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Dipartimento di Scienze della Produzione Animale, Facoltà di Medicina Veterinaria, Università degli Studi di Udine, 33010 Pagnacco (Ud), Italy and
Federal Research Institute for Agriculture in the Alpine Regions, A 8952, Irdning, Austria
1To whom correspondence should be addressed. E-mail: bruno.stefanon{at}dspa.uniud.it.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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KEY WORDS: • modeling • neural networks • nitrogen excretion • purine derivatives • cows
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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–3
). The excretion of urinary nitrogen in ruminants depends on the protein intake, the protein absorption in the intestine, the biological value of the protein absorbed and the efficiency of nitrogen capture by rumen microrganisms (4
). The excretion of purine derivatives (PD)3
in the urine has been used to predict microbial protein synthesis in ruminants (5
–9
). The excretion of PD is related to the absorption of exogenous purines in the gut, which is related to the amount of microbial yield leaving the rumen. The total excretion of urinary PD can be partitioned into an exogenous fraction related to rumen microbial synthesis and an endogenous contribution associated with the turnover of purines at tissue level. Some authors (6
,8
) have proposed that the PD endogenous fraction is a function of metabolic live weight (LW). Other authors (10
) have proposed that the endogenous excretion of PD in cattle varies according to the physiological status of the cows, thus giving a different endogenous PD excretion for dry and lactating animals. An examination of the factors affecting the excretion of urinary nitrogen and PD in dairy cows requires a large dataset obtained under a wide selection of dietary and nutritional conditions and advanced modeling tools to study the relationship between the different factors involved. New techniques for data analysis have recently been introduced. Neural networks are different from conventional statistical tools (e.g., correlation and linear regression) and represent an alternative method of investigation. The so-called neurocomputing techniques provide an alternative to programmed computing because they are based on standard transformations and do not require prearranged algorithms or rules (11
). An introduction to artificial neural networks
An artificial neural network (ANN) is a parallel distributed structure devoted to information processing, consisting of processing elements. As described by Hecht-Nielsen (11
) the processing elements of the network, called nodes, are related to each other by connections; each connection is assigned a weight and each node can receive any number of input connections and can have any number of outgoing connections that fan out the same signal. A generic processing element is provided with a local memory and has a transfer function that can use the local memory and the input signals to generate the output signal. Sarle (12
) has described neural networks as a "bunch of neurons," "simple linear or nonlinear computing elements interconnected in often complex ways and often organized into layers." A particular neural network structure, the multi-layer perceptron (MLP), is discussed in this article. Such a structure is a supervised neural network consisting of three different layers of nodes: input, hidden and output layers. Nodes within the same layer are not connected to each other horizontally but have vertical connections to those of preceeding and following layers (Fig. 1
). The term supervised refers to the type of training scheme adopted during the adaptation phase, when the neural network is exposed to a particular dataset according to a training schedule. In supervised training, the network is supplied with a series of input and output pairs, then the adaptation takes place by comparing the correct output value used for the training process with the model actual output (an estimation of the correct output). As discussed by Sarle (12
), MLP are flexible, nonlinear models able to approximate virtually any function and can be used when there is "little knowledge about the form of the relationship between the independent and the dependent variables"; the complexity of MLP models can be changed "by varying the number of hidden layers and the number of hidden neurons in each hidden layer." If the number of neurons in the hidden layers is small, then the MLP is a parametric model and an alternative to polynomial regression (12
). This new approach can be used for some real-world applications, such as sensor processing, pattern recognition, data analysis and control. Roush and Cravener (13
) used neural networks to predict amino acid contents in feed ingredients, and recently Berg et al. (14
) developed a neural network to predict pork carcass composition from electromagnetic scanning. Neural networks in agriculture would be widely applied if accurate predictions could be obtained using a small number of key variables easy to measure on farms. In this respect, networks with a small number of input variables would be ideal, and their performance, therefore, could challenge those of a traditional multiple regression analysis.
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The present study is based on the hypothesis that neural network models can be used to study complex physiological aspects like those governing the use of nitrogen in the rumen and the excretion of total nitrogen in the urine of cows.
In this study, a comparison of ANN with traditional linear regression methods has been carried out with the aim of: predicting urine nitrogen excretion using simple parameters measurable at a farm level, predicting the urinary excretion of PD by means of simple parameters affecting microbial synthesis in the rumen, and examining the role of LW and milk yield (MILKY) as possible factors affecting the excretion of PD in cows.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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The database used to develop and test the model consisted of 177 nitrogen balances carried out on dry (four experiments) and lactating cows (three experiments) at the Department of Animal Production Science of the University of Udine and at the Federal Institute for Alpine Studies at Irdning (Austria). Methodological and technical details of the trials are reported in the study by Gruber et al. (15
) and in other published articles (16
–19
). All of the trials were conducted according to the approved national protocols regarding experiments with animals. The intake of non-structural carbohydrates (CHOINT) was calculated by subtracting crude protein (CP), neutral detergent fiber (NDF), ash and ether extract from dry matter (DM) intake. This gives an estimate of nonstructural carbohydrates (NSC) intake, because the difference between NDF and NDF-bound protein (20
) was not accounted for. In situ rumen degradability trials for CP and non-protein dry matter (NPDM) of the forages and the concentrates fed to the cows were carried out according to the standards described by the Commissione Proteine nella Nutrizione e nell’Alimentazione dei Poligastrici (21
), and data were fitted to the model proposed by Ørskov and McDonald (22
). The amount of CP and NPDM effectively degraded in the rumen were computed using the rumen outflow rate for forages and concentrates as predicted by the equations proposed by Owens and Goetsch (23
). The following variables were selected as direct inputs or indirectly used to calculate the input variables: DM intake (DMI; g/d), CP intake (CPINT; g/d), CHOINT (g/d), NDF content of the diet (NDFC; % DM), effective degradability of NPDM (DegNP; g/d) effective degradability of nitrogen (DegCP; g/d), MILKY (kg/d) and LW (kg). The output variables were daily urinary excretion of nitrogen (NURI; g/d) and daily PD nitrogen (PDN) excretion (g/d, calculated as the sum of allantoin and uric acid nitrogen). The original database was split in two for modeling purposes. A first training dataset (n = 130) was used to develop two multiple linear regressions (MLR) aimed at predicting NURI and PDN (24
). The same dataset was then used to obtain two ANN models (25
) devoted to predict NURI and PDN by means of the same variables chosen to develop the regression equations. A second challenge dataset (n = 47) was used to validate the MLR and ANN models. The main dietary, rumen and animal parameters used in the training and in the challenge datasets are presented in Table 1
.
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The linear model equation to predict NURI was developed using five variables: CPINT, DegNP, NDFC, LW and MILKY. The intercept of the MLR equation did not result significantly different from 0, and, consequently, model with no intercept was recomputed. The second objective of the modeling exercise was to develop an MLR equation to predict PDN with the aim of highlighting the parameters affecting microbial synthesis and the related PDN excretion. A third objective was to investigate the role of LW and milk production level in determining PDN metabolic excretion. For this reason the following variables were adopted as regressors: LW, CHOINT, the ratio between NPDM and CP effectively degraded in the rumen (DNPDCP; g/g), and MILKY per unit of DMI (MILKDM; kg milk/kg DMI). As in the first case, the intercept did not result significantly different from 0, and a model with no intercept was adopted.
Developing an ANN.
Using the same variables as in the linear regression models, the software package NEURAL CONNECTION, Version 2.0 (25
) was used to fit a truly connected MLP model to the training dataset. Fully connected means that every node in each layer is connected to every node in the layer above and below. The structure of the MLP chosen is as follows.
The total input of the jth node of the hidden layer is:
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where wij is a weight associated with the connection from input layer "i" and hidden layer "j," bj is the bias and xi is the input variable.
The value passed to the single output node from the jth node of the hidden layer is:
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where 
h is the logistic (sigmoidal) transfer function of the hidden layer; note that the use of a logistic transfer function does not imply that there is a direct sigmoidal relationship between input and output layers. Then:
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The output of the MLP is:
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where djk is a weight associated with the connection from hidden layer "j" and output layer "k," co is the bias and yj is the passed variable of the hidden layer.
The value passed to the single hidden node to the output layer "k" is:
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The transfer function o of the output layer is linear.
The software package NEURAL CONNECTION, Version 2.0 (25
) calculates the bj, wij, co and yjk by means of a back propagation learning rule. This involves repeatedly adjusting the parameters of the model until the error between the predicted values and actual outputs is minimized. The MLP is susceptible to a phenomenon of overtraining, i.e., the model tends to model the noise element of the data as well as the signal. To overcome this, a second training test dataset is used to monitor the predictive capabilities of the model. In the present study the training dataset was randomly split into a training dataset (n = 117, i.e., 90% of the data) and a training test dataset (n = 13, i.e., 10% of the data). The model error was evaluated by the software both on the training and the training test datasets by calculating mean square error between the correct and the actual output values.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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The input variables were included in the linear regression and neural network models because of their potential role in explaining the output variables. CPINT is a direct determinant of NURI as a fraction of dietary protein degraded in the rumen and fermented to produce ammonia escaping in the portal blood (26
). Dietary amino acids absorbed in the gut that are in excess of tissue requirements can be deaminated in the liver and converted to urea. NDFC and DegNP affect rumen environment and nutrient availability for microbial populations. Microbial synthesis and protein fermentation affect ammonia escape from the rumen and, therefore, nitrogen excretion in the urine. The amount of fiber in the ration (NDFC) affects rumen pH (27
). The NDF content of forages has been negatively correlated with CP potential degradability (28
), and a high NDF forage content has been associated with low CP effective degradability in both roughages and concentrates (29
). DegNP can be compared with carbohydrate availability in the rumen, the lack of which can lead to an increased bacterial fermentation of protein (30
) and, consequently, to ammonia production and nitrogen escape in the portal blood. Recent models based on metabolizable protein have assumed that a fraction of the absorbed amino acids supports milk production (31
). For this reason MILKY has been chosen to control the partition of the absorbed protein toward milk production. LW was introduced in the model because metabolic LW affects endogenous urinary nitrogen (32
). The prediction of the urinary excretion of PDN was the second objective of this study. Several researchers have suggested that the metabolic fraction of these compounds is related to animal body mass (6
,8
); therefore, LW was also included in the MLR and ANN models. CHOINT was taken into account because NSC can be rapidly fermented in the rumen (20
). The ratio DNPDCP was considered because microbial synthesis is affected by protein and carbohydrate (or energy) availability in the rumen (33
–36
), the latter being represented in the present case by DegNP. Stefanon et al. (10
) suggested that the amount of PD degraded in the tissues can be higher in lactating cows than in dry cows. To isolate the effect of MILKY on metabolic PDN, the ratio between the amount of milk produced per each unit of DMI was computed (MILKDM). A preliminary correlation analysis of the training dataset revealed a strong correlation between MILKY and DMI and that both variables were correlated to PDN excretion. For this reason, the effect of milk production was expressed in terms of a milk:DMI ratio.
Selection of the ANN.
The complexity of a model varies according to the number of hidden layers and the number of neurons in each hidden layer (12
). Increasing the number of nodes in the hidden layer usually improves the performance of the MLP over the training set, however such an advantage is not necessarily reflected on the training test set. Given a certain number of input variables and a certain number of outputs to predict, the neural network architecture is determined by the number of the nodes in the hidden layer. The optimal number of the nodes in the hidden layer is chosen on the basis of the MLP performance measured on the training test set. Adding new nodes in the hidden layer may lead to better results in terms of model prediction ability but on the other hand the model might learn the error (i.e., "the noise") associated with the data. Should this happen, the neural network would lose its predictive power. Some researchers applying Neural Networks have proposed methods to achieve the best model performance; these are concerned either with the best architecture, i.e., the number of nodes to be considered in the hidden layer (37
,38
), or with a strategic interruption of the training phase (39
). In the present study the best model architecture was selected by testing a wide selection of nodes in the single hidden layer of the MLP. A range of one up to fifteen nodes in the hidden layer were studied, monitoring the model performance in terms of the error computed on the training set and the training test set. The error computed on the training test set was used to avoid overtraining as well as to choose the best model architecture. Addition of additional nodes in the hidden layer was evaluated in terms of performance on the training test set. The architecture showing the lowest error on the training test set was then chosen as the best model. The best model architecture for NURI and PDN presented, respectively, four and five nodes in the hidden layer.
Comparison between neural networks and linear equations performances.
The coefficients and statistics of MLR for NURI and PDN are reported in Table 2
. The selected variables always entered in the model with a high level of statistical probability, for both the dependent variables. The parameters of the ANN, reported in Table 3
, refer to the weights of each node of the networks, which can be used to reproduce the ANN model (for details see the ANN: model development paragraph and formulas reported in Fig. 1
).
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. Coefficients of determination of the predicted vs. observed values (according to a linear regression equation as PRED = a + b x OBS) and analysis of the residuals were calculated both for model formulation based on the training dataset (n = 130) or model evaluation based on the independent challenge dataset (n = 47). With regard to NURI, when tested in terms of model fitting (n = 130), the ANN model performed slightly better in terms of coefficient of determination and of SE (0.891 and 15.57, respectively) than the MLR model (0.861 and 17.33 for R2 and SE, respectively). The plot of the residuals (predicted - observed) vs. the observed values indicate that they were randomly distributed for both the models (Fig. 2
), exhibiting a non-significant mean bias and a slight linear bias (Table 4)
. With reference to PDN prediction, in terms of model fit (n = 130), the ANN proved to be clearly superior to MLR (R2 = 0.844 and 0.759, SE = 1.6024 and 1.9482 for ANN and MLR, respectively). In contrast, the analysis of residuals revealed for both methods a higher linear bias, as is evident from Figure 3
, showing an under-prediction for PDN excretion above the threshold of 20 g/d.
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. The intercept and the slope of the regression equation PRED = a + b x OBS, resulted significantly different from 0 and 1, respectively. The mean bias computed on the residuals was not significant, but both ANN and MLR statistics revealed a higher significant linear bias (-0.3847 and -0.4199, respectively; P < 0.0001) with respect to that computed for the training dataset, as expected. The regression analysis of predicted and observed values for PDN obtained by ANN and MLR showed only slight differences, because the coefficients of determination were very similar (0.688 and 0.666 for ANN and MLR, respectively) and the intercept and the slope significantly differed from 0 and 1, respectively (Table 4)
. The mean bias was not significant, but again the linear bias was significant for both models (-0.3847 and -0.3064 for ANN and MLR, respectively; P < 0.0001).
The results so far presented suggest some difficulties in the application of neural networks to biological systems. Such systems involve a higher level of complexity than do many physical systems, which can often be successfully modeled by ANN (40
).
Neural networks scenario and model response.
The neural network models obtained for PDN and NURI (training dataset, n = 130) were further evaluated in terms of their response to input variations. The behavior of the output was tested when varying inputs according to sound nutritional and physiological dairy concepts. Such an investigation is available as an option in the NEURAL CONNECTION, Version 2.0 software (25
). Basically, the response of the model is checked by varying an input variable under study against another input variable set to a desired value, while all remaining inputs are kept at their mean value. An arbitrary value between the highest and the lowest value of the training dataset was chosen for each input variable under study. Such a value was increased or decreased by 5% and the corresponding response of the output of the model was recorded. This analysis provides a graphical description of the relationship between a single input variable and the output. Given the large amount of figures needed to show all the input variables effects on NURI and PDN, here only the effect of LW and MILKY on NURI, the effect of CHOINT and DNPDCP on PDN, and the effect on LW and MILKDM on PDN are presented as graphical responses.
The response of the neural network model to MILKY variation is showed in Figure 4A
. The response in terms of NURI to a change in MILKY was studied from a starting value of 17.9 kg/d, against a CPINT fixed at 2291 g/d. A 50% reduction in MILKY generates a 24% increase in NURI excretion (Fig. 4A
), whereas an increase of MILKY from 17.9 kg/d to 26.8 kg/d (+50% MILKY) causes a lower urinary nitrogen excretion of 11.9%. When a fixed amount of protein digested is available, an increased requirement for MILKY causes a lower amount of nitrogen wasted in the urine, a result consistent with current concepts in dairy cow physiology (41
).
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. Starting from a cow body weight of 647 kg against a fixed value in CP intake of 2030 g/d, a 20% increase in LW induces a 7.2% higher NURI excretion, whereas a reduction of LW from 647 to 517 kg (-20%), generates a 14.7% lower NURI excretion. This behavior is consistent with the well-known relationship between endogenous urinary nitrogen and cattle body weight (32
). The behavior of the model to simultaneous changes in MILKY and LW is depicted in the surface response graph Figure 5
. In this case, the neural network correctly predicts a higher NURI when the LW is increased from 500 to 800 kg, whereas the combined effect of a lower MILKY causes a further increase of NURI.
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,42
) providing more energy available to microbial population.
The model also reacted to variations in the ratio of non-protein DM degraded to CP degraded (DNPDCP). A change of -50% and +50% of the basic value of 10.3 of DNPDCP ratio against a fixed value of CHOINT of 4523 g/d, respectively, resulted in a 38.6% increase and in a 24.8% decrease of PD excretion. The ratio between non-protein DM degraded and the CP degraded is a gross index of the balance between energy and nitrogen availability in the rumen. Stokes et al. (43
) reported lower bacterial efficiencies (grams of bacterial N per kilogram of DM digested) as a result of a wider NSC:degradable protein intake ratio in experiments with continuos cultures. This behavior can be confirmed in the present model by the surface response graph in Figure 6
, which shows a reduction of PDN when CHOINT increases if DNPDCP is contemporarily increased.
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shows the interaction between LW and MILKDM. This surface response graph shows PDN variations within the range of 6–12 g/d, below the threshold of 20 g/d, where the ANN model exhibits lower accuracy of prediction (Fig. 3)
. In general terms, although an increase in MILKDM always generates a higher PDN response, an increase in LW results in a tendency of PDN to decrease, at least at high values of MILKDM. For instance, an increase of MILKDM from 0 to 2 when the LW is fixed at 494 kg (left side of the surface graph) induces a 72% increase in PDN, whereas the variation is lower (+61%) when the LW is fixed at 800 kg (right side of the surface graph). Despite this apparent inconsistency (i.e., lower PDN excretion when increasing LW), it should be noted that a larger body mass implies a higher rumen volume and, consequently, a lower passage rate of digesta given a certain level of DMI. As is classically recognized, decreasing passage rate would drive a lower microbial efficiency because of the increased proportion of energy expended on microbial maintenance (23
,44
). Furthermore, a lower passage rate in the rumen causes an increased recycling of microbial DM. These effects lead to a lower microbial matter net flow rate and, consequently, of microbial purines from the rumen. The surface response graph in Figure 7
shows an increased PDN excretion with high milk production cows (i.e., higher MILKDM). This effect could be explained by more intensive purine degradation in lean tissue as a consequence of an increased tissue turn over in high milk potential cows. This scenario supports the observations by Stefanon et al. (10
) of a larger endogenous PDN excretion in lactating vs. dry cows and would also suggest that the metabolic PDN excretion is correlated to MILKY production. This latter observation needs to be validated experimentally.
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FOOTNOTES |
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3 Abbreviations used: ANN, artificial neural network; CHOINT, non-structural carbohydrates intake; CP, crude protein; CPINT, crude protein intake; DegCP, effective degradability of nitrogen; DegNP, effective degradability of non-protein dry matter; DMI, dry matter intake; DNPDCP, ratio between non-protein dry matter and crude protein effectively degraded in the rumen; LW, live weight; MILKY, milk yield; MILKDM, milk yield per unit of dry matter intake; MLP, multi-layer perceptron; MLR, multiple linear regression; NDF, neutral detergent fiber; NDFC, NDF content of the diet; NPDM, non-protein dry matter; NURI, urinary total nitrogen excretion; PD, purine derivative; PDN, purine derivative nitrogen.
Manuscript received April 19, 2001. Initial review completed July 23, 2001. Revision accepted September 27, 2001.
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LITERATURE CITED |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONLITERATURE CITED |
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