Comparing some mathematical functions to describe growth pattern in quail

Document Type : Research Paper

Authors

• Marzieh Jahan ¹
• Ali Maghsoudi ²
• Mohammad Rokouei ¹
• Hadi Faraji-Arough ³

¹ Department of Animal Science, Faculty of Agriculture, University of Zabol, Zabol, Iran.

² Department of Animal Science, Faculty of Agriculture, Tarbiat Modares University, Tehran, Iran

³ Department of Ostrich, Special Domestic Animals Institute, Research Institute of Zabol, Zabol, Iran.

Abstract

Keywords

• Richards’ function
• inflection point
• non-linear regression
• Japanese quail
• modeling

Main Subjects

• Animal Breeding and Genetics

Extended Abstract

Introduction

The global population growth and diversification of food preferences have led to an increase in the consumption of quail meat and eggs worldwide. Quail has become one of the smallest domesticated birds raised for egg and meat production due to its desirable characteristics. Numerous studies have been conducted on the genetic capacity of quail growth, body weight yield, and growth curve. Growth is an essential biological indicator that refers to an increase in body mass per unit of time. Growth curve parameters that can be interpreted biologically can correct the changes caused by the environment. The aim of this research is to compare some parameters of the growth curve in two wild and spotted Italian quail strains.

Methodology

The present investigation was carried out at the Special Livestock Research Institute of Zabul University. The study employed growth data from 1182 wild quails, comprising 905 females and 277 males, and 674 Italian spotted quails, comprising 499 females and 175 males. Prior to incubation, the eggs were collected, numbered, and disinfected. The chicks were identified by assigning a flight number immediately after hatching, and their one-day weight was recorded with an accuracy of 0.01 g. The birds were weighed at five-day intervals until the age of 45 days. The growth curve parameters were estimated using Gompertz, Logistic, Lopez, Richards, and von Bertalanffy functions. The functions were analyzed using the R software package nlme.

Results

Tables 4 and 5 show the goodness of fit criterion and parameters of the five nonlinear regression functions Gompertz, Logistic, Richards, Lopez, and Von Bertalanffy for wild and Italian quail based on their species. Table 4 displays the goodness of fit for each function. In wild quail, the Richards function was the best function for both female and male sexes based on the Akaike criterion, with the lowest Akaike value of 182592. 0 and 57187. 90, respectively. The logistic function was the worst function for both sexes, with the highest Akaike value of 182667. 70 and 57210. 70. The Bayesian information criterion gave similar results, with the Richards function being the best function for both sexes. Based on the mean squared error, the Richards function had the lowest value for both male and female sexes. Overall, the Richards function was the most suitable function for describing the growth curve in both female and male wild strain quail. For Italian spotted quail, the Richards and Gompertz functions were the best functions for both female and male sexes based on the Akaike criterion, with the lowest AIC value of 15636. 90 and 5650. 60, respectively. The logistic function was the worst function for both sexes, with the highest AIC value of 15667. 80 and 5657. 50. The Bayesian information criterion gave similar results, with the Gompertz function being the best function for both sexes.

Discussion

The study of growth functions in quail has been conducted for approximately three decades, in contrast to the long history of sigmoid-shaped curves commonly referred to as growth curves. Most studies have investigated only one growth function to compare different groups of birds based on breed, strain, food treatment, selection purpose, and other factors. However, selection significantly affects the parameters of the growth curve in different breeds of birds, including quail. Various nonlinear functions have been used to model the growth pattern of different bird species. The present study suggests that using a function with more parameters, such as Richards, may lead to more accurate fits. The complexity of the function itself may affect the modeling of growth curve data.

Conclusion

After analyzing the goodness of fit values of various functions, it can be inferred that all functions performed well in describing the weight data of the two quail strains under consideration. However, the results of this study indicate that Richard's growth function was more effective in characterizing the growth pattern of both male and female wild Japanese and spotted Italian quail strains. Therefore, it can be recommended as a suitable function for this trait.

Given that the two strains were managed under the same breeding system in this study, it can be concluded that their growth patterns were similar. The comparable growth patterns and the use of the same functions to describe growth in both strains further support the notion that they share many similarities in terms of growth. Consequently, it is feasible to breed these two strains together under a single management system. This study also highlights the importance of increasing the number of records and shortening the weighting intervals to determine the appropriate function effectively.