Ann. Hum. Genet., Lond. (1963), 27, 167 Prwted in Great Britain 157 Pattern of correlations in the skeleton of the growing hand BY DAVID HEWITT Department of Social Medicine, Oxford University As a matter of common observation, people who are large in any one dimension of the skeleton (e.g. stature) tend also to be above average in other dimensions (e.g. span). Because of such correlated variations any analysis which treats body dimensions one at a time is over- simplified and cannot give much insight into the genetic control of size and form. When dimen- sions are considered more than one at a time, some degree of simplification is still a practical necessity, and a number of investigators have attempted to supply this by postulating a hierarchy among the many factors which must influence size. For instance, in the terminology suggested by Wright (1932) one might assume growth in various parts of the body to be under the control of ‘general, group and special size factors’. A crucial difficulty with this three-tier hierarchy is that the composition of the measure-groups, which are to correspond with the group size-factors, normally has to be decided on the basis of empirical data. Consequently, sampling errors (and frequently measurement errors also) will influence not only the estimates obtained but also the definition of the quantities to be estimated. This difficulty arises in Wright’s (1932) method, it underlies the treatment of multiple measurements by factor analysis (e.g. Burt & Banks, 1947 ; Tanner & Burt, 1954), and is seen most clearly in the work of Olson & Miller (1958) who choose an arbitrary level of the sample correlation coefficient to define the presence of ‘bonding ’ between measures. In the present study it was hoped to by-pass this difficulty by concentrating on the skeleton of the hand, chosen as an area of the body in which highly plausible groupings of the measures could be laid down a priori. That is, each of the nineteen short bones of the hand could be regarded as a member of two intersecting groups defined in advance : one consisting of all bones on the same finger, and one consisting of all bones in the same ‘row’ (metacarpals, and proximal, medial or terminal phalanges). The raw material consisted of antero-posterior teleoroentgenograms of the hand and wrist taken in the course of the Oxford Child Health Survey (Acheson,Kemp & Parfit, 1955). Twenty- three measurements were recorded for each film examined: the length of each short bone (excluding the growth cartilage plate and epiphysis), and the maximum breadth of the shaft of each proximal phalanx except that of the thumb. Each measurement was obtained by applying a transparent rule marked in half-millimetre units directly to the negative film on a viewing box. Only one hand was measured on each film, normally the right unless faulty posing made the left preferable. The main series of films related to 198 children all X-rayed within a fortnight of their second birthdays, and comprised 99 pairs of full sibs (27 boy pairs, 29 girl pairs, 43 mixed pairs). For 19 of these pairs (38 children) the same measurements were also obtained from films taken on or near the h t, third, fourth and fifth birthdays, with repeat measurements of the 2-year-old films from which it was estimated that the standard error of measurement of a single bone length was 0.24 mm. Two-year-old films of an additional thirteen unrelated children were also measured (see Part I1 below). Other relevant information available on the Oxford children 11-2
Transcript
Ann. Hum. Genet., Lond. (1963), 27, 167 Prwted in Great Britain
157
Pattern of correlations in the skeleton of the growing hand
BY DAVID HEWITT
Department of Social Medicine, Oxford University
As a matter of common observation, people who are large in any one dimension of the skeleton (e.g. stature) tend also to be above average in other dimensions (e.g. span). Because of such correlated variations any analysis which treats body dimensions one at a time is over- simplified and cannot give much insight into the genetic control of size and form. When dimen- sions are considered more than one at a time, some degree of simplification is still a practical necessity, and a number of investigators have attempted to supply this by postulating a hierarchy among the many factors which must influence size. For instance, in the terminology suggested by Wright (1932) one might assume growth in various parts of the body to be under the control of ‘general, group and special size factors’. A crucial difficulty with this three-tier hierarchy is that the composition of the measure-groups, which are to correspond with the group size-factors, normally has to be decided on the basis of empirical data. Consequently, sampling errors (and frequently measurement errors also) will influence not only the estimates obtained but also the definition of the quantities to be estimated. This difficulty arises in Wright’s (1932) method, it underlies the treatment of multiple measurements by factor analysis (e.g. Burt & Banks, 1947 ; Tanner & Burt, 1954), and is seen most clearly in the work of Olson & Miller (1958) who choose an arbitrary level of the sample correlation coefficient to define the presence of ‘bonding ’ between measures.
In the present study it was hoped to by-pass this difficulty by concentrating on the skeleton of the hand, chosen as an area of the body in which highly plausible groupings of the measures could be laid down a priori. That is, each of the nineteen short bones of the hand could be regarded as a member of two intersecting groups defined in advance : one consisting of all bones on the same finger, and one consisting of all bones in the same ‘row’ (metacarpals, and proximal, medial or terminal phalanges).
The raw material consisted of antero-posterior teleoroentgenograms of the hand and wrist taken in the course of the Oxford Child Health Survey (Acheson, Kemp & Parfit, 1955). Twenty- three measurements were recorded for each film examined: the length of each short bone (excluding the growth cartilage plate and epiphysis), and the maximum breadth of the shaft of each proximal phalanx except that of the thumb. Each measurement was obtained by applying a transparent rule marked in half-millimetre units directly to the negative film on a viewing box. Only one hand was measured on each film, normally the right unless faulty posing made the left preferable. The main series of films related to 198 children all X-rayed within a fortnight of their second birthdays, and comprised 99 pairs of full sibs (27 boy pairs, 29 girl pairs, 43 mixed pairs). For 19 of these pairs (38 children) the same measurements were also obtained from films taken on or near the h t , third, fourth and fifth birthdays, with repeat measurements of the 2-year-old films from which it was estimated that the standard error of measurement of a single bone length was 0.24 mm. Two-year-old films of an additional thirteen unrelated children were also measured (see Part I1 below). Other relevant information available on the Oxford children
11-2
DAVID HEWITT included assessments of skeletal maturity, a variety of external measurements and, in most cases, a record of the parents' heights.
At age 2 there was no important difference between the sexes in respect of bone length. The mean of forty-three brother-sister differences for the aggregate length of nineteen bones was + 2.64 mm., which was only 1.08 times its standard error and only 0.6 yo of the mean aggregate. This small difference has been ignored in the calculation of covariances (see Appendix Table), which are of the intraclass type and computed without any grouping of observations. All the covariances were first computed for the twenty-seven girl pairs alone, but these are not reported separately as their pattern was indistinguishable from that obtained from the pooled data on all ninety-nine sib pairs.
In aggregate breadth of the proximal phalanges there was a more substantial male excess, amounting to 3.3 yo of the girls' mean and highly significant (P < 0.001). No further use was made of the breadth measurements. The following interclass estimates were obtained : 27 boy pairs, + 0.603 ; 29 girl pairs, + 0.437 ; 43 mixed pairs, + 0.439.
Table 1. Diagrammatjc r e ~ r e ~ e n t a ~ i o n of .the metacarpals and phalanges of 198 children showing : (i) reference letter, (ii) mean length (mm.) at age 2 years, (iii) mean increment between ages 1 and 3 years, ( iv) variance (mm.z) at age 2 years
Terminal
Medial
Little d
6.505 I
1.70 0.441 9
D
8.3232
1'1378 1.99
Proximal 148232 3.28 1'0747
9
Metacarpal 21.5328 6-21 2'1212
Ring d
8.0379 1'79 0'4770
9
12.5278 2.91 1.0534
Q
19.2475 4'49
.8
23'5934 6.5 I
2.5070
1'5071
Middle '9
7'7399 1-57
x 0.4563
13'0556 2-91 0.9465 3
4.80 1.4197
"4
26. I 389 7.16
20.13 I3
2'7091
Index d4-
6.8258 I .64 0.3826
B
10.5303 2.38 0.8324
9
18,0783 4'13 1'2703 9
28.0858 7.68 2.9043
Thumb Y
9.6894 I .79 0.5361
Table 1 portrays the hand in diagrammatic form, each cell representing one of the nineteen
(i) the reference letter used in the text to refer to that bone; (ii) the average length in 198 2-year-old children; (iii) the average absolute increment between ages 1 and 3 years in 38 children, and (iv) the variance of 198 measurements at age 2. It may be noted that throughout the hand the average length and the average increment for
a given bone exceeds that of the bone distal to it on the same finger, and that this pattern also holds for the variances, with the single and important exception 97 > V. The longest meta- carpal is on the index finger (g), the longest proximal and medial phalanges are on the middle finger (9 and S), the longest distal phalanx is on the ring finger (8). As would be expected,
bones and containing
Correlations in the skeleton of the growing hand 159 there is a close relationship between absolute increment through the interval 1-3 years and absolute length at 2 years. For the fourteen phalanges this relationship is adequately fitted by the rule that length at age 2 is approximately 4.4 times the 1-3 increment; each metacarpal is between 5 and 6 mm. shorter than this rule would suggest.
PART I. GENERAL CONSIDERATION OF THE BONE LENGTHS OF THE HAND
In most of the following analyses it has been convenient to omit the three bones of the thumb, both to reduce the labour of computation and to avoid the necessity of allocating bone %! to a particular row. (Though always referred to as a metacarpal this bone has its epiphysis at the proximal end, so that its X-ray appearance is that of a phalanx.) An additional advantage of excluding the thumb was that this made the postulated group factors for fingers and rows fully orthogonal. It was proposed to study the variations in length of the remaining sixteen bones in terms of the following model, in which environmental effects are ignored.
The measured length of an individual bone at a particular age can be represented as the sum of five independent components : one being the response to an inherited factor H which affects the whole hand (and possibly the entire skeleton), one the response to a factor F which affects all bones on the same finger, one to a factor R which affects all bones in the same row, one to a factor P affecting the particular bone only, and one representing measurement error. A measure- ment of bone d, expressed as a deviation from the population mean, can therefore be written as (aHH + a,F’ + a,R’ + a,P” + e)
in which the factors H , F, R and P as well as the error term vary about a mean of zero, and the coefficients a are constants for bone A? in the given population. The primes are inserted to identify one out of the four F-factors, one out of the four R factors and one out of the sixteen P factors. It is assumed that the sib correlations in respect of each growth factor have the same true value p (but see Table 5 below for evidence on this point), so that it will be appropriate when using sib data to define the scale of measurement for all these factow as that on which
var ( H ) = var (F) = var (R) = var (P) = (l/p) mm.
On this basis the expected covariance between sibs in respect of bone d will be
E {cov (dd)} = a& + a: + a& +a$ the product and error terms all vanishing. The expressions for expected covariance between sibs in respect of different bones will always involve less than four growth factors. In particular, if the bones are neither on the same finger nor on the same row, only the most general factor H will be involved, e.g. E (COV (dF)} = aIJH or, more conveniently
By appropriate addition and subtraction of the log covariances one may obtain estimates of the sixteen coefficients aH, b,, . . . , r, and hence estimate the contribution made by H to each co- variance. It is then possible to determine the average relative magnitude of the contributions by all four types of factor (see Table 2). In order to obtain values for the contributions by individual F and R factors, it would be necessary to reduce each same-finger and same-row covariance by the estimated contribution from H and then to proceed through a second cycle of calculations based on the reduced log covariances. Finally, the covariance attributable to each
8 {log cov (ds)} = log a H 3. log fH.
160 DAVID HEWITT special factor could be obtained as a residual. For reasons which will appear, neither the second nor the third cycle of estimation was carried out, but least-squares estimates of the sixteen coefficients associated with H were obtained as follows. Among the 136 sib covariances relating to the sixteen bones under study (see Appendix Table) there are seventy-two which involve only the general factor H . Writing (AF), (AG) ... (LR) for log COP (dg), log cov (d3) ... log cov (YB), and a, b, ... r for loga,, logb, ... logr,, we seek to minimize the sum of the 72 terms
((AF) -a - f )2 + ((AG) -a - g)2+ . .. + ((LR) - 1 - r)2.
Differentiating with respect to a, b, ..., r in turn and equating to zero we obtain a set of sixteen simultaneous equations of which the first is
9a + f +- g + h+ k + 1 + m + p + q + r = (AF) + (AG) + (AH) + (AK) + (AL) + (AM) + (AP) + (A&) + (AR)
and the other fifteen can be written down from symmetry. The general solution of these equations is
in which i is the estimated log of the coefficient of H for the ith bone and W , X , Y and Z stand for certain sums of log-covariances, namely
i = (l/lSO) (20W+2X-4Y-Z)
W : those linking the i th bone with the nine bones in other fingers and rows; X : those linking the ith bone’s 3 finger-neighbours with its three row-neighbours; Y : those linking bones which differ in finger and row from the ith bone and from one another
2: the remaining thirty-six log covariances for pairs of bones which are neither on the same
The sixteen estimated coefficients of H obtained in this way are shown in the right-hand
On the basis of these coefficients the proportionate contributions made by H to any sib
a, x e, = 0.3819 x 0.4351 = 0.1662,
(eighteen in all) ;
row nor on the same finger.
column of the Appendix Table.
covariance can be estimated as in the following example:
cov (d8) = 0.2253.
Proportionate contribution of H = 0.1662/0.2253 = 0.7377.
Proportionate contributions of H were computed for all 136 of the sib covariances in the Appendix Table and were found to have the average values shown in Table 2. If it can be assumed that each type of factor makes the same proportionate contribution to the variation in length of each of the sixteen bones, then these averages will estimate the quantities defined in the right-hand column of Table 2 where H , F, R and P stand for the proportionate contributions made by the four types of factor. On this basis the contribution to the total genetic variation is judged to be:
factors affecting the whole hand factors affecting whole fingers factors affecting whole rows factors affecting particular bones
81.7 yo 0.7 yo
13-0 yo 4-6 yo
Though this analysis attributed an unexpectedly large weight to row as against finger factors, the result may be considered reasonable on embryological grounds.
Correlations in the skeleton of the growing hand 161
However, during the preparation of Table 2 a finding emerged which brought the adequacy of the theoretical model into question. According to this model the seventy-two covariances for pairs of bones differing in both finger and row (more precisely their logs) should deviate from the fitted values only as a result of sampling error, so that each should be equally likely to exceed or fall short of its fitted value. In fact the deviations were seen to follow a pattern depending on whether the bones concerned were in adjacent rows (e.g. H and Q) or separated by one or two intermediate rows. Thus, of thirty-six covariances between bones on different fingers and in adjacent rows, twenty-six exceeded their fitted values (the average ratio between observed and fitted values being 1.056), while of the thirty-six covariances between bones on different fingers and non-adjacent rows, only eight exceeded the fitted value (average ratio 0.965). There was also some suggestion of a similar, though much weaker effect when the same seventy-two deviations were classified by adjacency or non:adjacency of the fingers. Hence to make the model fully adequate it would have been necessary to introduce additional group factors intermediate between that for the whole hand and those for the single rows and fingers. Unfortunately, this degree of complication would also render the model virtually useless for the purpose of estiination.
Table 2. Average proportionate contribution made by the general factor H to various classes of sib covariance
No. of Proportionate Theoretical Claw covariances contribution value
Same bone 16 0817 H / ( H + R + F + P ) Same row, 24 0863 H / ( H + R) Same finger, 24 0.991 H / ( H + fl) Different finger, 72 I ‘000 H / H
different finger
different row
different row
In view of this finding it was decided that estimates of the individual coefficients of F and R could have little meaning, so the second and third cycles of computation mentioned above were not completed. Instead it was decided that the best practicable summary of the covariation amongst lengths of the hand bones would be in terms of ro coefficients (Falconer, 1960). For a pair of measures x and y such a coefficient may be defined as
where the subscripts i and j refer to the members of a sib pair. It may be noted that if the measures x and y have the same degree of heritability then ro will have the same ‘true ’ value as the ordinary phenotypic correlation between the two measures in the same individual, but that, unlike the latter, its estimate will not be subject to attenuation by measurement errors.
Table 3 summarizes the 136 available rG coefficients by giving average values of 100r: for sixteen groups of bone-pairs classified by their finger and row relationship. The top left-hand cell of Table 3 refers to the sixteen coefficients which are by definition equal to unity. Reading down each column of the table it will be seen that rG is substantially lower for bones in adjacent rows than for bones in the same row, and lower again for bones separated by an intermediate
162 DAVID HEWITT row than for those in adjacent rows, but that in the fourth line of the table (which summarizes correlations between metacarpals and distal phalanges) there is little or no further fall. Reading along the lines of Table 3 it will be seen that bones on adjacent fingers are almost as highly correlated as bones on the same k g e r (except in the same-row line, where the difference between I00 and 93 may reflect the operation of special factors for particular bones). Separation by one or by two intermediate fingers does, however, involve a fall in r: by about 4 percentage points in each case.
Table 3. Summary of lOOr& among sixteen hand bone lengths. Figures in brackets are the numbers of values of 100rg on which the average i s based. I n the marginal totals marked * the same-bone correlations have been given a weight of eight rather than sixteen to make them more comparable with other marginal totals
Finger r 1
Next Next Same Same Adjacent but one but two Average
Same roo (16) 93 (12) 88 (8) 85 (4) 92 (32)* Adjacent 78 112) 77 (18) 74 (12) 68 16) 75(481 Next but one 59 (8) 61 (12) 56 (8) 5 0 (4) 58 (32) Next but two 59 (4) 57 (6) 57 (4) 5 2 (2) 57 (16) Average 76 (32)* 75 (48) 71 (32) 66 (16)
The pattern of correlations shown in Table 3 implies that bones on the periphery of the region studied should have a lower average degree of integration with the system as a whole-because they are adjacent to only one other row or finger instead of two. This was in part confirmed (see Table 4) inasmuch as the average values of 100rg were lower for the index and little finger than for the two central fingers, and lower for terminal phalanges than for proximal and medial phalanges. However, the average degree of correlation was somewhat higher for metacarpals and for proximal phalanges than might have been expected if the hand were an isolated system. This last finding had a parallel in the estimates (based on 140 of the same 198 children) of the same measure of loo$ between 2-year-old standing height and the aggregate length of each row of bones, namely:
height x metacarpals 55 height x proximal phalanges 55 height x medial phalanges 48 height x terminal phalanges 38
The relatively large degree of ‘autonomy’ in the distal parts of the hand was seen again when the adjacent-row correlations were averaged in sets of sixteen:
metacarpals x proximal phalanges 84 73
medial phalanges x terminal phalanges 69 proximal phalanges x medial phalanges
The cross-covariance used in the numerator of each rCf value can also be used as the numerator of a sib correlation coefficient. The statistic r, = cov (xixj)/cov (xi yJ can be interpreted as an unbiased estimate of the sib correlation in respect of the factor(s) which influence both character x and character y. Altogether 120 ( = 16 x I+) values of r, were obtained, ranging from 0.464
Correlations in the skeleton of the growing hand 163
(for %and A) to 0.746 (for W and 6’)) with an average of 0.609. There was some pattern in the differences among these coefficients (see upper figures in Table 5) inasmuch as
(i) within each finger the terminal phalanx had the highest average value of rs; (ii) the overall average values for the fingers followed a consistent ranking from the little
finger down to the index finger. Table 5 also shows (lower figures) the conventional intraclass estimates of sib correlation
( r = cov (xixj)/var (2 ) ) for each of the nineteen short bones of the hand. These estimates average only 0.500, or one-sixth less than the unbiased estimates. The downward bias in the conventional estimates seems to have been less serious for the proximal and medial phalanges than for the terminal phalanges (where a given measurement error is largest in relation to the true variance), or for the metacarpals (where measurement errors may have been absolutely greater because of the more complicated shape of the silhouette).
Table 4. Average of fifteen values of lOOr& for each of sixteen hand bone lengths Finger
Table 5 . Unbiased (upper Jigure) and conventional (lower Jigure) estimates of sib correlation in respect of factors affecting bone length
Finger
Row Little Ring Middle Index Thumb Average
Terminal 0.662 0.496
Medial 0.628 0.470
Proximal 0.592 0.470
Metacarpal 0.595 0512
Average 0.619 0.487
0.660 0.573 0.574 0’459 0.604 0.552
0.594 0.465 0.608 0.5 I 2
0.644 0.632 0.621 -
0.608 0.578 - 0.597
0.516 0.447 0.536 -
0.502 0.463 -
0.610 0.612 - 0.606 0’559 0’599 0’534 -
0.591 0‘579 0’595
0.607 0.602 - 0.609
-
- 0409 0.485 0453 -
0.497 0’499 0,508 0.500
PART 11. SPECIAL CONSIDERATION OF THE FIFTH MEDIAL PHALANX
Among many heritable anomalies of the hand skeleton possibly the commonest is the flexion deformity of the fifth digit which has variously been termed camptodactyly, streblomicro- dactyly (Byrne, 1959) and clinodactyly (Anderson & Klintworth, 1961 ; Hersh, De Marinis & Stecher, 1953). A regular feature of this deformity is that bone @I is shorter than ‘normal’. Hersh et al. (1953) conclude that the defect is transmitted as an autosomal dominant with slight lack of penetrance, and that it has a prevalence of about 1 in 1000. Their prevalence estimate seems unduly low since this condition is one of the most regular stigmata of mongolism, which
164 DAVID HEWITT alone is commoner than 1 in 1000 births. Clearly any prevalence estimate must be influenced by the degree of flexion considered necessary to establish the diagnosis. The consultant radio- logist who reviewed the Oxford Child Health Survey iilms identified twenty-three out of 669 children as having a ‘crooked fifth digit ’, a prevalence of 3-5 % (Kemp, 1959). Ten of these twenty-three were among the 198 children studied in Part I, measurements of bone lengths for the other thirteen were also obtained from 2-year-old hand films.
The sex ratio in this ‘affected’ group (17 male/6 female) was significantly (P < 0.05) higher than in the survey as a whole, and the proportion of first-born children slightly but not signifi- cantly raised. Hand films were also available for some of the mothers of these children: in several instances these showed conspicuous shortening of the fifth medial phalanx without flexion deformity.
On comparing the hand bone lengths of the twenty-three ‘affected’ with 188 ‘normal’ children it a t once appeared that the ‘affected’ group were shorter not only in bone 98 (by an average of 19 yo), but also in each of the other medial phalanges (by an average of 7 %), and to a Iesser extent in every one of the remaining fifteen short bones of the hand (average of 3 %). Shortening of other bones on the little finger (sl, %,B) was not especially marked (3%). The mean standing height of the ‘affected’ children was fully an inch below the standard for Oxford 2-year-olds (Acheson et aE. 1955), which was clearly a significant difference (P < 0.01) and again amounted to a shortening of about 3 %. The skulls of the ‘affected’ children tended to be shorter in the antero-posterior’diameter (P < 0-05) but not transversely (P > 0.70). Weight, inter- cristal breadth, calf circumference, carpal maturity and I.Q. (measured at age 5) showed no significant differences, but the points score for the maturity of the hand epiphyses (Acheson, 1954) was significantly lower in the ‘affected’ group, and this was not solely due to a low score for the epiphysis of bone 9. Finally, the fathers and mothers of ‘affected’ children were on average shorter but slightly heavier than those of other Oxford children. From these com- parisons it appears that the ‘abnormal’ shortening of bone 9? which underlies this deformity is correlated with shortening in other longitudinal dimensions of the hand and of the skeleton as a whole. (This is also what happens when the condition is due to trisomy, since mongols, besides being generally stunted, tend to have relatively round skulls.)
Reverting now to the original series of ninety-nine sib pairs-that is, to a sample selected without reference to any peculiarity of the little finger-it may be noted from Table 4 that the growth of &? is less well integrated with hand growth generally than is the case with any of the other fifteen bones studied. One way in which such a situation could come about would be through the operation of some unusually selective growth factor which inflated the variation of 9Y without imposing the usual amount of correlated variation on neighbouring bones. It is in fact possible to confirm that the total amount of genetic variation in 9 ’ s length is, in a particular sense, excessive. Fig. 1 shows the relationship between the sib covariance for each of the bones d, &?, . . . , 4P and the corresponding average Iengths in the unselected sample. The point repre- senting A?, marked with a cross, is an obvious outlier. The fitted line has been drawn through the mean points for the longer and shorter nine bones of the remaining eighteen. On comparing the 97 point with the fitted line we may say either
(i) that the sib covariance is about twice ‘too large’ for a bone of 93’s average length; or (ii) that averages about 40 yo ‘too short’ for a bone with the observed amount of genetic
variation. (Note that this 40% is more than twice the, difference between ‘affected’ and
Correlations in the skeleton of the growing hand 165
‘normal’ children, so that (ii) amounts to the assertion that 9’ is too short in the population as a whole, not merely because of the presence of a few abnormal individuals.)
is absolutely as well as relatively larger than that for its proximal neighbour, a situation which does not arise anywhere else in the hand and thus violates the general pattern of relative magnitudes within fingers (see also Table 1).
A detail which favours (i) against (ii) is that the sib covariance for
X
Bone length (rnrn.)
Fig. 1. Relationship between mean length (mm.) of each of nineteen hand bones (horizontal) and corresponding sib covariance (vertical). Plotting of values given in Table 1 and Appendix Table. x refers to bone g.
It would not necessarily follow from (i) that there exists any peculiar factor affecting B- such as segregation of a major gene-to which the other bones are less than usually responsive. It would be equally legitimate to postulate an exaggerated sensitivity of A3 (present throughout the population) to some quite general growth factor. Indeed, the H-coefficient estimated for B in Part I was outstandingly large in relation to the length of this bone, so that if one plots H-coefficients instead of sib covariances in Fig. 1 the appearance is not greatly changed. This idea of exaggerated responsiveness also accords with the results of the analysis presented in Table 6, where mean parental height has been used as the best available index of inherited factors controlling longitudinal dimensions of the skeleton as a whole. In thirteen families the height record was missing for one or both parents; from the remaining 172 children there were distinguished fifty-four whose parents’ mean height equalled or exceeded 69 in. (1753 mm.), and fifty for whom this mean was less than 67 in. (1702 mm.). Stature in the taller group of parents exceeded that in the shorter group by an average of 4.27 in. (108 mm.) or between
166 DAVID HEWITT 6 and 7 %. In Table 6 the upper figures show for each bone the absolute difference between the children of the taller and shorter parents. In only three instances out of a possible fourteen does the tall-short difference for a particular bone exceed that for the bone proximal to it, the largest excess being that for compared with V. The tall-short difference is also considerably greater for L% than for its row-neighbours F, and 8. If it is appropriate to express the tall-short differences as percentages of the average bone length (see lower figures in Table 6) then the response to a putatively ‘general’ size factor is seen to be much greater in 98 than in any other bone.
Table 6. Average absolute difference (mm.) and percentage difference in bone length between jijty-four children of ‘tail’ parents and Jifty children of ‘short’ parents
The present investigation was undertaken and completed without knowledge of the much earlier study by Lewenz & Whiteley (1902) which covered some of the same ground. The raw material for the earlier study (see Pfitzner, 1892-93) differed from the Oxford material in having been obtained post mortem, from a relatively small sample, and from both hands of unrelated, adult subjects. Lewenz & Whiteley retained thumb measurements in their analysis but only considered within-finger and within-row relationships, that is only sixty-four of the 136 bone- pairs dealt with in Part I above. Their values for the intrasubject, phenotypic correlations tend to be considerably lower than the estimates of correlation obtained in the present study, partly, no doubt, because of attenuation by measurement errors. If their coefficients of correlation between the same bone on the right and left hands of the same subject are interpreted as measuring the reliability of Pfitzner’s measurements, then an appropriate correction can be applied and this brings their within-row correlations up to the level of those given in Table 3. Even with this adjustment, however, Lewenz & Whiteley’s within-finger correlations remain smaller than those of the present study. This could mean that row-factors are more important, relative to the general factor, in an adult population than at age 2 years.
Though their analysis was incomplete Lewenz & Whiteley were able to detect the two main features shown by Table 3, namely
( a ) the greater influence of row than of finger factors (‘each bone being on the average more nearly related to the corresponding bone on the next digit than to the adjacent bone on the same digit ’) ;
(b) the more inteme correlations between adjacent than non-adjacent bones, which they termed a ‘rule of neighbourhood’.
Correlutions in the skeleton of the growing hand 167
On account of this latter finding Lewenz & Whiteley characterized the correlations among hand bone lengths as being ‘organic’ rather than ‘homotypic’. A similar rule has been found by Holt (1961) to apply to dermal ridge-counts.
If there are high correlations between the lengths of homologous bones in the hand and foot there would be some basis for interpreting the otherwise incongruous findings concerning bone 3?. It is conceivable that the phenomena described in Part I1 are merely incidental to continuing evolutionary modification of the human foot. Wood Jones (1949) suggests that after the assump- tion of an erect posture some selective advantage may be gained by having only two phalanges on the fifth toe, and Venning (1953) has confirmed that variation in the number of phalanges on this toe is under genetical control. When the medial phalanx is absent from the fifth toe the medial phalanges of the other toes tend to be short; if this and other related morphological variations occur simultaneously a more general shortening of the bones of the foot is found (Venning, 196 1).
One way in which an evolutionary shortening of one bone relative to another could come about is by delay in the commencement of some phase of growth. It is therefore relevant that of all nineteen epiphyses in the hand that of bone 3? is normally the last to begin ossifying (Greulich & Pyle, 1950). It may also be more than a coincidence that the second last in this ossification order is bone Jtr which, according to Table 6, also exhibits the second largest percentage difference between children of short and of tall parents.
SUMMARY
From radiographs of the hand taken at the age of 2 years the lengths of nineteen bones were determined for each member of ninety-nine sib pairs. An attempt was made to account for the variation of these lengths in terms of additive contributions from a general factor, group factors (one for each finger and one for each row) and special factors (one for each bone). The analytic model proved to be inadequate because of relatively high correlation between bones in the same neighbourhood, whether or not they belong to the same finger or row. Terminal phalanges were estimated to have a relatively low degree of integration with the hand as a whole and with stature, but a high degree of sib resemblance. A special study was made of the medial phalanx of the fifth finger, leading to the suggestion that this bone is involved in a common finger deformity because it is hyper-responsive to general growth factors.
The Oxford Child Health Survey is supported by a grant from the Medical Research Council.
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