Egg production forecasting: Determining efficient modeling approaches

SUMMARY

Several mathematical or statistical and artificial intelligence models were developed to compare egg production forecasts in commercial layers. Initial data for these models were collected from a comparative layer trial on commercial strains conducted at the Poultry Research Farms, Auburn University. Simulated data were produced to represent new scenarios by using means and SD of egg production of the 22 commercial strains. From the simulated data, random examples were generated for neural network training and testing for the weekly egg production prediction from wk 22 to 36. Three neural network architectures—back-propagation-3, Ward-5, and the general regression neural network—were compared for their efficiency to forecast egg production, along with other traditional models. The general regression neural network gave the best-fitting line, which almost overlapped with the commercial egg production data, with an R² of 0.71. The general regression neural network-predicted curve was compared with original egg production data, the average curves of white-shelled and brown-shelled strains, linear regression predictions, and the Gompertz nonlinear model. The general regression neural network was superior in all these comparisons and may be the model of choice if the initial overprediction is managed efficiently. In general, neural network models are efficient, are easy to use, require fewer data, and are practical under farm management conditions to forecast egg production.

DESCRIPTION OF PROBLEM

Accurate modeling of commercial layer strains during various phases of the egg production cycle, via an easy-to-use procedure, may lead to a better understanding of egg production behavior under new and changing conditions. Such models, in turn, will lead to efficient feed and nutrient intake balances, an improved environment, and enhanced farm profits.

Modeling commercial egg production, however, is a complex and challenging task, mainly because of the nonlinear nature of the egg production curves. Commercial layer flocks typically begin hen-day production (HD) around wk 20, starting slowly around 5% (i.e., 5% of the flock is laying an egg once a day) and with production increasing exponentially for the next 3 to 4 wk until peak production of 95 to 97% HD is achieved around wk 28. This is referred to as phase I of the production cycle, and it lasts until wk 36 to 38. Weeks 39 to 52, referred to as phase II of the production cycle in commercial layer operations, maintains egg production steadily at around 90% HD. Egg production, although maintaining a fairly steady level, slowly begins declining, and this is exacerbated further during phase III (wk 53 to 72), reaching a point of unprofitability around 60% HD. (This HD distribution, broadly depicted in Figure 1, is a general egg production pattern; the individual HD curve is dependent on the specific layer lines, farm management conditions, and other related factors.) At this stage, a decision is usually made either to molt the flock (nutrient restriction and light reduction to force the flock out of production) or to replace the flock with younger birds. In Figure 1 presented here, the average HD percentage curves of most US commercial egg-laying strains are averaged as white-shelled and brown-shelled layers. Data for these production curves were obtained from Roland [1]. Fitting such curves to well-defined mathematical or statistical models is complicated because of the varying shapes and natures of these curves during the 3 phases of the egg production cycle. Factors contributing to curve variations include genetic potential, feed and feeding formulation, ambient temperature, light pattern, and myriad other factors.

Figure 1.

Comparative egg production curves of brown-shelled vs. white-shelled commercial layer strains. Color version available in the online PDF.

Published egg production models using mathematical and stochastic approaches are available. Such approaches, however, are either too complex, as in the case of the compartmentalization model [2], or require too many variables to determine production, as in the case of the stochastic model [3], making such models impractical under most commercial situations. Other models, such as the Gompertz nonlinear model, produce nonsensical results and are unsuitable for the kinds of variables and production data at hand, as shown in this article. A regression equation predicted with feed consumption as the predictor variable gives a fragmented and simplistic view because feed consumption may not be the only contributing factor in egg production.

The present research used a simple approach with only 1 variable, egg production (by classifying the variation in it), to model egg production by using simulation and artificial intelligence approaches of neural networks and genetic algorithms. The neural network models were subsequently compared with other linear and nonlinear models to find an appropriate approach for egg production modeling.

MATERIALS AND METHODS

Comparative egg production and feed consumption data of 22 commercial layer strains were obtained from a comparative layer study conducted at the Poultry Research Farms, Auburn University [1]. Two hundred forty hens of each of the 22 commercial strains [10 brown-shelled egg layers (1 to 10) and 12 white-shelled egg layers (11 to 22)] were reared in an environmentally controlled layer house with ad libitum feed and water. Daily egg production data on each of the 240 hens from each strain were collected and adjusted for hen mortality. Data were summarized into mean weekly HD percentage and mean weekly feed consumption in grams. The data were analyzed using the GLM procedure of SAS version 9.1 [4] to compare egg production and feed consumption among the 22 strains. Significant means were further classified using all pairwise Tukey and Duncan tests. The NLIN procedure of SAS was used to determine production parameters for the Gompertz nonlinear model to predict egg production. Regression models, to predict egg production with feed consumption, were developed using the REG procedure of SAS.

The comparative average egg production percentage of the 22 strains for phase I (wk 22 to 36) are given in Figure 2, and Tables 1 and 2 provide egg production and feed consumption means, respectively, for the entire production cycle from wk 22 to 66.

Figure 2.

Comparative egg production of 22 US commercial strains from wk 22 to 36. Each line represents phase I egg production of 22 strains from wk 22 to 36, whereas the respective symbols on each line represent each week’s egg production. Color version available in the online PDF.

Table 1.

Egg production comparisons of US commercial strains from wk 22 to 66¹

US commercial strains	Egg production %	Comparison by Duncan test	Mean
Strain 1	90.76	Strain 16	91.67a
Strain 2	85.98	Strain 7	91.4ab
Strain 3	90.44	Strain 8	91.31ab
Strain 4	90.76	Strain 1	90.76abc
Strain 5	89.87	Strain 4	90.76abc
Strain 6	89.16	Strain 3	90.44abc
Strain 7	91.4	Strain 5	89.87abcd
Strain 8	91.31	Brown-shelled average	89.78bcd
Strain 9	89.18	Strain 21	89.58bcd
Strain 10	88.87	Strain 23	89.51bcd
Brown-shelled average	89.78	Strain 9	89.18cd
Strain 11	88.18	Strain 6	89.16cd
Strain 12	85.82	Strain 20	89.02cd
Strain 13	80.8	Strain 10	88.87cde
Strain 14	83.96	Strain 11	88.18def
Strain 15	84.69	Strain 18	87.24efg
Strain 16	91.67	White-shelled average	86.89fg
Strain 18	87.24	Strain 22	86.73fg
Strain 20	89.02	Strain 24	86.51fg
Strain 21	89.58	Strain 2	85.98 gh
Strain 22	86.73	Strain 12	85.82gh
Strain 23	89.51	Strain 15	84.69hi
Strain 24	86.51	Strain 14	83.96i
White-shelled average	86.89	Strain 13	80.8j

^a–jMeans in the column with the same letter are not significantly different at P < 0.05.

¹Strains 1 to 10 are brown-shelled and strains 11 to 22 are white-shelled, arranged in descending order for multiple comparisons.

Table 2.

Feed consumption comparisons of US commercial strains from wk 22 to 66¹

US commercial strains	Feed, g/bird per day	Comparison by Duncan test	Mean
Strain 1	113	Strain 6	122a
Strain 2	107	Strain 4	118b
Strain 3	111	Strain 8	118b
Strain 4	118	Strain 7	117b
Strain 5	114	Strain 12	115c
Strain 6	122	Brown-shelled average	114c
Strain 7	117	Strain 5	114c
Strain 8	118	Strain 1	113c
Strain 9	112	Strain 9	112d
Strain 10	111	Strain 3	111d
Brown-shelled average	114	Strain 10	111d
Strain 11	106	Strain 2	107e
Strain 12	115	Strain 16	107e
Strain 13	96	Strain 24	107ef
Strain 14	102	Strain 21	107ef
Strain 15	101	Strain 11	106efg
Strain 16	107	Strain 22	106fg
Strain 18	104	Strain 23	106fg
Strain 20	104	White-shelled average	105gh
Strain 21	107	Strain 18	104hi
Strain 22	106	Strain 20	104i
Strain 23	106	Strain 14	102j
Strain 24	107	Strain 15	101j
White-shelled average	105	Strain 13	96k

^a–kMeans in the column with the same letter are not significantly different at P < 0.05.

¹Strains 1 to 10 are brown-shelled and strains 11 to 22 are white-shelled.

Weekly egg production means and SD were determined from wk 22 to 66 for each of the 22 commercial strains and were used in the monte Carlo procedure of @Risk 4.0 software [5] to simulate percentage egg production data. The simulated data thus generated were a reflection of new scenarios and were used in NeuroShell2 software [6] to train various neural network models. Six simulations were performed, each with 1,000 iterations. On each of 15 sets of mean and SD data, representing each week of production from wk 22 to 36, 20 data points were randomly drawn, to train the neural networks, for a total of 300 observations. Similarly, for testing the neural networks, 10 random data points were drawn (Table 3). Each of those 20 and 10 random observations, representing each week of egg production, was arranged in a single row of a spreadsheet to determine neural network training and testing examples, respectively.

Table 3.

Random samples of simulated data using strain 1 means and SD

Item	Week
	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36
For training epochs, egg production %	6.67	32.09	82.94	96.62	102.52	90.59	96.46	98.62	95.09	96.82	99.55	93.35	98.77	101.16	91.13
	12.62	24.40	40.49	98.56	101.77	90.69	89.17	98.89	94.88	97.06	90.57	98.31	110.05	94.50	92.19
	21.11	33.30	74.09	103.92	86.29	94.44	91.61	101.98	93.85	97.93	86.13	89.72	81.20	92.69	104.61
	54.44	48.34	38.30	95.40	93.46	99.92	94.25	96.60	105.47	99.12	98.35	98.20	85.01	98.08	97.08
	10.86	78.37	106.94	62.99	96.52	91.00	98.87	99.08	96.01	105.06	104.29	94.57	107.11	96.00	95.72
	24.06	47.75	82.23	85.80	89.64	94.25	90.30	103.28	99.36	107.47	91.69	89.08	94.50	89.29	88.26
	14.16	52.19	71.28	67.41	98.35	92.03	94.92	101.88	105.76	98.60	86.28	81.82	95.77	82.56	83.87
	19.67	73.86	79.00	104.25	98.18	98.60	84.20	94.34	98.78	92.66	100.46	101.16	90.71	105.86	106.52
	40.96	50.92	97.52	96.40	90.55	92.38	95.18	99.36	94.93	95.64	106.39	102.36	99.28	97.75	96.60
	54.21	49.90	118.46	105.95	102.85	99.37	90.48	95.10	91.31	87.70	82.96	108.58	93.50	101.97	96.29
	46.47	44.69	98.81	86.63	89.50	94.98	99.91	96.69	93.60	97.98	89.83	106.85	96.20	92.04	94.57
	13.17	40.50	63.15	101.56	106.61	95.86	101.47	101.21	100.31	97.35	104.35	103.36	79.56	84.65	100.82
	12.49	51.23	65.03	88.76	95.36	101.16	100.94	97.00	89.60	99.58	101.03	94.53	99.51	93.44	98.80
	26.99	2.82	66.88	83.16	112.90	102.51	95.67	98.30	97.96	100.32	95.81	90.52	102.71	101.97	95.54
	14.77	59.28	31.04	99.02	97.64	91.61	92.38	98.97	105.09	95.51	89.78	90.01	101.96	113.56	99.19
	35.62	17.94	87.58	105.48	83.93	96.13	101.73	102.64	98.44	101.64	94.61	83.75	93.91	90.36	93.69
	14.60	74.14	98.53	81.33	97.60	91.96	96.28	97.61	95.50	103.25	101.89	97.86	104.68	105.04	99.63
	42.90	61.18	78.70	94.70	98.08	95.01	87.62	96.94	101.92	98.18	101.48	96.46	94.02	105.94	94.39
	30.53	64.85	63.12	88.93	84.80	93.22	89.83	98.96	100.61	99.72	94.04	102.16	97.69	97.02	99.24
	29.65	39.60	40.62	88.90	91.90	89.95	93.41	98.40	101.53	110.37	96.47	88.56	87.01	102.45	96.56
For testing epochs, egg production %	5.03	60.58	39.86	120.67	103.52	94.73	96.69	95.09	94.95	105.84	103.59	92.25	89.34	93.65	95.61
	13.40	66.64	70.72	88.80	96.09	92.23	97.21	100.99	99.21	92.55	91.28	89.42	95.78	106.56	96.39
	29.34	60.30	74.44	72.91	100.38	95.72	94.04	102.49	104.02	92.62	82.46	98.68	103.24	97.47	93.56
	2.73	6.43	66.67	82.79	109.14	91.58	88.87	101.08	93.21	99.98	83.20	95.21	94.94	89.34	94.67
	47.82	38.96	60.64	74.77	86.99	92.88	88.72	93.29	98.32	96.08	108.46	106.44	93.47	93.06	92.31
	30.01	67.06	92.53	88.75	106.32	94.50	98.11	97.34	93.69	106.93	87.17	103.23	84.59	103.07	99.73
	44.40	53.75	99.02	99.25	89.51	89.25	99.10	98.86	101.02	103.41	91.11	89.46	93.41	99.48	85.05
	39.70	48.59	70.26	77.28	93.74	96.76	96.79	97.99	96.89	102.73	98.23	90.62	96.06	92.95	100.67
	9.13	57.89	89.52	79.38	82.62	96.61	95.02	99.03	101.44	100.54	102.18	91.09	94.28	92.79	91.58
	10.21	68.89	69.86	77.95	103.82	96.24	102.74	102.83	101.32	99.28	90.86	97.16	94.09	103.44	93.63

Beginning from the first observation, the first 4 egg production observations were used as inputs, whereas the fifth observation was used as the output, to constitute 1 training example, referred to as an epoch in the neural network literature and comparable with replicates in biological experiments. The second training example consisted of the second, third, fourth, and fifth observations as inputs, whereas the sixth observation was used as the output to represent the second training example. This process was iterated until all the training examples from wk 22 to 36 were generated, for a total of 105 examples. (Week 22 training epochs are given in Table 4.) Various neural networks, using NeuroShell2, were then trained on those training epochs until no further improvements were observed in these models. At that point, the training was stopped. The neural networks trained to predict the phase-I egg production curve were tested by using randomly drawn simulated-test data, which were arranged similarly to the training data. However, the neural networks were not previously exposed to such test data. A brief description on the inner workings and data manipulation of the neural network is given below.

Table 4.

Training and testing epochs developed for the neural network training and testing

Age	Epoch	Input 1	Input 2	Input 3	Input 4	Output
Training example, egg production %
wk 22	Epoch 1	6.67	12.62	21.11	54.44	10.86
wk 22	Epoch 2	12.62	21.11	54.4	10.86	24.06
wk 22	Epoch 3	21.11	54.44	10.86	24.06	14.16
wk 22	…	54.44	10.86	24.06	14.16	19.67
wk 22	…	10.86	24.06	14.16	19.67	40.96
wk 22	…	24.06	14.16	19.67	40.96	54.21
wk 22	Epoch 7	14.16	19.67	40.96	54.21	46.47
Test example, egg production %
wk 22	Epoch 1	5.03	13.4	29.34	2.73	47.82
wk 22	Epoch 2	13.4	29.34	2.73	47.82	13.01
wk 22	Epoch 3	29.34	2.73	47.82	30.01	44.4
wk 22	…	2.73	47.82	30.01	44.4	39.7
wk 22	…	47.82	30.01	44.4	39.7	9.13
wk 22	…	30.01	44.4	39.7	9.13	10.21
wk 22	Epoch 7	44.4	39.7	9.13	10.21	60.58

Neural Networks

A neural network is a computer program (series of instructions) that loosely behaves like a biological brain. Millions of neurons in the biological brain work together in parallel, each trying to solve a tiny bit of a complex problem. This type of problem solving (i.e., to divide and conquer) seems very efficient for “fuzzy” data (data that are not very clear), for making decisions based on past experiences, and for associating and applying the acquired knowledge to new situations.

Neural networks learn by example. To train a neural network under supervision for a specific problem, it needs to be shown good examples in which the inputs and outputs are already known. On the basis of these examples, the network builds a model for the problem. Training data can be obtained from historical problem data in which the outcomes are already known, by creating sample problems and solutions with the help of experts, or through empirical research where feasible.

A typical neural network usually has 3 layers of “neurons,” each of which is connected to the neurons in the next layer (Figure 3). Each connection has a “weight” associated with it. Input values in the first layer are weighted and passed on to the hidden layer. Neurons in the hidden layer produce outputs by applying an activation function to the sum of the weighted input values. These outputs are then weighted by the connections between the hidden and output layers. The output layer produces the desired results.

Figure 3.

Schematic view of a neural network. X1 to X5 = input layers of data; Z1, Z2 = output layers of results. Color version available in the online PDF.

The network “learns” by adjusting its interconnection weights repeatedly so that the output neurons produce results close to the correct outputs in the training data. Eventually, if the network learns the problem, the weights become stable. The real power of the trained network lies in producing good results for data that it has never encountered before.

When a network with back-propagation architecture is presented with the training set, the neuron transforms sums of inputs into weights that are transferred to other neurons. The difference between the predicted output and the actual training output is computed. The error is propagated backward through the hidden layer to the input layers. The connection weights between neurons and layers are adjusted until the output error is minimized. All the training set data are presented until the network is able to duplicate the training set with success. This trained neural network can then be used to predict outputs when given inputs on which it has not been trained. Further information on neural networks and their use to predict other poultry-related variables can be found in previously published papers [7, 8]. A detailed description of neural networks is available [9].

RESULTS AND DISCUSSION

The mean HD percentage and feed consumption of 22 commercial strains from wk 22 to 66 are given in Tables 1 and 2, respectively. Brown-shelled strains (1 to 10) on average consumed significantly more feed (114 g/d) and produced more eggs (89.78%) than did white-shelled strains (11 to 22), which, on average, consumed 105 g of feed/d with 86.89% egg production (P ≤ 0.05). Strain 6 consumed the highest amount of feed (122 g/d), strain 7 had the highest egg production (91.4%), and strain 13 consumed the lowest amount of feed (96 g/d) and also had the lowest egg production (80.80%). Detailed comparisons among respective strains, using the Duncan multiple range test, are given in Tables 1 and 2 for egg production and feed consumption, respectively. As expected, brown-shelled strains, in general, consumed more feed and produced more eggs compared with white-shelled strains.

Regression analysis for egg production using feed consumption as the independent variable (predictor), from wk 22 to 66 for all strains, resulted in the prediction equation 4.0428 + 0.7663feed consumption, whereas using the phase-I (wk 22 to 36) data, the prediction equation was −47.28 + 1.2883feed consumption. The corresponding egg production results using these equations for wk 22 to 66 and wk 22 to 36, respectively, are given in Figures 4 and 5, whereas Figure 6 compares the 2 predictions with the actual egg production percentage of strain 1 and the general regression neural network-predicted egg production. Beginning from wk 22, both regression models overpredicted until wk 24, when they leveled off; slightly underpredicted until wk 29; and then overpredicted until wk 36. The general regression neural network overpredicted until wk 24 (with a lesser differential than the regression models), but from wk 25 to 36 it predicted perfectly, overlapping the actual egg production curve.

Figure 4.

Predicted egg production percentage using the linear regression equation −4.0428 + 0.7663feed consumption, determined from data from wk 22 to 66. Color version available in the online PDF.

Figure 5.

Predicted phase I egg production percentage using the linear regression equation 47.28 + 1.2883feed consumption, determined from data from wk 22 to 36. Color version available in the online PDF.

Figure 6.

General regression neural network comparisons (GRNN) with linear regression equations and strain 1 egg production. Egg production % = phase 1 (wk 22 to 36) actual egg production data of strain 1; GRNN wkly average = egg production predicted with the general regression neural network; RegPred wk 22 to 36 = egg production predicted using the regression equation −47.28 + 1.2883feed consumption; RegPred wk 22 to 66 = egg production predicted using the regression equation 4.0428 + 0.7663feed consumption. Color version available in the online PDF.

The Gompertz model of the equation, egg production = A exp[(−log(A/B) exp(−Kt)], was used to predict egg production [10]. The 3 parameters, A (maximum egg production), B (the intercept at wk 0), and K (the rate constant), as well as t (the time of egg prediction at weekly intervals), were initially determined from the egg production data of 22 commercial strains from wk 22 to 66. The maximum egg production (A) was 95%; the intercept at wk 0 (B; assumed at wk 21) was 5%; and the rate constant (K) was calculated to be 0.082. These parameter values were then used in the NLIN procedure of SAS to determine the nonlinear parameters to be used for the egg production prediction and were 6.05E09, 80.6, and 0.00018, respectively, for A, B, and K. Beginning from t = 22 to 66, weekly egg production was determined from wk 22 to 66 and is given in Figure 7. The Gompertz model produced nonsensical results (which did not change when converted to log or log natural) in absolute values; however, the overall curve showed a linear trend in egg production from wk 22 to 66. This is unlike the characteristics of the actual production curves, which begin exponentially, achieve a plateau, and then steadily decline. The Gompertz prediction equation used in this research seems unsuitable for the prediction of egg production, even though such an equation had been used successfully to predict several growth variables across many species. These results are being reported for further critique and model or parameter modifications. The main argument for using such a Gompertz model was that egg production, particularly during the initial surge, mimics exponential growth, tapering off once the peak production is achieved. Other models, such as neural networks, were also inefficient during this initial surge of egg production but were very efficient afterward.

Figure 7.

Nonsensical egg production percentage from wk 22 to 66 using the Gompertz nonlinear model. Color version available in the online PDF.

Results of the neural network models are given in Table 5 and Figures 8, 9, and 10. The 3 neural network models—back-propagation-3, Ward-5, and general regression—were trained using the data simulated from strain 1 data means and SD. The general regression neural network model produced the best-fitting curve, compared with the other 2 models, with an R² value of 0.715 when exposed to test data and selected for further comparisons. The detailed results of all 3 neural network models are given in Table 5. The general regression-predicted phase-I curve compared with the original strain 1, average curves of brown-shelled egg strains and white-shelled egg strains, and results are given in Figures 8, 9, and 10, respectively. In all 3 of these comparisons, the general regression network overpredicted initially, but then tapered off from the initial surge. For the brown-shelled egg strains, however, the initial overprediction was less stark than the other 2 comparisons. Apart from the initial anomaly, the general regression neural network predicted egg production with great accuracy. Egg production, particularly during wk 22 to 25, when it quadrupled in only 3 to 4 wk, is difficult to predict with any of the models used. If this area of the production curve is managed efficiently, the neural network will be the most successful model, given the ease of use, data requirements, and expediency under commercial conditions. Neural network models, in general, are efficient, are easy to learn, and use and require fewer data than most of their counterparts. Models are useful to a certain extent; beyond that, it still depends on the variable being modeled and on human expertise. A combination of knowledge based-prediction and expert opinion may make the best forecast under any given circumstance, and egg production is certainly not an exception.

Table 5.

Neural network model comparisons using simulated egg production data¹

Parameter	BP-3	GRNN	Ward-5	Linear regression
R2	0.681	0.715	0.697	0.3597
r2	0.78	0.75	0.76	0.3591
Mean squared error	136.09	121.51	129.38	Root mean square error 10.98
Mean absolute error	7.81	7.28	7.40	CV 12.43
Minimum absolute error	0.04	0.12	0.09
Maximum absolute error	46.54	43.54	48.40
Correlation coefficient r	0.88	0.86	0.87
Percentage within 5%	45.71	49.52	50.48
Percentage within 5 to 10%	25.71	24.76	20.95
Percentage within 10 to 20%	16.19	15.24	18.10
Percentage within 20 to 30%	5.71	2.86	4.76
Percentage over 30%	6.67	7.62	5.71

¹BP-3 = 3-layer back-propagation neural network model; GRNN = general regression neural network; Ward-5 = 5-layer Ward neural network.

Figure 8.

General regression neural network (GRNN) phase-I egg production comparison with the actual strain 1 curve. Egg production % = wk 22 to 36 egg production of strain 1; GRNN wkly average = egg production predicted with the general regression neural network. Color version available in the online PDF.

Figure 9.

General regression neural network phase-I egg production comparison with the average curve of brown-shelled egg strains. Brown average = average egg production data of brown-shelled strains (strains 1 to 10); GRNN wkly average = egg production predicted with the general regression neural network. Color version available in the online PDF.

Figure 10.

General regression neural network phase-I egg production comparison with average curves of white-shelled egg strains. White strain average = average egg production data of white-shelled strains (strains 11 to 24); GRNN average = egg production predicted with the general regression neural network. Color version available in the online PDF.

CONCLUSIONS AND APPLICATIONS

1. Data simulations offer an efficient alternative to empirical studies, new scenarios, replacement of missing data, or their combination if historical data distributions can be effectively manipulated within biological and computational bounds by using either empirical evidence or expert-based opinion.

2. Neural network models can successfully replace traditional mathematical and statistical models in predicting future egg production in layers. These models are easier to use, require fewer variables, and can be more efficient compared with their mathematical counterparts in predicting egg production and other such physiological variables.

3. Further research, particularly in bird nutrient requirements, may advance our understanding of neural network models.