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Published December 11, 2014
Female Traits, Ovary and Follicle Characteristics,
and the Conditional Probability of Normal
Oocyte Development After Superovulation
of Beef Cows'
R. C. Greer*, R. B. Staigmillert, and J. J. Pamsh"
*Department of Agricultural Economics and Economics,
Montana State University, Bozeman 59717;
+Fort Keogh Livestock and Range Research Laboratory, ARS,
U.S. Department of Agriculture, Miles City, M T 59301;
and *Department of Meat and Animal Science,
University of Wisconsin, Madison 53706.
regressors not been added to the model a simple,
single equation would have represented oocyte
development response; given an oocyte at aspiration only one variable, cumulus quantity, was
found to condition the probability of normal
development directly. However, the complete
model included four additional equations: 1) the
probability that an oocyte was recovered at
aspiration was conditional on the plane of nutritional treatment and progesterone concentration
in follicular fluid; 21 cumulus quantity was conditional on the presence on a corpus luteum, follicle
size, and progesterone concentration; 3) progesterone concentration was dependent on plane of
nutrition; and 4) corpus luteum w&s conditional on
plane of nutrition. The estimated model provided
some insight into the complexity of oocyte development response and the role nutrition may
Play.
ABSTRACT: The proportion of transferable beef
embryos obtained after superovulation, follicle
aspiration, and in vitro maturation and fertilization has been small. To seek possible explanations, cows on different planes of nutrition were
treated with exogenous gonadotropin and oocytes
were isolated from their ovaries. The record for
each oocyte included characteristics of the follicle, ovary, and cow from which it was obtained
and the response to in vitro maturation, fertilizstion, and development. The sample was used to
obtain estimates of the relationships among the
variables. The logistic function with the probability of normal development as the dependent
variable was the basic equation of the statistical
model. When an explanatory variable was itself a
result of the biological system, an equation
explaining variation therein was added to the
model. Had equations representing endogenous
Key Words: Follicles, Ovaries, Nutrition, Oocytes Viability
J. Anim. Sci. 1992. 70:263-272
Introduction
at reasonable cost. This limitation rests with the
female gamete. Large numbers of female gametes
can be harvested from ovaries obtained at
slaughter plants or from selected females. But
these oocytes then must undergo a progressive
series of biological changes Imaturationl before
they can be fertilized and develop into embryos.
Techniques for maturing,fertilizing, and developing these oocytes into transferable embryos are
available (see reviews by Staigmiller, 1988; LeibGried-Rutledge et al., 1989). However, the success
rate of such procedures is still relatively low,
A major limitation in the application of embryo
transfer technology to production of domestic
animals is obtaining a large number of embryos
'Published with the approval of the Director of the Montana
Agric. E-. Sta. Journal series no. 5-2097.
Received December 5, 1990.
Accepted August 20. 1991.
263
GREER ET AL.
264
ranging from 20 to 40%. The low success rate
raises the question of whether there are qualitative differences in the harvested oocytes that
affect potential for complete development into
transferable embryos. Criteria for selecting 00cytes based on differences in oocyte quality are
limited and rather subjective (Leibfried and First,
1979). Similarly, females, ovaq, and(or1 follicle
characteristics that may influence the number or
quality of oocytes are not well established (Fukui
and Sakuma, 1980; Katska and Smorag, 1984;
Leibfried-Rutledge et al., 1985; Grimes and Ireland, 1986).
The objective of this study was to investigate
the relationships among factors related to oocyte
quality Ke., the complete biological integrity of an
oocyte as measured by its ability to undergo early
embryonic development in vitro after in vitro
maturation and fertilization). The fundamental
postulate for this study was that oocyte development is a result of systematic relationships within
a biological system and thus can be represented
by a system of equations. Data were individual
records of 401 follicles aspirated from ovaries of
33 FSH-treated beef cows that were included in an
experiment to determine the influence of nutrition
on ovarian function. This data sample was used to
estimate parameters of a model describing oocyte
development response to variation in characteristics of the female, the ovary, the follicle from
which the oocyte was aspirated, cumulus cells,
and the oocytes themselves.
Materials and Methods
Data Sample
The data were observations on various characteristics of recovered and fertilized oocytes, the
follicles from which the oocytes were aspirated,
the ovaries on which the follicles were located,
and the cows from which the ovaries had been
surgically removed. Data were collected on 401
follicles from the ovaries of 33 cows. In part the
experiment was designed to determine the effect
of nutrition and body condition on oocyte development. Thus a 2 x 2 factorial arrangement was
implemented with 17 cows initially placed on a
low plane of nutrition and 16 cows placed on a
high plane of nutrition. Cows were maintained a t
these feed levels for 60 d to provide treatment
groups with either a low 0 or high 0 body
condition. For the next 20 d (one estrous cycle,
2Mention of trade names or companies does not constitute
an implied warranty or endorsement by the authors, USDA, or
Montana Agricultural Experiment Station
and referred to as the final nutrition phase) onehalf of the cows in each group were switched to
the other plane of nutrition. The result was four
treatment groups: LL (n = 91, LH, HL, and HH (n
= 8 each). Estrous cycles were synchronized for
the final nutrition phase by giving two injections
of prostaglandin 12 d apart; the second injection
was given at the time of the change in nutrition (d
01. On d 12 the cows received an implant of
Norgestomet (Cera Laboratories, Overland Park,
KSP and on d 15 through 19 received injections of
pFSH (total dose = 15 mgl twice daily. Prostaglandin was injected on d 18,the implant was removed
on d 19, and the ovaries were surgically removed
on the morning of d 20. After ovariectomy,
characteristics of the ovaries were recorded and
the follicles 2 7 mm in diameter were aspirated.
Follicles 1 7 mm were selected because they
represented the population of follicles from which
ovulations would have occurred had ovulation
been permitted. After aspiration, recovered 00cytes (n
290) were matured and fertilized in
vitro. Methods for handling ovaries and in vitro
maturation were those described by LeibfriedRutledge et al. (19871, except that oocytes were
incubated individually in 10-pL droplets so that
the fate of each could be recorded. Maturation
was based on expansion of the cumulus cells or
absence thereof. Fertilization was as reported by
Parrish et al. (19861 using semen from a bull of
known fertility. After fertilization, oocytes were
incubated for 48 h as described by LeibfriedRutledge et al. (1987) to permit embryonic development. Development was assessed by staining the
embryos and counting the number of nuclei.
Concentration of steroid hormones in follicular
fluid was determined by RIA previously validated
in this laboratory (Staigmjller et al., 1979; Moseley
et al., 19841.
3
:
Statistical Model
"he 401 records in the data sample included
observations on the variables defined in Table 1.
Normal oocyte development is represented by the
binary variable ND (indicating normal development), which is equal to 1 when development
response was 8, 9, or 10, or equal to 0 otherwise.
The first statistical tests considered traits and
characteristics of each cow and the response to
the plane of nutrition. Cow was the unit of
observation and linear models with ordinary least
squares methods were applied to test for systematic variation when the variable of interest
was a continuous variable. When the variable of
interest was a categorical variable, the binomial
formula was applied.
The statistic& analysis then turned to estimating parameters of a model describing relations
OOCYTE DEVELOPMENT RESPONSE
among management variables, cow traits, ovary
and follicle characteristics, and their influence on
oocyte recovery and development. Normal oocyte
development was represented by the restricted
variable ND equal to 1 when normal development
occurred, or 0 when development did not occur.
The variable ND was the dependent variable in
the statistical model, and it was interpreted as the
probability of normal oocyte development. The
explanatory variables were factors hypothesized
to condition the probability distribution of normal
development, and the null hypotheses were that
coefficients on the explanatory variables were
equal to zero.
The basic equation of the statistical model was
the logistic function as follows:
where NDi = probability of normal development
for the ith oocyte with the observed sample values
being 1 if normal development and 0 otherwise; Xij
= values of the J traits, characteristics, and other
factors hypothesized to condition the probability
of normal development for the ith oocyte; a, =
the unknown parameters to be estimated; and 6
= the ith random disturbance term. The logistic
function was chosen because its sigmoid shape
corresponds to a cumulative distribution function
and is not subject to the shortcomings of a linear
model (for a complete discussion see Fomby et al.,
1984, or Kmenta, 1971). Because the function is
intrinsically nonlinear, maximum likelihood procedures were applied to obtain parameter estimates White et al., 19901. Selection of the best fit
model was based on t statistics associated with
the coefficients, robustness of the coefficient
estimate in terms of sensitivity to equation specification, residual variance, log of the likelihood
Table 1. Data sample variables defrntions
Variables
Definitions
CA
cow w e , Yr;
Plane of nutrition, L = low, H = high;
Cow body condition score at end of nutrition phase, sum of two technicians' scores on a 1 (thin] to 10 0 scale;
Weight of the ovary on which the follicle was located, g;
1 when CL was located on right or left ovary, respectively, = 0 otherwise, both variables = 0 then no CL was present;
CL weight, g;
Number of follicles
7 mm in diameter on the same ovary as FN;
Number of follicles 2 7 mm in diameter on the same ovary as F";
1 when follicle 0 was on R or L ovary, respectively, = 0 otherwise;
Surface diameter of follicle, p ~ z n ;
1 when follicle was largest follicle from either ovary from the cow, =
0 otherwise;
Volume of follicular fluid, &
Concentration of progesterone in follicular fluid; ng/mL;
Concentration of &adiol in follicular fluid, ng/mL;
Concentration of androstenedione in follicular fluid, ng/mL;
oocyte quality,
1 - uniform cytoplasm,
2 - Pycnotic,
3 = Degenerative or clear cytoplasm,
cumulus quantity,
1 = Nude to very sparse cumulus cells,
2 = Corona only,
3 = Corona + 1 egg diameter cumulus,
4 = Corona + 2 egg diameter cumduq
cumulus q w t y ,
1 - Good,
2 = Pycnotic;
Development response, 1 = Germinal vesicle intact,
2 = Germinal vesicle breakdown,
3 = Clumped chromatin,
4 = Metaphase plate a: or ID
5 = Pronuclei,
6 1 Fragmented,
7 1 2 nuclei,
8 = 3 to 4 nuclei,
e = 5 to 8 nuclei,
10 = > 8 nuclei
TRT
BCS
OWT
CUR or LP, binary
CLWT
FL.7
FG7
FS(R or U,binary
Fz
DOMF, binary
Fv
p4
E2
A4
OQ,qucllitative
CQN, qu&itf&tive
CQL, qualitative
DR, qualitative
265
R or L is the last letter of a variable symbol it designates side location of that variable.
GREER ET AL.
266
function, and the logic of the specification.
Given the basic equation, consideration of the
variables (Table 1) that might influence ND led to
the conclusion that the appropriate model was
more than a simple, single equation. Among the
possible explanatory variables were female traits
and ovary and follicle characteristics that were
themselves responses of the biological system. As
such they were considered random variables and
the model was expanded to include an equation
for each endogenous explanatory variable. Thus,
the complete statistical model was a set of
simultaneous equations that expressed the various interdependent responses of the biological
system leading to oocyte development (e.g., female traits and ovary, follicle, and oocyte characteristics, and the s’ubsequenteffects on the probability of normal oocyte development).
occurrence of physiological events that happen
through time that condition a response or generate an effect. Within the sample, all cows of a
given age also had the same reproductive history-3-yr-old cows were primiparous, and so on.
Thus, in this data sample, age, parity, or any
other term describing reproductive history were
synonymous; age was selected for its simplicity.
Because it is the occurrence of discrete events
that may be important, the analyses considered
categorical age variables in addition to the
seemingly continuous variable, age.
It was hypothesized that cow body condition
score (BCS) would vary with treatment group. The
initial parameter estimates obtained with ordinary least squares procedures were
Results and Discussion
with SE of the coefficients in parentheses, R2 =
.715, and SE of the estimate = 1.684. It was
concluded that the estimated coefficients on LL
and LH were significantly different from zero but
not significantly different from each other. The
estimated coefficient on HL was not significantly
different from zero. Thus,it was inferred that the
determinant of BCS was the initial plane of
nutrition, H vs L. Although the plane of nutrition
had changed for the LH and HL cows, the number
of days on the alternative feeding level (the
2 O d final nutrition phase) was such a short period
that & response to change in nutrient quantity
had not yet been manifested in changed BCS.
Because no other variables, including cow age, or
interactions among variables were found to explain variation in BCS, the model judged to best
fit the data sample was as follows:
Cow Traits
Sample means, SD, and minimum and maximum values for the quantitative variables in the
data sample are presented in Table 2. Although
all are not explicitly included in the subsequent
detailed discussion of the results, all were included in the statistical analyses, first, to determine whether these variables were sigruficantly
affected by the plane of nutrition, and, second, to
determine whether these variables should be
included as explanatory variables in the ND
model. One variable deserves discussion; cow age
is reported in years. Yet, simple time is probably
not the important dimension, rather it is the
Table 2. Variable means, standard deviations,
and minimum and maximum values
Variable
33 Cow@
CA, v
BCSb
o m ,8
o n ,8
n 7 R , No.
FL7L. No.
FG7R, No.
FG7L, No.
401 Follicles
-
Fz,
m,
Pd,n g / d
Ez,
A4, n g / d
Min.
4.80
11.24
11.55
9.87
30.87
26.58
6.33
5.82
2.19
3.00
4.64
5.00
19.17
19.69
4.36
4.79
3.00
10.00
6.00
3.01
17.00
23.44
20.04
11.25
552.21
675.46
62.12
1.78
2.71
460.41
1,049.90
69.68
4.33
3.71
5.00
7.00
1.00
1.00
7.00
40.00
27.00
.oo
.oo
= 13.750
BCSi
- 4.7500LLi - 5.125OLHi + .125OHLi
(.8183)
(-8421)
(.8421)
=
13.812 - 4.9890Li
(.56961
Max.
SD
Me-
BCSi
80.00
113.00
15.00
17.00
23.00
4,250.00
10,679.00
524.00
40.1 1
aVariable symbols BS defined in Table 1.
’sum of two technicians’scores on a 1 (thin)to IO vat scale).
with SE of the coefficient in parentheses, R2 =
.712, and SE of the estimate = 1.635.
Presence of a corpus luteum (CL)(CL= 1) was
related to initial plane of nutrition and cow age.
However, effects attributable to each could not be
separated with the data sample. All 16 cows
(including six 3-yr-olds) on the high plane of
nutrition had a CL,whereas 7 of the 17 cows on
the low plane of nutrition did not have a CL. Six of
the seven cows without CL were 3-yr-01ds1leaving
only two 3-yr-old cows on the low plane of
nutrition that did have a CL. There was no
difference in presence of a CL attributable to
changing the plane of nutrition during the experimental period. Because the variables conditioning
OOCYTE DEVELOPMENT RESPONSE
the probability of a CL, cow age 3, and L were
themselves binary, the estimated logit model
parameters exactly reflected the proportions of
3-yr-oldcows having or not having a CL.Thus, the
following conditional probability statements regarding the presence of a CL were derived from
the data sample:
RCL
P(-CL
P(CL
P(-CL
RCL
I
I
I
I
CA3
CA3
CAO
CAO
IH)
&
&
&
&
L)
L)
=
=
L)
=
L)
=
=
.25
.75
3889
.1111
1.0
where L denotes a cow on initial low plane of
nutrition; H denotes a cow on initial high plane of
nutrition; - denotes not, the characteristic was not
present; CA3 denotes a 3-yr-old cow; and CAO
denotes a cow > 3 yr old.
Results with respect to two other variables, CL
location and dominant follicle location, were in
part consistent with past results, and in part
raised a question to be researched and a hypothesis to be tested with much larger data samples.
Although the number of cows in the present
sample is small, the possibility of a nutritional
effect on relative right-left ovary activity was
raised by the CL and dominant follicle distributions (Table 3). Previous studies with dairy cows
found that ovulations occurred slightly but significantly more often on the right ovary than on the
left ovary (Kidder et al., 1952). If the point estimate
of the probability of right location is taken to be
.56 and because only the initial plane of nutrition
affected CL location (the final nutrition phase was
started just before ovulation), then among the L
cows the proportion 4 of 10 CL right ovary,
although < .5, certainly was not surprising.
However, among the H cows the 12 of 16 CL right
ovary seemed disproportionate, and so the probability was calculated as follows:
):(
(.56)l2(.44I4
=
.0649.
This probability and the probability of observing
12 or more from a sample of 16
k
2 (F)
=
(.56)k(.44)'6 -
=
.0984
12
were neither small nor large. Although they were
in the range that would often lead to rejecting the
null hypothesis, they were not considered persuasive evidence for or against a plane of nutrition
affect. Consideration of the dominant follicle
location distributions only increased curiosity.
Again, among the L cows, whether LL or LH, and
even among the HL cows, the distributions (Table
267
Table 3. Number of cows, by treatment, showing
location of the corpus luteum (CL) of the previous
cycle, and the location of the dominant follicle
Dominant
follicle location
CL location*
Treatmentb
NO
LL
LH
4
3
HL
HH
CL
L ~ R
Right
Left
Right
3
2
2
6
4
4
5
6
0
3
2
2
-
3
4
5
8
-
*Location of the CL was dependent only on the initial plane
of nutrition, because the change to the second plane (beginning
of the f i i nutrition phase) was after ovulation.
bL = low plane of nutrition; H = high plane of nutrition.
3) were not surprising. However, the probability of
observing the HH distribution, 8 out of 8 dominant
follicle right, is very small
c)
(.56)* =
.0097
and further focuses on the need for additional
research to understand the mechanism that apparently makes the right ovary more actke and
the possible role of plane of nutrition.
Variation in other cow characteristics, CL
weight, ovary weight, the number of follicles < or
> 7mm, the total number of follicles and the
proportion of oocytes/embryos that develoFed
normally, was not explained by or attributable to
treatment group, cow age, or BCS. Of course,
ovary weight was highly correlated, .74, with the
number of follicles > 7 mm, and correlated, .42,
with the number of follicles < 7mm (i.e., heavy
ovaries had a large number of follicles).
In summary, it was the initial plane of nutrition, not the change in plane of nutrition during
the experimental period that had important effects on BCS and presence of a CL. The interesting results that raised questions in need of further
research were found when the previously reported
probability of right ovary location, .56, was applied to the CL and dominant follicle location
distributions. Although the power of any statistical test was low because of the small number of
cows in the study, the calculated probabilities of
observing the H distributions were small enough
to raise the conjecture that the mechanism making the right ovary more active than the left is in
fact responsive to plane of nutrition.
Oocyte Developmeni
For the analysis of oocyte development the unit
of observation was the individual follicle. First,
within the sample of 401 observations, 115 oocytes
GREER ET AL.
268
developed normally; thus, the success rate, or the
unconditional probability of normal oocyte development from this sample of aspirated follicles,
was 115/401 = .287. Second, there were four
distinct possible outcomes: 1) an oocyte was not
recovered at aspiration (111 follicles);2) the oocyte
was lost in the laboratory during the experiment
(66 oocytes); 3) the oocyte developed normally
(ND);or 41 the oocyte did not develop normally
(109 oocytes). The objective was to determine
whether plane of nutrition, cow traits, and ovary
and follicle characteristics entered the logistic
function as explanatory variables to condition the
probability of normal development. Given that
some of the possible explanatory variables were
themselves responses of the system, and thus
random variables, a potential estimation problem
had to be considered. The problem was the
possible correlation between a stochastic regressor and the equation disturbance term. When a
regressor is correlated with the equation disturbance term the parameter estimators are biased
and inconsistent, a problem that even maximum
likelihood procedures will not resolve m e n t a ,
1971). Correlation between the equation disturbance and explanatory variables representing
female traits and ovary and follicle characteristics seemed likely because all were generated
within the same system or unit of observation.
The problem was solved by expanding the model
to include an equation for each endogenous
explanatory variable. Adding equations not only
solves the estimation problem, but the explicit
relations among system responses and among
system responses and basic determinants furthers
understanding of the complexity of the biological
system.
The best fit statistical model representing the
relations leading to normal oocyte development
included five equations and the implicit relation
between the plane of nutrition treatment and the
presence of a CL. Two of the equations along with
the implicit relation represented the biological
system in terms of the conditional probability that
an oocyte was recovered at aspiration. The three
remaining equations then represented the biological system in terms of the conditional probability
that a recovered oocyte developed normally. The
equations and parameter estimates are presented
in Table 4.
Through the testing of many specifications only
two variables, concentration of progesterone in
follicular fluid (P3 and plane of nutrition, were
found to condition the probability that an oocyte
was recovered at aspiration (Equation 2, Table 41.
Because P4 w&s itself a response of the biological
system, an equation explaining variation therein
was added to the model. The distribution of P4
concentration was skewed to the right, and
therefore the values were transformed to LnW4).
With Ln(P41 the dependent variable, measures of
equation fit improved, and the best fit specification included only the binary variables LL and LH
[Equation 1, Table 4). The distinction between LL
and LH in terms of P4 was the only time in the
analyses with the follicle as the unit of observa-
Table 4. Parameter estimates for the system of equations describing the relations among plane of nutrition,
cow traits, follicle characteristics, and normal oocyte development
Equation
number
Dependent
variableB
Ekplanatory variables
Constant
CQN34
P4
L
LL
LH
-.86690
-.47492
(.0886)
CL
n b
~ncwc
SEE^
401 observations
1
6.4881
-4
LO88 lIe
2
224 observations
3
ORA
2.1023
w
6.2856
4
4
CQNW
5
ND
-.000538 -1.1020
(.00013) L2784)
-2 14.86
h4P
-.83488 -37608
(.0879) (.1008)
-2.8258
-.57054
.762
(.23)r
.001039
(.000479)
1.2124
C.2798)
.577
(.2d
1.2700
.13566
(.3385) LO5591
-137.01
(64F
-145.36
(65s
is the Ln of progesterone concentration; ORA equal 1. when an oocyte was recovered at aspiration; CQN34 equal 1. when
cumulus quantity was 3 or 4; ND is normal development.
bFZ is diameter of the follicle, millimeters.
cLn[L) is Ln of the likelihood function for the logistic function.
dSEE is standard error of the estimate for the linear equation estimated by ordinary least squares.
eNumbers in parentheses me absolute value of the standard error of the coefficient.
‘Adjusted R2.
gpercentage of correct predictions within the sample.
OOCYTE DEVELOPMENT RESPONSE
269
Table 5. Number of follicles with progesterone (Pb]
concentration greater than 1,000 ng/mL
by treatment
Treatments
Total no.
of follicles
LL
146
LH
06
HL
98
62
HH
*L
= low plane of
Follicles with P4 > 1,000
ng/mL
No.
Proportion
2
10
18
14
.014
.lo4
.la8
226
nutrition; H = high plane of nutrition.
tion that the changing plane of nutrition during
the experimental period had a significant effect
on the result. The effect of plane of nutrition is
shown by the number of follicles with P4 > 1,000
ng/mL for each treatment group mable 5).
The low plane of nutrition not only decreased
P4, but it also decreased the probability of
recovering a n oocyte. Equations 1 and 2 in Table 4
represent the biological system in terms of the
likelihood that an oocyte was recovered. The
relations as well as the cow trait responses to
plane of nutrition are depicted in a tree diagram
in Figure 1. The rectangular node with the L
represents the low initial plane of nutrition, a
management choice variable, and the two smaller
rectangles represent the LL and LH subsets. The
oval nodes represent the system responses, and
the arrows represent the causal relations; the +
Table 6. Calculated conditional probability
that an oocyte was recovered at aspirationa
RORA =
1IL and PJ
100
200
300
.7205
.7095
400
.7870
.6753
.6635
.a14
.6302
.6267
.6141
S490
.4822
.4160
2 4 18
.lo61
.6984
500
600
700
600
000
1,000
1,500
2,000
2,500
4,000
5,500
1/1 + e-(2-1029- l.lMo
RORA I 1)
is oocyte recovered at aspiration.
*Eq-tion:
p4); ORA
HORA =
1IH and P3
b o g e a t e r one.
.8858
.a803
.a745
.a685
.a623
.a558
.a491
.a421
.8348
.a273
.7856
.7371
.6620
.4898
.3006
- .000536
Figure 1. Tree diagram of the initial cause-effect
relations among plane of nutrition (L), cow trait, ovary
and follicle characteristics, and the probability an
oocyte was recovered at aspiration (ORA);
DOMF is
dominant follicle.
or - immediately above the arrow indicate the
direction of the effect. For instance L, compared
with H, has a two-part effect on the probability
that an oocyte was recovered at aspiration; L
directly decreases the probability, whereas LL
and LH by different amounts decrease the P4
concentration, which, given the negative sign of
the estimated coefficient and smaller P4, then
increases the probability that an oocyte was
recovered at aspiration. Although the indirect
effect of nutrition (decreasing P41 offset the direct
effect, the net effect of L was to decrease the
probability that an oocyte was recovered. The
effects are shown by the calculated example
conditional probabilities that an oocyte was recovered presented in Table 6. For a given P4
concentration there was a smaller probability
that an oocyte was recovered when the cow had
been on the low plane of nutrition than when the
cow had been on the high plane of nutrition.
These results point to the need for further
investigation and understanding of the role and
mechanisms through which nutrition affects physiological responses.
The finding that the cow trait responses to the
plane of nutrition experiment with L acting to
decrease the probability of a CL and BSC were
separate from oocyte development is made clear
in Figure 1. Although there w ~ l scorrelation in the
observed values of BCS and P4,when the effect of
the common basic determinant plane of nutrition
was removed there was not a discernible causeeffect relation, hence no arrow in Figure 1;
similarly no arrows appear for other variables for
which no cause-effect relation was discernable.
270
GREER ET AL.
One further outcome, the probability that the
oocyte was lost during the maturation, fertilization, or development periods after treatment with
FSH,must be considered before explicitly considering the phenomenon of primary interest, normal
oocyte development. To concentrate on the three
remaining outcomes, lost during the experiment,
ND, and not ND, it was decided to truncate the
data sample, to delete from the sample those
observations in which an oocyte was not recovered at aspiration. Thus, the sample became
290 observations, because the oocyte was lost
during the experiment for 66 of the observations.
To test for systematic loss of oocytes during the
experiment, several specifications regressing the
restricted dependent variable, oocyte lost during
the experiment, on other variables in the data
sample were estimated. None of the estimated
coefficients were significantly different from zero
nor were statistics measuring the fit of the
regressions significnatly different from zero.
Thus, it was concluded that the loss of oocytes
during the experiment was a random occurrence
not related to variables in the data sample, and
the data sample was truncated again to remove
those observations in which the oocyte was lost.
Within the truncated sample, the unconditional
probability of ND was 115/224 = 5134. Normal
development was affected by cumulus quantity,
which in turn was influenced by the presence of a
CL, follicle size (FZ), and P 4 concentration. The
model best representing the truncated data sample was a system of three equations, Equations 3,
4, and 5 in Table 4. Two were logistic functions
representing the conditional probability of occurrence for the restricted dependent variables ND
and CQN34, and the third represented P4 concentration.
After testing many specifications, only one
variable in the data sample was found to directly
condition ND, Equation 5. The variable was a
categorization of oocyte cumulus quantity, which
was recorded in the data sample as one of four
values, Table 1. During estimation there was no
discernable difference in response or effect between cumulus quantity values l and 2, nor was
there a discernable difference between cumulus
quantity values 3 and 4. There waa, however, a
difference between the two subsets. Thus, a
binary variable was constructed (Le., CQN34 = 1
when cumulus quantity was a 3 or 4, = 0
otherwise).
Because CQN34 was itself a response of the
biological system, another equation, Equation 4,
Table 4, was added to the model. Three explanatory variables, P4, CL, and FZ, entered the
equation and thus acted to condition the probability that cumulus quantity was either 3 or 4. It
should be remembered that CL was a binary
variable, and the presence of a CL was itself a
conditional probability, conditioned by the plane
of nutrition treatment and cow age. It should be
noted that CL included cows from both the high
and low planes of nutrition and of different ages
and both CL right and CL left ovary. The
possibility of influence by ipsilateralcontralateral
c o n f i i a t i o n of the CL and the follicle from
which the oocyte was aspirated was tested by
constructing variables representing the disjoint
subsets. Estimation results did not support side or
ipsilateral-contralaterrtl configuration as significant explanatory variables because there was not
improvement in the measures of fit. Thus, the
conclusion was that "simply" the presence of a CL
was important in conditioning the probability of
CQN34. The low plane of nutrition and inseparable cow age effect, however, had an indirect effect
as they conditioned the probability that a CL was
present and P 4 concentration.
The second variable acting to condition the
probability of CQN34 was a continuous variable,
FZ, measuring the diameter of the follicle lin
millimeters)from which the oocyte was aspirated.
It should be noted that FZ and follicular fluid
Table 7. Calculated probabilities cumulus quantity
was 3 or 4 given corpus luteum (CL) and selected
progesterone (P4)and follicle size (PZ)valuesa
Zonditional probability, N o CL
100
200
300
400
500
600
700
800
900
1,000
1,500
100
200
300
400
500
600
700
800
900
1,000
1,500
.2262
.2772
.3347
.2449
.2ea
.3582
.2646
.3207
.3824
.2854
.3437
.4072
.3070
.3675
.4325
.3295
.3920
.4582
3529
.4170
.4841
.4425
3770
.5100
.4017
.4682
.I5360
.4269
.5617
.4942
.5560
.6216
.e830
Conditional probability, CL was present
3770
.4425
.5105
.5773
.e417
.4017
.4683
5360
A024
.e653
.4269
.4942
.5617
3270
,6880
.4525
.5201
.5871
3510
.7088
.4783
5460
.0120
.e742
.7308
SO43
.5716
A364
.e966
.75M
.7181
.7696
.5302
,5968
.6601
.5560
.e210
.MI30
.7386
.7875
.5815
,6457
.7050
.7582
.8044
.e065
.e691
.7262
.7767
.8202
.7216
.7727
.8168
.8540
.8847
.1452
.1586
.1730
.1884
.2048
.2222
2407
.2602
.2807
.3021
.4212
-
.1823
.1983
.2153
.a34
2525
.2726
.2937
.3157
3385
.3622
.4884
-
OOCYTE DEVELOPMENT RESPONSE
volume were highly correlated, r = .87. Regression results with either as a regressor were
essentially identical. Thus, it could not be con
cluded that one explained more of the variation
than the other. The specification including size
was selected because its measurement is obtained
first, thus facilitating use as a decision variable.
The inference from the positive coefficient was
that as follicle size increased the probability that
cumulus quantity was 3 or 4 increased. None of
the variables in the available data sample were
found to significantly explain variation in follicle
size, thus no equation was added to the model.
Including P4 as an explanatory variable in the
CQN34 equation led to interesting inferences.
Recall from earlier results with the full sample
(401 observations) that as P4 increased the probability that an oocyte was recovered decreased.
Now with the truncated sample and the positive
estimated coefficient, it was inferred that as P4
increased the probability that cumulus quantity
was 3 or 4 increased. From the two results, the
inference was that truncating the sample by
deleting those observations from which an oocyte
was not recovered removed observations with
large P4 values. Comparison of the sample means
supported the inference;with 401 observations the
mean P4 was 675 and with 224 observations, the
mean P4 was 482.
Again, with P4 entering the system a second
time as an explanatory variable, the Ln(P41equation was reestimated with the truncated sample.
There was very little difference in the estimated
coefficients on LL and LH (Equations 1 and 3,
Table 4); no other variables entered as significant
explanatory variables, and the intercept was
271
smaller, reflecting the effect of sample truncation.
Thus,the consistency of the estimates, the robustness, increased confidence that the structure of
the relation was properly modeled.
The influence of the three explanatory variables in conditioning the probability CQN34 is
shown by the example calculations presented in
Table 7; the unconditional probability in the
truncated sample was 116/224 = .5179. For a
given follicle size and P4 concentration the probability that CQN was 3 or 4 was greater when a CL
was present than when there was no CL.
In appearance, the ND equation (Equation 5,
Table 4) was quite simple and straightforward.
Because CQN34 was binary, there were only two
conditional probabilities to be calculated:
P(ND
P(ND
= 1
=
1
I
I
CQN34 = 01 = .3611 and
CQN34 = 11 = .6552
This apparent simplicity, however, masks the
complexity of the system because 1) cumulus
quantity was conditional on the presence of a CL,
FZ, and P4;2) P4 was dependent on LL and LH; 3)
CL was conditional on L and an apparent, but
inseparable, influence from cow age; 41 the estimates were conditional on an oocyte being recovered; and 5) the probability an oocyte was
recovered was conditional on L and P4.
The complexity of the total system, the various
responses to the plane of nutrition followed by the
effects on subsequent responses, may be represented by incorporating the results of Equations 3,
4, and 5 into the initial tree diagram, Figure 2.
The objective of this research was to identify
variables in the data sample that ostensibly
\
+
-
Figure 2, Tree diagram of the cause-effect relations conditioning the probability of normal oocyte development;
ORA is the probability that an oocyte was recovered at aspiration, DOMF is dominant follicle, FZ is follicle size
(millimeters) and CQN34 is the probability that cumulus quantity was 3 or 4.
GREER ET AL.
272
affected oocyte development response, variables
that conditioned the probability of normal oocyte
development. The variables and combinations of
variables in the data sample were specified as
independent regressors in the logit model. Had
the research been done with the view that the
variables in the data sample, other than ND,were
predetermined variables the conclusion would
have been that cumulus quantity alone conditioned the probability of normal oocyte develop
ment after treatment with FSH. The model would
have been a very simple single equation, a single
explanatory variable model with no recognized
plane of nutrition effect or effects from attendant
traits, characteristics, and hormone levels. Rather, this research recognized that when regressors
in the model were themselves results of the
biological system additional equations explaining
variation in the endogenous regressors should be
specified and parameter estimates obtained;
responses of the biological system should be
traced back to the basic determinants that initiated and motivated the system. The system of
equations selected as best representing the data
sample revealed a complex system, a model
consisting of five equations with a sixth relation
implicit. The implicit relation was the plane of
nutrition (and perhaps cow age1 effect on the
presence of a CL.The five equations represented
P 4 concentration and the conditional probabilities
of recovering an oocyte, cumulus quantity, and
ND. From the results, the high plane of nutrition
clearly acted to increase the probability of normal
oocyte development after treatment with FSH.
The effect, however, was an indirect effect working through other system responses, the probability an oocyte was recovered at aspiration, the
presence of a CL,P4 concentration, and cumulus
quantity.
Implications
Research often focuses on one trait or characteristic: normal oocyte development. But, aa
clearly shown here, if other response variables
are considered, predetermined errors result. The
more grievous errors are the errors in logic and
understanding of the biological system; the probability of normal oocyte development is not simply
conditioned by cumulus quantity. The plane of
nutrition also plays an important role. Working
toward complete specification provides insight
and generates an additional hypothesis and a
question relative right-left ovary activity is
responsive to plane of nutrition, but what are the
basic determinants of the loss of oocytes or of
follicle size? Identifying and obtaining measurements on basic determinants whose values are
generated outside of but initiate or motivate the
system would seem to be a high research priority.
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