a contribution to the genetics of milk gland activity in cattle

A CONTRIBUTION T O T H E GENETICS OF BY GERT B O N N l E R ANIMAL UREEDING INSTITUTE, WIAD, ELDTOM'I'A, S W E D E N of samples of milk, all of which have equal percentages of fat or,

A CONTRIBUTION T O T H E GENETICS OF

BY GERT B O N N l E R

ANIMAL UREEDING INSTITUTE, WIAD, ELDTOM'I'A, S W E D E N

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

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 T h e studies in

which 19 are identical, 7 are fraternal and 3 are uncertain as to the nature of' the twinships Table 1, in which some of the statistical

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

influencie from this dif Ferential treatment on the differences between

Tlie numbrr of genes in crction - - A more searching analysis (still

ever, be made T h e average mean squares, corresponding to the com-

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 compa- risons between other mean squares by dividing the latter by the former

GERT BONNIER

102

0,0713 0,0765

Iktween groups of

different fat pcr-

cen tages

tages

Hetween twin pair

u n re1 ate d an im a1 s)

ter

unccrtain twins

b ' i t h i n cows (error)

Total

> 0 , 0 5

>0,06

fat percentages

I

Protein

~-

Degrees 1

Meau Freedom

4 5

503

168

45

82

1401

2144

4,2830

P

Lactose Mean square

0,ma

0,4018

0 , i a a s

0 , 1 8 8 2

0 , 1 9 2 0 0,1950

I'

Q 0,001

> o I o 5

lactose, 18 in number (13 identical, 3 fraternal and 2 uncertain),

have been selectrd, and the mean squares corresponding to the

1 7 x 18

= 153 dif'ferences IJelweeri two such twin pair means have

2

I~ec~11 computed As above, these 153 inean squares are divided by O,n7i3

1:tblr.s (Table 3 for protein and Table 4 €or lactose) Finally, all ratios :ire classified in groups with a grouping unit of 0,s and the distributions

o f the figures If we look at Table 3, wc find, for instance, that [ h e

MILE GLAND ACTIVITY IN CATTLE 1 03

the t w o twin means and on the other the average mean square between

means of t w o identical twins ( 0 o m f o r protein and 0 1523 f o r lactose)

No of twin pair

I n tlie barn

For referen-

ce to Tables

3 and 4

4- 3

8- 9

106.107

119-120

12 1-122

205-206

213-214

725-726

818-819

8111 x11 2

736-737

8O7-8O8

8.iO-8 31

7 I 6 -7 17

123- 121

20 1-202

2O3-20J

21 5-21 0

92 1-922

117-118

906-907

915-916

4 J7 -758

617 - 648 ,

15- 16

c -

1

2

3

1

5 (i

7

8

9

10

11

12

13

14

15

16

17

18

Nature of

t w inship

Identical

.9

s

>

>>

>

s

7

>

Uncertain

Fraternal

>

*

Uncertain Identical

2

Fraternal

u

>

>

Uncertain

Ratio

"rotein i Lactose

0 738

0 400

0 328

0 180

0 829

1 021

0 389

0 586

1 293

0 878

0 839

0 797

1 397

1 409

1 224

1 449

2 756

1 659

0 610

1 793

0 637

2 460

2 006

1 060

0 929

1 344

0 405

0 374

0 147

1 175

0 600

0 681

0 41s

1 268

0 899

0 936

1 229

0 603

0 721

0 823

0 545

1 404

1 020

1 883

2 658

1 530

1 380

1 450

1 229

1 312

2 104

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

TABL,E

I I

3,899 1.005

- 1,541 1,984 2,180 4,093

- 2,819 3,846 2,476 2,346 2.347

- 8 - 2,239 2,257 5,302 9,525 3,985 5,418 6,568

- 9 - 1,073 1,471 3,207 3,235 1,158 1,613 2,611 1.822

- ~

- 1,328 0,956 2,677 3,110 1,149 2,351 1,816 2,802 1,239 2,350 2,659 1,208 2,599 1,418 2,855 2,920 4,683 1,387 0,820

3,559 5,783 3,l

9,986 9,677 5,525 1,724 2,254 1,472 4,249 1,397 3,108 3,925

1,966 3,263 6,878 2,053 3,527 2,389 1,94

0,926 1,878 2,821 1,435 0,866 3,764

- 1,977 1,538 5,278 7,280 2,340 2,718 2,547 1,760 1,601 1,ilG 2,130 1,009 0,601 2,198 0,386

- 3,047 3,161 4,938 7,469 2,640 2,281 4,337 3,156 1,518 2,567 3,403 1,490 1,447 5,669 1,641 1,484

-

- 2,343 2,601 5,362 0,125 4,555 4,251 3,196 1,354 1,835 2,809 4,477 1,914 1,815 2,462 0,817 0,920 2,652

TABLE

0,423 0,662 0,5i8 1,245 0,681

0,658 0,708 2,664 1,063 0,298 1.677

- 2,770 0,651 0,84i 0,625 1,558

0,951 1.698

1,979 1,756

- 3,006 0,620 0,749 1,188 1,753 0,568 1,222 1,004 0,550 2,173 1,274 0,846

1,210 2,317 1,616 1,680 2,690 2,540 1,827 4,028 1,831 1,356 1,742 1,206

3,823 7,887 9,184 7,331 8,i~ 7,610 4,858 1,154 6,201 5,751 7,089 3,314 3,956

- 1,289 2,219 1,186 2,338 1.725 2,089 2,022 1,889

- 2,285 1,352 1,146 2,762 1,923 1,436 2,i46 2,833

1,963 1,910 0,91i 1,671 3,438 1,297 1,962 1,237 1,461 3,422 1,82J

- N I0 -

- - w c: I3 l i w I t & c cc 1 3 w G e3 c: 1

- w w 1 i

w i n e n 0

- N N -

0,i

e l

4

Y , ,

v

MILK GLAND ACTIVITY IN CATTLE

between the second and third is b , then the dil'l'erence between the first

.~ 1 0 7

-~

2

t

20

a,

10

CT

c

L

0

20

10

se

0

Ratio

Fig 1 Graphs correspoiiding to the distributions of the mean square ratios in Table 5 Crosses -= comparisons between identical twins; triangles = comparisons between fraternal twills; dots = comparisons between unrelated animals (= between

fraternal twins, with only 3 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 7

The curves are fitted by free-hand

108 GERT BONNIER

f 21/1,3x7 X 1 , t z = 4,m, which is very much less than 11,397 T h e other reason is randoin variation When two pairs are compared, all

will automatically be included in the coinputation of tlie mean square

autoniaticnlly excluded Thus, if the first and the second pairs :ire

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

the first pair, this group will contribute to the mean square correspond- ing 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

identical 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 1 But it gives

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

lair to concludc that several pairs of genes are in action Hence we a r e probably concerned here with a case of polygenic effect

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

large ratio\ in one of the tables do not at a11 correspond to large ratios

_ _ -

MILK GLAND ACTIVITY IN CATTLE 109

in the other table Grouping the ratios as in Table 5 with a grouping

sets of genes are in action when the percentage of protein and the per-

SUMMARY

(1) It has been shown in a n earlier article that in cow's inilk the

are chiefly genetically delermined

( 2 ) 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

levels of fat percentages

LITERATURE CITED

1 BONNIER, G and HANSSON, A 1946 Studies on niotiozggous cattle twins VII

On thc genetical determination of tlie iiitcrdependency between thc per- centages of fat, protein, and lactosc i n tlie inilk - 8 c t a A4 gricult~ ~ r z Siiecana ( I n prcss.)