## 2 Materials and Methods  
### Literature Review  
Different methods can be used in order to forecast egg production rates, from models that use a small number of inputs to models that require a complex set of parameters. The further review is dedicated to nonlinear and machine learning approaches found in the literature, resulting in the selection of multiple models used for practical implementation and validation. The application of nonlinear regression models for fitting a poultry egg production curve has been popular for several decades--a variety of nonlinear models (the incomplete gamma model by [PERSON] [27], modified gamma model by [PERSON] [28], model by [PERSON] and [PERSON] [29], Compartmental model by [PERSON] [30], Modified Compartmental (also called Logistic-Curvilinear [23; 31]) model by [PERSON], [PERSON], and [PERSON] [32]) have been proposed. Several authors have analysed and compared the traditional nonlinear models for egg production curve fitting:  
* [PERSON], [PERSON], [PERSON], and France's [33] research demonstrated the applicability of three Narushin-Takma models (NT1, NT2, NT3) to fit several poultry-related characteristics (such as egg production, egg weight, feed conversion ratio, etc.) of  
Figure 1: The concept of a cyber-physical model (**a**) and the interrelationship of data in the proposed data structure (**b**) [14]. broiler breeder flocks. The performance of these models was compared with 5 others--Gompertz, Modified Compartmental, Richards, Adams-Bell, and Lokhorst. It was concluded that the NT3 model showed the best performance, measured by 4 goodness of fit criteria (MSE, R2, AIC, and BIC). * [PERSON] et al. [34] in their study selected 7 models to determine their applicability to fit weekly egg production curves in order to compare production between different selection lines of laying hens. The results of this study stated that several nonlinear models--Logistic, Persistency, Segmented Polynomial, and the Modified Compartmental model, specifically, had adequate fitting qualities and, therefore, could be applied for the egg production curve, whereas the rest of the evaluated models', i.e., Compartmental (I and II) and McNally, performances were lacking in comparison. * [PERSON]. [PERSON] et al. [23] compared three nonlinear models (Compartmental, Modified Compartmental and Adams-Bell) with an Artificial Neural Network approach to fit the egg production curve of broiler breeders. Based on the evaluation criteria, the authors concluded that the ANN model had the best performance, but the Modified Compartmental model outperformed the rest in fitting the egg production curve between the selected traditional nonlinear models. This also increased the credibility of results published by [PERSON] et al. [34]. * [PERSON] and [PERSON] [21] in their study analysed the performance of four traditional nonlinear regression models (Adams-Bell, Compartmental, McNally, and Logistic model [35] together with the least square support vector machine (LSSVM) model). It was concluded that LSSVM had the best performance followed by the Adams-Bell model from the selected nonlinear model category, but its performance was better only by a narrow margin, and, as stated by the authors, all of the tested models fit the laying hens' production curve quite well. * [PERSON] [36] compared the performance of four nonlinear models (Wood, McNally, Compartmental, Modified Compartmental) focusing on how well they fit the production curve of Fayoumi layers. The results of the study suggested that the Modified Compartmental model proved to have the best fit. * [PERSON] et al. [18] in their research investigated the effects of different diets (focusing on variation in concentrations of three essential amino acids) on egg production of laying hens.