Author Institution: The Ohio State Universit

Rife, David C.

The Ohio Journal of Science

KnowledgeBank at OSU

SIMPLE MODES OF INHERITANCE AND THESTUDY OF TWINS1D. C. RIFEThe Ohio State UniversityTwins, both monozygotic and dizygotic, are of inestimablevalue in the study of the interaction of heredity and environ-ment in the development of human traits. With the exceptionof mutations which may occur during the life of the individual,intra-pair variations in monozygotic twins are due to factorsother than heredity. Many implications easily follow in theinterpretation of experimental data based on the study oftwins, not all of which are necessarily true. One such implica-tion is that when intra-pair variation in some trait is greaterin dizygotic than in monozygotic twins, such differences are ameasure of the extent to which heredity is responsible for thetrait. While it is true that the differences between the twotypes of twins are due largely to heredity, yet it must be remem-bered that dizygotic twins are as similar in hereditary make-upas brothers and sisters, and thus such comparisons give usonly a partial estimate as to the role played by hereditaryfactors. Comparisons of monozygotic twins with foster sibsor unrelated pairs of individuals reared in orphanages shouldgive a more accurate basis for evaluating the role of heredity.Dizygotic twins and sibs, however, should also be included insuch studies. Members of twin pairs are contemporaries, andthus have more similar environments than sib or random pairswith age discrepancies. Moreover, the prenatal environmentof twins, due to crowding and possible imbalances of fetalblood supply, is different from that of single born individuals.While such conditions would not affect many genetic traits,such as blood types and skin pigmentation, yet it has beendemonstrated that left-handedness and associated traits occurwith greater frequencies in both types of twins than in singleborn individuals. Recent studies of dermatoglyphics (Cum-mins, Leche, and McClure, 1932; Leche, 1933) have broughtxGenetic Studies of Monozygotic Twins, No. VI.281•282 D. c. RIFE Vol. X X X V I I Iout evidence that handedness has a genetic basis. As dizygotictwins and sibs have, on the average, the same degree of geneticsimilarity, comparisons of dizygotic twins with sibs shouldgive us a measure of the part the unusual prenatal environmentof twins plays in bringing about intra-pair differences. Differ-ences between monozygotic twins reared together, minus thedifferences between dizygotic twins and sibs, should give us amuch more accurate estimate of the part played by heredity,than comparisons only of the two types of twins.The erroneous statement is sometimes made (Rosanoff et al.,1937) that although studies of twins are of great value in esti-mating the relative parts played by heredity and environmentin the etiology of various traits, such data tell us absolutelynothing in regard to the mode of inheritance. It has recentlybeen shown (Cotterman, 1937) that intra-pair sib comparisonscan be used in the determination of whether or not a giventrait could be due to single factor inheritance, although notnecessarily indicating which phenotype is dominant. Similarmethods can be employed in the analysis of data obtained fromdizygotic twins, and may also be made to include a single pairof factors with incomplete dominance, sex-linked and sex-influenced factors.A SINGLE PAIR OF FACTORS, WITH AND WITHOUTDOMINANCEFor a single pair of allelomorphs with incomplete dominance,A and a, let us allow p to represent the frequency of gene A,and q the frequency of gene a. Then, in a population whichhas reached quilibrium,p + q = 1Alsop2 + 2pq + q2 = 1p2 = frequency of genotype AA2pq = frequency of genotype Aaq2 = frequency of genotype aaLet us designate individuals of dominant phenotype by D,those of blending phenotype by I, and those of recessive pheno-type by R. Table I shows all the possible types of matings,their frequencies, and also the relative frequencies of the sixpossible dizygotic twin or sib pair combinations.No. 6 THE STUDY OF TWINS 283Totaling, we find the frequencies of the various types ofpairs to be as follows:In an allelomorphic pair where dominance is complete, indi-viduals would necessarily be D or R, and pairs DD, DR andTABLE IRR. The frequency of DD pairs would be the sum of thefrequencies of DD, II, and DI pairs with incomplete dominancewhich equals 3^p(4 + 5p — 6p2 + p3). Similarly, the fre-quency of DR pairs would equal the sum of DR and RI pairswith incomplete dominance, which is 3^(1 — p)2 (4 — p). Thefrequency of RR pairs would be the same for complete as forincomplete dominance, 3^(1 — p)2(2 — p)2.*The writer is indebted to Mr. C. W. Cotterman for aid in the simplification offormulae.MATINGSOFFSPRING284 D. c. RIFE Vol. XXXVIIITABLE IIASINGLE PAIR FACTORS WITH BLENDINGGENEFREQUENCIESNo. 6 THE STUDY OF TWINS 285GENEP.01.05.10.15.20.25.30.35.40.45.50.55.60.65.70.75.80.85.90.95.99FREQUENCIESq99.95.90.85.80.75.70.65.60.55.50.45.40.35.30.25.20.15.10.05.01TABLE IlBCOMPLETE DOMINANCEDD.0101235025.05293906.111025.1731328125.2384.3056640625.374025.4425640625.5104.5766890625.640625.7014390625 ..7584.8108140625.858025.8994140625.9344.9624453125.983025.995687065.9998255025DR.019552995.089121875.15795.208621875.2432.263671875.27195.269871875.2592.241621875.21875.192121875.1632.133371875.10395.076171875.0512.030121875.01395.003621875.000148995RR.9703235025.857937065.731025.6182453125.5184.4306640625.354025.2875640625.2304.1816890625.140625.1064390625.0784.0558140625.038025.0244140625.0144.0074328125.003025.00068906.0000255025Table II shows the expected ratios of the various types ofpairs, for different values of p and q, for both complete andincomplete dominance. It can readily be seen that the amountof information concerning the inheritance of a trait conveyedby obtaining the ratios of the various types of pairs dependsupon the number of pairs studied, and also, to some degree,upon the frequencies of the genes involved. If the frequencyof the recessive gene (where dominance is complete) were .80,the ratio obtained from the various types of pairs is approxi-mately the same as when q has a frequency of .60, but in this286 D. C. RIFE Vol. XXXVIIIinstance the total numbers of the two phenotypes in the popula-tion studied would enable us to determine which gene wasdominant. At a frequency of approximately .70 for q, DDand RR pairs occur with equal frequency, and DR pairs attheir maximum frequency, .27+. We would not, of course,determine which phenotype was dominant. If, in a groupof dizygotic twins or sib pairs, the percentage of DR pairssignificantly exceeds 27%, Variation in the trait cannot bedue solely to inheritance, baled on a single pair of autosomalgenes with complete dominance.In a trait where dominance is incomplete, the situation ismore complex, because there are six instead of three types ofpairs. Consequently, a much larger number of pairs would benecessary to obtain an accurate ratio. There is some com-pensation for this difficulty, in that where six instead of threetypes of pairs are included in the ratio, the precision of our ratiosis likewise greater. If not enough pairs can be collected forsignificant ratios of all six types, pairs may be classed as con-cordant or discordant, the former group being the sum ofDD, II and RR pairs, and the latter group the sum of DI, RIand DR pairs. Where dominance is complete, concordantpairs would of course include DD and RR pairs, and discordantwould still include only DR.There has been considerable data brought together byvarious investigators, giving ratios of concordant to discordantTABLE IIIFrequencies- , - ,.quencies MatingsNo. 6 THE STUDY OF TWINS 287dizygotic twin pairs, in respect to a number of traits. Unfor-tunately, almost without exception, only one type of concordantpair is considered, and moreover, the twins have been selectedfor the trait in question. Thus we have no way of knowing,from such data alone, the frequencies of the various phenotypes.in the population as a whole.SEX-LINKED FACTORSWhen dealing with sex-linked factors, we have nine typesof pairs, depending on sex as well as trait phenotype. Table IIIshows the various types of matings, and the ratios of thevarious types of pairs.Totaling, we find the frequency of each type of combinationto be as follows:DDt? = p3 + % P2q + Hpq2 = 3^P(1 + P)DR d» = p2q + pq2 = p(l - p)RRc? = q3 + % pq2 + 3^P2q = WX - p) (2 - p)DD 9 = p3 + 3 p2q + % pq2 = i^p (3 - p2)DR 9 = pq2 = p(l - p)2RR 9 = q3 •+ 3^pq2 = WX ~ P)2 (2 - p)D D ( ? 9 = p3 + 2p2q + y2 pq2 = ^P ( l + 2p - p2)DR<?9 = p2q + 2pq2 = p(l - p) (2 - p)RR cf 9 = 3^pq2 + q3 = WX - P)2(2 - p)Table IV shows the various ratios for the three types ofpairs for various gene frequencies. It will be noted that thevarying percentages of discordant male pairs form a symmetrical distribution, the highest value being .25 where bothgenes have a frequency of .50. This frequency is, of course,the same as that for random male pairs in the general population.While the fact that nine types of pairs existing in sex-linkedfactors introduces greater complications, there is some com-pensation in that differences in the occurrence in the twosexes would rather easily become apparent, and the only othertype of inheritance likely to show such sexual discrepancieswould be that involving sex-influenced factors.SEX-INFLUENCED FACTORSIn a single factor trait which shows reversal of dominancein the two sexes, we can readily obtain the expected ratios atvarious gene frequencies for both male and female pairs byreference to Table II. Suppose, for example, male pairs fit288 D. C.RIFE Vol. XXXVIIITABLE IVSEX-LINKED FACTORS• 3 1 ^No. 6 THE STUDY OF TWINS 289single factor inheritance with complete dominance, withp at a frequency of .10, and q at a frequency of .90. Ifsex-influenced, female pairs should fit the same mode ofinheritance, but at a value of .90 for p. and .10 for q.TABLE vp.01.05.10.15.20.25.30.35.40.45.50.55.60.6570.75.80.85.90.95.99Q.99.95.90.85.8075.70.65.60.5550.45.40.35.30.25.20.15.10.05.01S E X - I N F L U E N C E D F A C T O R SDD.0194794975.1499296875.151975.1969359375.22562412109375.246975.24606093752416.2366859375.234375.2376859375.2496.2730609375.310975.3662109375.4416.5399359375.744975.8164359375.9606714975DR.019849005.033634375. 10305.263128125.3328.392578125.44205.480878125.5088.525628125.53125.525628125.5088.480878125.44205.392578125.3328.263128125.10305.033634375.019849005cf 9 PAIRSRR.9609714975.8164359375.744975.5399359375.4416.3662109375.310975.2730609375.2496.2376859375.234375.2366859375.2416.2460609375.246975.2412109375.2256. 1969359375. 151975.1499296875.0194794975In unlike-sexed pairs, we find upon examination of Table I,the following ratios:DD = 2p3q + % p2q2 + - p (1 + p)DR = 2p3q + 2pq3 + 4.5p2q2 = p(l - p) (4 + p - p2)RR = + M P2q2 + q4 = - p)2(4 - p2)Table V gives the ratios at various gene frequencies.290 D. C. RIFE Vol. xxxvurIt can readily be seen that where a trait is dependent solelyon heredity, based on a single pair of allelomorphs, the ratioof concordant pairs and discordant pairs may be of value insuggesting the mode of inheritance. Just how precise theinformation may be depends upon the number of pairs investi-gated, and the gene frequencies. If no discordant pairs arefound in identical twins, and if fraternal twins show significantlymore than 27% of discordant pairs, where only two phenotypesare known and where the sex of the pairs does not affect theratios, we can be sure that more than a single pair of genes isinvolved in the expression of the trait in question.TABLE VIMatingsd1 9AO X AAAO X AOAO X 0 0AO X BBAO X BOAO X ABAA X AAAA X AOAA X OOAA X BBAA X BOAA X AB0 0 X AA0 0 X AOOO X 0 0OO X BB0 0 X BOOO X ABBB X AABB X AOBB X 00Frequency.0245. 1225.1575.00175.03325.01050.0049.0245.0315.00035.00665.00210.0315. 1575.2025.00225.04275.0135.00035.00175.00225Proportion ofDiscordant Pairsin Progeny0.375.5.5.75.50000.5.50.500.550.50Proportion ofTotal0.0459375.07675.00875.0264375.005250000.003375.001050.0787500.021375.006750.008750No. 6 THE STUDY OF TWINS 291TABLE VI— [Continued]Matingstf1 9BB X BBBB X BOBB X ABBO X AABO X AOBO X 0 0BO X BBBO X BOBO X ABAB X AAAB X AOAB X 0 0AB X BBAB X BOAB X ABFrequency.000025.000475.00015.00665.03325.04275.000475.009025.00285.00210.01050.0135.00015.00285.0009Proportion ofDiscordant Pairsin Progeny0.5.5.5.75.50.3755.5.5.5.5.5.375Total discordantProportion ofTotal0.0002375.000075.0033750264375.02137500.00336975.001425.00105.00525.00675.000075.001475.0003375.35440725MULTIPLE ALLELOMORPHSWhile it is possible to set up tables for ratios of varioustypes of pairs at given gene frequencies for series of three ormore allelomorphs, similar to those given for single pairs ofallelomorphs, the complications are tremendously increasedand their practical applications in determining modes ofinheritance would not seem to be sufficient to justify theirconstruction. If the frequencies of the various genes andtheir interactions are known, however, such knowledge may beof value in twin diagnosis. Let us consider how the blood groupsmay be of value in this connection.Genes A and B show incomplete dominance in respect toeach other, but both are dominant to gene O. The frequenciesof these genes vary, of course, depending upon race. In NorthAmerican Whites (Snyder, 1927) the relative percentages ofthe blood groups are approximately: A—42, 0—45, B—10,292 D. c. RIFE Vol. XXXVIIIand AB—3. Allowing p to equal the frequency of gene A,q the frequency of gene B, and r that of O, we obtain thefollowing genotypic ratio: AA—.07; AO—.35; BB—.005;BO—.095; 00—.45; and AB—.03. Let us now determinewhat percentage of fraternal twin and sib pairs would beexpected to be discordant in blood group. As shown inTable VI, this can be accomplished by tabulating the fre-quency of all types of matings, and determining what percentageof paired offspring would be discordant. As shown in Table VIwe should find such variation in approximately 35% of fraternaltwins, in North American Whites.Various research workers (Diehl and von Verschuer, 1933;Levit, 1935; Rife, 1934-37) have used blood grouping as con-firmatory evidence of monozygosity, and in a total of several,hundred pairs, assumedly monozygotic twins have nevershown intra-pair variation in blood groups. There is thepossibility, however, that selection for monozygosity mayhave been too rigid, and thus some less similar pairs ofmonozygotic twins classed as dizygotic. In a large groupof twins, separated into classes according to zygosity, we shouldexpect, if selection for monozygosity has not been too rigid,approximately 65% of the dizygotic twins to be of the sameblood group. If the percentage of concordance exceeds thisfigure significantly, we may be justified in assuming thatselection for identity has been too rigid, and that some of theassumedly dizygotic twins are monozygotic.The M and N blood reactions may also be of use in thisconnection. In North American Whites (Wiener, 1934; Hyman,1935) the relative proportions of the three types are MN—50,M—28, and N—22. M and N are a pair of allelomorphslacking dominance. The frequency of gene M is therefore.53 and that of N, .47. Referring to Table Ha, we find thatthe ratio of discordant types (sum of ratios in columns 4, 5and 6) in blending inheritance, with gene frequencies of from.45-.55 to .50-.50 is approximately 40%. As the M and Ngenes and the blood group genes have been shown not to belinked (Wiener, 1932), the proportion of sib and dizygotictwin pairs showing concordance in both traits should approxi-mate .65 X .60 = .39. In a similar manner, more independenttraits whose mode of inheritance and gene frequencies areknown could be added to the formula, thereby increasing itsefficiency.No. 6 THE STUDY OF TWINS 293CONCLUSIONSComparisons of identical with fraternal twins are of primaryimportance in obtaining partial evaluations of the relative rolesplayed by heredity and environment in bringing about variationin human traits. Where simple types of inheritance areinvolved, data obtained from fraternal twins may be of valuein suggesting the exact mode of inheritance. Such data, whilenot affording the most efficient method for determining mannersof inheritance, are valuable by-products of twin studies primarilydesigned with other objectives in mind. In twin diagnosis,data taken from assumedly dizygotic twins concerning theoccurrence of traits, whose manners of inheritance are known,may be of value in determining whether or not selection formonozygosity has been too rigid.REFERENCESCotterman, C. W. 1937. Indication of Unit Factor Inheritance in Data Com-prising but a Single Generation. Ohio Journal Science 37: 127-140.Cummins, H., S. Leche, and K. McClure. 1931. Bimanual Variation in PalmarDermatoglyphics. The American Journal of Anatomy 48: 199-230.Diehl, Karl and O. F. von Verschuer. 1933. Zwillingstuberkulose. GustavFischer, Jena.Hyman, Harriet S. 1935. Genetic Studies of the Agglutinogens M and N. TheJournal of Immunology 29: 223-237.Leche, Stella M. 1915. Handedness and Bimanual Dermatoglyphic Differences.The American Journal of Anatomy 53: 1-51.Levit, S. G. 1936. Proceedings of the Maxim Gorky Medico-Genetical ResearchInstitute. State Publishing House for Biological and Medical Literature,Leningrad.Rife, D. C. 1933. Genetic Studies of Monozygotic Twins. Journal of Heredity24: 339; 1938, ibid. 29: 83-90.Rosanoff, Aaron J., L. M. Handy and Isabel Rosanoff Plesset. 1937. The Etiologyof Mental Deficiency, with Special Reference to Its Occurrence in Twins.Psychological Monographs XLVIII, No. 4.Snyder, L. H. 1929. Blood Grouping in Relation to Clinical and Legal Medicine.The Williams and Wilkens Co., Baltimore.Wiener, A. 1932. Method of Measuring Linkage in Human Genetics, WithSpecial Reference to Blood Groups. Genetics 17: 335-350.. 1934. Blood Groups and Blood Transfusion. Charles C. Thomas Co.,Springfield, 111.

Simple Modes of Inheritance and the Study of Twins

https://kb.osu.edu/bitstream/1811/2971/1/V38N06_281.pdf

Simple Modes of Inheritance and the Study of Twins

Abstract

Similar works

Full text

Available Versions

KnowledgeBank at OSU