Livestock Research for Rural Development 30 (10) 2018 Guide for preparation of papers LRRD Newsletter

Citation of this paper

Modelling egg production in Sasso dual-purpose birds using linear, quadratic, artificial neural network and classification regression tree methods in the tropics

A Yakubu, O I A Oluremi1 and Z N Ibrahim

Department of Animal Science, Faculty of Agriculture, Nasarawa State University, Keffi, Shabu-Lafia Campus, P.M.B. 135, Lafia, Nasarawa State, Nigeria.
1 Department of Animal Nutrition, College of Animal Science, University of Agriculture, Makurdi, Nigeria


The use of robust algorithms in the prediction of egg production is gaining more prominence in recent times. This study, therefore, aimed at estimating egg number from the age (weeks) of Sasso dual-purpose chicken breed using two traditional regression tools (Linear and Quadratic functions) and two robust models [artificial neural network (ANN) and classification regression tree (CRT)]. Such prediction will enable better understanding of the trend of egg production, thereby aiding management decisions to boost production. A total of Fifty four (54) 30-week old Sasso hens were randomly allocated to individual cages. Out of these, records on thirty eight surviving birds with consistency in lay were utilized. Egg records totaling 760 were divided into five different ages (weeks): 31-34; 35-38; 39-42; 43-46 and 47-50.

The prediction of egg number from age using both linear and quadratic functions followed a similar pattern. The corresponding R2, adjusted R2, RMSE and significance level were 66.0%, 66.0%, 0.72 and p<0.001 (Linear); 67.0%, 67.0%, 0.71 and p<0.001 (Quadratic). However, in the ANN model, R2, adjusted R2, RMSE and significance level were 70.3%, 70.2%, 0.67 and p<0.001 between the actual egg number and the predicted egg number. The predicted mean weekly egg value using ANN model (4.70) also appeared similar to the observed value of 4.69. The CRT approach revealed that optimal egg production goes beyond 48 weeks of age with R2 value of 70.3%. Both ANN and CRT models appear to have more predictive power than the Linear and Quadratic functions. Therefore, they could be exploited in the estimation of egg number in laying birds with better accuracy in a tropical environment.

Key words: algorithms, forecasting, layers, optimality


There is growing demand for livestock and their products as a result of increase in incomes, urbanization and population in many parts of the third world countries (Brankaert et al 2000; Marwa et al 2018). Egg production involves the use of layers with good genetic potential. However, the age of birds remains one of the important factors required for improved quantity of eggs (Nwogu and Acha 2014). The use of mathematical models in the poultry industry has been proposed (Sakomura 2004). Accurate modeling of commercial layers at different ages of egg production may facilitate better understanding of egg production dynamics which could eventually lead to a great improvement in poultry farm profits (Ahmad 2011).

Traditional regression approaches such as linear and quadratic models have been applied in the poultry industry. However, these approaches are not robust enough and the regression coefficients may be prone to large standard errors. Burnham and Anderson (2002) reported that linear predictive equations may be biased in the estimation of parameters and inconsistent among the model selection algorithms. Artificial Neural Network (ANN) is an alternative predictive model. It is a machine learning tool which explores information from the input variables and target variable to train a model that maps the relationship function between the response and predictor variables, thereby permitting future predictions (Bishop 2006; Felipe et al 2015). It processes data using a set of interconnected neurons or nodes, just like a biological brain with millions of neurons working in parallel, each trying to solve a tiny bit of a complex problem.

A neural network works by taking the values of predictor or input fields and feeding them into the algorithm as an input layer. The input values in the first layer, according to Ganesan et al (2014) 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 plus a bias value. The model can be used for early detection of problems and adjust the production curve of commercial eggs (Morales et al 2016). Classification and Regression Tree (CRT), a tree-based non-parametric algorithm,is another tested robust model in applied sciences. A binary classification tree is created by partitioning a subset into two smaller subsets recursively and error estimated using a ten V-fold cross validation. This technique is structurally simple and outputs can be visualized easily (Karabağ et al 2010; Yakubu 2012).

Sasso birds are dual-purpose chicken breed developed in France. The birds, which have been tested and found adaptable to the tropical environment (Yakubu and Ari 2018), were recently introduced into Nigeria, Sub-Saharan Africa. However, there is dearth of information on the use of statistical regression models to predict egg production in Sasso birds. This study therefore, aimed at predicting egg number from the age (weeks) of laying Sasso hens using four different algorithms.

Materials and methods

Location of study

The experiment was conducted at the Poultry Unit of the Livestock Section of the Teaching and Research Farm, Faculty of Agriculture, Nasarawa State University, Keffi, Shabu-Lafia Campus, Lafia. The farm lies on latitude 08 º 35N and longitude 08º 33E within the guinea savannah zone of North Central Nigeria. The experiment took place in the hot-dry season. The average environmental Temperature-Humidity index (THI) and average rainfall value during the study period were 79.9 and 4.19 mm, respectively (MUFAN 2017; NIMET 2017).

Management of birds

A total of Fifty four 30-weeks-old Sasso hens were used in the study. The birds, which were individually kept in cages, were allotted randomly with eighteen birds per replicate. There was a tag attached to each bird for identification. The birds were fed commercial layer mash and supplied clean water ad libitum throughout the duration of the experiment (March-July). Routine vaccination and medication were also strictly carried out. Other management practices were as described by Yakubu et al (2010). International Council for Laboratory Animal Science and NC3Rs ARRIVE (Animals in Research: Reporting In Vivo Experiments) guidelines on research ethics were strictly followed.

Collection of eggs

Egg collection was done twice daily (morning and evening) in the course of the experiment. Egg records were divided into five phases of production: week 31-34, week 35-38, week 39-42, week 43-46 and week 47-50. These phases corresponded to five different ages. Out of the fifty birds initially stocked, records on thirty eight surviving birds with consistency in lay were used for further analysis.

Statistical analysis

Descriptive statistics of egg production were calculated based on age. The relationship between egg number and age was established using Linear and Quadratic regression functions. The linear and quadratic models fitted were: as follows:

(1) Linear model: Y= b0 + b1X + e

(2) Quadratic model: Y= b0+ b1 X + b2 X2 + e


Y = egg number

b0 = the intercept

X = age of birds

b1and b2 = coefficients of regression

e = residual which was randomly distributed.

Both models above were validated using coefficient of determination (R 2), Adjusted R2, RMSE (Root mean squares error) and significance level.

The Artificial Neural Network (ANN) model involved the use of Multilayer Perceptron (MLP). The MLPs are usually trained by error back propagation algorithm (Ahmad 2011).

The input parameter in this study was age of birds (weeks) whereas the ANN output was egg number. A total of 760 egg records were utilized. 70% of the data were used for training the network while the rest of the data (30%) were used for testing to validate the output. The more the number of hidden layers and neurons, the more complex the problem is. The minimum and maximum numbers of units in hidden layer used to develop the current MLP network were 1 and 50, respectively. Error minimization was obtained by Scaled conjugate gradient. The synaptic weights (weighted contributions) were exported to XML file for future prediction of new data sets. R2, Adjusted R2 and RMSE were used to determine the efficiency of the ANN output. In order to determine the optimal age for egg production, the Classification and Regression Tree (CRT) growing method was applied. The model was subjected to cross-validation with 10 sample folds to estimate error. The minimum change in improvement was set to default (0.0001). Every other step was as described in Yakubu (2012). The unexplained variation in egg number was calculated as:

S2e = risk value ÷ S2y


S2e = unexplained variation in the number of eggs

S2y = variance of the dependent variable

1-S2e = explained variation in the number of eggs

SPSS (2015) statistical software was used for the analyses.


The mean egg numbers were 3.33, 3.69, 4.83, 5.76 and 5.85 for ages 31-34, 35-38, 39-42, 43-46 and 47-50 weeks old birds (Table 1). The average weekly egg production for combined ages (pooled data) was 4.69. While the lowest mean value of egg production was recorded in 31-34 weeks old birds, the highest was obtained in their 47-50 and 43-46 weeks old counterparts.

Table 1. Descriptive characteristics of egg production





Mean egg

Error of Mean





































The pattern of the prediction of egg number from age using both linear and quadratic functions appeared similar. The corresponding R2, adjusted R2, RMSE and significance level were 66.0%, 66.0%, 0.72 and p<0.001 (Linear); 67.0%, 67.0%, 0.71 and p <0.001 (Quadratic) (Table 2).

Table 2. Regression equations of the estimation of egg number




Adjusted R2




Y = -2.77 + 0.18X






Y = -8.67 + 0.46X -0.003X2





Y = egg number, X = age, R2 = coefficient of determination; RMSE= Root mean squares error

Neural network indicating the input nodes (week 34-50), hidden node and output node (egg number) is shown in Figure 1. Each input was synaptically connected to the output node which comprises Bias, one accumulator (H term), and the response variable (egg number). The relative error (0.290) for training the network was nearly the same with that of testing (0.321) gave some confidence that the ANN model was not overtrained and that in future cases, the error scored by the network would be close to the present error values. The regression line indicated a good fit. R2, adjusted R2, RMSE and significance level were 70.3%, 70.2%, 0.67 and p<0.001 between the actual egg number and the predicted egg number. The summary statistics of observed and predicted egg number of Sasso hens using ANN are shown in Table 3. The predicted mean weekly egg value using ANN (4.70) appeared similar to the observed value of 4.69. The standard error of the mean of 0.04 was the same for the observed and predicted egg number.

Figure 1. Schematic representation of the three-layered artificial neural network. There was a single hidden layer with one unit which
increased the computational efficiency of the ANN model. Weighted sum of the inputs (ages 34; 38; 42; 46 and 50 weeks)
and bias term were passed to the activation level through the transfer function to produce the output (egg number).

Table 3. Descriptive statistics of the actual and predicted egg number using artificial neural network

Egg number





Error of Mean







ANN Predicted






In the CRT model (Figure 2), a total of nine nodes were obtained, five of which were terminal (Nodes 3, 4, 5, 7 and 8). Node 0 is the root node representing the response variable, egg number. Although, all the terminal nodes recorded 20% gain, Node 8 appeared to be the best as it recorded the highest predicted mean egg number (5.85) compared to Node 7 (5.76), Node 5 (4.83), Node 4 (3.70) and Node 3 (3.33). It also had a lower (0.16) variance (error term) than Node 7 (0.22), Node 3 (0.50), Node 4 (0.62) and Node 5 (0.78). The variance of the root node in the present study was 1.53. The risk value and its associated standard error were 0.45 and 0.03, respectively. The explained variation in egg number by the regression model was found to be 70.3%.

Figure 2. Regression tree for the prediction of egg number from age of bird. The tree displayed the optimal age (weeks)
for egg number. Birds that are 48 weeks older are expected to produce more eggs than those of earlier ages.


The coefficient of determination (R2) is often taken as a measure of the validity of a regression model or a regression estimate. It reflects the fraction of variation in the Y-values that is explained by the regression line. In this wise, R2 implies that 66.0% (Linear) and 67.0% (Quadratic) of the variability between the egg number and age have been accounted for. The current values appear high enough and reliable in predicting egg number. In a related study, Okoro et al (2017a) reported that egg production fitted into a linear function with R2 value of 38.1%.

The three-layered artificial neural network revealed the great contribution of ages 43-46 weeks and 47-50 weeks to egg number prediction by virtue of their grey lines. This is because the dark lines represent weights less than 0 (take away from the effect) while the grey lines represent weights greater than 0 (add to the effect) (Anonymous,

The higher predictive performance of ANN model over both linear and quadratic functions in the present study may be attributed to the fact that the degree of robustness and the ability to tolerate fault are greater in ANN compared to the two other models. This is congruous to the submission of Savegnago et al (2017) with regard to the efficiency of ANN model. According to Ahmad (2011), ANN model gave the best fit while predicting egg production with an R2 value of 0.71. However, theirs was for weekly egg production from week 22 to 36 of age. Similarly, Ghazanfari et al (2011) reported that ANN model could provide an accurate prediction of egg number of layers based on age. Ahmad et al (2001) reported that ANN (MLP) gave a better fit when compared to linear regression. The use of ANN as a more reliable model than the traditional regression functions for the prediction of egg number was also accentuated by Wang et al (2012) and Semsarian et al (2013) in different perspectives. It has also been applied in the prediction of egg size in the food industry (Soltani et al 2015).

From the regression tree of the present study, it appears there is tendency for the birds to produce more eggs at ages greater than 48 weeks. This means that the active productive life and optimal egg production go beyond 48 weeks of age. The implication of this is that continuous egg production for a relatively long period is guaranteed and this could boost sale with a corresponding increase in farm revenue. The coefficient of determination value obtained in the present study was high enough and exactly the same with that of the ANN model above, an indication that the CRT model fitted well. Therefore, it can be relied upon to predict egg number. In their own study, Nwogu and Acha (2014) reported that hens were at their best at ages between 34.5 and 54.5 weeks and that for optimum egg production, they should not be kept far beyond 54.5 weeks. However, Okoro et al (2017a) submitted that the optimal age for egg production was 63.7 weeks. Regression tree methodology has been used to predict egg size in chickens (Okoro et al 2017b).



This project was partially supported by the Senate research grant (NSU/REG/2005) of Nasarawa State University, Keffi (NSUK). Many thanks to Prof E B Sonaiya, Principal Investigator (PI), , the Co-PI, Prof Mrs O A Adebambo and the National Project Coordinator, Dr O Bamidele of African Chicken Genetic Gains-Nigeria (ACGG-Ng) project for the donation of the Sasso birds.


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Received 8 September 2018; Accepted 24 Septemeber 2018; Published 1 October 2018

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