A SEARCH FOR QUANTITATIVE TRAIT LOCI AFFECTING ASYMMETRY OF MANDIBULAR CHARACTERS IN MICE

Transcription

1 Evolution. 51(3) pp A SEARCH FOR QUANTITATIVE TRAIT LOCI AFFECTING ASYMMETRY OF MANDIBULAR CHARACTERS IN MICE LARRY J. LEAMY,l ERIC J. ROUTMAN,2 AND JAMES M. CHEVERUD J I Department of Biology, University ofnorth Carolina at Charlotte, Charlotte, North Carolina I ljleamy@ .uncc.edu 2Department ofbiology, San Francisco State University, San Francisco, California Department ofanatomy and Neurobiology, Washington University School ofmedicine, Saint Louis, Missouri Abstract.-An interval mapping procedure was used to search for and describe the effects of any quantitative trait loci (QTLs) for directional asymmetry (DA) and fluctuating asymmetry (FA) of IO bilateral mandible characters in house mice. It was hypothesized that more QTLs would be found for DA than for FA. but that any discovered for FA should tend to exhibit dominance. All mandible characters were triply measured and 76 microsatellite markers were scored in an average of 471 mice from the F 2 intercross of the Large (LG/J) and Small (SM/J) inbred strains. A total of 16 QTLs significantly affected DA in nine of the 10 mandible characters. and this was more than the 9.5 expected by chance alone. These QTLs were found on seven of the 19 chromosomes. often at or near locations of QTLs affecting the mean of the two sides for various dimensions on the mandible. It was concluded that there is genetical variability for DA in these characters. although its level was low (4.4% of the total variation in this particular F 2 population). Eleven QTLs were detected for FA. suggesting that there is very little genetic variability for FA, at least as seen in the mandible characters in this particular F 2 population. As hypothesized. however. these QTLs did tend to exhibit dominance. Key words.-directional and fluctuating asymmetry. mandibular characters in mice. quantitative trait loci. Received September 3, Accepted January Are there genes that affect variation in the differences almost always found between right and left sides of bilateral characters? It often has been assumed that nondirectional variation in such differences, referred to as fluctuating asymmetry (FA), may be purely environmentally controlled (Palmer et al. 1994). It is possible that FA is truly not heritable if the same genes govern both sides of such characters (Leamy 1997) and exhibit no differential expression on these sides, and if no other genes act singly or epistatically on the separate sides. In contrast to the situation for FA, a heritable basis has long been assumed for directional asymmetry (DA). and antisymmetry (AS), two other forms of asymmetry. DA occurs when one side of a bilateral character is consistently larger than the other, and examples of DA in various characters such as the mammalian heart are common throughout the animal kingdom (Van Valen 1962). Antisymmetry is characterized by a bimodal or platykurtotic right minus left side distribution, and although apparently not as common as DA, is well known (e.g., see McKenzie and Clarke 1988). From an evolutionary point of view, it is important that we understand the genetical basis of both FA and DA. FA is widely regarded as a measure of developmental stability (Waddington 1957; Zakharov 1994), and thus increasingly has been used to compare developmental stability levels in populations subjected to genetic or environmental stressors such as inbreeding, hybridization, parasitic infections, pollution, and sexual selection (Zakharov 1989; Parsons 1990; Graham 1992; Palmer et al. 1994). In most of these sorts of comparisons, it has been necessary to assume FA has no genetical basis (Palmer and Strobeck 1992; Zakharov 1992; Palmer et al. 1994). On the other hand, the presumed heritable basis for DA has led to the hypothesis that this form of asymmetry (or other heritable forms such as AS) may have given rise to more pronounced, macroscopic asymmetries such as seen in claw size in fiddler crabs (Palmer et al. 1994) The Society for the Study of Evolution. All rights reserved. 957 Clearly, however, we understand little about the evolutionary relationships among FA, DA, and various other asymmetries. The evidence for or against genetic variability for both FA and DA is not extensive and rests primarily on observations of differences especially in FA between inbreds and hybrids (Thoday 1958; Leamy 1984; Clarke 1994) and on heritability estimates of these asymmetries. The majority of the relatively few studies acceptably estimating heritabilities of FA have produced low, usually nonsignificant estimates (McGrath et al. 1984; Leamy 1986, 1997). Heritability estimates for DA, although also typically low in magnitude, have been significant for some characters (Cheverud et al. 1990). But traditional heritability studies tell us nothing about the number, location, and mode of action of potential genes that might affect these asymmetries. For example, if there are such genes affecting FA or DA, are they few or many in number; are they spread throughout the genome; are they identical to the genes affecting the separate sides of the characters themselves; for those affecting FA, do they exhibit dominance as might be expected given our knowledge of differences in FA between inbreds and hybrids; do the same genes affect both DA and FA? Fortunately. modern advances in both molecular and statistical genetics (Lander and Botstein 1989; Dietrich et al. 1992, 1996) now allow us to begin to answer these and related questions. In this paper we report the results of an interval mapping study designed to search for and measure the effects of any quantitative trait loci (QTLs) for FA and DA in 10 mandibular dimensions in mice. Based primarily on the literature as briefly outlined above, it is hypothesized that: (I) some QTLs will be found for DA; and (2) fewer QTLs (if any) will be found for FA in these mandibular characters. but based on the results of inbred/hybrid comparisons, those discovered will tend to exhibit dominance.

2 958 LARRY J. LEAMY ET AL. MATERIALS AND METHODS The Population and Characters The mice used in this study were the F 2 progeny of F 1 hybrids produced by crossing the Large (LG/J) and Small (SM/J) inbred strains obtained from the Jackson Laboratory. The LG/J strain originally was selected for large size by Goodale (1941) and the SM/J strain was selected for small size by MacArthur (1944). When received by the Jackson Laboratory, selection was abandoned and both strains were inbred via sib mating (Chai 1956a). Sufficient numbers of generations of inbreeding were accomplished so that both strains were considered to be basically isogenic; that is, all genes, including those affecting body size, were assumed to be fixed in each strain. In a series of studies on these strains, Chai (I956a,b) found that the mean body weight at 60 days of age was 13.6 g for mice in the Small strain and 37.4 g for mice in the Large strain, and he estimated that 11 or more genes were responsible for this difference. In the first QTL study on the F 2 generation from crosses between these strains, Cheverud et al. (1996) found between seven and 17 QTLs, located on 16 of the 19 autosomes, affecting body weights at various ages. DNA was extracted from the spleens of mice in the Large and Small strains following a protocol that previously has been described (Routman and Cheverud 1994, 1995). Both strains were screened for 472 microsatellite loci using PCR amplification techniques modified from Dietrich et al. (1992). The amplification products were visualized with the use of ethidium bromide staining on 5-6% agarose gels (Routman and Cheverud 1995). Over 200 (47%) of these loci were found to be polymorphic between the two strains (Routman and Cheverud 1994, 1995). Of these polymorphic loci, 76 that mapped in representative areas on the 19 autosomes were chosen for scoring in the F 2 mice (see Table 1, Fig. 1). The X chromosome was not represented because only two polymorphic loci were found on this chromosome (Routman and Cheverud 1995) and they mapped quite close to each other. Ten single-pair matings of Large mice X Small mice originally were made, and this resulted in 41 FI hybrid mice. When these FI mice reached at least 70 days of age, they were randomly (single-pair) mated and males were removed from the cages when females became pregnant. Over about a three-month period of time, F I parents produced multiple litters of varying size that altogether resulted in a total of 535 F 2 mice. All F 2 litters were weaned at 21 days and sexes were caged separately. All mice in this F 2 generation were weighed at 10 weekly intervals starting at seven days of age and were sacrificed after the last weighing at 70 days of age. After sacrifice, spleens were removed from all F 2 mice and their skeletons were prepared by exposure to dermestid beetles. The 76 microsatellite loci were scored in the F 2 mice following the same procedure as already outlined for the Large and Small strains. One locus, DlOMit20, was used only as a dominant marker since the heterozygote could not be distinguished from the SM/J homozygote. In addition, some loci were not resolvable in all mice, so the loci varied in their sample sizes (Table 1). Table 1 gives the positions of the 76 microsatellite loci based on recombination percentages in the TABLE 1. Microsatellite loci scored in the F 2 hybrids of SM/J and LG/J. The interval length in Haldane cm following the locus and the sample size (n) are given. NA indicates that the recombination between loci approached 50%. Interval Interval Locus length n Locus length n DIMit DIOMit DIMit DlOMit DIMit DlOMitlO DIMitll DlOMitI4 473 DIMitI DllMit DIMitI7 515 DllMit D2Miti NA 520 DllMitI D2MitI DllMitI D2Mil DllMil D2Mit DI2Mit D3Mit D12Mit D3Mit DI2Mit D3Mit D12MiI D3MitI DI2Nds2 470 D3Mit DI3Miti D4Mil D13Mit D4MitI D13Mit D4Mit DI4Ndsi D4MitI DI4Mit D4Mit D14Mit7 505 D5Mit DI5MitI D5Mit6I DI5Mit D5Mil DI5Mit D5Mit DI5Mil D5Mit DI6Mit D5Mil DI6Mil5 518 D6Miti D17Mit D6Mit D6Nds D17Mi D6MitI5 508 DI7Mit D7Mit2I D18Mit D7Ndsi D18Mit D7MitI DI8Mit8 508 D7Mil DI9Mil D7Nds4 523 DI9MitI D8Mit DI9Mit2 467 D8Mit D9Mit D9Mit D9Mit D9MitI9 511 F 2 mice themselves derived from the MAPMAKER 3.0b program (Lander et al. 1987; Lincoln et al. I992a). These positions also are shown as a genetic map in Figure 1. The 76 loci defined a total of about 1500 cm, including 55 intervals with an average interval length of 27.5 cm. It should be noted that this distance of 1500 cm represents the total between the markers used here and is not strictly comparable to the total length of the mouse genome estimated in other studies from wide crosses (Dietrich et al. 1996). Further details regarding the mapping procedures used in this study can be found in Routman and Cheverud (unpubl.). Left and right sides of the mandible in each F 2 mouse were separated at the mandibular symphysis, placed under a Wild microscope, and scanned into a Mac computer with the use of Adobe Photoshop. Five points around the periphery of each mandible (Fig. 2) were recorded in millimeters in x,y space with the NIH program IMAGE. Euclidean distances

3 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY DlMil3 DlMit20 tnuur DIMitl1 DIMil14 D2Mitl D2Mill7 D2Mil28 D2Mit22 D3Mit54 D3Mit3 D3Mit22 D3Mitl2 D4Mit2 D4Mill7 D4Mil45 D4Mitl6 D4Mitl3 D5Mit47 D5Mit61 D5Mil6 D5Mit26 D5Mit32 D6Mitl D6Mit9 D6Nds5 D6Mill5 D7Mit21 D7Ndsl D7Mitl7 D7Mit9 D7Nds4 DBMit8 DBMit56 D9Mit2 D9Mit4 D9Mit8 D9Mitl9 DlOMit2 DlOMit20 DIOMitlO DlOMitl4 DlMitl7 D3Mit32 D5Mit DllMil62 Dl2Mit37 D14Ndsl D13Mill DI5Mil13 Dl7Mit46 Dl8Mitl2 Dl9Mitl6 Dl6Mit2 Dl2Mit2 Dl8Mitl7 D19Mit14 Dl7Mitl6 Dl5Mit5 DllMil64 Dl2Mit5 D14Mit5 Dl6Mit5 DllMit15 Dl2Mit6 Dl3Mit9 Dl5Mit2 Dl7Mit39 Dl4Mit7 Dl8Mit8 DllMitl4 Dl2Nds2 Dl9Mit2 D15Mit42 DllMit48 FIG. 1. Dl3Mit35 Relative positions of microsatellite markers scored in F 2 mice from an original cross of LGIJ with SMIJ. I25eM calculated between each pair of points resulted in the creation of 10 interlandmark distances on both left and right sides. referred to as mandible characters Mi-MIO (Fig. 2). These five points were chosen because they proved to be highly repeatable (see below) in preliminary measurement trials. and Ramu. Coronoid proce 1 Condylar proce 5 Angular proce FIG. 2. Outline of a mouse mandible showing the five landmark points that were digitized. MI = I to 2; M2 = I to 3; M3 = I to 4; M4 = I to 5; M5 = 2 to 3; M6 = 2 to 4; M7 = 2 to 5; M8 = 3 to 4; M9 = 3 to 5; MID = 4 to 5. precision of measurement is a very important consideration in any asymmetry study (see Palmer 1994). Each mandible was measured three times so that three separate estimates of the 10 distances were available for both left and right sides of the mandibles in each mouse. Statistical Analysis Right minus left differences for each of the three estimates of the 10 mandible characters in all F 2 mice first were plotted and several outliers (amounting to about 1/7 of I% of the total values) eliminated according to criteria given in Sokal and Rohlf (1995). An assessment of the significance of DA and FA for each of the 10 mandible characters then was obtained from a mixed model, two-way analysis of variance. In this model, "individuals" is a random factor (a - 1 df where a = the number of mice) that assesses variation in size or shape among individual mice, "sides" (l df) is a fixed factor that assesses DA, the individuals X sides interaction (a - I df) assesses nondirectional asymmetry (typically FA). and the error assesses variation in replicate measurements (Leamy 1984; Palmer 1994). In these analyses, sex effects were taken out with the use of sex as a covariate, and mean squares for sides were tested over the individuals X sides

4 960 LARRY J. LEAMY ET AL. interaction, whereas mean squares for the interaction were tested over the error (replicate measurement) mean squares. In determining significance, all probabilities generated from F-tests in these analyses were assessed via the sequential Bonferroni procedure (Rice 1989). These analyses also were used to obtain estimates of the precision of the replicate measurements. Variance components were calculated for the individuals, interaction, and error sources of variation, and once completed, the magnitude of the error variance relative to that for the interaction (FA) variance, provided a measure of measurement error (see Palmer 1994). After this preliminary assessment of DA, FA, and the precision of measurement, all analyses made use of the mean of the three repeat measurements for each mandible character. It was useful first to obtain the mean of the two sides for each character so that QTL results for these characters could be compared with those for their asymmetries. Means of the left and right sides, (R + L)I2, therefore were calculated for each of the 10 mandible characters, averaged over all repeats, and then sex-adjusted via linear regression. Basic statistics, including correlations, also were calculated for these characters to provide some description of their variation and covariation. Right minus left side differences (R - L) next were calculated for each of the 10 characters, averaged over repeat measurements, and sex-adjusted via regression as before. The effect offour different covariates (litter size, parity, dam, and experimental blocks; see Cheverud et at. 1996) on these differences also was tested, but none reached statistical significance when evaluated by sequential Bonferroni tests (Rice 1989), and thus no adjustments were necessary. If the mean of these signed differences significantly differed from zero (using t-tests and the sequential Bonferroni procedure to evaluate significance), then DA was assumed to be present (Van Valen 1962; Leamy 1984). Even if significant DA was not detectable for any given character, however, signed differences for that character were used to assess DA in the QTL analysis since different alleles of a QTL could act to produce DA in opposite directions (right side larger than left side and vice versa) that could cancel each other and produce a mean difference of zero. Variation in the signed differences for each of the mandible characters also was assessed by the calculation of skewness and kurtosis statistics to discover if it was normally distributed, as expected if this variation represented classical FA (Van Valen 1962; Palmer 1994), and/or whether there was any evidence of antisymmetry. Antisymmetry usually is suggested by a platykurtotic distribution that is detected by a significant, negative kurtosis statistic (Palmer and Strobeck 1992). To assess fluctuating asymmetry, it was necessary to construct a measure for each character that would adequately reflect the variation rather than the mean (as for DA) of right minus left differences. The unsigned or absolute differences of the right minus left sides were used for this purpose, since they are unbiased estimators of the standard deviation of the differences (Kendall and Stuart 1951; Palmer 1994). Foreach character, the mean of the right minus left differences was subtracted from right minus left differences in all mice to correct for DA, and then the absolute values of these differences, IR - LI, were used to assess FA. Statistically correcting for DA prior to estimating FA is a common practice (Soule 1967; Leamy 1984) that effectively sets the mean of the signed distribution of differences to zero as is expected if the distribution represents FA. Palmer (1994) has argued that such a correction is statistically valid for any characters exhibiting DA, but does not eliminate potential genetical variation for DA affecting this asymmetry, and thus yields characters that may contain unknown mixtures of DA and FA variances. However, the measure of FA used here (unsigned differences between sides) effectively assesses the variability of right minus left differences about a mean, and it would seem to make little difference whether this mean is zero or significantly different from zero (Hutchison and Cheverud 1995). Nonetheless, it should be borne in mind that "FA" as described throughout this paper represents DA-corrected FA. Fortunately, it was possible to calculate correlations between DA and DA-corrected FA-values for each of the mandible characters to discover whether they are phenotypically related, and to compare QTL results for them as well to see whether their genetic bases are similar. Once estimates of DA (signed differences of sides) and FA (unsigned differences of sides after correction for DA) were calculated for each of the 10 mandible characters, it was appropriate to test whether they significantly scaled with a measure of overall size of the mice. Palmer (1994) has explained how scaling effects can sometimes be a problem in asymmetry studies, especially if the magnitude of asymmetry depends on the mean character size itself and the mean size varies among samples (in this case, genotypes of QTLs). Regression coefficients of DA- and FA-values on the mean of the two sides, (R + L)I2, therefore were calculated for each of the 10 characters and tested for significance using the sequential Bonferroni procedure (Rice 1989) to detect any scaling effects. Significant associations of the mean of two sides with the signed difference of these sides, however, may be produced from differences in the variances of the two sides and may not necessarily be informative. For this reason, DA- and FA-values also were regressed on 70-day body weight to discover whether these asymmetries were related to this other, perhaps more appropriate, measure of body size. Since the asymmetries for the mandibular dimensions all were derived from 10 interlandmark distances closely related to each other, it was appropriate to assess the covariation among all DA-values and among all FA-values. All pairwise correlations for the DA-values, and for the FA-values, therefore were calculated and tested for significance again using the sequential Bonferroni procedure (Rice 1989). A principal components analysis (Harman 1967) also was conducted on these correlations for the DA-values and for the FA-values to further analyze covariation in these characters. Once principal components were constructed, component scores also were calculated for each individual and subjected to the same QTL analyses as the means and differences of the 10 characters themselves. QTL Analyses A search for QTLs affecting the mean of the sides, and the signed (DA) and unsigned differences between sides (FA),

5 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY 961 for each of the 10 mandible characters was accomplished with the use of the MAPMAKERlQTL 1.1b program (Paterson et al. 1988; Lander and Botstein 1989; Lincoln et al. 1992b). This program uses a maximum-likelihood model to solve for additive and dominance genotypic values and the percentage of effect for putative QTLs in every 2-cM interval between flanking (molecular) markers. It also calculates a LOD score for each interval, a score that represents a ratio of the 10glO likelihood that a QTL exists to the 10glO likelihood that it does not exist in that interval. Thus LOD scores are highest where the existence of a QTL is most probable and therefore were used to indicate the probability of QTLs being present. With the large number of LOD scores calculated for so many chromsomes and characters, multiple comparisons considerations dictated that the level of statistical significance for any single score needed to be adjusted. Adjustments previously were made in the body weight study using these same mice (Cheverud et al. 1996) on the basis of the distribution of LOD scores obtained in QTL analyses run on 500 samples of random normally distributed traits (N[O, I]) obtained from simulations. Thus for each of the 19 chromosomes analyzed, those LOD scores obtained less than 5% and I% of the time, respectively, were used as the critical values for the 5% and I% significance levels (see Cheverud et al. 1996). The 5% critical values ranged from (chromosome 16) to (chromosome 5), whereas the I% critical values varied between (chromosome 17) and (chromosome 5). These same critical values were used for the LOD scores generated from the mandibular characters as well, so that if the LOD score for any character equaled or exceeded the critical value for that particular chromosome, the null hypothesis of no QTL effect was rejected. For all chromosomes, a single QTL model that included both additive and dominance genotypic effects first was fit to the data. If statistically significant results were obtained according to the explanation above, the patterns of LOD scores and additive/dominance effects were examined to determine whether a second QTL might be present on the chromosome. Typical patterns that suggested two QTLs were either abrupt changes in the sign of additive/dominance effects or biomodal distributions of LOD scores. If a second QTL seemed likely for any character and chromosome, a two-qtl model was employed. Significance for such two-qtl models was indicated when there was a statistically significant improvement in fit over the one-qtl model. In addition, for any QTLs found to be significant for the DA and FA characters, an additive model was tested for significance and also subtracted from the full model to determine significance of dominance effects. This was done to assess the relative importance of additive and dominance effects in both types of asymmetry. The model embodied in the MAPMAKERlQTL 1.1b program described above is most appropriately applied to normally distributed quantitative data such as would be expected for the means of the sides and signed differences between sides for each of the 10 mandible characters. Although this program was applied to the unsigned differences between sides (FA characters) as well, such values typically are not normally distributed (see Palmer 1994). In addition to this model, therefore, a nonparametric approach provided by the MAPMAKERlQTL 1.9 program (Kruglyak and Lander 1995) also was used for these FA characters. Although this program does not estimate additive and dominance genotypic values and percentages of variation, it does produce a Xw-statistic that was used in place of LOD scores to test for significance of QTLs affecting any of the 10 FA characters. The critical values for all Xw-values were determined by converting the 5% and I% critical LOD scores for each chromosome (see above) to Xw-values using the formula given by Kruglyak and Lander (1995). These Xw-values were used for significance testing only for one-qtl models since this nonparametric approach has not yet been extended to include two QTL models. In interpreting the overall results of the parametric and nonparametric mapping runs, conclusions about the presence or absence of QTLs affecting DA (or FA) in the 10 mandible characters were based on the total number of QTLs expected to be significant by chance alone. Since the individual significance of QTLs was based on the 5% and I% critical cutpoints derived as already explained for each of the 19 chromosomes, the total number of significant QTLs expected by chance alone at the 5% level was assumed to be 10 characters x 19 chromosomes x 0.05 = 9.5. At the I% level, 10 x 19 x 0.01 = 1.9 significant QTLs were expected by chance alone. Thus, if the number of QTLs significantly affecting (P < 0.05) DA or FA in the 10 mandible characters exceeded 9 or 10 (or exceeded 2 if significant at the 1% level), this was more than expected by chance alone and it was concluded that some of these QTLs were genuine. These probability arguments apply only if the 10 (DA or FA) characters are all independent. Because this could not be assumed, however, resort was made to the results of QTL runs on the component scores generated in the PCA analyses of the DA and FA values. These components, four of which were generated from the DA analyses and five from the FA analyses (see below), are independent (Harman 1967). Using the same logic as above, therefore, the number of QTLs expected by chance alone to significantly affect the principal components of the DA values would be 3.8 (4 components x 19 chromosomes x 0.05) at the 5% level and 0.76 (4 components X 19 chromosomes X 0.0 I) at the I% level. For the FA analyses, the comparable numbers would be 4.75 (5%) and 0.95 (1%). RESULTS Basic Statistics The results of the two-way analysis of variance of repeated mandible measurements are given in Table 2. Degrees of freedom for all sources of variation except sides were variable, since the 10 characters differed some in their final sample sizes. The percentage contributions to the total variance for both the individuals X sides interaction and the error variance components also are given so that precision of measurement can be assessed. As may be seen, differences among individual mice are highly significant for all mandible characters, and differences of sides are significant as well for eight of the 10 characters. Thus significant DA is detectable in all characters except M8 and MID. Significant FA is in-

6 962 LARRY J. LEAMY ET AL. TABLE 2. The analysis of variance (mean squares and components of variance x 10 4 ) of the 10 mandible characters. Percentage contributions for the interaction (nondirectional asymmetry) and error (replicate measurement variation) sources of variation for all mandible characters also are given. ** = p < Trait Individual (I) Sides (S) df MS ur.s rye df MS rye Ml ** ** ** M ** ** ** M ** ** ** M ** 19,451.3** ** M ** ** ** M ** 81,502.9** ** M ** ** ** M ** ** M ** ** ** MIO ** ** I x S Error dicated for all 10 characters by their highly significant interaction mean squares. and the percentage contribution of FA to the total variation is sizable. ranging from about 8% (M9) to 24% (M5) and averaging 16.1%. By contrast. measurement error. assessed by the percentage contribution of the error variance. averages only 2.7% of the total variation across all 10 characters. Put another way, measurement error contributes on average 2.7/(16.1) = 16.8% of the withinindividual, nondirectional variation. Table 3 gives basic statistics for the mean of the sides and for the signed and unsigned differences between sides for each of the 10 mandible characters. Sample sizes are somewhat variable, but most are near or greater than 500. The average size of the characters (mean of both sides) ranges from slightly over 3 mm (M6) to almost 12 mm (M9), with standard deviations averaging about Coefficients of variation (not shown in Table 3) for these 10 characters average 3.35, suggesting that the mandible characters exhibit a fairly low level of overall variation. Correlations between each pair of characters (also not shown in Table 3) range from to and all are significantly different from zero. The means of the right minus left (signed) differences between sides (Table 3) are negative in sign for all 10 characters, indicating that the left side is larger than the right. All means except those for M8 and M 10 are significantly different from zero, confirming that these two characters exhibit "pure" FA whereas the other eight characters exhibit significant DA. Expressed as a percentage of the mean of the two sides, DA is prominent for M6 (3.3%), M3 (2.2%), M2 (2.1 %), and M5 (1.6% ), but is less so for M 1 (1.1 %), M4 (0.8%). and especially M9 (0.3%) and M7 (0.2%). Skewness and kurtosis statistics also are given in Table 3 for the 10 signed differences, and none reached significance in the sequential Bonferroni tests. Thus we may conclude that right minus left (signed) differences are normally distributed for all 10 characters. Regressions of the signed differences between sides on the mean of the sides (Table 3) were significant for four of the 10 characters, but coefficients of determination (,.2) for these four cases were very low ( ). Further, regressions of the signed differences on another measure of body size, weight at 70 days, were not significant for any of the 10 mandible characters and thus no corrections for scaling were made for these signed differences. Means of the unsigned differences between sides (Table 3), used as measures of FA, all reach statistical significance. Regressions of these values on the mean of the two sides (and on 70-day body weight) were not significant for any of the 10 characters, suggesting no correction needed to be made for scaling in these characters. Correlations of the signed and unsigned differences between sides for each pair of the 10 mandibular characters are given in Table 4. For the signed differences (DA-values), correlations range from to +0.77, averaging Of the 45 total correlations for these DA-values, 26 are sig- TABLE 3. Basic statistics for the mean of the sides and for the signed and unsigned differences of the sides for the 10 mandible characters. Regression of differences of the sides on the mean of the sides also is given. * = P < 0.05; ** = P < " Mean of sides Signed differences Unsigneddifferences Mean SD Mean Skew Kurt. Regression Mean Regression MI ± ** ± ± 0.004** ± M ± ** ± ± 0.004** ± M ± ** ± ± 0.004** 0.00 ± 0.Q15 M ± ** ± ± 0.004** ± M ± ** ± 0.034** ± 0.003** 0.05 ± M ± ** ± ± 0.002** ± M ± ** ± 0.019* ± 0.003** ± M ± ± * ± 0.003** 0.00 ± M ± ** ± ± 0.004** 0.01 ± MI ± ± 0.027** ± 0.004** 0.03 ± 0.016

7 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY 963 TABLE 4. Correlations of signed (below diagonal) and unsigned (above diagonal) differences between left and right sides for each pair of the 10 mandibular characters. '" = p < 0.05; """ = p < MI M2 M3 M4 M5 M6 M7 M8 M9 MID Ml 0.55""" 0.42""" M2 0.77""" 0.31 "'''' """ """ M3 0.68""" 0.62""" """ M4-0.15'" -0.26""" """ M """ """ 0.33"'''' 0.07 M6-0.17""" """ M7 0.15* "'''' -0.16'" 0.16'" """ 0.31 """ M """ -0.25""" """ 0.46""" """ 0.19""" M """ """ 0.58""" """ 0.46""" 0.32""" MI '" 0.45""" "'''' 0.57""" -0.44""" 0.51 """ nificantly different from zero. For the unsigned differences (FA-values), the range for the correlations is somewhat less, -O.II to , and the mean is Nonetheless, 15 of these 45 total correlations also reach statistical significance. So overall there is much evidence of significant, though relatively weak, covariation among the DA characters and among the FA characters. Principal components analysis results also demonstrated this integration for both DA and FA, four components accounting for over 84% of the total variation in DA and five components accounting for over 74% of the total variation in the FA characters. Spearman (nonparametric) correlations between DA and DA-corrected FA-values for each of the 10 characters also were calculated as described earlier, the values varying from to Using the sequential Bonferonni procedure to evaluate significance, none of these values were even close to significance (P > 0.05). Therefore DA and (DA-corrected) FA in each of the mandible characters appear to be independent measures. Interval Mapping Although the thrust of this study was to search for QTLs affecting DA and FA in the mandible characters, interval mapping runs were done for the mean of the two sides for each of these characters to provide a frame of reference for the asymmetry analyses and to discover whether the same QTLs affected both the mean of the sides and differences of the sides. The results of these analyses for the mean of the sides are summarized in the appendix, where the locations of potential QTLs (those locations with significant LaD scores) for one or more of the characters are listed. Locations are given in terms of intervals from the proximal flanking marker(s), where these intervals were defined by clusters of significant LaD scores for the various characters. It is possible that multiple QTLs affecting different mandible characters might be represented in some of these intervals, but they would have to be fairly close together on the chromosome since the maximum interval range (see Appendix) is 22 cm. As may be seen, there are 34 different intervals where at least one QTL affecting the mandible characters probably resides. All 19 autosomes contain putative QTLs for one or more of the 10 mandible characters, and the number of such QTLs affecting these characters varies from five (M4) to 15 (M9). There are also 16 instances where there are two QTLs at different locations on the same chromosome that affect the same mandible character. For example, there are two QTLs on chromosome I that both affect M3, M5, M9, and MIO. Although not shown in the appendix, each of these QTLs contributes from 1.6% to 18.3% (averaging 4.32%) of the total variation in the characters. In general, therefore, QTLs for the mandible characters are plentiful and are scattered throughout the genome, and there is variation in the number affecting each of the 10 different characters. Table 5 provides descriptive data for all putative QTLs (those whose LaD scores reached significance at the 5% or 1% level) affecting DA in each of the 10 mandible characters. Six QTLs reach significance at the 1% level, and this is more than the 1.9 expected by chance alone. Locations for these QTLs are provided by the number of cm past the proximal flanking marker in Table 5 and are depicted in Figure 3. As may be seen, 12 QTLs at specific locations on seven of the 19 chromosomes are identified as affecting DA in various mandible characters. Chromosome 3 contains two QTLs (at clearly different locations) that both affect DA in M I. In addition, three QTLs affect more than one mandible character: for example, the QTL located 34 cm from DJ 3Mit9 significantly affects DA in M7, M9, and MIO. Only three of these (QTL on chromosome 13 affecting DA in M 10 and QTLs on chromosome 15 affecting DA in M3 and M4) appear to be roughly in the same location as the QTLs for the means of the sides themselves for these specific characters (see appendix). Other QTLs, however, are in or near the intervals for the mean of the sides for other characters; for example, the QTL at 34 cm past DJ3Mit9 on chromosome 13 affecting DA in M7 is precisely in the same location as a QTL affecting the mean of the sides for both M8 and M10. Still other QTLs affecting DA do not appear to be the same as those affecting the mean of the sides for any of the mandible characters. On average, these QTLs (Table 5) contribute 2.8% of the total variance in DA for each of the characters, a percentage somewhat less than that of 4.3% for the average contribution of QTLs to the mean of the sides of the mandible characters themselves. The QTLs for DA in the mandible characters also have additive genotypic values whose absolute average is 0.023, nearly identical to the average of for the absolute values of the dominance genotypic values. Additive genotypic values are significant for 15 of the 16 total cases whereas dominance genotypic values are significant in eight cases although there is more power to detect significance in

8 964 LARRY J. LEAMY ET AL. TABLE 5. Descriptive data for all DA characters (DA 1 = DA in M 1, etc.) with significant LOD scores in the QTL analysis. a = additive genotypic value. d = dominance genotypic value. % = % of total variation explained. * = p < 0.05; ** = p < Chromo Marker em Trait LOD '7c a d 3 D3Mit54 4 DAI 3.32** * * 3 D3Mit12 70 DAI * * 5 D5Mit6 0 DA9 2.74* ** IO DlOMit2 12 DA6 2.19* * * DA8 3.70** ** * IO DlOMit2 30 DA9 2.92** ** D12Mit2 12 DA6 3.26** ** D13Mitl 50 DA5 2.60** ** * 13 D13Mit9 34 DA7 2.16* ** DA9 1.89* * DAIO 2.21* * 0.030* 15 D15Mit5 0 DA3 2.26* ** -0.Q17 DAIO 2.02* * D15Mit5 14 DM 2.19* ** D15Mit42 26 DA8 2.55** * 0.025* 18 D18Mit17 44 DAIO 1.88* ** the tests for additivity than in those for dominance (Falconer 1989). Of the 16 total additive genotypic values, 13 are negative in sign, which indicates that the Small-strain alleles generally tend to produce greater DA than alleles in the Large strain. DA in this experiment was assessed as right minus left side differences (where a mean difference of zero would indicate no DA), so greater DA here means greater negative right minus left differences. Although not shown here because presentation of the detailed mapping information seems more appropriate for the DAl DA6,8 DA9 FA6 DA9 FA3 DAl FA FA8 FAlO DA6 FAlO FA7 DA5 FA4 DA3,lO DA4 FA5 DAlO FA3 FA9 125eM DA8 DA7,9,lO FIG. 3. Relative positions of QTLs significant for directional asymmetry (DA) and fluctuating asymmetry (FA) in the IO mandibular characters.

9 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY 965 TABLE 6. Descriptive data for all FA characters (FA6 = FA in M6, etc.) with significant parametric LaD scores or nonparametric X w values in the QTL analysis. a = additive genotypic value, d = dominance genotypic value. % = % of total variance explained. * = P < 0.05; ** = p < Chromo Marker em Trail LOn x. iff a d 4 D4MitJ6 20 FA6 2.14* 3.29* * 0.011* 5 D5Mit32 10 FA6 2.47* 3.48* ** D7Mit9 0 FA3 2.86** 3.45* ** 11 Dl1Mit62 24 FA8 2.88** ** 12 DJ2Mit37 10 FA ** * DJ2Mit * 13 DJ3MitJ 10 FA * * 15 DJ5MitJ3 0 FA4 2.07* 3.20* ** 15 DJ5Mit2 0 FA5 1.82* 3.46** ** DJ9MitJ6 0 FA3 1.77* 2.84* J * 19 DJ9MitJ4 38 FA9 1.82* ** individual DA characters, interval mapping was conducted as previously described for the first four principal components assessing DA in each of the mandible characters. Results of these runs showed QTLs on chromosomes 3, 5, 10, and 15 affecting these DA components. Three of the four QTLs reached significance at the I% level, and this is considerably greater than the roughly one component (0.72) expected to reach significance at this level by chance alone. Table 6 provides descriptive data for all putative QTLs significantly affecting DA-corrected FA in each of the 10 mandible characters. The number of QTLs with significant (P < 0.05) LOD scores is 10, including two on chromosome 12 affecting FA in M 10. Of the eight QTLs that could be tested with the non parametric approach described earlier, six also yield significant Xw-values although the two that do not (QTLs at 24 cm past DIIMit62 and at 38 cm past D19Mit14) narrowly miss significance (critical Xw-values for chromosome II = 3.11 and for chromosome 19 = 2.82). Further, an additional QTL on chromosome 13 (at 10 cm past D13Mitl) affecting FA in M3 had a significant Xw-value (but not LOD score). Thus the parametric and nonparametric approachs yield reasonably compatible results that suggest that as many as II or as few as seven QTLs affect FA in the mandible characters. This total number of QTLs is less than the 16 found for DA, as hypothesized. and also is much closer to the 9.5 expected by chance alone at the 5% level. Only three QTLs significantly affected (P < 0.05) pea components derived from the FA characters, less than the 4.75 expected by chance alone (again at the 5% level). The QTLs significantly affecting FA appear entirely different from those previously found affecting DA in these mandible characters. For example, five QTLs affect FA in the five characters showing the greatest amounts of DA (M6, M3, M2, M5, and M I; see Table 3) whereas the remaining five characters with least amounts of DA (including M8 and MIO, which show no significant DA) are affected by six QTLs. This random pattern of ranking suggests that the DAcorrected FA measures are truly different than those for DA alone and have a separate genetic basis. As further evidence of this, the locations of the QTLs for FA (Table 6) do not coincide with those for DA (see Fig. 3) in any case and in fact are within the QTLs intervals defined for the mean of the sides for the specific characters involved only for the two QTLs on chromosome 12 affecting FA in MIO. Like those for DA. however, several of these QTLs affecting FA are similar in location to those affecting the mean of the sides for other characters (consult Appendix). The average percentage of variation accounted for by the QTLs is 3.1 %, similar to that for those QTLs affecting DA, but again less than that for the QTLs affecting the mean of the sides of the mandible characters. Dominance genotypic values for the FA characters vary in sign (six negative, five positive), but the mean of their absolute values (0.021) is significantly higher (P < 0.0I) than that for additive genotypic values (mean = 0.008). Further, nine of the dominance values, but only three of the additive genotypic values, reach significance. Given that dominance is harder to detect than additivity in these models, this clearly suggests that dominance is important in the action of these QTLs influencing FA. DISCUSSION Directional and Fluctuating Asymmetry The basic objective of this study was to search for QTLs affecting asymmetry, and the mandibular characters measured in the F 2 mice appeared to be well suited for this purpose. Precision of measurement was quite good, so it seems fair to assume that the use of the means of each of the triplymeasured distances provided reasonably precise estimates of these characters on both left and right sides of the mandibles and their differences (asymmetries). Also, the signed differences between sides for all characters were well behaved, showing no evidence of skewness or kurtosis that would indicate anti symmetry, or of any scaling with overall body weight. DA was significant for eight of the 10 mandible characters, but based on the phenotypic and genetic independence for the DA- and FA-values as already detailed, it seems reasonable to believe that the measures of FA in each of these eight characters were free of any effects of DA. The precision of measurement no doubt contributed to the levels of integration seen among the DA-values and the FAvalues. Thus the average correlation among DA-values of (mean of absolute values = +0.26) found here matches that found for the mean of the two sides of nine mandibular characters in random-bred mice that were measured only once (Leamy 1993), and is well above that of the mean of absolute correlations of calculated among DA values in 10 os-

10 966 LARRY J. LEAMY ET AL. teometric characters in inbred and hybrid house mice (Leamy 1984). The anatomical proximity and/or near colinearity of the mandible dimensions no doubt contributes to this integration as well, and the highest correlations (see Table 4) do seem to be ascribable to "neighborhood effects" (see Leamy 1984). Leamy (1993) also found persistent DA among eight of nine mandible characters in random-bred house mice, with left sides generally being larger than right sides in most of these characters. There also was a surprising degree of integration among the FA values for all 10 characters since a number of the 45 total correlations were significantly different from zero even using the sequential Bonferonni procedure. The average correlation of was higher than that of calculated from FA in mandible dimensions in the random-bred population already mentioned (Leamy 1993). In addition, as was the case for DA, the first principal component extracted from these FA intercorrelations appeared to be a general one that described overall FA. These findings suggest that there may exist an individual asymmetry parameter, or lap (see Leamy 1993) that somehow is acting to produce concordance of FA-values among these different characters in each individual. laps generally have not been found in asymmetry studies (see Leamy 1993; Palmer 1994), but presumably the large sample size used here, the triple measuring of the mandibles, and the anatomical similarity of the dimensions all have acted to bring about this level of integration. On the other hand, there is a very high matrix correlation of the pairwise correlations ofda- and FA-values (r = +0.80), so perhaps some of this apparent integration of FA-values is in fact due to general directional asymmetry affecting these mandible dimensions. In any event, FA is normally viewed as an attribute of the sample rather than the individual, and any interpretation of these subtle asymmetries in individuals probably needs to be made with some caution (Palmer 1994). QTLs for Directional Asymmetry As hypothesized, there seems little doubt that this study identified a significant number of QTLs for DA in the mandible dimensions. QTLs with highly significant (P < 0.01) LaD scores were found on chromosomes 3, 10 (two loci), 12, 13, and 15 (see Table 5). Even if the two sites on chromosome 10 are considered to represent the same QTL, this still means there are four QTLs discovered for DA when only 1.9 are expected by chance alone. Perhaps more persuasive is the fact that three QTLs had significant (P < 0.01) LaD scores for the principal components, where less than 1 (0.76) was expected by chance. As in any interval mapping study, some of these putative QTLs may have been produced by chance alone and be spurious; if so, they cannot be separated from real QTLs affecting DA. Nonetheless, it seems safe to conclude that the overwhelming majority of the QTLs identified as significant are real and are specifically influencing DA in these characters. A genetical basis for DA long has been hypothesized (see Palmer and Strobeck 1992), but as far as is known, this is the first study to explicitly locate such QTLs for DA. The genetical basis discovered here for DA in the mandible characters, however, is extremely weak at best. The average percentage of the total variation of DA contributed by each QTL is nearly 3%, but there are so few QTLs affecting DA that their cumulative effect ranges from 0% (DA in M2) to only 9.5% (DA in M9). The total additive and nonadditive genetical variance, or broad-sense heritability (Falconer 1989) of DA in these characters, in fact, averages only about 4.4%. Although extremely low, this level of genetic variation is very close to the broad-sense heritability estimates of 0% to 11% (average about 3%) calculated by Leamy (1984) for DA in 10 osteometric characters in inbred and hybrid house mice. If these results prove to be at all general, they suggest that broad-sense heritability estimates of DA should be so low as to be nondistinguishable from zero in all but the most robust designs. It will be recalled that it was primarily alleles from the Small strain that produced increased DA (greater negative right minus left differences) for most of the mandible characters. There was no necessary a priori reason to suspect that the action of alleles at any QTLs affecting DA would be in this direction, nor is there any evidence that this is a scaling effect. Thus regressions of signed differences on the mean of the sides were significant only for four of the 10 characters (and two were positive, two negative in sign), and there was no association of the signed differences with body weight. Although some of the QTLs identified as affecting DA acted additively, others exhibited a significant level of dominance. The sign of the dominance genotypic value varied, however, suggesting that heterozygotes of different QTLs produced either increased or decreased DA levels (compared to that of the mean of the homozygotes) in these mandible characters. It was instructive to discover that several QTLs significantly affected signed differences between sides for both M8 and MlO, in spite of the fact that neither character exhibited significant overall DA. What this suggests is that different alleles at these loci are acting to produce either positive or negative differences between sides that cancel each other to produce a mean difference of zero. To pursue this further, means for DA in both of these characters were calculated for the homozygous (L/L = Large; SIS = Small) and heterozygous (LIS) genotypes of the molecular marker closest to each of the five QTLs significantly affecting DA in these characters (see Table 5). These means, as well as the results of an analysis of variance with Tukey's unplanned comparisons among the three groups, are shown in Table 7. As may be seen, genotypic differences were significant in all five instances, confirming the significant interval mapping results for all five QTLs. For four of these QTLs, the SIS homozygotes produce negative right minus left differences whereas L/L homozygotes produce positive (or trivial negative) right minus left differences, and thus tend to cancel each other as hypothesized. For the QTL nearest D15Mit5, the reverse pattern is true. The amount of DA produced is significantly different from zero for four of the homozygotes but for only one of the heterozygotes. Unplanned comparisons show that the differences between Large and Small homozygous genotypes are significant in four of the five instances. If there exist two alleles at a locus that act additively and also have roughly equal but opposite effects on the direction of the differences between sides (i.e., the side bias parameter of Palmer et al. 1994), then DA could be generated if one

11 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY 967 TABLE 7. Means and sample sizes (in parentheses) for DA in M8 (DA8) and in MIO (DAIO) for each of the three genotypes (LIL = Large, SIS = Small, SIL = heterozygote) of the molecular marker closest to the QTLs significantly affecting DA in these traits. Results of an analysis of variance (P = probability) and Tukey's unplanned comparisons between the three groups also are given. * = P < 0.05; ** = P < Means Marker Trait SIS SIL LlL P Tukey's test DIOMit2 DA (125) ** (242) * (123) LIL-SIS* LIL-SIL* D15Mit42 DA * (121) (264) (114) LIL-SIS* SIS-SIL* D13Mit35 DAIO * (119) (221) (140) LIL-SIS* SIS-SIL* D15Mit5 DA * (113) -0.Ql5 (264) (116) SIS-SIL* D18Mit8 DAIO (121) (241) (121) LIL-SIS* allele is more frequent than the other (especially if it is fixed). In the F 2 mice here, frequencies of alleles at each of the segregating loci were approximately equal and thus both M8 and MlO exhibited no apparent overall DA. But by using the means (and standard deviations) of signed differences in each homozygote as well as a total sample size of 500, it can be shown that there would be significant DA in all five cases if the Small allele were fixed and in three of the five cases if the Large allele were fixed. Many other models are possible, including those that include dominance or overdominance and interactions (epistasis) between several loci, although the particular model discussed here probably is not overly unrealistic given the trends shown in Table 7. These results suggest that there can be genetic effects on DA even in bilateral characters that exhibit the classical FA distribution in which the mean of the signed differences between sides is zero. It was interesting that the QTLs identified as affecting DA in a specific mandible character such as M1 often were in locations close to those for QTLs affecting the mean of the sides not for the specific character itself but for other characters (i.e., M2, M3, etc.). In addition, however, these QTL sites often matched those of some of the QTLs discovered by Cheverud et al. (unpubi.) for 21 different mandible dimensions in these same F 2 mice. For example, the QTL 0 cm from D5Mit6 on chromosome 5 affecting DA in M9 (distance from base of incisor to tip of angular process; see Fig. 2) is identical in location to one affecting coronoid base length in the mandible (trait 11 of Cheverud et al., unpubi.). Therefore it is possible that this QTL identified by Cheverud et al. (unpubi.) as affecting a different, and smaller, region in the mandible may in fact also be causing DA in the longer distance of character M9. Other explanations are possible, but these QTLs for DA must in some way be differentially influencing growth, and thus size, on each side of the mandible. To say these QTLs affect certain mandible dimensions, however, is still to beg the question of the actual nature of these genes. Although this study was not designed to answer this sort of question, some inferences about potential candidate genes for these QTLs are possible from a study of map positions of genes given in the Mouse Genome Database (1995). A search for such genes at or near positions where QTLs affecting DA were found (see Table 5) reveals several possibilities. On chromosome 15, for example, the thyrotropin releasing hormone receptor (Trhr) locus is very near that for the QTL on chromosome 15 affecting DA in M3 and MlO; and the platelet derived growth factor, endothelial cell (Ptgfec) locus is near that for the QTL affecting DA in M8. Similarly, on chromosome 13 is a growth-arrest-specific-l (Gas}) locus that is very near that for a QTL affecting DA in M7, M9, and MlO. Whether the QTLs discovered here are truly the same as these known genes obviously is purely speculative, but it is reasonable to believe that a genetic basis for DA might be found at loci reponsible for products such as growth factors and hormone receptors. QTLs for Fluctuating Asymmetry Although there seemed to be ample evidence for QTLs affecting DA, this was less so for QTLs affecting FA, as hypothesized. The number of QTLs identified as significantly affecting FA was at most II, not much different from the 9.5 expected by chance (5% level) alone. There were three QTLs with LOD scores significant at the 1% level, slightly more than the 1.9 expected by chance, but the Xw-values for only one QTL reached significance at this level in the nonparametric approach. Further, the number of significant QTLs for the five principal component characters was only 3, and this is less than the 0.05 X 5 X 19 = 4.75 expected by chance alone. Thus, these 11 QTLs may well represent genuine loci influencing FA, but they cannot necessarily be distinguished from those expected by chance alone. Clearly, therefore, the evidence for a genetical basis for FA is less than that found for DA in these mandible characters. This conclusion fits well with the theoretical expectations of many investigators that there should be little or no genetical variability for FA (see Palmer 1994), making it a particularly useful measure of developmental stability in various populations (Zakharov 1989, 1992; Parsons 1990; Graham 1992). It has been suggested, however, that dominance and epistatic interactions of genes throughout the genome are important in producing FA (see Livshits and Smouse 1994). In this regard it is interesting that the QTLs for FA were fundamentally different from those for DA in that they overwhelmingly exhibited dominance. Dominance has been implicated in numerous previous studies comparing FA between inbred and hybrid individuals (Leamy 1984; Palmer and Strobeck 1986; Livshits and Smouse 1994), and it is appears to be indicated for FA in the mandible characters here as well. It is reasonable to think that most or all of the QTLs for FA discovered here playa role in establishing the level of developmental stability attained in the F 2 mice. Waddington (1957) certainly envisioned such genes, but with rare excep-

12 968 LARRY J. LEAMY ET AL. TABLE 8. Means of the means. (R + L)/2. and differences, (R L). of the two sides for the 10 mandible characters in F 1 mice. The sides x individuals interaction components (CTfxs X 10 4 ) also are given for the F) and F 2 generation and compared in individual F-tests. * = p < ** = p < " Mean ITT. s F-sla- (R + L)/2 R - L F, F, tisuc MI ** M ** J.l2 M ** M M M ** J.l9 M M M * MIO ** tions (see Davies et al. 1996). it has been difficult to isolate them or to know how they function. Resort to the Mouse Genome Database (1995) suggests the possibility that candidate genes for at least some of these QTLs may be those that govern the production of hormones and/or hormone receptors. For example. the QTL on chromosome 15 affecting FA in M4 maps very close to the growth hormone (Gh) locus and the QTL on chromosome 11 affecting FA in M8 is close in position to the growth hormone receptor (Ghr) locus. Growth hormone affects skeletal growth through chondrocyte differentiation and proliferation (Barton et al. 1989). so both of these loci could well be involved in mandible growth and resultant asymmetry. Once again such possibilities must remain speculative. but at the minimum they do provide potential insights into the mechanisms responsible for developmental perturbations. Finally. it seems appropriate to ask how optimal this F2 population. originating from a cross of the Large and Small inbred strains. was for detecting QTLs for FA. FA levels do not always significantly differ between various inbred strains and their F I hybrid progeny (see Leamy 1992). and where so. it would not be surprising to discover few or no genes for FA in the F2 progeny produced from crossing these hybrids. Although too few original Large and Small mice were available to obtain adequate estimates of FA in the mandible characters. it was possible to estimate FA in the F, generation so that it could be compared to that already described for the F2 generation. For this purpose. therefore. 44 individual F) mice were triply measured and FA for each ofthe 10 mandible characters was calculated. as before. from the interaction component of variance obtained in two-way analyses of variance (see Table 8). Comparison ofthese FA measures between the F) and F2 generation (via F-tests) showed no significant differences (P > 0.05) for any of the 10 characters. suggesting that there is little or no genetic variability for FA in these characters in this population of mice. It would be most interesting, therefore, to repeat this sort of study using inbred strains known to have a level of FA significantly higher than that in their hybrid progeny. ACKNOWLEDGMENTS We thank S. Beyene, M. Butler, E. Cheverud, D. Irschick, and N. Vasey for help with laboratory work; G. Conroy for the use of digitizing equipment; S. Jacobs for computer assistance; S. Clark for help in preparing the figures; J. Graham for comments on an original draft of this paper; R. Palmer and G. Clarke for stimulating discussions of asymmetry; and two anonymous reviewers for useful revision comments. This research was supported by National Science Foundation grants BSR and DEB LITERATURE CITED BARTON. D. E. B. E. FOELLMER. W. I. WOOD. AND U. FRANCKE Chromosome mapping of the growth hormone receptor gene in man and mouse. Cytogenet. Cell Genet. 50: CHAI. C. 1956a. Analysis of quantitative inheritance of body size in mice. I. Hybridization and maternal influence. Genetics 41: b. Analysis of quantitative inheritance of body size in mice. II. Gene action and segregation. Genetics 41: CHEVERUD, J. M., D. FALK. C. HILDEBOLT. A. J. MOORE. R. C. HELKAMP. AND M. VANNIER Heritability and association of cortical petalias in rhesus macaques imocaca mulatta). Brain Behav. Evo!. 35: CHEVERUD. J. M., E. J. ROUTMAN, E A. M. DUARTE. B. V. SWIN DEREN. K. COTHRAN. AND C. PEREL Quantitative trait loci for murine growth. Genetics 142: CLARKE, G. M The genetic basis of developmental stability. I. Relationships between stability. heterozygosity and genomic coadaptation. Pp in T. A. Markow. ed. Developmental instability: its origins and evolutionary implications. Kluwer Academic Publishers, Dordrecht. DAVIES. A. G., A. Y. GAME, Z. CHEN. T. J. WILLIAMS. S. GOODALL. J. L. YEN. J. A. McKENZIE. AND P. BATTERHAM Scalloped wings is the Lucilia cuprina Notch homologue and a candidate for the Modifier of fitness and asymmetry of diazinon resistance. Genetics 143: DIETRICH. W.. H. KATZ, S. LINCOLN. H.-S. SHIN, J. FRIEDMAN. N. DRACOPOLI. AND E. S. LANDER A genetic map of the mouse suitable for typing intraspecific crosses. Genetics 131: DIETRICH, W. E. J. MILLER. R. STEEN, M. MERCHANT. D. DAMRON BOLES, Z. HUSAIN. R. DREDGE, M. DALY. K. INGALLS. T. O CONNOR. C. EVANS. M. DEANGELIS. D. LEVISON, L. KRUG LYAK. N. GOODMAN. N. COPELAND, N. JENKINS. T. HAWKINS. L. STEIN. D. PAGE. AND E. LANDER A comprehensive genetic map of the mouse genome. Nature 380: FALCONER, D. S Introduction to quantitative genetics. Longman Press, New York. GOODALE, H Progress report on possibilities in progeny test breeding. Science 94: GRAHAM, J. H Genomic coadaptation and developmental stability in hybrid zones. Acta. Zoo!. Fennica 191: HARMAN. H. H Modern factor analysis. Univ. of Chicago Press. Chicago. HUTCHISON, D. W. AND J. M. CHEVERUD Fluctuating asymmetry in tamarin (Saquinus) cranial morphology: intra- and interspecific comparisons between taxa with varying levels of genetic heterozygosity. J. Hered. 86: KENDALL, M. G. AND A. STUART The advanced theory of statistics. Hafner, London. KRUGLYAK. L., AND E. S. LANDER A nonparametric approach for mapping quantitative trait loci. Genetics 139: LANDER, E. S., AND D. BOTSTEIN Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps. Genetics 121: LANDER. E. S. P. GREEN. J. ABRAHAMSON, A. BARLOW. M. DALEY. S. LINCOLN AND L. NEWBURG MAPMAKER: an interactive computer package for constructing primary genetic linkage maps of experimental and natural populations. Genomics I: LEAMY, L Morphometric studies in inbred and hybrid house

13 QUANTITATIVE TRAIT LOCI FOR ASYMMETRY 969 mice. V. Directional and fluctuating asymmetry. Am. Nat. 123: Directional selection and developmental stability: evidence from fluctuating asymmetry of dental characters in mice. Heredity 57: Morphometric studies in inbred and hybrid house mice. VII. Heterosis in fluctuating asymmetry at different ages. Acta Zoo I. Fennica 191:1 I I-I Morphological integration of fluctuating asymmetry in the mouse mandible. Genetica 89: Genetic analysis of fluctuating asymmetry for skeletal characters in mice. J. Hered. 88: LINCOLN, S., M. DALY, AND E. LANDER. 1992a. Constructing genetic maps with MAPMAKERJEXP 3.0. Whitehead Institute technical report, 3d ed., Cambridge, MA b. Mapping genes controlling quantitative traits with MAPMAKERlQTL 1.1. Whitehead Institute technical report, 3d ed., Cambridge, MA. LIVSHITS, G., AND P. E. SMOUSE Relationship between fluctuating asymmetry, morphological modality and heterozygosity in an elderly Israeli population. Pp in T. A. Markow, ed. Developmental instability: its origins and evolutionary implications. Kluwer Academic Publishers, Dordrecht. MACARTHUR, J Genetics of body size and related characters. I. Selection of small and large races of the laboratory mouse. Am. Nat. 78: MCGRATH, J. w., J. M. CHEVERUD, AND J. E. BUIKSTRA Genetic correlations between sides and heritability of asymmetry for nonmetric traits in rhesus macaques on Cayo Santiago. Am. J. Phys. Anthropol. 64: McKENZIE, J. A., AND G. M. CLARKE Diazinon resistance, fluctuating asymmetry and fitness in the Australian sheep blowfly, Luci/ia cuprina. Genetics 120:2 I MOUSE GENOME DATABASE (MGD) Mouse genome informatics project. Jackson Laboratory, Bar Harbor, Maine. World Wide Web (URL: PALMER, A. R Fluctuating asymmetry analyses: a primer. Pp. 335 in T. A. Markow, ed. Developmental instability: its origins and evolutionary implications. Kluwer Academic Publishers, Dordrecht. PALMER, A. R., AND C. STROBECK Fluctuating asymmetry: measurement, analysis, patterns. Ann. Rev. Ecol. Syst. 17: Fluctuating asymmetry as a measure of developmental stability: implications of non-normal distributions and power of statistical tests. Acta Zool. Fenn. 191: PALMER, A. R., C. STROBECK, AND A. K. CHIPPINDALE Bilateral variation and the evolutionary origin of macroscopic asymmetries. Pp in T. A. Markow, ed. Developmental instability: its origins and evolutionary implications. Kluwer Academic Publishers, Dordrecht. PARSONS, P. A Fluctuating asymmetry: an epigenetic measure of stress. BioI. Rev. 65: PATERSON, A. E. LANDER, J. HEWITT, S. PETERSON, S. LINCOLN, AND S. TANKSLEY Resolution of quantitative traits into Mendelian factors by using a complete linkage map of restriction length polymorphisms. Nature 335: RICE, W. R Analyzing tables of statistical tests. Evolution 43: ROUTMAN, E., AND J. M. CHEVERUD A rapid method of scoring simple sequence repeat polymorphisms with agarose gel electrophoresis. Mammal. Genome 5: Polymorphism for PCR-analyzed microsatellites: data for two additional inbred mouse strains and the utility of agarose gel eletrophoresis. Mammal. Genome 6: SOKAL, R. R., AND J. F. ROHLF Biometry. 3d ed. Freeman, San Francisco, CA. SOULE, M. E Phenetics of natural populations. II. Asymmetry and evolution in a lizard. Am. Nat. 101: THODAY, J. M Homeostasis in a selection experiment. Heredity 12: VAN VALEN, L A study of fluctuating asymmetry. Evolution 16: WADDINGTON, C. H The strategy of the genes. MacMillan, New York. ZAKHAROV, V. M Future prospects for population phenogenetics. SOY. Sci. Rev. F. Physiol Gen. BioI. 4: Population phenogenetics: analysis of developmental stability in natural populations. Acta Zool. Fenn. 191: Appearance, fixation and stabilisation of environmentally induced phenotypic changes as a microevolutionary event. Pp in T. A. Markow, ed. Developmental instability: its origins and evolutionary implications. Kluwer Academic Publishers, Dordrecht. Corresponding Editor: T. Markow ApPENDIX Locations (interval in cm) of putative QTLs for the mean of the two sides for each of the 10 mandible characters. Chr. Interval Range Characters DJMit20-J M3, M5, M9, M 10 DJMit7-5.J 0 M8 DJMitJ4-JO M2, M3, M5, M8, M9, MI0 2 D2Mit28-O-J M7, M8, M9, MIO 3 D3Mit3-6.O-J2.0 6 M6, M8, M9 3 D3Mit22-0.O-J2.0 6 MI, M2, M3, M7, M8 3 D3MitJ MI 4 D4Mit2-26.O-D4MitJ7-0 4 MI, M2, M3, M5, M8, MI0 5 D5Mit6J M8 6 D6MitJ-0 0 M6 6 D6MitJ-J M 1, M2, M3, M4, M5 6 D6Mit9-JO.O-D6Nds5-J Ml, M2, M3, M4, M5, M7, M9, MIO 7 D7Mit2J-J M4, M7, M9, MIO 7 D7NdsJ -J2.O-D7MitJ M7, M8, M9 8 D8Mit M6, M7, M9, MIO 9 D9Mit4-J2.0 0 M6 10 D1OMit M7, M9, MIO 10 DJOMit20-J4.O-DJOMitJO MI, M2, M3, M6, M7, M8, M9 11 DJ JMit MI, M3 II DJ JMitJ5-8.O-J6.0 8 M5, M6, M8 11 DJ JMitJ4-8.O-J6.0 8 M7, M9, MIO 12 DJ 2Mit37-6-DJ2Mit M5, MIO 12 DJ2Mit2-J8.O-DJ2Mit MI, M8 12 DJ2Mit6-J4.0 0 M6 13 DJ3MitJ-J Ml, M2, M3, M4, M7, M8, M9, MIO 13 DJ3Mit9-J M5, MI0 14 DJ4Mit5-8.O-J Ml, M2, M3, M6, M7, M9, MIO 15 DJ 5Mit5-8.O-J6.0 8 M3, M4, M5 15 DJ5Mit2-1O.0-J8.0 8 Ml, M2 16 DJ6Mit2-J M5, M9 17 DJ7Mit2-J MI, M2, M5, M7, M9, MIO 18 DJ8MitJ2-0.O-DJ8MitJ MI, M6 19 DJ9MitJ Ml, M2 19 DJ9MitJ4-J4.0 0 M5, M8