NationalLibraryOfScotland/medical-history-of-british-india huggingface dataset:
74 THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
has been the same as employed by Sanders, i.e., study a factor first, get its elimina
tion factors, apply them to the data and then study the next factor.
Season of the year was studied first, the idea being to see the extent of milk
yield variation as caused by it, in order to decide if the data from the two different
herds—Pusa and Military Dairy Farms—could be combined into one for the study
of other factors without serious loss of accuracy. It was observed that no definite
seasonal variation in milk yield existed in our data, the variation for different
calving months being quite erratic. Hence after its study the data from the two
sources was all put together and studied for other factors. Since S. P. has been
found to be least affected by interrelations of factors, the only relation noticed
being a slight decrease in its value with advanced age, which in the author's
opinion is not very serious, it was studied first, and the correction factors worked
out for it. These were then applied to the data which was next used for the study
of the variations of milk yield with age.
VARIATION OF LACTATION MILK YIELD AS AFFECTED BY : A. SEASON OF TH
YEAR.
From a table drawn to show the variation of the total lactation milk yield
with the month in which a cow calves for the 1274 Military Dairy Farms'
records, the statistical constants given in Table VI were worked out.
TABLE VI.
Variation of milk yield with season of year.
Month of calving
January .
February .
.
.
March
April
.
.
.
May .
.
.
.
June
July .
.
.
.
August .
.
.
September.
October
November
December.
Mean of 12 months
Mean milk yield
3851 ╤ 75 lbs.
4223 ╤ 70 „
4124 ╤ 79 „
3808 ╤ 93 „
4125 ╤ 98 „
4646 ╤ 143 „
4264 ╤ 137 „
4017 ╤ 151 „
4214 ╤ 217 „
4301 ╤ 131 „
4781 ╤ 140 „
4087 ╤ 110 „
4204
Standard deviation
1281 ╤ 53 lbs.
1384 ╤ 50 „
1677 ╤ 56 „
1669 ╤ 66 „
1654 ╤ 69 „
1684 ╤ 101 „
1659 ╤ 97 „
1679 ╤ 107 „
2089 ╤ 154 „
1593 ╤ 93 „
1928 ╤ 103 „
1745 ╤ 78 „
1587
Co-efficient of varia
tion
33.28 ╤ 1.52 per cent.
32.77 ╤ 1.30
„
40.67 ╤ 1.56
43.84 ╤ 2.04
40.11 ╤ l.94
36.24 ╤ 2.44
„
38.91 ╤ 2.58
41.81 ╤ 3.09
49.57 ╤ 4.45
„
37.04 ╤ 2.43
40.33 ╤ 2.49
42.69 ╤ 2.23
„
39.77
The mean milk yield for the different calving months varies between 3,800
and 4,800 lbs. with an average of 4,204 lbs. for all the 12 months, and the standard
deviation lies in the neighbourhood of 1600 though it is rather exceptionally high
STATISTICAL STUDIES, INDIAN DAIRY CATTLE 75
for the months September and November, when it well nigh reaches 2,000 lbs.
The co-efficients of variation which vary from 32 to 50 per cent. with an average
of about 40 per cent. are rather high when compared with those for other
biological data as given by Gowen [ 1924 ] where the highest reported is only
38.2 per cent. although the majority of them fluctuate between 3 and 25 per cent.
Table VII gives what might be called the effect of the season of the year on
lactation milk yield in our data, as compared with the same as obtained by other
workers, for it gives the differences of the means of different calving months from
the mean milk yield of 12 months.
TABLE VII.
Effect of the Season of year on milk yield. Differences in mean milk yield from mean
of 12 months.
Month of calving
January .
February
March .
.
.
April
May
June
July
August .
September
.
October .
November
.
.
December
For present data
—353
+ 19
— 80
—396
—79
+442
+ 60
—187
+ 10
+ 97
+577
—117
Sanders' [ 1923 ]
Penrith
+153
—162
—192
—326
—369
—1040
—642
—473
+ 544
+ 1334
+ 744
+ 450
Sanders' [ 1927 ]
Norfolk
(uncorrected)
+196
+333
+68
+108
—236
—496
—318
—363
—218
+214
+226
+490
Sanders' [1923]
N. Somerset
+562
+331
+169
+13
+87
—377
—259
—503
—280
+215
+88
+387
A comparison of our figures with others at once shows that this variation in our
data is quite erratic, e.g., in between the months December to May with sub-normal
yield, there is the month of February which has a mean slightly above the normal,
and in the months July to November—giving a higher mean than the mean of 12
months—is August whose yield is sub-normal. Furthermore, it will be seen that our
figures lack smoothness which is so very characteristic of the figures given for
other workers, for the peaks reached in our data during the two seasons are quite
sudden, whereas had these figures been really influenced by the influence of the
season of the year the variation ought to have been quite continuous and gradual.
These conclusions about the abrupt variations of milk yields for different
calving months are further supported by Table VIII, which gives the differences
between the mean yields for different calving months together with the probable
errors of these differences.
76
THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
TABLE VIII.
Significance of the differences between the monthly means.
—
January .
February .
March
April
May
June
July
August .
September
October .
November.
December.
January
—
..
..
..
..
..
..
..
..
..
..
..
February
—342 ╤ 69
—
..
..
..
..
..
..
..
..
..
..
March
—273 ╤ 74
+99 ╤ 71
..
..
..
..
..
..
..
..
..
..
April
+43 ╤ 80
+415 ╤ 78
+316 ╤ 82
—
..
..
..
..
..
..
..
..
May
—274 ╤ 83
+98 ╤ 81
+1 ╤ 85
—317 ╤ 90
—
..
..
..
..
..
..
..
June
—795 ╤ 109
—423 ╤ 107
—522 ╤ 110
—838 ╤ 115
—521 ╤ 117
—
..
..
..
..
..
..
July
—413 ╤ 105
—41 ╤ 104
+140 ╤ 107
—456 ╤ 112
—139 ╤ 113
+382 ╤ 134
—
..
..
..
..
..
August
—166 ╤ 114
+206 ╤ 112
+107 ╤ 115
—209 ╤ 119
+108 ╤ 121
+ 629 ╤ 140
+247 ╤ 138
—
..
..
..
..
September
—363 ╤ 154
+9 ╤ 154
+90 ╤ 155
—406 ╤ 159
—89 ╤ 161
+432 ╤ 182
+50 ╤ 173
—197 ╤ 178
—
..
..
..
October
—450 ╤ 102
—78 ╤ 100
—177 ╤ 103
—493 ╤ 109
—176 ╤ 111
+343 ╤ 131
—37 ╤ 127
—284 ╤ 135
—87 ╤ 170
—
..
..
November
—930 ╤ 102
—568 ╤ 106
—657 ╤ 108
—973 ╤ 113
—656 ╤ 115
—135 ╤ 135
—517 ╤ 132
—764 ╤ 139
—567 ╤ 179
—480 ╤ 130
—
..
December
—236 ╤ 90
+ 136 ╤ 88
+37 ╤ 89
—279 ╤ 98
+38 ╤ 100
+559 ╤ 121
+177 ╤ 119
+70 ╤ 124
+127 ╤ 164
+214 ╤ 115
+694 ╤ 120
—
STATISTICAL STUDIES, INDIAN DAIRY CATTLE 77
Since with the same means the same figures though with opposite sign would
be obtained in the lower left half portion of Table VIII as are given in its upper
right half, these are omitted. It will be seen that the only significant differences—
differences at least four times their P. E's, and which are printed in bold type—
are between the means of the 2 months June and November and those of the
remaining months, all other differences except a few stray ones scattered here
and there being quite insignificant.
Again a comparison of the mean milk yields for different calving months with
their corresponding mean S. P. and D. P. shows that the mean total and both S. P.
and D. P. of cows calving in each month show a marked resemblance, e.g., both
the D. P. and S. P. are below the average for the months December to May—
months with lower mean yields—and above the normal for other months—months
with higher mean yields ; and since the effect of the season of the year
is only very slight on milk yield as compared with the same for S. P. and
D. P., in the author's opinion, majority of these seasonal variations of milk yield
in this data would be cancelled when the due allowance is made for the seasonal
variation of S. P. and D. P. The only variations that might still remain, though
these too will be very much reduced, will be for the months June and November—
months with exceptionally high yields for no apparent reason.
The consideration of all this has led the author to believe that there does not
exist in this data any very great effect of the season of the year on the lactation
milk yield, and that any differences that do exist between the means of different
calving months and the average of 12 months, are perhaps merely due to the
fact that the cows of different grades of production are not equally distributed in
different calving months, i.e., cows calving in months from June to November have
a larger proportion of high producers amongst them than those calving in the
months December to May—a claim to disprove which we have unfortunately no
data at hand for it can best be seen by the study of the drop curves for different
calving months, though there is some presumptive evidence in its favour.
The work of Sanders [1927,1] has proved conclusively that the seasonal
variation in milk yield, which is the result of the variations of the monthly drop of
milk yield—persistency factor of lactation curve—from month to month is
"nutritional rather than meteorological" and is an inverse index of the herd
management, e.g., he has shown from Norfolk data the effect of young grass in
spring in putting up the yield—spring flush due to the very succulent nature of
grass and its high nutritive value—, which is followed by a decline as the grass
78 THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
gets older and therefore deteriorates in its nutritive value ; furthermore that this
seasonal variation is much more pronounced in Penrith than in Norfolk because of
the feeding of roots and other succulent foods to Norfolk cows as compared with
Penrith ones during the hot months when pastures parch and dry off and therefore
there is scarcity of succulent food and whatever grass there is, it is very fibrous
and low in nutritive value.
A consideration of the above results as reported by Sanders together with a
study of the actual conditions under which the animals of our data have made their
records further supports the claim that these differences in milk yield means for
different calving months cannot be very significant, for the system of herd manage-
ment at these Military Dairy Farms is more or less perfect as an attempt is always
made to keep the feeding and management conditions quite uniform throughout
the year by stall feeding. Adequate protection from inclemencies of weather is
always provided by way of proper housing. Supply of succulent fodder is ensured
all the year round, either in the form of green fodder—there being no pastures—or
silage when green fodder is not available, though in the winter months roots, etc.,
are also fed, and during the months roughages are of poor quality they are supple-
mented by a fixed though liberal concentrate allowance. Under such ideal con-
ditions of herd management it is only too natural that there be no very great sea-
sonal variation of milk yield. That such is very probably actually the case is
shown by the results given above, hence no corrections have been applied for this
factor to the data. In this connection it might as well be noted that it is by no
means the intention of the author to imply that the lactation milk yield of a cow
cannot be affected by her month of calving. That such an effect is possible
is fully realized though its presence in the data reported is rather doubtful. This
conclusion, however, requires further investigation.
VARIATION OF LACTATION MILK YIELD AS AFFECTED BY :—B. SERVICE PER
The distribution of the S. P. and its relations with the other three factors in
our data have already been discussed. In the present section an attempt has been
made to study the effect of S. P. on total lactation milk yield. To do this a
correlation surface was drawn for these two variables, i.e., milk yield and S. P. and
the mean milk yields worked out for the different service-period intervals, a study
of which showed the variation of milk yield with S. P. to be quite regular and
definite, the means for successive S. Ps. being quite smooth running. The main
statistical constants as derived from the same table are given in Table IX.
STATISTICAL STUDIES, INDIAN DAIRY CATTLE
79
TABLE IX.
Correlation of milk yield with S. P.
Mean milk yield
Standard deviation of milk yield
Mean S. P. . . .
Standard deviation of S. P.
Correlation coefficient
„
ratio milk yield on S. P.
n 2 — r 2
Equation of fitted curve .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
where
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4069 ╤ 28 lbs.
1612 ╤ 20 „
123.8 ╤ 1.7 days.
100.66 ╤ 1.2 „
+ .339 ╤ .015
.389 ╤ .015
.0364 ╤ .0067
—.00417x.
Y = 5960 - 3033, e.
Y = lactation yield lbs.
e = natural base of neparian
logarithms.
x = S. P. in days.
The value of correlation coefficient is fairly high and is many times its probable
error and consequently is quite significant, meaning thereby that milk yield and
S. P. are causally correlated. The correlation ratio, as would be expected, is higher
than correlation coefficient though the difference between the two .050 ╤ .014 is not
quite significant, it being only 3.57 times its P. E.
The value of n 2 — r 2 , the test for linearity of regression is .0364 ╤ .0067,
which, though low as these values generally are, is quite significant, it being 5.43
times its P. E. This would mean that the relation between mean lactation milk
yield and S. P. is not linear in nature, and in fact a study of the mean milk yields
for different S. Ps. quite justified this conclusion, for the mean yields increased at
a decreasing rate for successive S. P. intervals apparently tending to a limit. More
over the fact that the relation between mean lactation yield and S. P. can be linear
is quite belied by the modern researches about the form of lactation curve, for
linearity would mean that a cow never served would milk indefinitely whereas
Brody, Ragsdale and Turner [1923] have shown that " the form of the equation
for the lactation curve is the form that also describes the course of a monomolecular
reaction, that there is present some material of the nature of a catalyst which acts
as a necessary intermediary in the chemical process involved, and that the catalyst
is very slowly and continuously destroyed in accordance with the differential
—kt "
equation dy/dt - a e
Keeping in view all these different considerations, it was decided to fit a logarith-
-cx
mic curve of the form y = A—Be
to the mean milk yields for different S. Ps.
Trial gave the curve,
—.00417x
y = 5960 — 3033 e.
whose fit to the actual means for different S. Ps. is shown in Figure 3. It will be
seen that the fit of theoretical curve to observational means is very good indeed.
B
80 THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
Length
of
service
period
in
days.
Fig. 3. Effect of the length of service period on total lactation milk yield.
STATISTICAL STUDIES, INDIAN DAIRY CATTLE 81
According to this curve the lactation yield of an average cow would be 3,033
lbs. only if conception occurred at once after calving and 5,960 lbs. as a limit if breed-
ing were indefinitely postponed. From this equation a set of correction factors as
given in Table X, has been derived by using standard S. P. of 85 days, for making
allowance for varying lengths of S. P.
TABLE X.
Corrections to total yield for S. P. (standard S. P.=85 days, mean yield for 85 days
S. P.=3,832 lbs.).
Service
period
9.5
29.5
49.5
69.5
89.5
109.5
129.5
149.5
169.5
189.5
209.5
249.5
289.5
329.5
369.5
409.5
Corresponding
mean total yield
from smooth curve
lbs.
3,045
3,278
3,493
3,690
3,872
4,039
4,193
4.334
4,464
4,584
4,694
4,888
5,051
5,192
5,310
5,410
3832
Value from 2
(correct factor)
1.258
1.169
1.097
1.038
0.989
0.948
0.914
0.884
0.858
+0.835
0.816
0.784
0.758
0.738
0.721
0.709
Per cent. correction
to apply
+25.8
16.9
9.7
3.8
—1.1
5.2
8.6
11.6
14.2
16.5
18.4
21.6
24.2
26.2
27.9
29.1
Per cent. correc-
tion from Pen-
rith data (1)
+ 26.0
17.0
9.7
3.9
—1.0
5.0
8.5
11.4
14.0
16.2
18.1
21.2
23.7
25.6
27.2
28.5
B 2
82
THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
85 days S. P. has been selected as the standard, as with this S. P. and a nor
mal gestation period of 280 days the cow will calve at yearly intervals. Since a
long S. P. increases the lactation milk yield and a short one depresses it, a per
centage as given in Table X for corresponding S. P. must be added to lactation yield
for all S. Ps. below 85 days, and a percentage subtracted from it for all periods higher
than 85 days. For the sake of comparison, the elimination corrections for Penrith
as obtaired by Sanders [1923] and recalculated to a standard of 85 days S. P. are
also included in Table X. It will be seen that the two sets of figures agree admira
bly well though our corrections are a trifle lower for the S. Ps. below 85 days and
a trifle higher for the S. Ps. above 85 days.
The correction factors given for varying lengths of S. P. shew very clearly the
very great potency of S. P. in influencing the total lactation yields for a reference
to Table X will show that milk yielded by a cow in a lactation must be raised by
26 per cent. if she is served 9.5 days after calving, and lowered by 28.5 per cent. if
she is left empty for 409.5 days after calving, in order to see what she would have
produced with a S. P. of 85 days. It must, of course, be mentioned that these
correction factors for different S. Ps. are strictly true for the mid-value of the
intervals. But since the variation of milk yield with S. P. is a continuous one, more
accurate results would be obtained if the corrections for the S. Ps. lying in the
intervals, the means of which are only given in Table X, be interpolated by ordinary
linear interpolation ; especially will this be necessary for very low S. Ps. when the
mean lactation yields are rising very rapidly with successive S. Ps.
CAUSES OF VARIATION OF MILK YIELD WITH S. P.
It is generally realized that the length of lactation is determined to a very
great extent by the length of its S. P. The problem has been the subject of study
at different places all over the world with more or less similar results regarding the
extent of correlation existing between these two variables. Ellinger [1910?], for
instance, dealing with Red Danish breed got a very high value of correlation co
efficient between these two variables r = +.943 ╤ .005. Sanders [1927, 1], how
ever, working on the same problem got the following results :—
1st calvers
Others .
.
.
.
.
.
r
+.795
+.758
╤
╤
.008
.008
.811
.760
n
╤
╤
.008
.005
regression equation
35.70
33.30
+
+
0.105
0.109
S. P.
„
As will be seen, the value of r is quite high though it is much lower than that
of Ellinger, and close agreement between r and n justifies the use of a linear regres
sion equation. Both these sets of correlation coefficients, however, seem to the
author rather high and therefore over-estimating the true physiological rela
tionship existing between these two variables. In fact, Sanders himself admits
STATISTICAL STUDIES, INDIAN DAIRY CATTLE
83
this fact in his work, for according to him " there always are some very long
S. Ps. being associated with only moderately long lactations and these are often
excluded automatically from the data by the farmers selling the cow before she
conceived."
There seemed little evidence, however, of this defect in our data, and it was,
therefore, thought that the value of r obtained from it would approximate more
nearly the true physiological relationship than the same of Sanders' or Ellinger's.
A correlation surface was therefore drawn between these two variables, a close study
of which revealed that whereas there appeared to be quite a high value of r bet
ween the two variables, i.e., a high value of S. P. seemed to be generally asso
ciated with a long lactation, there were good many cases where the S. P. had
been longer than the lactation length accompanying it, this being especially true
for very long S. Ps. This led the author to the belief that the length of lactation,
though generally governed by S. P., tended to a limit even though the length of
the S. P. be infinitely increased, and therefore the true relation between the two
variables is not linear in nature as given by Sanders, for on the basis of Sanders'
linear equations a cow once in milk will milk infinitely provided she is kept away
from the bull, and that the lactation length increases regularly at the rate of 10.5
weeks for every 100 days the date of service is deferred in first calvers. All these
beliefs are quite substantiated by the statistical constants given in Table XI and as
derived from the said correlation surface.
TABLE XI.
Correlation of S. P. with lactation length.
Mean S. P.
Standard deviation S. P. . .
.
.
Mean length of lactation
....
Standard deviation length of lactation
r
n
.
n 2 —
r 2
.
.
.
.
.
.
.
123.8 ╤ 1.78
100.66 ╤ 1.25
291.69 ╤ 1.23
70.64 ╤ 0.91
+.524 ╤ .013
.590 ╤ .001
.0735 ╤ .0095
As expected the value of r is considerably lower than that of Sanders or Ellin¬
ger, though it is still quite high and highly significant. The value of n is nearly
quite significantly higher than that of r , n—r being .066 ╤ .017 or 3.88 times
its P. E., and the value of n 2 —r 2 does not permit the use of linear equation to
describe the function. All this means that though the relation between these two
84
THE INDIAN JOURNAL OF VETERINARY SCIENCE AND ANIMAL HUSBANDRY [ I, II
variables is not quite linear, their degree of correlation is quite high, i.e., a high
S. P. will go with a long lactation period.
Again though no similar statistical constants for the relationship existing
between the lactation length and total milk yielded in it are known to the author
to have been determined as between S. P. and lactation length, yet it is common
knowledge that the total amount of milk produced during any lactation, i.e., from
parturition to the end of lactation or until recurrence of parturition, is greatly
influenced by the length of time over which the lactation extends. From the
correlation surface drawn for these two variables for our data the statistical cons
tants given in Table XII were obtained:—
TABLE XII.
Correlation of milk yield with lactation length.
Mean milk yield
Standard deviation milk yield
.....
Mean lactation length
....
,
.
Standard deviation lactation length
....
r
n
n 2 — r 2
4069 ╤ 28 lbs.
1612 ╤ 20 „
291.69 ╤ 1.23 days
70.64 ╤ 0.91 „
+.695 ╤ .009
.723 ╤ .008
.0397 ╤ .007
Although the value of r as given above does not represent the true physiolo
gical relationship between the two variables, for the length of lactation is generally
a controlled factor in most herds, yet its very high positive value leaves no doubt
in its significance. The value of n 2 —r 2 is again interesting ; for it together with
the value of r shows that though with longer lactation periods one gets more milk
yet the rate of increase is not expressed by a linear equation but is represented in
some other form.
The above discussion about the relations between the S. P., lactation length
and milk yield therefore goes to explain the cause of the variation of lactation
milk yield with S. P., for it clearly brings out that since S. P. and lactation length
and lactation length and lactation milk yield are all positively correlated, a longer
S. P. in a cow results in a longer lactation and therefore more milk yield as
against shorter one in which the length of lactation and consequently the milk
yield are both reduced.
Before this discussion about the causes of variation of milk yield with S. P.
is left off, it must of course be mentioned that this is not the only way in which