INTRODUCTION
Production traits in dairy cattle are under the influence of many genetic
and environmental factors and the interactions between them both linearly
and nonlinearly. Dairy production traits including milk yield and milk
fat percentage are of the most important economic traits in Iran`s dairy
industry. So, prediction of these traits is of importance to find prospective
high yielding cows and improving the economic proficiency of dairy farms.
Also, much of the selection of superior bulls is based on their ability
to produce high yielding cows (Salehi et al., 1998). Accuracy rate
of finding high producing cows is important, because feeding, breeding,
maintenance, veterinary and other costs can be saved for superiors and
also by misculling cows of high genetic value, good sources of gene pool
will be lost.
In many countries, analysis of milk yield for 305 day lactation period
is a foundation for dairy cattle genetic evaluations. So, implementing
mathematical models for prediction of 305 day production in subsequent
lactations from previous lactations or predicting total lactation yield
from early records would be useful.
In comparison with regression methods or timeseries analyses, Artificial
Neural Network (ANN) represents a different new approach. The relationship
between two or more independent variables on a dependent variable can
be obtained applying Multiple Linear Regression (MLR) method. Regressions
show the extent and direction of associations between characters in the
units of measurements. A MLR explains the linear causeconsequence relationships
between some independent variables (x_{1}, x_{2}, ...,
x_{n}) and a dependent variable (y). Artificial Neural Network
(ANN), like biological neural network, is made up from some sets of neurons.
These neurons process the presented input and matching output to input
in a supervised manner and extract nonlinear relationships between those
input and output. ANN consists of a set of neurons which are connected
by weighted links that pass signals from one neuron to another. During
training, the weights become adjusted to reduce error between actual and
desired output. This error is minimized until it reaches to a certain
objective value (Md Saad et al., 2007).
ANN proposes an approach that is completely different from those offered
by conventional methods. It solves particular problems through a learning
system by typical inputs and specific desired outputs. (Grzesiak et
al., 2003). The usefulness of any mathematical model depends on how
well it can mimic the biological process of milk production and adjusts
for factors affecting it (Olori et al., 1999). In ANN identifying
patterns and relationships between the input and the corresponding output
in a sample data set refers to the fact that optimal net performance depends
on the recognition and extraction of nonlinear relations through the
training step which form the ANN structure (Lacroix et al., 1995).
Using this relation in the simulation stage, ANN can anticipate the output
of the problem in a complex biological system from known input. In practice,
ANNs have been primarily used in engineering, economics, or even in detection
of heart abnormalities (Md Saad et al., 2007). Recently, they also
have been used in some areas of animal genetics and husbandry, such as
detection of clinical disease (Yang et al., 1999), estimating meat
quality (Brethour, 1994), prediction of slaughter value of bulls (Adamczyk
et al., 2005), evaluation of physiological status of cows (Molenda
et al., 2001), detection of mastitis in dairy cattle (LópezBenavide
et al., 2003), to predict swine daily gain in different ambient
temperatures (Korthals et al., 1994), prediction and classification
of dairy cows based on milk yield in one period (Salehi et al.,
1998) and prediction of 305 day milk production from part lactation records
(Lacroix et al., 1995).
The aim of this research was comparing the predictive ability and the
accuracy of ANN and MLR methods for predicting 305 day adjusted kilogram
Milk Yield (MY) and Milk Fat Percentage (%MF) of the second lactation
using information from first lactation as a tool for recognition of more
producer cows of high genetic merit as the parents of the next generation.
MATERIALS AND METHODS
The data was provided by the Animal Husbandry Division, Agricultural
Organization of the Ministry of Agriculture in Isfahan, Iran, which was
consisted of collected information from 32 Holstein dairy herds milked
during 1995 to 2002. From the available herds, four medium sized herds
were selected randomly for final investigations. Records were restricted
to cows with completed second lactation. Followed by this restriction,
a sample of 1880 cows with records was made available for further studies.
The sample data was consisted of cows` registration number, purity (%
Holstein blood which was 65.5±19.43 in the sample), first and second
parities milk yield and fat percentage, corrected for 305 days in milk
and some other information on the first parity of cows. Then, the data
structure was rechecked and the data was introduced to MATLAB (2006) software
for further processing.
Ten variables of the first parity (as inputs) plus two variables of 305
day MY and %MF from the second parity (as outputs) were assigned to each
cow for both ANN and MLR (Table 1). In order to achieve a better learning
for ANN, first lactation 305 day MY was classified into 9 production levels
including milk production <2000 kg as the first and >9000 kg as
the ninth level and the middle levels of 1000 kg difference. Salehi et
al. (1998) concluded that data classification would lead to a better
network learning.
Table 1: 
Variables used in the experimental data sets 

*: %Holstein blood 
Normality distribution of each set was tested using Statistical Analysis
Software (SAS, 1997). For ANN, the minimum and maximum values of each
variable (Table 1) were mapped to the mean and standard deviation of 0
and 1, respectively. In order to construct the network, the neural network
toolbox of MATLAB (2006) was used. The constructed network was a back
propagation artificial neural network which had 3 layers of input, hidden
and output with 10, 10 and 2 neurons in each, respectively. For input
and hidden layers, tangent hyperbolic transfer function and for output
layer, purline transfer function were used (MATLAB, 2006). The net learning
function updated the weight and bias values relative to LevenbergMarquardt
optimization algorithm (Hagan and Menhaj, 1994). The net trained in 100,000
cycles of processing elements.
Cows were assigned to two groups:
Group 1: Included 1850 cows. Data of the second parity corresponding
to the first period were used to design ANN and MLR for both MY and %MF.
This part of data was divided into 925 training and 925 verification sets.
The training set was used to obtain and modify the weights by ANN and
to obtain the related regression coefficients by MLR. Verification set
was used to control the size of network error during the training step
and consequently to control the approximation ability of the network (Grzesiak
et al., 2006).
Group 2: Thirty cows were randomly selected from 1880 cows as
a simulation set. The simulation set was used to test both ANN and MLR
by predicting second parity MY and %MF from first parity information and
then comparing the results of ANN anticipations and the results taken
from MLR regression coefficients with the observed values.
MATLAB (2006) and SAS (1997) softwares were employed to run ANN and MLR
analyses, respectively. The criterions used to compare the results of
ANN and MLR anticipations with the actual observed data were: (1) adjusted
coefficient of determination, (2) root of mean square error, (3) SD_{ratio},
(4) Pearson`s coefficient of correlation between observed and predicted
values, (5) relative mean error of prediction and (6) Theil`s inequality
coefficient.
Where:
R^{2}_{A} 
= 
Adjusted coefficient of determination 
n 
= 
No. of records 
k 
= 
No. of predictors or independent variables 
R^{2} 
= 
Coefficient of determination 
Where: 
RMSE 
= 
Root of mean square error 
n 
= 
No. of records 
y_{i} 
= 
Observed value 
í 
= 
Estimated value by ANN or MLR 
Where: 
Sd_{ratio} 
= 
Ratio of error standard deviation to the total standard
deviation 
e_{i} 
= 
Individual error 

= 
Mean of error values 
y_{i} 
= 
Observed value 

= 
Mean of observed values 
r_{p} = δ_{ip}/δ_{i}
δ_{p} 
(4) 
Where: 
r_{p} 
= 
Pearson`s correlation coefficient between observed and predicted
values 
δ_{ip} 
= 
Covariance between observed and predicted values 
δ_{i} 
= 
Standard deviation of observed values 
δ_{p} 
= 
Standard deviation of predicted values 
Where, Ψ is the relative mean error of prediction and the other symbols
are as the same as for the previous formulas.
Where, I
^{2} is Theil`s inequality coefficient (Theil, 1979) and
the other symbols are as the same as for the previous formulas.
The above coefficient is the sum of three other model`s inequality coefficients.
I^{2} = I^{2}_{O}+
I^{2}_{B}+ I^{2}_{E} 
(7) 
The components of Eq. 7 are as follows:
Where: 
I^{2}_{O} 
= 
Prediction bias 

= 
Mean of observed values 
í_{m} 
= 
Mean of predicted values 
Where, I
^{2}_{B} represents the error resulting from predictions`
inadequate flexibility.
Where, I
^{2}_{E} represents the error resulting from insufficient
convergency between direction of changes in the observed values and changes
in the predicted values.
RESULTS AND DISCUSSION
Regression coefficients estimated by MLR method for MY and %MF are shown
in Table 2. These estimated regression coefficients obtained from the
train set were used to make evaluations for the test set. ANN and MLR
predictions were compared to the observed values by their mean differences
to the mean of observed values (Table 3). Although MLR showed very low
differences close to zero for train and verification data sets, finally,
ANN predictions had lower differences with the observed data, may be due
to the fact that MLR has no learning ability and it only finds linear
relationships between data. The variability parameters (SD, CV) were also
closer to those for observed data for ANN than MLR. Grzesiak et al.
(2003) using test day records to estimate 305d lactation yield, derived
only 13.2 kg higher and 91.3 kg lower milk yield than the average of actual
yield for ANN and MLR predictions, respectively.
Some quality parameters are shown for ANN and MLR for both MY and %MF
by Table 4. SD_{ratio} was lower and R^{2}_{A}
was higher for ANN relative to MLR. Also for ANN, SD_{ratio} deceased
and R^{2}_{A} increased in the test step. These findings
show the relative advantage of ANN to MLR. Better quality parameters for
ANN relative to MLR have been also reported by Grzesiak et al.
(2003, 2006). Regardless of the method of evaluation, SD_{ratio}
and %RMSE were lower and R^{2}_{A} was higher for %MF
relative to MY, which show that the input variables may better justified
the changes in %MF than MY. Due to training and verification abilities
of ANN, its quality of prediction drastically improved in the test step.
However, it was not expected from MLR to show any considerable improvement
in the test step relative to the previous steps. SD_{ratio} value
less than 0.4 shows a good quality of the model, whereas values lower
than 0.1 mean that the model would be close to ideal (Grzesiak et al.,
2006). In this study, low R^{2}_{A} values were derived
for MLR, which showed that the chosen independent variables alone, could
not explain well the changes in the dependent variable by MLR method.
R^{2}_{A} = 0.70 implies a very good fitness for the model.
While, R^{2}_{A}< 0.40 shows a nonappropriate model
(Olori et al., 1999). Although, R^{2}_{A} was low
in the verification set, the final predictions by ANN for the test data
set had a high R^{2}_{A}.
Table 2: 
Estimated regression coefficients using MLR method 

MY: Milk Yield; %MF: Milk Fat Percentage, Correlation
coefficients (β) are in the same sequence as the input variables
represented in Table 1 
Table 3: 
Descriptive parameters for the observed and predicted (by ANN and
MLR) data 

MY: Milk yield; %MF: Milk fat percentage; OBS: Observed
value; ANN: Artificial neural network prediction; MLR: Multiple linear
regression prediction; DIFF: Difference from the mean of observed
values; t: All DIFF`s have no significant difference from zero (p>0.05) 
Table 4: 
Quality parameters for ANN and MLR methods 

MY: Milk yield; %MF: Milk fat percentage; SD_{ratio}:
The ratio of error standard deviation to the total standard deviation;
R^{2}_{A}: Adjusted coefficient of determination;
RMSE: Root of mean square error; %RMSE: RMSE divided by the mean
of performance 
In other studies which have used partial records to predict full lactation
records, higher R
^{2}_{A} values were estimated, including
R
^{2}_{A} = 0.79 by Wood (1967) and R
^{2}_{A}
= 0.94 by Olori
et al. (1999). Grzesiak
et al. (2003) reported
RMSEs equal to 501.7 and 544.76 kg milk yield in the test step for ANN and
MLR, respectively. Also, Salehi
et al. (1998) estimated RMSE values
ranging from 445 to 554 kg depending on the network system and the average
of herd milk production. The reason for the differences between the results
of these studies and the results of the current study refers to different
data structures used to train ANN. For example, they have used test day
records to calculate 305 day milk production with more or less extended
data from other regions with more input variables.
Table 5: 
Predictive measures for ANN and MLR 

MY: Milk yield; %MF: Milk fat percentage; r_{p}:
Correlation coefficient with the observed data (p<0.001); Ψ:
Relative mean error of prediction; I^{2}: Theil`s inequality
coefficient; I^{2}_{O}: Prediction bias; I^{2}_{B}:
Prediction inflexibility; I^{2}_{E}: Insufficient
convergency between direction of changes in the observed and predicted
values 
Table 5 shows some parameters related to predictive ability
of ANN and MLR for both MY and %MF. As shown in this table, on average,
r
_{p} values were higher and Ψ and I
^{2} values were
lower for ANN relative to MLR, which were in favor of ANN. These values
showed a same situation for %MF, which support the results of
Table
4 regarding better fitness of both ANN and MLR for %MF relative to MY.
For both ANN and MLR, r
_{p} increased for the test data set. Both
Ψ and I
^{2} decreased in the test step for MY, while they increased
for %MF.
Considering final predictions obtained in the test step (Table 5), except
I^{2}_{O} for %MF, all of the three criterions of I^{2}_{O},
I^{2}_{B} and I^{2}_{E} were lower in
both MY and %MF for ANN relative to MLR, which shows that ANN predictions
are less bias and more flexible and the direction of changes in the observed
and predicted data are more in convergence for ANN than MLR.
The most important part of Theil`s coefficient (I^{2}) was related
to I^{2}_{E}, which represents an error resulting from
a lack of full convergency in the direction of changes between the observed
and predicted values, particularly for the neural network. This result
was in agreement with the results obtained by Grzesiak et al. (2006).
The major use of any predictive process is to support accurate decisions
which are dependent on a prior knowledge to make possible outcome(s).
The results of this study showed that both MLR and ANN can be used to
predict second parity production from first parity information. MLR models
are simple to design and define parameters. However, the results showed
that ANN systems have the ability to predict second parity 305 day milk
yield and fat percentage with a higher accuracy. Correlations between
the observed values and predictions, together with the other quality parameters
and predictive measures had better situations for ANN relative to MLR.
Also, ANN predictions showed lower deviations from the observed data,
but this difference between ANN and MLR was slight and can be negligible.
Adding new data requires a new statistical model, whereas a neural network
system can update itself with new data. Finally, ANN can be improved with
more additional input variables and training with more actual data to
get more accurate predictions.
ACKNOWLEDGMENT
The authors would like to acknowledge Isfahan University of Technology
for supporting financially P. Hosseinia`s M.Sc. Thesis.