected sibs can then be estimated for each sibship and a likelihood ratio criterion, which is a x2 with a n undefined number of degrees of freedom, is calculated for the model. Subtracting the smaller likelihood ratio criterion from the larger between a pair of models gives the likelihood ratio that is equivalent to a x2 with one degree of freedom. In their discussion of the method, Morton et al. (1971) have stated that a goodness-of-fit comparison between the two models requires the estimation of three parameters (i.e., d, t, and z) in the two-allele single-locus model and two parameters (i.e. T and Z) in the polychotomized normal distribution of liability model. This guideline is followed in the present study. In their discussion of the method, Morton et al. state that Limited experience suggests that discrimination between model 1 [two-allele single locus] and quasicontinuous model 3 will often be difficult. Dominance and a high ratio SEGREGATION ANALYSIS OF DENTAL TRAITS of recurrence risk to incidence favor model 1. Lack of dominance and a low or moderate ratio of recurrence risk to incidence suggest quasi-continuity but do not rule out a discontinuous model, which, with more parameters, is necessarily more flexible. With this in mind, the recurrence risks and the recurrence risk to incidence ratios are calculated and are relied on in the interpretation of the results of the complex segregation analysis. A high recurrence risk to incidence ratio and dominance would tend to improve the chances that a n underlying major gene would be detected should one exist. However, in those cases when the recurrence risk to incidence ratio is low and the quasicontinuous model is accepted, but the recessive model gives the best fit of the single gene models, it is not possible to completely rule out the existence of a major gene. In those cases, the recommendation for further study of that character must be made. Because high or low frequencies are a potential source of difficulty for the statistical analysis, the trait frequency, when approaching 0 or 1, also has a role in the interpretation of the results of the complex segregation analysis. Under Gruneberg’s (1952) model for quasicontinuous inheritance, a character is under the control of many genes, with alleles that have either positive or negative effects on its development. The number of positive alleles must add up to a certain threshold value for the trait to be expressed. When a quasicontinuous trait has a high frequency in a population, it would be expected that many of the individuals affected with the trait have values well above the threshold, whereas the values of most nonaffected individuals would be just below it. Therefore, matings of the most informative type, affected x nonaffected, would tend to produce many affected offspring, mimicking the dominant pattern. When such a trait is a t low frequency, most affected individuals would have values just above the trait threshold, and the values among the nonaffected individuals would tend to be well below the threshold. In this case, the affected x nonaffected matings would tend to produce few affected offspring, mimicking the recessive pattern. 45 RESULTS Table 4 presents the results of the complex segregation analysis. Information contained therein for each run includes the recurrence risk, the recurrence risk to incidence ratio; the model with the best fit to the data (which is that yielding the lowest likelihood ratio criterion), the best estimate of transmissibility (T) when the polychotomized normal distribution of liability is selected, the likelihood ratio between the model with the best fit and the model with the second best fit, the level of significance of that likelihood ratio, and any other models producing likelihood ratio criteria that are not significantly different from that produced by the model with the best fit at the P < 0.05 level. The following is a discussion of the results for each of the characters studied. Winging Winging produces a highly significant likelihood ratio ( P < 0.001), favoring the polygenic model, with a transmissibility estimate of 0.19. Having used a n earlier segregation analysis method that was also developed by Morton (1959), Escobar et al. (1976) proposed that a major gene with a dominant allele for affection is involved in the development of winging. In the present study, the singlegene model with the best fit is recessive rather than dominant. The recurrence risk to incidence ratio is somewhat low, which, as was mentioned, may inhibit the detection of discontinuity, particularly when there is a lack of dominance. Given these findings, judgement on the mode of inheritance of winging must await further study. Central incisor procumbency Another positional variant of the upper central incisors, procumbency, shows best fit to the quasicontinuous model with a transmissibility of 0.47 when examined at the 011 breakpoint and to a discontinuous model with a dominant allele for affection when analyzed a t the 112 breakpoint. The significance level a t the 0/1 breakpoint is quite high ( P < 0.001); at the 112 breakpoint, P is just barely < 0.05. These findings may suggest that the detection of dominance at the 112 dichotomy is a statistical error. On the other hand, the frequency a t the 0/1 breakpoint is fairly high, which can interfere with the detection of a dominant major gene. A definite conclusion Winging UIl Procumbency UI1 Procumbency UI1 Insetting U12 Insetting U12 Insetting UI2 Labial convexity UI1 Labial convexity UI1 Labial convexity U12 Labial convexity UI2 Interruption grooves UI1 Shoveling UI1 Shoveling UI1 Shoveling U12 Shoveling U12 Shoveling U12 Shoveling UI2 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI2 Double-shoveling U12 Double-shoveling UC Double-shoveling UP1 Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge LC Distal accessory ridge LC Distal accessory ridge LC Accessory cusps UP1 Accessory cusps UP2 Hypocone (cusp 4) UM1 Traititooth >O Sibs observed 83 83 83 82 82 82 83 83 82 82 72 83 83 82 82 82 82 83 83 83 83 82 82 77 76 77 77 77 77 80 80 80 77 75 83 Categorization of grades normal/ affected 2-411 011-3 0-112-3 0-112-6 0-2/3-6 0-314-6 011-4 0-112-4 011-4 0-112-4 Abs/Pres 0-213-6 0-3/4-6 0-112-7 0-2/3-7 0-3/4-7 0-415-7 0/1-6 0-112-6 0-213-6 0-314-6 0/1-6 0-112-6 0/1-6 011-6 011-5 0-1/2-5 0-213-5 0-3/4-5 011-5 0-112-5 0-2/3-5 AbsiPres AbsiPres 0-314-6 62 62 60 60 60 62 62 68 68 51 49 49 57 57 57 57 54 54 54 54 65 65 62 54 28 28 28 28 14 14 14 50 48 56 ~~ 63 Both parents observed 1 4 0 3 12 24 0 1 10 33 37 0 17 14 6 25 10 10 18 7 7 10 4 7 9 3 14 10 5 11 31 13 9 18 28 21 16 11 11 1 55 19 13 31 5 16 41 47 1 31 39 48 4 55 1 25 14 17 20 23 12 26 17 0 27 5 42 5 24 48 6 45 3 1 51 1 0 36 0 51 32 21 18 42 6 1 43 3 35 13 0 30 0 56 2 4 15 2 34 10 3 11 2 Number of parents affected TABLE 2. Number o f sibships used in the analysis and break down by number ofparents affected ? 20 21 21 22 22 22 21 21 14 14 21 34 34 25 25 25 25 29 29 29 29 17 17 15 22 49 49 49 49 66 66 66 27 27 27 Hypocone (cusp 4) UM1 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Metaconule (cusp 5) UMl Carabelli’s trait UM1 Carabelli’s trait UM1 Lingual cusp number LP1 Lingual cusp number LP2 Lingual cusp number LP2 Lingual cusp number LP2 Transverse ridge LP1 Transverse ridge L P l Transverse ridge LP2 Transverse ridge LP2 Groove pattern LM1 Groove pattern LM2 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM2 Metaconulid (cusp 7) LM1 Deflecting wrinkle LMl Deflecting wrinkle LM1 Deflecting wrinkle LM1 Protostylid LM1 Protostylid LM1 Protostylid LM1 Protostylid LMI Protostylid LM2 Protostylid LM2 Maxillary torus Mandibular torus Maxillary arch form Mandibular arch form X 0-1/24 0-213-8 0-314-8 0/1-8 0-1/2-8 0/1-3 011-3 0-1/2-3 0-112-3 0/1-8 0-314-5 0-415 011-5 0-213-5 0-3/4-5 0/1-5 0-112-5 0-2/3-5 011-5 011-4 0/1-3 0-112-3 0-2/3 Y/+, 0-415-6 011-6 0-1/2-6 0-213-6 0-314-6 011-5 011-7 0-112-7 0-112-8 0-112-8 0-213-8 0-314-8 011-2 0-112 on-2 0-112 Yli, x 83 75 75 75 75 83 83 83 80 76 76 76 80 80 73 73 82 73 80 80 74 74 74 83 83 83 74 83 82 82 82 83 83 83 83 76 76 82 83 83 83 ~~ 56 61 61 61 61 56 57 57 58 51 51 51 57 57 50 50 37 28 33 33 43 37 37 54 54 54 44 59 45 45 45 55 55 55 55 47 47 29 45 48 51 21 11 43 27 24 ~~ 35 34 24 34 35 46 11 15 0 0 4 29 49 22 43 50 25 37 46 0 6 11 40 24 0 4 20 7 17 26 28 34 44 37 51 0 10 10 23 17 9 23 17 9 7 8 7 21 10 25 19 20 9 12 4 2 20 21 23 5 27 11 19 32 28 6 22 14 7 20 12 5 1 27 23 9 12 7 0 56 24 16 1 1 23 19 3 13 3 2 3 3 1 0 0 38 13 1 6 2 0 0 0 0 0 1 16 z 13 0 1 6 1 14 50 42 25 4 27 14 14 14 14 27 26 26 22 25 25 25 23 23 26 26 45 45 47 47 31 37 37 29 29 29 30 24 37 37 37 28 28 28 28 29 29 53 38 35 32 __ Categorization of grades normal/ affected 2-4/1 011-3 0-112-3 0-112-6 0-213-6 0-314-6 011-4 0-112-4 011-4 0-112-4 Abs/Pres 0-213-6 0-314-6 0-112-7 0-2/3-7 0-314-7 0-415-7 Oil-6 0-112-6 0-213-6 0-314-6 011-6 0-112-6 011-6 011-6 011-5 0-112-5 0-213-5 0-314-5 011-5 0-1/2-5 0-213-5 AbsPres AbsiPres 0-314-6 Raitltooth Winging UI1 Procurnbency UI1 Procurnbency UI1 Insetting U12 Insetting U12 Insetting U12 Labia1 convexity UI1 Labial convexity UI1 Labial convexity U12 Labial convexity U12 Interruption grooves UI1 Shoveling UI1 Shoveling UI1 Shoveling U12 Shoveling U12 Shoveling U12 Shoveling U12 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling U12 Double-shoveling U12 Double-shoveling UC Double-shoveling UP1 Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge LC Distal accessory ridge LC Distal accessory ridge LC Accessory cusps UP1 Accessory cusps UP2 Hypocone (cusp 4) UM1 396 394 394 369 369 369 393 393 371 371 205 389 389 368 368 368 368 393 393 393 393 370 370 274 303 264 264 264 264 283 283 283 310 281 422 Sibs observed 60.0 18.8 15.0 9.9 5 32 113 131 - - - 100.0 44.7 11.6 22.3 69.6 14.5 73.1 52.0 24.0 50.0 4.2 100.0 8.3 47.8 37.7 16.4 48.0 21.6 14.3 6.0 44.4 36.0 20.7 6.3 75.0 8.7 71.4 48.1 (%) Incidence 7 38 69 - 266 69 69 152 25 88 175 215 9 161 198 237 20 253 7 27 1 112 23 200 26 127 221 26 212 24.5 88.8 16.5 90.0 60.4 25.5 71.8 6.1 95.4 7.8 51.2 55.0 20.6 70.4 34.8 18.2 7.3 93.9 43.5 25.4 6.1 91.4 9.2 92.3 74.9 83.3 73.9 42.4 11.7 71.0 45.6 14.8 23.9 8.5 92.9 (%) Sibs observed Incidence 0 40 79 99 67 78 128 72 41 57 80 69 34 128 49 42 58 17 23 25 8 20 27 11 64 44 20 51 131 62 78 97 104 50 126 86 22.9 82.3 33.3 90.7 73.1 48.0 66.7 10.5 90.2 5.0 57.0 58.6 38.8 57.7 42.2 27.8 17.1 87.7 57.5 42.0 8.8 88.3 14.3 95.2 70.7 88.2 78.3 36.0 0.0 75.0 59.3 27.3 35.9 6.8 90.0 ~ - 25 13 2 17 1 265 - 72.0 46.2 50.0 29.4 0.0 95.1 - - 92.5 75.8 85.0 74.5 42.9 - 173 124 60 47 14 - 95.5 - 154 264 10 9 61 10 156 43 12 3 205 30 4 96.2 10.0 44.4 73.8 50.0 80.1 44.2 33.3 33.3 98.0 70.0 75.0 - - 79.5 146 - 32.2 91.9 18.8 95.3 77.5 59 209 16 148 40 ~ Number of parents affected 1 2 Sibs Incidence Sibs Incidence observed observedI (%) (%I TABLE 3. Number of sibs observed and trait incidence in the sample and i n each type of sibship based on number ofparents affected 55 55 48 160 160 109 109 109 109 122 122 122 122 68 68 52 94 187 187 187 187 238 238 238 116 105 137 98 98 98 95 95 100 94 100 Sibs observed ? 24.5 91.0 7.0 85.7 51.0 17.3 72.6 6.3 96.4 7.3 47.9 53.1 15.0 70.6 33.0 16.5 5.5 93.4 37.7 22.1 4.9 92.6 7.4 92.3 84.0 82.4 72.2 42.8 12.3 70.6 43.7 13.4 25.0 7.6 89.1 (%I Incidence Hypocone (cusp 4) UM1 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Metaconule (cusp 5) UM1 Carabelli’s trait UM1 Carabelli’s trait UM1 Lingual cusp number LP1 Lingual cusp number LP2 Lingual cusp number LP2 Lingual cusp number LP2 Transverse ridge LP1 Transverse ridge L P l Transverse ridge LP2 Transverse ridge LP2 Groove pattern LM1 Groove pattern LM2 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM2 Metaconulid (cusp 7) LM1 Deflecting wrinkle LM1 Deflecting wrinkle LM1 Deflecting wrinkle LM1 Protostylid LM1 Protostylid LM1 Protostylid LM1 Protostylid LM1 Protostylid LM2 Protostylid LM2 Maxillarv torus Mandibdar torus Maxillary arch form Mandibular arch form 0-314-5 0-415 011-5 0-213-5 0-314-5 011-5 0-112-5 0-213-5 011-5 011-4 011-3 0-112-3 0-213 011-8 0-112-8 0-213-8 0-314-8 011-8 0-1/2-8 011-3 011-3 0-112-3 0-112-3 Yl+,X YI+,X 0-415-6 011-6 0-112-6 0-213-6 0-314-6 011-5 011-7 0-112-7 0-112-8 0-112-8 0-2/3-8 0-314-8 011-2 0-112 011-2 0-112 422 227 227 227 227 420 423 423 313 292 292 292 316 316 291 291 347 223 307 307 235 222 222 415 415 415 237 420 378 378 378 413 413 413 413 270 270 370 398 401 404 21.9 91.5 81.8 33.2 63.8 39.2 13.1 36.1 20.0 8.2 8.4 8.6 93.7 63.2 12.4 28.8 23.0 18.2 7.7 8.5 3.3 13.8 11.3 57.6 32.7 5.5 47.4 93.4 87.2 63.0 15.9 7.6 61.9 21.5 9.3 38.7 21.9 9.6 93.4 53.5 40.2 - 58.1 18.1 26.7 23.6 20.1 10.4 10.7 5.2 19.6 13.0 43.4 25.5 - 43 144 120 165 169 230 121 153 138 123 53 __ 106 - 72.2 34.1 58.6 21.1 6.4 20.1 10.6 6.1 7.1 7.1 51.9 19.4 4.2 21.6 18 88 29 57 78 139 170 212 113 239 - 27 36 144 102 - 66.7 11.9 5.4 45.4 18.2 9.3 26.6 11.0 8.8 12 84 259 108 214 182 94 136 181 - - - 31.5 73 - 55 38 21 107 76 44 18 59 35 102 47 106 92 101 40 40 8 9 104 104 131 47 12 2 75 90 39 42 16 40 34 78 ._ 22 43 68 08 01 23 11 81 30 59.6 32.8 9.6 .. 45.1 93.0 80.9 54.6 15.8 0.0 60.4 27.2 16.7 44.9 42.6 8.3 50.0 48.0 28.9 7.7 38.1 87.5 85.0 20.6 54.5 47.4 4.8 44.9 26.3 15.9 5.6 23.7 85.7 65.7 14.9 33.0 29.3 23.8 7.5 5.0 0.0 22.2 - 21 10 5 95 32 - - 158 48 2 44 13 0.0 64.2 40.6 - - - 94.3 60.4 0.0 36.4 30.8 - - - 94.7 65.1 49.2 0.0 40.0 93.4 89.6 53.8 79.5 72.7 28.6 70.6 58.8 42.9 209 109 61 4 5 61 77 13 39 11 7 17 17 7 - 0.0 61.9 80.0 - 1 65.6 92.7 89.6 74.0 62.5 50.0 89.5 90 150 125 73 8 2 76 137 34 34 34 34 136 128 128 100 99 99 99 105 105 104 104 198 146 172 172 112 116 116 152 152 152 106 122 185 185 185 143 143 143 143 109 109 223 166 149 135 3fi.3 46.0 97.1 91.2 64.7 14.7 12.5 60.9 23.4 7.0 40.4 21.2 11.1 91.4 45.7 51.9 6.7 18.2 91.1 78.5 33.7 64.3 42.2 18.1 40.8 23.0 7.2 10.4 4.1 94.6 63.8 7.6 25.2 17.5 11.9 3.5 7.3 0.9 9.9 11.4 57.0 Categorization of grades normaliaffected 2-411 011-3 0-112-3 0-112-6 0-213-6 0-314-6 011-4 0-112-4 011-4 0-112-4 AbsPres 0-2/3-6 0-314-6 0-112-7 0-213-7 0-314-7 0-415-7 011-6 0-112-6 0-213-6 0-314-6 0/1-6 0-112-6 Oil-6 Oil-6 011-5 0-112-5 0-2/34 0-3/4-5 011-5 0-1/24 0-2/3-5 AbsPres AbsiPres 0-3/4-6 Traititooth Winging UI1 Procumbency UI1 Procumbency UI1 Insetting U12 Insetting UI2 Insetting U12 Labial convexity UI1 Labial convexity UI1 Labial convexity UI2 Labial convexity U12 Interruption grooves UI1 Shoveling UI1 Shoveling UI1 Shoveling U12 Shoveling U12 Shoveling U12 Shoveling U12 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling UI1 Double-shoveling U12 Double-shoveling U12 Double-shoveling UC Double-shoveling UP1 Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge UC Distal accessory ridge LC Distal accessory ridge LC Distal accessory ridge LC Accessory cusps UP1 Accessory cusps UP2 Hypocone (cusp 4) UM1 16.9 85.9 13.7 87.1 54.7 20.8 66.7 8.3 94.1 7.8 45.4 50.7 27.1 66.0 36.2 18.2 4.0 92.3 39.9 30.0 9.7 88.9 11.4 97.8 70.1 79.0 67.2 29.6 9.6 67.7 38.6 12.1 25.9 5.6 91.7 Recurrence risk (%) 68.9 96.6 82.8 96.8 90.6 81.5 92.9 136.5 98.6 100.3 88.7 92.2 131.8 93.7 103.9 99.9 55.1 98.3 91.6 117.9 159.2 97.3 124.4 99.5 93.6 94.8 91.0 69.7 82.1 95.4 84.8 81.7 108.3 65.0 98.7 Recurrence risk to incidence ratio (%) Likelihood ratio 22.708 14.560 3.852 4.355 24.351 46.322 6.874 22.003 19.324 21.283 16.008 20.072 33.473 30.803 17.562 5.140 1.585 9.327 29.779 19.716 5.140 33.768 5.543 10.081 26.185 20.727 25.231 19.841 16.105 4.444 8.645 12.158 2.601 27.145 8.224 Model with best fit Polygenic T = 0.19 Polygenic T = 0.47 Dominant Polygenic T = 0.54 Dominant Dom in a nt Recessive Polygenic T = 0.44 Polygenic T = 0.35 Polygenic T = 0.16 Dominant Dominant Dominant Recessive Recessive Dominant Dominant Polygenic T = 0.51 Dominant Dominant Dominant Polygenic T = 0.38 Dominant Polygenic T = 0.19 Recessive Polygenic T = 0.04 Polygenic T = 0.00 Polygenic T = 0.07 Polygenic T = 0.04 Polygenic T = 0.46 Polygenic T = 0.13 Polygenic T = 0.20 Dominant Polygenic T = 0.08 Recessive 0.001 0.001 0.05 0.05 0.001 0.001 0.01 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.025 n.s. 0.005 0.001 0.001 0.025 0.001 0.025 0.005 0.001 0.001 0.001 0.001 0.001 0.05 0.005 0.001 ns. 0.001 0.005 Significance (P<) Recessive Polygenic T = 0.29 Other models not reiected TABLE 4. Results of the complex segregation analysis: recurrence risk to incidence ratio, model with best fit, likelihood ratio, and significance Hypocone (cusp 4) UM1 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Hypocone (cusp 4) UM2 Metaconule (cusp 5) UM1 Carabelli’s trait UM1 Carabelli’s trait UM1 Lingual cusp number LP1 Lingual cusp number LP2 Lingual cusp number LP2 Lingual cusp number LP2 Transverse ridge LP1 Transverse ridge LP1 Transverse ridge LP2 Transverse ridge LP2 Groove pattern LM1 Groove pattern LM2 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM1 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Hypoconulid (cusp 5) LM2 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM1 Entoconulid (cusp 6) LM2 Metaconulid (cusp 7) LM1 Deflecting wrinkle LM1 Deflecting wrinkle LM1 Deflecting wrinkle LM1 Protostylid LM1 Protostylid LM1 Protostylid LM1 Protostylid LM1 Protostylid LM2 Protostylid LM2 Maxillary torus Mandibular torus Maxillary arch form Mandibular arch form 0-415-6 011-6 0-112-6 0-213-6 0-314-6 011-5 011-7 0-112-7 0-112-8 0-112-8 0-213-8 0-314-8 011-2 0-112 011-2 0-112 Yl+,x Yl+, x 0-314-5 0-415 011-5 0-213-5 0-314-5 011-5 0-112-5 0-213-5 011-5 011-4 011-3 0-112-3 0-213 011-8 0-112-8 0-213-8 0-314-8 011-8 0-112-8 011-3 011-3 0-112-3 0-112-3 43.6 90.8 83.4 65.9 17.2 9.3 55.9 17.9 10.6 31.7 28.1 12.5 91.5 44.0 34.5 2.0 21.2 88.7 77.3 31.5 58.7 32.8 9.1 32.2 15.5 11.9 7.4 10.9 91.9 57.7 11.0 19.9 18.4 12.4 3.6 5.7 3.3 11.6 6.9 50.3 30.2 91.9 97.2 95.7 104.6 108.4 122.4 90.3 83.1 114.8 82.0 128.1 130.4 98.0 82.3 85.7 35.7 96.7 96.9 94.6 95.0 91.9 83.6 69.6 89.1 77.4 145.0 87.8 127.5 98.1 91.3 88.7 69.2 79.9 68.2 47.1 67.1 100.0 84.5 61.2 87.4 92.6 Recessive Polygenic T = 0.00 Recessive Recessive Polygenic T = 1.00 Polygenic T = 0.51 Dominant Dominant Polygenic T = 0.29 Dominant Dominant Dominant Polygenic T = 0.36 Recessive Recessive Polygenic T = 0.11 Polygenic T = 0.37 Polygenic T = 0.18 Polygenic T = 0.30 Dominant Dominant Dominant Polygenic T = 0.20 Dominant Polygenic T = 0.42 Polygenic T = 0.59 Polygenic T = 0.18 Dominant Polygenic T = 0.23 Polygenic T = 0.19 Polygenic T = 0.11 Polygenic T = 0.06 Dominant Polygenic T = 0.10 Polygenic T = 0.00 Polygenic T = 0.04 Dominant Dominant Polygenic T = 0.00 Recessive Polygenic T = 0 25 _ _ 7 678 17.299 8.635 0.938 22.403 11.750 2.024 30.791 2.882 12.342 13.882 30.661 17.306 15.773 27.043 16.114 20.933 4.619 11.650 17.426 15.315 16.534 4.400 16.865 28.981 20.628 4.025 4.318 10.040 19.352 16.094 12.536 31.551 11.729 17.327 8.624 23.435 15.491 11.302 53.109 28.585 n- ni __ 0.001 0.005 ns. 0.001 0.001 ns. 0.001 n.s. 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.05 0.001 0.001 0.001 0.001 0.05 0.001 0.001 0.001 0.05 0.05 0.005 0.001 0.001 0.001 0.001 0.001 0.001 0.005 0.001 0.001 0.001 0.001 0.001 Polygenic T Dominant Polygenic T = = 0.22 0.38 52 C.R. NICHOL likelihood ratio comparing the best quasicontinuous and discontinuous models and the strength of a possible major gene is a one-toLateral incisor insetting one correspondence. However, the percentInsetting of the lateral incisor yields best age contribution of a single locus to the disfit to the single-gene model with a dominant continuity of the genetic background for a allele for affection for two of the three break- trait should correspond in some way to the points (213 and 314) a t which it was tested. At ability to detect this discontinuity. the third breakpoint (1/2), the polygenic Shoveling model with a transmissibility estimate of Six separate runs of shoveling are per0.54 is accepted a t the P < 0.05 level. Given that the significance level in the two cases formed in this study. Two different breakwhen the dominant model is selected is high points (314 and 415) are tested on the central ( P < 0.001), whereas at the other breakpoint incisor, and four breakpoints (213, 314, 415, the significance level is lower and the fre- and 5-6) are examined on the lateral. In each quency is quite high (90.0%), it is logical to case, the model showing the best fit was a reject the latter case and propose that inset- discontinuous one, although on the lateral incisor at the 5-6 breakpoint the quasicontinting has dominant major gene inf’Iuence. uous model is not rejected. The reason for the Incisor labial convexity inability to discriminate between models at Labial convexity is examined at two break- this breakpoint is probably the low trait frepoints on both the central and lateral inci- quency (7.3%) and a low recurrence risk to sors. On the central, at the 011 breakpoint, incidence ratio (55.1%). For both cases on the the single gene model with a recessive allele central incisor the allele for affection in the for affection yields the best fit to the data. best model is dominant, with a P of < 0.001. At the 112 breakpoint, the recessive mod- However, for the lateral incisor the degree of el, which gives the lowest likelihood ratio cri- dominance of the allele for affection is not terion of the three single gene models, is the same in all cases. At the two lower breakrejected by a polygenic model with a trans- points, the allele is suggested to be recessive; missibility estimate of 0.44. For the lateral a t the two higher dichotomies, the best fit is incisor, the quasicontinuous model is ac- to a dominant model. Given that the best fit cepted a t both breakpoints. The transmissi- in all six runs is to the single-gene model, a bility estimate is 0.35 a t the 011 breakpoint proposal of a major gene for shoveling can be and 0.16 at the 112 dichotomy. One can note made. Dominant gene involvement in the that, in three cases when the quasicontin- development of shoveling seems clear for the uous model is accepted, the trait frequency is central incisor. The situation for the lateral either very high (95.4% for U12 a t the 011 incisor is more confusing, but it seems undichotomy) or quite low (6.1 and 7.8% for UI1 likely that shoveling has different genetic and UI2, respectively, at 112 division). Also, etiologies for each incisor. Therefore, the a significant sex difference in incidence is most logical conclusion would be to dismiss seen on 12 a t the 112 breakpoint. Again, no the findings of recessiveness a t the two lower final answer on the genetics of this trait can breakpoints as statistical error and propose dominant major gene influence on shoveling be put forward at this time. for both teeth. A significant sex difference in Interruption grooves trait frequency is noted for shoveling of the Quasicontinuity is overwhelmingly re- lateral incisor a t the 213 breakpoint. jected for interruption grooves on the maxillary lateral incisors. The single locus model Double-shoueling with a dominant allele for affection produces Double-shoveling is tested on four different better fit to the data than does any other model a t the P < 0.001 level. If the level of teeth and for a total of eight dichotomies of significance of the likelihood ratio can be the observational scale. On the central inciused to estimate the strength of the major sor, the quasicontinuous model with a transgene for a trait, then such a major locus for missibility estimate of 0.51 yields best fit a t interruption grooves plays a very large role the 011 breakpoint. For the other three dichoin the development of the character. It is tomies tested on this tooth, the discontinuous doubtful that the relationship between the model with a dominant allele for affection is on the mode of inheritance of this trait also depends on further analysis. SEGREGATION ANALYSIS OF DENTAL TRAITS accepted. For the lateral incisor, the polygenic model (T = 0.38 in this case) is again accepted a t the 011 breakpoint, and the dominant model is chosen for the 112 dichotomy. The polygenic model with transmissibility estimate of 0.19 yields best fit for the canine, which is tested only at the 011 division of the scale. For the premolar, the single-gene model with a recessive allele for affection is selected. From the observation that the polygenic model is selected for presencelabsence on all three anterior teeth, one might be led to the conclusion that trait presence is under the influence of many genes, whereas expression is influenced by a major gene with a dominant allele for stronger degrees of affection. However, in all cases when the polygenic model is the best fit, the trait frequency is > 90%. It is more likely that this high frequency is causing methodological problems, and the quasicontinuous findings can be dismissed. Also, significant sex differences in the trait frequencies occur a t the 01 1 breakpoint for both the incisors. The findings of recessive major gene influence for labial (or, more correctly in this case, buccal) marginal ridges on the premolar, as opposed to the dominant allele influence noted for the anterior teeth, could indicate that there are different genetic backgrounds for these two morphologically similar traits. On the other hand, this might be some sort of statistical aberration, as is suspected for lateral incisor shoveling. Canine distal accessory ridge The canine distal accessory ridge is tested using four dichotomies of the upper canine scale and three divisions of the lower canine standard. In all seven cases, the model using the polychotomized normal distribution of liability is selected. For the upper canine, all transmissibility estimates are quite low (ranging from 0 to 0.07), suggesting a n overwhelming environmental influence on the character on that tooth. The transmissibility estimates are higher for the mandibular canine, ranging from 0.13 to 0.46. Two problems with the distal accessory ridge are worthy of note. First, as mentioned, the canine distal accessory ridge is the most sexually dimorphic morphological feature of the human dentition. In this sample, very significant ( P < 0.001) sex differences in trait frequencies are found in all runs, except for those at the 011 and 112 breakpoints on the upper canine. Second, this trait has one of 53 the worst records for percentages of sibships with one or both parents not being observed. The reason for this is that canine distal accessory ridge is affected by relatively minor degrees of attrition and is frequently totally obliterated by the age of 30 years. Given this, the analysis of this trait in this sample is highly dependent on making the assumption of equal fertility among parents, which if not true could yield unreliable results. Premolar mesial and distal accessory cusps The presence of mesial and distal accessory cusps on the upper premolars yields best fit to a discontinuous model on the first premolar. However, there is not significant discrimination between the dominant and recessive estimates of the degree of dominance for the allele for affection. Both the recessive and dominant models reject the polygenic model a t the P < 0.005 level. For the second premolar, the greatest correspondence is to a quasicontinuous model with a low transmissibility estimate (T = 0.08). The results for the first molar suggest discontinuity in trait inheritance, implicating a major gene, but it is impossible to estimate the degree of dominance at this time. On the second premolar, there is a very low transmissibility estimate, suggesting large environmental influences. Also, the trait frequency (8.5%)and recurrence risk to incidence ratio (65%) are both low. Each of these factors could make the major gene, if it exists, impossible for this method to detect. The results point to the existence of a major gene on the first premolar, although, at this time, the degree of dominance is in question, and it is unlikely that the genetics, of this feature are different on the second premolar. Also, note that there are significant sex differences in trait frequencies for both teeth, and possible sex-linkage could be causing some of the problems noted. Hypocone (cusp 4) Expression of the hypocone is tested a total of six times on two teeth. On the first molar, the recessive single locus model was accepted at both breakpoints (314 and 415) tested. For the second molar, the recessive model is a significantly better fit ( P < < 0.001) at the 21 3 breakpoint. At the 112 breakpoint the recessive model is the best fit, but the quasicontinuous model with a transmissibility estimate of 0.38 is not rejected. At the other two scale divisions tested on this tooth, the 54 C.R. NICHOL polygenic model is a significantly better choice. At the presence/absence level (Oh) the transmissibility estimate is 0; a t the 314 breakpoint the estimate is 1. It is apparent that, if a major gene exists for this trait, the allele for greater trait expression is recessive. In all six cases, including the two when the single gene model was rejected, the best estimate of the degree of dominance for the allele for affection out of those tested was 0. In that both tests of the first molar hypocone give best fit to the recessive model, a proposition of major gene influence for first molar seems reasonable. It is unlikely that the genetics of the hypocone are different on the second molar. Some of the difficulties in the results for the second molar could be due to high frequency and overwhelming environmental influence at the 0/1 breakpoint, high frequency at the 112 breakpoint, and low frequency a t the 314 breakpoint. Significant frequency differences between the sexes occur at the 213 breakpoint on M2 and at the 314 breakpoint on both molars. Metaconule (cusp 5) The metaconule of the upper first molar does not provide a significant level of discrimination between a discontinuous model with a dominant allele for affection and a quasicontinuous model with a moderate level of transmissibility (T = 0.51). A factor that may be the cause of the inability of the method to distinguish between models is the relatively low incidence of the trait in the sample (7.6%). Possibly, a major gene with a dominant allele for affection exists for this trait, but it does not contribute to discontinuity in trait inheritance with such strength that it results in rejection of additive multifactorial inheritance in-a sample of this size with the low level of incidence observed. Carabelli’s trait Carabelli’s trait of the maxillary first molar undergoes two analyses of its probable inheritance. At the 0/1breakpoint the dominant model is accepted overwhelmingly accepted (P < < 0.001). At the 1/2 breakpoint there is not significant discrimination between this model and the polygenic one with a transmissibility estimate of 0.22. Using Morton’s and MacLean’s (1974) complex segregation analysis method, and trichotomizing the trait with cusp forms as affected, other forms of the trait as intermediate, and absence as normal, Kolakowski et al. (1980) have found evidence of a weak major gene for Carabelli’s trait. The findings of this study are in agreement with the suggestion of major gene influence on this trait. Significant frequency differences between sexes are seen at both dichotomies. Premolar lingual cusp number The presence of multiple lingual cusps on the lower premolars yields best fit to a quasicontinuous model with a low to moderate estimate of transmissibility (T = 0.29) for the first premolar a t the presencelabsence (1/2) level. On the second premolar, the greatest correspondence is to a discontinuous model with a dominant allele for affection for all three breakpoints tested. Probably, a major gene exists for the trait, but its influence is weakened away from the center of the trait field. Other evidence, such as the trait frequency (9.3%) and the transmissibility levels selected for the polygenic model (estimates of T for P2 range from 0.38 to 0.941, suggests that the center of the field for this character is on the second premolar rather than the first. Different genetics for the trait on each tooth are unlikely. Transverse ridge The transverse ridge of the lower premolars is analyzed a t two different dichotomies of the observation scale for each of the two teeth. In both cases, the recessive model is accepted at one breakpoint, and the polygenic model is accepted at the other. For the first premolar the recessive model is chosen a t the 112 breakpoint; on the second the recessive model is selected at the 011 breakpoint. In both cases when the polygenic model produces best fit, the frequency approaches fixation. For the first premolar at the 011 breakpoint the frequency is 93.4%, and for the second premolar at the 112 breakpoint the frequency is 5.5%. There is also a very low recurrence risk to incidence ratio and a significant sex difference in frequencies on P2 at the 1/2 division. Because of these findings, the inclination is to reject the results indicating quasicontinuity and to go forward with a proposal of recessive major gene involvement in the development of the transverse ridge. Molar groove pattern The groove pattern of both lower molars demonstrates best fit to a model employing the polychotomized normal distribution of li- SEGREGATION ANALYSIS OF DENTAL TRAITS ability. For the first molar, the transmissibility estimate is moderate (T = 0.37), and, for the second, the estimate is somewhat low (T = 0.18). The groove pattern has been shown to be statistically associated with the size of molar cusps 5 and 6 (Nichol, 1985). Also, the presence of the Y-pattern has been noted to be related to the presence of the deflecting wrinkle (D.H. Morris, 1970). Because of the previous findings that the groove pattern is associated with several other crown features (and therefore may be the result of the presence andlor size of these characters), it is not surprising that the trait would correspond to a model in which the character is determined by many additive factors. Hypoconulid (cusp 5) The hypoconulid is examined a t five dichotomies, three on the first molar and two on the second. In three of the five cases, the discontinuous model with a dominant allele for affection is accepted. In the other two cases, the 3/4breakpoint on both M1 and M2, the data best fit the quasicontinuous model. The two findings of fit to the polygenic model occur in the analyses with the highest (81.8% on M1) and lowest (13.1% on M2) frequencies of the five runs for this trait. The findings of discontinuity for the other three analyses lead to a proposition of dominant major gene influence on the development of lower molar cusp 5. 55 incidence ratio is quite high (127.5%)in this case. The logical conclusion is that there is a major locus with a dominant allele for affection for this cusp. However, the caution must be put forward that a significant sex difference in trait frequency is found. Deflecting wrinkle The deflecting wrinkle of the lower first molar demonstrates best fit to the quasicontinuous model at all three of the possible breakpoints. In each case the estimate of transmissibility is low, ranging from 0.23 a t the 011 breakpoint to 0.11 at the 213 breakpoint. The presence of this character would appear to be under the influence of many additive genes modified by relatively strong environmental effects. Protostylid The protostylid of the lower molars is tested for a total of six dichotomies on two teeth. Four of the data runs yield best fit to the quasicontinuous model with low transmissibility estimates (ranging from 0 to 0.10). The other two analyses, both of which are a t the 112 breakpoint on each of the two teeth, give the greatest correspondence to the dominant model. Because this phenomenon occurred on both teeth, the findings for the second molar are retained even though the frequency was below the guideline stated earlier. From the transmissibility estimates found, it is evident that there is a tremenEntoconulid (cusp 6) dous amount of environmental influence on Cusp six is tested a t the presencelabsence the development of the protostylid trait. The level on both the first and second molars and findings of possible dominant major gene efis further examined a t the 112 and 213 break- fects at one breakpoint are potentially interpoints on the first molar. In all cases, except esting, but determination of whether this has for the 011 dichotomy on the first molar, some meaning awaits further analysis. which corresponds to the dominant model, the polygenic model gives best fit. In two of Maxillary and mandibular tori the cases when the polygenic model is acTwo different situations are found for the cepted, the trait frequency (8.2% for the 213 dichotomy on M1 and 8.4% for the 011 divi- maxillary and mandibular tori. The maxilsion on M2) and the significance levels for lary torus demonstrates best fit to a singlerejection of the dominant model are low. locus model with a dominant allele for affecThese findings cast suspicion on the results tion. On the other hand, the mandibular tofor these two runs. The results for this trait rus shows best fit to a polygenic model with do not make the proposition of a major gene a transmissibility estimate of 0. Proposition a straightforward one, but they at least raise of a major gene with a dominant allele for affection is indicated for the maxillary torus. the possibility that such a gene exists. For the mandible, problems of low incidence Metaconulid (cusp 7) and low recurrence risk to incidence ratio Cusp seven of the lower first molar shows exist, and overwhelming environmental inbest fit to the single-gene model with a dom- fluences on the development of the mandibinant allele for affection. The recurrence to ular torus make it impossible to say just what 56 C.R. NICHOL the inherited portion of the trait’s develop- three tests show significant correspondence to the polygenic model. Two of these three mental background might be. give best fit to the recessive submodel when Maxillary and mandibular arch form the single locus model is examined. These Wide forms of the two arches also demon- results bear out the contention that, with strate correspondence to different models. For dominance and a high incidence to recurthe maxilla, the wide forms yield best fit to a rence risk ratio, detection of discontinuity is discontinuous model with a recessive allele enhanced. On the other hand, low recurrence for affection. The likelihood-ratio in this case risk to incidence ratio and lack of dominance is very significant ( P < < 0.001). For the are suggested to inhibit detection of disconmandible, the best fit is to the polygenic tinuity. The results seem to bear this out, in model with a transmissibility estimate of that, for the 11 runs where the recurrence 0.25. A relatively strong major gene with a risk to incidence ratio is < 70%, ten give recessive allele for affection by wide arches significantly better fit to the polygenic model, is suggested for the maxilla, whereas multi- and the other does not produce significant factorial inheritance, including fairly strong discrimination between the two models. In environmental effects, is apparent for the five of the ten runs where quasicontinuity is mandible. It should also be noted that there favored, the best fit under tests of the single is sexual dimorphism for this trait on the gene model is to the recessive submodel. mandible in this sample, with males more An overall view of the results suggests that frequently having a wide arch. the polygenic model is favored a t high or low levels of trait incidence. In 30 of the 39 cases when the polygenic model is favored, the trait DISCUSSION frequency is below 20% or above 80%, The results of the 76 individual runs of the whereas this is true in only 11 of the 37 cases complex segregation analysis produce 39 when the single-locus model is the best fit. cases showing best fit to the polychotomized The potential effects of high and low frequennormal distribution of liability model. In 38 cies on the results of the segregation analysis of the 39 instances, the likelihood ratio is were mentioned above. In all, 14 of the 76 significant, and in the other a dominant sin- runs have trait incidences > 80%. An inorgle gene model is not rejected. The other 37 dinate number of these (12) show signifiruns show that the two-allele single-locus cantly greater correspondence to the quamodel is the best fit to the data. For 34 of sicontinuous model than to the single-locus these the likelihood ratio is significant, and model. For 8 of the 12, the dominant submofor the other three the quasicontinuous model del is the best fit in the analysis of the single is not rejected. Dominance of the allele for gene model. Fears that confusion of domiaffection is indicated in 26 of the 37 instances nance and quasicontinuous inheritance could when the single-gene model is the best fit occur when a trait is a t high frequency seem and in 24 of the 34 runs when the polygenic to be realized. In 27 runs the incidence is < model is rejected. 20%.For 17 of these 27, the goodness-of-fitto Discussed above was the possible relation- the polygenic model is significant. In the ship between the recurrence risk to incidence other ten runs, eight when the single gene ratio and the goodness-of-fittest between the model is a significantly better fit and two discontinuous and quasicontinuous models. when discrimination between the models is Analysis of the results of the segregation not significant, the dominant submodel is seanalysis reveals that some of the concerns of lected as the best of the single-gene models the developers of the method are realized. In in all cases. The 17 instances when the qua11 runs the recurrence risk to incidence ratio sicontinuous model is selected show a n equal is > 110%.In seven of these cases, the single- division (seven dominant, three additive, locus model yields significantly better fit to seven recessive) between dominance and rethe data than does the quasicontinuous cessiveness under tests of the single-gene model. In all seven instances the allele for model. The suggestion of these findings is affection is estimated to be dominant. Of the that there is a n inability of the model to four remaining tests, one favors the poly- discriminate between single-locus recessivegenic model, with a dominant single gene ness and quasicontinuity when the trait is a t model not being rejected. The remaining low frequency. SEGREGATION ANALYSIS OF DENI'AL TRAITS For some of the traits examined on more than one tooth, a proposition about the genetics of the character on one tooth is extended to another in the face of conflicting results from the complex segregation analysis. Under the two major models for dental development, the field model (Butler, 1939; Dahlberg, 1945) and the clone model (Osborn, 19781, a trait that occurs on more than one tooth has a genetic background shared between teeth rather than a separate genetic background for each tooth. It is therefore logical to extend a proposition about the genetics of a trait from one tooth to another, especially when complications of recurrence risk to incidence ratios or frequencies call the results from one tooth into question. Given these reasons for rejecting the results of certain data runs, the results of the complex segregation analysis suggest major locus involvement in the development of 13 of the 24 traits examined. Nine of theseinsetting of UI2, interruption grooves of UI2, incisor shoveling, incisor and canine doubleshoveling (as was mentioned above; premolar buccal marginal ridges may not be genetically linked to double-shoveling of the anterior teeth), Carabelli's trait of UM1, multiple lingual cusp of the lower premolars, the hypoconulid of LM1 and LM2, cusp 7, and the maxillary torus-show indication that the allele for affection by the trait is dominant. Three traits-the hypocone of UM1 and UM2, the transverse ridge of the lower premolars, and the maxillary torusgive evidence of a recessive allele for affection. Premolar double-shoveling also suggests recessiveness, but further study is necessary to determine whether this finding is a statistical error or if in fact the trait is separate from double-shoveling on the incisors and canine. One character, accessory cusps of the upper premolars, does not give a clear picture on the degree of dominance of the major gene indicated in the results. Five other traits-procumbency of UI1, labial convexity of UI1 and UI2, metaconule UM1, and cusp 6 of LM1 and LM2, and protostylid of LM1 and LM2-give hints of major gene influence, but definite conclusions on their true mode of inheritance must await further study. The results for the remaining six traits show that their development is under the control of many genes. However, the results in two of these cases-winging of UI1 and the mandibular torus-are suspect because of 57 findings of low recurrence risk to incidence ratios. Two others of these six-the distal accessory ridge and the mandibular arch form-show significant sex differences in frequencies, which may call the results into question. Therefore, only two characters-the groove pattern of LM1 and LM2 and the deflecting wrinkle of LM1-give clear results indicating their polygenic origin. Overall, the transmissibility estimates found for the polygenic model tend to be low. Being magnanimous and taking the highest estimate of transmissibility from any of the runs for a trait on each tooth, the average for the 38 traits is only 0.36. These findings suggest that there is a large amount of environmental influence on the development of dental morphological variants. However, this conclusion must be qualified by recognizing that there are observational difficulties for many of these characters (Nichol and Turner, 1986). Although the traits analyzed in the present study generally have observational discrepancies that have been found to be nondirectional, and would therefore cancel out in population studies of large samples, it must be recognized that the difficulties in accurately replicating observations may well result in overestimation of the environmental influences on these characters. Valid transmissibility estimates must await the development of more refined observational technique. Certainly this analysis has left open many questions about the mode of inheritance of the dental morphological characters examined. In 20 of 76 data runs, there are significant differences between the sexes for the trait frequency, meaning 11 of 24 traits examined show some evidence of sexual dimorphism. If any of these characters are under the influence of sex-linked genes, the conclusions drawn about their mode of inheritance could be in error. The possibility of sex effects on dental trait development certainly warrants the future testing of sex-linkage models, to determine whether these are due to sex-linked genes, or other circumstances such as sex differences in growth factors. Also, more intensive analysis of these characters using more advanced methods of segregation analysis is needed to verify the presence of the major genes proposed here; to estimate the relative contributions of major genes and the multifactorial backgrounds; and to investigate the relative contributions 58 C.R. NICHOL of genetic, familial environmental, and ran- Falconer DS (1965)The inheritance of liability to certain diseases, estimated from the incidence among reladom environmental effects on trait developtives. Ann. Hum. Genet. 295-76. ment and expression. Garn SM, Lewis AB, and Kerewsky RS (1965) X-linked inheritance of tooth size. J. Dent. Res. 44t439-441. Goose DH (1971)The inheritance of tooth size in British families. In AA Dahlberg (ed.): Dental Morphology and The author would like to recognize the conEvolution. Chicago: University of Chicago Press. tributions to this study of Dr. and Mrs. A.A. DH, and Lee GTR (1971) The mode of inheritance Dahlberg. Without their tremendous and ex- Goose, of Carabelli’s trait. Hum. Biol. 43t64-69. tended effort in putting together the collec- Gruneberg H (1952) Genetical studies on the skeleton of tion from which the sample used in this study the mouse. IV. Quasi-continuous variation. J. Genet. 51t95-114. came, this analysis would not have been possible. The information that they gave me Harris EF (1977) Anthropologic and genetic aspects of dental morphology of Solomon Islanders, Melaabout the collection and Dr. Dahlberg’s in- the nesia. PhD Dissertation, Arizona State University, sightful comments about the dentition were Tempe. also invaluable. I would also like to thank Harris EF (1980) Sex differences in lingual marginal ridges on the human maxillary central incisor. Am. J. Dr. C.G. Turner I1 under whose guidance Phys. Anthropol. 52541448. with study was performed and with whose Hrdlicka A (1920) Shovel-shaped teeth. Am. J. Phys. encouragement it was submitted for publicaAnthropol. 3.429-465. tion. The three anonymous reviewers also Jorgensen KD (1955)The dryopithecus pattern in recent deserve thanks for their comments, which Danes and Dutchmen. J. Dent. Res. 34t195-208. have resulted in the final form of this paper. Kaul V, and Prakash S (1981) Morphological features of Finally, I wish to acknowledge Dr. M.Y. Is- the J a t dentition. Am. J. Phys. Anthropol. 54:123-127. can, who organized the session at the annual Kieser JA, and Preston CB (1981) The dentition of the Lengua Indians of Paraguay. Am. J. Phys. Anthropol. meetings of the American Association of 55,485-490. Physical Anthropologists where this paper Kolakowski D, Harris EF, and Bailit HL (1980)Complex was originally presented and who oversaw segregation analysis of Carabelli’s trait in a Melanethe organization of the papers from that ses- sian population. Am. J. Phys. Anthropol. 53r301-308. 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