A CONTRIBUTION T O THE GENETICS OF MILK GLAND ACTIVITY IN CATTLE BY GERT BONNlER ANIMAL UREEDING INSTITUTE, WIAD, ELDTOM'I'A, SWEDEN I N a study of the composition of milk, based on comparisons between a number of twin pairs, it was found that the percentages of protein and of lactose at fixed levels o / percentages of frrt are chiefly genetically determined (BONNIERand HANSSON,1946) That is to say: in two sets of samples of milk, all of which have equal percentages of fat (or, more correctly, have fat percentages the range of variation of which is only 0,i % ) , the differences between the means of the two sets in protein percentage or in lactose percentage are within the limits of random variation if the two sets are taken from two identical twins, whereas, Irom a statistical point of view, the means of the two sets may be very widely apart it' they are talten froin two unrelated cows The studies in question are based on 2245 samples taken from 29 pairs of twins of which 19 are identical, are fraternal and are uncertain as to the nature of' the twinships Table 1, in which some of the statistical figures are given, is a n excerpt froin Tables and of the article cited Tlie orders of magnitude of the P's are found by coinparing the ratios of the mean square\ in question by ihe error mean square In most of the cases the two twins of a pair had been treated or fed differently but, so far, it has not been possible l o show any certain influencie from this dif Ferential treatment on the differences between protein or lactose percentages :kt fixed percentages of fat Tlie numbrr of genes in crction - - A more searching analysis (still always made by comparisons zuithin groups of fat percentages, the grouping unit of which is 0,i ) of the genetical relationships can, however, be made T h e average mean squares, corresponding to the comparisons between the means of two identical twins, 0,0713 for protein and 0,1523 for lactose, may be said to constitute a measure of the average differcnce an animal would show if it did live two different lives These mean squares have therefore been used as a common base for comparisons between other mean squares by dividing the latter by the former Thus each mean square corresponding to the difference of the means of two twins of each separate twin pair has been divided by the above- 102 GERT BONNIER TABLE , Aiiulysis of vuriuiice of ihe diljerences between percentages of protein and of the differences between percentages of lactose ut fixed fat percentages Degrees Freedom Iktween groups of different fat pcrcen tages A t fixed fat percentages Hetween twin pair means (=between u n re1ate d an im a1s) Cow versus twin sister identical twins unccrtain twins fraternal twins b ' i t h i n cows (error) Total 45 I Protein Lactose ~- Meau P I' 0,ma 4,2830 503 168 45 Mean square 0,4018 0,0713 >0,05 0,iaas 0,0765 >0,06 0,1882 82 0,1920 1401 2144 0,1950 Q 0,001 > oIo5 Appr = 0,oa Appr = , o i iiientioned figures These ratios are given in Table Furthermore, lwin pairs for which this ratio is less than , for proteiii as well as lor lactose, 18 in number (13 identical, fraternal and uncertain), have been selectrd, and the mean squares corresponding to the x 18 = 153 dif'ferences IJelweeri two such twin pair means have I~ec~11 computed As above, these 153 inean squares are divided by O,n7i3 for protein and by O,IYXJ for lactose and the ratios are collocated in two 1:tblr.s (Table for protein and Table €or lactose) Finally, all ratios :ire classified in groups with a grouping unit of 0,s and the distributions ;\re computed for the 19 identical pairs, the fraternal pairs and for the 153 twin pair combinations (Table , Fig 1) Before trying to interpret the tables it inay be well lo explain some o f the figures If we look at Table 3, wc find, for instance, that [ h e ratios are: for p:iirs 9-1 1, 1,387, lor pairs 9-14, , , thus two moderate ratim But the ratio for p:iirs 11-14 is very inuch larger, 11,397 And there are other cases of a inore or less similar kind It may 5rem natural to expect that, if we have three pairs, and if the difference MILE GLAND ACTIVITY IN CATTLE ~ 03 ~ TABLE Ratios between, on the one hand, the mean squures between the two twin means and on the other the average mean square between means of two identical twins ( o m f o r protein and 0.1523 f o r lactose) Ratio No of twin pair For reference to Tables and I n tlie barn 48- 106.107 119-120 12 1-122 205-206 (i Nature of t w inship Identical s > >> 213-214 725-726 818-819 8111 x11 736-737 8O7-8O8 8.iO-8 31 I -7 17 123- 121 20 1-202 2O3-20J 215-21 92 1-922 10 11 12 13 14 15 16 17 18 738 400 0.328 0.180 0.829 1.021 0.389 586 i Lactose 344 405 374 0.147 175 0.600 0.681 0.5 0.41s > 1.293 s 878 1.268 1.2 > 839 899 936 Uncertain I dentical Fraternal 797 229 1.397 603 721 0.823 > * Uncertain Identical 0.8 1.409 1.224 1.449 2.756 1.659 0.9611 610 1153 117-118 906-907 915-916 c4 J7 -758 617 -648 ., 15- 16 "rotein Fraternal u 1.793 637 460 > 2.006 1.060 Uncertain 929 > 1.3 545 1.404 020 1.883 2.658 1.530 380 450 1.229 1.312 104 1.O i s between tlie first a n d the second a s well as that between the second aiid the third is sinall then also the difference between the first and the third ought to be small 'There are two reasons for this not always being the case Suppose first that all three pairs were represented only within one a n d the same group of f a t percentages If the numeric value of the difference between tlie first and the second pair is a and ~ 17 14 15 16 13 12 11 10 Xn Twin I i I I 0,938 , I _ 1,751 2,224 ' G 3,846 2,476 2,346 2,180 4,093 1.005 2.347 2,819 1,541 1,984 - - 3,899 6,247 I 1.822 2,611 1,613 5,418 1,902 6,568 1,158 3,985 3,493 5,525 2,a6 ~ 0,603 2,498 1,370 3,925 3,108 1,397 3,764 0,866 1,435 2,821 0,817 0,920 1,641 1,484 0,386 2,652 2,462 1,815 1,914 4,477 5,669 1,447 1,490 3,403 2,198 0,601 1,009 2,130 2,567 1,ilG 1,878 4,249 1,764 0,820 1,239 1,998 1,835 1,518 2,809 1,354 3,156 1,760 1,601 1,94 I 0,926 0,569 1,472 3,196 4,251 4,555 2,254 4,337 2,281 4,992 2,547 2,718 2,640 0,125 2,340 2,453 I 2,193 2,389 3,527 2,053 1,387 1,724 9,677 5,362 7,469 6,878 9,986 7,280 2,601 3,263 3,l I 4,938 3,161 1,538 1,966 5,783 5,278 2,343 3,047 1,977 1,31I 3,559 1,624 1,848 18 17 _ 4,683 2,8c1 3,746 2,855 2,920 1,700 1,418 i - 16 I 2,802 1,816 2,351 1,149 7,092 6,467 2,599 3,110 3,235 9,525 2,766 2,938 2,944 1,208 2,677 3,207 5,302 0,975 2,548 0,468 2,557 ~ 0,601 2,659 1,328 2,350 1,073 1,471 2,257 4,059 - 10 0,956 - - 2,239 0,847 - i ~ - TABL,E Rutios between, on the one hand, the mean squares of protein differences between two twin pair means and, on the other, the average mean square between means of two identical twins, 0,0713 c 17 1B '4 15 13 11 12 10 NO ~ l I 3,489 I1 1,766 0,699 , ~ 1,269 0,810 1,484 1,785 0,625 1,558 1.677 0,708 0,84i ],lily 0,298 2,770 2,051 1,063 0,651 2,664 0,658 2,288 - 'j 1,616 2,389 0,494 1,091 1,561 2,249 1,245 1.698 0,823 1,3i9 0,5i8 0,681 1,370 1,651 2,157 0,662 0,661 1,311 1,531 0,SZi 1,683 1,121 11 0,951 10 1,091 0,423 1,559 o,i89 2,150 1,188 1,203 0,771 0,998 1,756 1,979 0,636 I 16 1,461 1,82J 3,422 1,237 1,671 3,956 3,438 1,962 1,910 0,91i 1,297 1,672 3,738 0,943 2,833 3,314 , 2,i46 7,089 1,963 1,398 3,766 1,138 1,889 2,022 1,206 5,751 6,201 1,154 4,858 7,610 1,436 1,923 2,762 1,146 1,352 2,285 - 18 1,742 1,356 1,952 0,846 2,260 1,831 4,028 1,827 2,540 1,121 5,421 1,062 3,121 8,i~ 7,331 2,258 2,690 9,184 1,616 1,680 2,396 2,811 1.725 2,089 7,887 2,338 1,186 1,210 3,823 2,219 1,289 - 17 1,284 ' 7,740 1,613 ' 6,969 1.5 2,317 3,127 1,180 2,559 1,555 - 14 1,274 2,173 0,550 1,004 1,222 0,568 1,753 0,749 0,568 1,332 0,620 3,006 - 13 0,911 2,697 12 1,450 , ' i j of lactose differences between two twin pciir mectns and, on the other, the civerage mean square between means of two identical twins, 0,1523 TABLE Ratios between, on the one hand, the mean squares w c: I3 l i w I t & c.cc 13 r tG&ce& N I0 G e3 w - c: 13 - - - t i - = =: c t i "- - w w i "0 "- : I w "- i n e n 0,i e l " 0" 4 jai " -"0 "0 p -0 , -0 , h; p -,1 w - 4 -I e, m L* i.( - N N - "0 "0 w i l w in ,w ,j3 L1) Y,, v 107 MILK GLAND ACTIVITY IN CATTLE -~ ~ between the second and third is b, then the dil'l'erence between the first and the third may be either a - b or a f Suppose the latter to be Ihe case The inenn squares corresponding to the three differences are (1' b2 + O 2+ a h 'rliis means that if two of the figures then p , and in Table or are cr and 3!, the third may be of the order ol' magnitude n p 4-2 vag This explains several of the cases, but not all And, ~ + , se 40 t k 30 a, CT c 20 10 L a 30 20 10 Ratio Fig Graphs correspoiiding to the distributions of the mean square ratios in Table Crosses -= comparisons between identical twins; triangles = comparisons between fraternal twills; dots = comparisons between unrelated animals (= between twin pair means) The curves are fitted by free-hand (Therefore in the case of fraternal twins, with only groups represented, see Table 5, the fitting is very haphazardous.) For lack of space, the curves for unrelated animals are broken at the ratio-value of 108 GERT BONNIER lor inst:mce, not the csaniple given, as we have , : -k ~ 1,472 f 21/1,3x7 X , t z = 4,m, which is very much less than 11,397 The other reason is randoin variation When two pairs are compared, all groups of fat percentages in which both of the pairs are represented will automatically be included in the coinputation of tlie mean square of the pair means' difference But if only one of the pairs (or none) is represented within a certain group of fat peroentages, this group is autoniaticnlly excluded Thus, if the first and the second pairs :ire represented within the group of fat percentages 4,00-4,0!~ but not the Ihird pair, this group contributes to the mean square corresponding to the coinparison bctween the first and the second pair but not to the two reinaining comparisons Likewise, if the second and the third pairs :ire represented within the group of fat percentages 4,1il-4,19 but not the first pair, this group will contribute to the mean square corresponding to the comparison between the second and the third pair but not to the two rtmaining Comparisons Thus, none of these two groups of fat percentages will coiltribute to the mean square corresponding to the comparison between the first and the third pair Looking now at tlie distribution of the ratios (Table , Fig l ) , it is evident that the range ol' their variation is smallest for the intraidentical twin comparisons, somewhat larger for the intra-fraternal twin comparisoiils, and very much larger for the comparisons of twin pair means (i c for the comparisons between unrelated animals) This corresponds of course to the data pnt together in Table But it gives :I more apparent and visual picture of the facts The type of variation in the case of intra-identical twin comparisons must be due only to vxternal (and random) caiises If only one single pair of genes was responsible for the dil'fcrences between unrelated animals, there would be at most three different values round which the corresponding 153 ratios would vary And, likewise, if only very few pairs of genes did act, some peaks ought to be found in the curves of distribution of the 153 ratios Rut this does not appmr to be the case, and thus it seems lair to concludc that several pairs of genes are in action Hence we are probably concerned here with a case of polygenic effect It must be emphasized that the number of genes in action may br still greater, as it is possible that a certain gene difference which is aclive at one level of fat percentage may be inaclive at another level In such a case other gene differences must be active at that new level If the figures of Tables and are compared, it will be found thal large ratio\ in one of the tables not at a11 correspond to large ratios MILK GLAND ACTIVITY IN CATTLE 109 in the other table Grouping the ratios as in Table with a grouping unit of 0,s and computing the correlation of the 153 ratios for protein m d for lactose, a correlation cornefficientof 0,os is found The signification of this is that different - or at least partly different sets of genes are in action when the percentage of protein and the percentage of lactose are determined at a certain level of fat percentage SUMMARY (1) It has been shown in an earlier article that in cow's inilk the percentages of protein and of lactose at fixed levels of fat percentages are chiefly genetically delermined ( ) A comparison of the variation in the percentages of protein a n d of lactose at fixed levels of fat percentages between twin pair mean\ (i e between unrelated aninials) with the variation between the mean5 of two identical twins has led to the conclusion that several genes iniist be in action (3) It is also shown that different sets of genes are responsible for the percentages of protein and lor thc percentages of loctose at fixed levels of fat percentages LITERATURE CITED BONNIER,G and HANSSON,A 1946 Studies on niotiozggous cattle twins VII On thc genetical determination of tlie iiitcrdependency between thc percentages of fat, protein, and lactosc i n tlie inilk - c t a A4gricult~~rz Siiecana ( I n prcss.) ... one of the tables not at a1 1 correspond to large ratios MILK GLAND ACTIVITY IN CATTLE 109 in the other table Grouping the ratios as in Table with a grouping unit of 0,s and computing the correlation... percentages of protein and of lactose at fixed levels of fat percentages are chiefly genetically delermined ( ) A comparison of the variation in the percentages of protein a n d of lactose at fixed... when the percentage of protein and the percentage of lactose are determined at a certain level of fat percentage SUMMARY (1) It has been shown in an earlier article that in cow's inilk the percentages