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1 The Annals of uman Genetics has an archive of material originally published in print format by the Annals of Eugenics ( ). This material is available in specialised libraries and archives. We believe there is a clear academic interest in making this historical material more widely available to a scholarly audience online. These articles have been made available online, by the Annals of uman Genetics, UCL and Blackwell Publishing Ltd strictly for historical and academic reasons. The work of eugenicists was often pervaded by prejudice against racial, ethnic and disabled groups. Publication of this material online is for scholarly research purposes is not an endorsement or promotion of the views expressed in any of these articles or eugenics in general. All articles are published in full, except where necessary to protect individual privacy. We welcome your comments about this archive and its online publication.

2 OMOGAMY AN TE INTECOELATION OF CAPACITY T AITS BY BONSON PICE, P.. TE positive intercorrelation of desirable traits is generally considered to hold to the extent that no two such variates have been shown to correlate negatively in an adequate aampling of individuals, while low positive correlations are regularly reported. Largely in explanation of the relatively high correlations observed throughout desirable capacity traits, Prof. Spearman insists that there exist g and other major variates. Certain opponents of this view have long since pointed out that such an explanation is not readily reconciled with the particulate nature of inheritance. The great body of contemporary experimentation on intercorrelation problems, and the controversies over the generality or specificity of traits so revealed, nevertheless evidence small regard for genetical considerations. It is here suggested that the nature of human homogamy may well account for much observed intercorrelation. Positive correlations are of course positive only in so far as the desirable directions of the variates are generally agreed upon. On the view to be advanced, tunefulness and lightness of foot, for example, should be found positively correlated with each other but negatively correlated with desirable traits ) in general, in a society wherein the counterparts of these two characters were considered enviable. Since the desirable direction of any variate reflects accepted ideas, desired traits is perhaps a better expression. Goodness, as the term will be used below, is thus taken to mean simply a generally desired direction of variation. The discussion will be concerned with the effects of homogamy, and not with sex-associated factors or with selective mating in which some genotypes leave more offspring than others. Uniformity of environment and genetical variation in psychological traits are assumed. Let us consider a population in which good, average, and poor individuals occur as 1 : 2 : 1 in respect to the trait x and also in respect to the trait y. Let us assume that a single gene substitution causes the variation in each of the traits, that the heterozygote is intermediate, i.e. represents average, and that the x and y variates are uncorrelated in the population. Each individual may be considered as of one of the five groups : (1) poor in both traits, (2) poor in one and average in the other, (3) poor in one and good in the other, or average in both, (4) average in one and good in the other, and (5) good in both. The population may be represented as (5) (4) (3) (2) (1) AABB 2AABb 2AaBB asbb AAbb 4AaBb 2Aabb 2aaBb aabb oras

3 ~ BONSON PICE 23 If mating is perfectly homogamous for total goodness in these traits, a (5) individual will mate with another (5) individual, a (4) with another (4), a (3) with some other (3), etc. These matings, their relative frequencies, and the distributions of offspring for four children per mating are given in I of Fig. 1. Correlation between the x and y variates is shown to arise in the offspring population (Fig. 2). The result will be found to be the same when the two pairs of alleles are assumed to be linked as when assumed to be independently segregating. The effective mechanism here is correlation of trait x in individuals of the Mating I. Frequency (See IV below) or : 1. Matings and offspring offspring ' If mating were such that the direct marital correlations were unity: U If mating were such that the cross marital correlations were unity: E IV. The second generation matings from I are of the frequencies given there in italic figures. The offspring are found to be $18: V. If complete dominance is aasumed, there are three intermating classes. The offspring are found to be aa: VI. If three pairs of alleles are used, there are seven intermating classes, and intercorrelations of 0.14 are found in the offspring 2 13

4 24 INTECOELATION OF CAPACITY TAITS mating population with trait y in their mates. This we may refer to as cross homogamy, in order to distinguish it from the ordinary type of marital correlation which is also present and which we may call direct homogamy. Perfect homogamy in respect to the sum of the traits, and perfect equivalence of the traits in mating were of course gratuitous assumptions. It is necessary to assume that the marital correlation in respect to the sum of the traits is higher than the average of the direct marital correlations for the same traits, then cross marital correlation must be A(=s) B 1 B (=Y) E ; i: :p Fin. " 2. Intercorrelations E ri=o E ri=1/2 E j V. Ti= 15/119 VI. ri=1/7 A Fig. 3. Sibling correlations for the population of offspring in I of Pig. 1 A B A+B E (1) (2) (3) (4) r, = 3/ r, = 11.5 r, = 213 present. This may be seen from application of the Spearman-Brown relation for the correlation between the sum of several variates and the sum of another series of the same - variates, to the case of marital correlation: ere n = n' = the number of traits considered; ( n) is the sum of the traits for any individual of the mating population, and ( n') is the sum of the. same traits fsr his mate; Pi is the average intercorrelation of the traits (in either series of mates); and fnrli is the average of all the possible correlations between any of the variates in one

5 BONSON PICE 25 series of individuals and any of the variates in their mates. There are n2 correlations Of the type r,,,, and of these, n are direct marital coefficients (r,), and (n2-n) are cross marital coefficients (re). That is, Fnn, is equal to ni, - + (n- 1) Ic n2 Substituting this in the equation above, reducing, and writing r, for the marital coefficient in respect to the sum of the traits, I,+ (n- 1) Fc r, = ( 1). (n- 1) FJ In a different connection, Conrad* derived a numerically expressed relation equivalent to this. The relation is general for familial correlation of intraclass type. In mating populations of Fig. 1 these values are, I11 IV VI These effects should receive fuller genetical and statistical treatment than the present writer has been able to give them. owever, Wright? has worked out the limiting compositions of the population for certain degrees of assortative mating maintained in respect to a single trait determined by two pairs of alleles lacking dominance. This case is analogous to that for two traits, equivalent so far as homogamy is concerned, and each determined by a single gene substitution. Wright gives equations whereby the final incidences of the genotypes AAbb, AABB, and AABB, which incidences he calls y, z, and x respectively, may be found in terms of m, which corresponds to r,. Since the scatter is symmetrical, the correlation between the two pairs of alleles at equilibrium is determined by these incidences, and may be represented as r( = -Y ~ x+y+z *. S. Conrad, On kin resemblances in physique v. intelligence, J. edw. Psychd. (1931). 22,378. Conrad was concerned with eibling correlation, and chose the following valuea to represent possible data for several intelligence test funct,ions : n=ll, fi=0.o,?,=0.52, f,=0.37. These were shown to effect a sibling correlation of averages (r,=o.eo) higher than the average sibling correlation (?a) of 0-2. The matter turned however on the value assigned to F, and this was not noted. The opposite effect is evident if instead of 0.37 any figure leas than (=F,F,) is used. It is important to note that, for siblings in the offspring population of I of Fig. 1, them values are (see Fig. 3 above) n=2, r,=0.20, rd=o-0, ro=0.2o, r,=0-7. n, therefore, for sibling correlation, an P, higher than Fp, is actually found, the consequent rise in r, over Fd should be &B understandable in terms of the effects of cross marital correlation as in terms of current views of mental organisation. t S. Wright, Systems of mating, Ge7let4ea (1921),, 1.

2 INTECOELATION OF CAPACITY TAITS Wright s values for x, y, and z in terms of m need not be reproduced here ; upon substituting them in this expression, reducing, and solving for m, there is found,

6 2 INTECOELATION OF CAPACITY TAITS Wright s values for x, y, and z in terms of m need not be reproduced here ; upon substituting them in this expression, reducing, and solving for m, there is found, however, 7, + Fc Also, from (1) above, when n= 2, r,=-. l+ri Assuming equivalence of the traits in mating, rd=rc, and m=r,. It thus appeam that at equilibrium the cross or direct marital correlation then holding in respect to two pairs of alleles equals the intercorrelation reached between them. Since this condition is independent of the number of such pairs for which mating may be homogamous, we may place ri = Fa = Fc in (l), obtaining for the equilibrium intercombtion of n pairs of alleles lacking dominance and equivalent in respect to homogamy,... (2). It would seem dif icult to doubt that human homogamy has for long involved cross marital correlation in respect to desired traits, and an important cause of the intercorrelation of such traits is therefore indicated. The process which has been described is of course simply the throwing together or the association of traits which would otherwise be independently distributed in the population. To the extent that there is a common element in various concepts of the integration of personality and of character, it may be said that such expressions concern the predictability of one or several traits of the individual from one or several others, and this implies some degree of association of these traits in a group of individuals. In the present view, groups in differing circumstances should be expected to develop differing ideas concerning desirable traits, and, through corresponding variations in homogamy, eventually to reflect those differences in the integrations of character found in their prominent members. Similarly, intercorrelations should change as generally recognized concepts as to what is desirable are changed by the conditions and needs of the group concerned. Since the effects of cross homogamy are cumulative, it is clear that the lag between changed circumstances and their significant effects on intercorrelations may be a marked one. We should expect however to find differing sets of intercorrelatibns for groups which have long mated under different sets of conditions. The fact that high marital correlations are observed for those capacity traits which intercorrelate highly is here considered to be of more than incidental importance. If it be argued that such marital correlations reflect in part, or are raised by, non-genetic differences between social classes, then the same argument holds for the intercorrelations as obtained, and the presumption of a genetically causal relation between the two kinds of phenomena remains largely unaffected. It would appear likely that large numbers of genetically discrete traits which we have come to regard as comprising general mental capacity and versatility are simply traits for which mating has been crossly homogarnous, and that this is a primary source of their marked intercorrelation and seeming unity.

7 BONSON PICE 27 It appears from (2) above that for a marital coefficient of 0.75 maintained in respect to the sum of forty pairs of alleles determining general intelligence, the average intercorrelation throughout them would approach 0.07 at equilibrium if dominance were absent. Let us assume that the effect of dominance is to diminish this intercorrelation of the pairs to It may be seen from the relation for the correlation of sums or averages that the correlation between two mental functions each determined by twelve different such pairs would be If, say, four out of twenty of these pairs overlapped the tested functions, the correlation r~~+2+~~~+12~~s+lo+ll+~2+~~~+20~ would be These arbitrary values suggest that the structure of intercorrelations may be unlike that assumed or anticipated in contemporary factor analysis methodology. It has here been assumed that the alleles determining capacity traits are not only (i) many in kind and number, but also (ii) intercorrelated through cross homogamy. If (ii) is correct, the obliqueness variant in factor theory-that of allowing that the sought-for variates may be correlated-becomes a necessary line of attack. If (i) is correct, it is of course doubtful whether factor analyses can properly describe capacity functions in terms of a few variates. The Something which, as has been held, must cause the observed intercorrelations, may thus be in large part cross homogamy, and major variates may be much less necessary hypotheses than has been supposed. On the other hand, it is probable that there exist genes having pleiotropic effects in some degree analogous to the roles which have been assigned to so-called general factors. Proponents of major variates have apparently been little concerned with this possibility and the effectiveness of such genes in causing intercorrelations is yet to be explored. In the writer s view however, since solid evidence for either general or specific variates is lacking, the probable multiplicity of genetically discrete but slightly correlated determiners should receive no less emphasis in present-day intercorrelation theory than should the possible singularity of certain as yet hypothetical factors. SUMMAY In this paper it is noted that intercorrelation of otherwise uncorrelated traits arises as a result of cross inarital correlation. It is assumed that human homogamy is more marked in respect to a summation of generally desired traits than in respect to such traits considered singly, and it is noted that cross marital correlation is a consequence of such mating. The observed positive correlations among desirable traits are thus explained as due in major degree to cross homogamy. Probable effects of bionomic and social conditions on intercorrelations are also noted. To the extent that the present account of intercorrelation may be correct, modern efforts to resolve capacity traits into a few uncorrelated variates appear to be without promise of success, since the very importance of such traits will have associated their determiners in the general population. The intercorrelations which g has been presumed to illumine are seen primarily as consequences of the social and therefore marital importance which has attached to the abilities concerned.

Genetic basis of inheritance and variation. Dr. Amjad Mahasneh. Jordan University of Science and Technology

Genetic basis of inheritance and variation Dr. Amjad Mahasneh Jordan University of Science and Technology Segment 1 Hello and welcome everyone. My name is Amjad Mahasneh. I teach molecular biology at Jordan