مقایسه ی برخی توابع ریاضی برای توصیف الگوی منحنی رشد بلدرچین

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه علوم دامی، دانشکده کشاورزی، دانشگاه زابل، زابل، ایران

2 گروه علوم دامی، دانشکده کشاورزی،‌ دانشگاه تربیت مدرس، تهران، ایران

3 گروه علوم دامی، دانشکده کشاورزی،‌دانشگاه زابل، زابل، ایران

4 گروه شترمرغ، پژوهشکده دام‌های خاص، پژوهشگاه زابل، زابل، ایران

چکیده

صفات رشد (اوزان بدن در سنین مختلف)‌ در اغلب پرندگان، همواره در برنامه­های اصلاحی مورد توجّه هستند. تغییرات الگوی رشد را می‌توان با اندازه‌گیری وزن بدن در دوره‌های منظّم و با استفاده از توابع ریاضی (توابع منحنی رشد) بررسی کرد. برای این منظور، در مطالعه­ی حاضر، از اطّلاعات اوزان بدن انفرادی 1182 بلدرچین سویه­ی وحشی (905 ماده و 277 نر) و 674 بلدرچین سویه­ی خالدار ایتالیایی (499 ماده و 175 نر) استفاده شد. جوجه­ها پس از وزن­کشی در زمان تولد، جوجه­ها به سالن پرورش منتقل شدند و تمام وزن­کشی­ها در فواصل زمانی 5 روزه، تا سن 45 روزگی ثبت شدند. برای برآورد پارامترهای منحنی رشد، از توابع گمپرتز (Gompertz)، لجستیک (Logistic)، لوپز (Lopez)، ریچاردز (Richards) و وان برتالانفی (von Bertalanffy) استفاده شد. ارزیابی و رتبه­بندی نیکویی برازش توابع با معیار اطّلاعات بیزی (BIC)، ضریب آکایک (AIC)، میانگین خطای استاندارد (MSE)، و ضریب تعیین تصحیح شده () انجام شد. نتایج نشان داد که تابع ریچاردز برای توصیف الگوی رشد در هر دو سویه­ی بلدرچین وحشی ژاپنی و خالدار ایتالیایی و برای هر دو جنس ماده و نر، مناسب‌تر از سایر توابع بود. الگوی رشد نسبتاً مشابه و توابع یکسان توصیف­کننده رشد در دو سویه­ی بلدرچین وحشی ژاپنی و خالدار ایتالیایی مؤیّد این نکته است که این دو سویه مزبور، الگوی رشد نسبتا مشابه­ای دارند و امکان پرورش توأم آن­ها تحت یک مدیریّت واحد، وجود دارد. با مقایسه نتایج این مطالعه با سایر مطالعات مشابه، این پژوهش نشان داد که افزایش تعداد رکورد و کوتاه شدن فواصل وزن­کشی، می­تواند بر روی تعیین تابع مناسب، مؤثّر باشد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Comparing some mathematical functions to describe growth pattern in quail

نویسندگان [English]

  • Marzieh Jahan 1
  • Ali Maghsoudi 2
  • Mohammad Rokouei 3
  • Hadi Faraji-Arough 4
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 Animal Science, Faculty of Agriculture, University of Zabol, Zabol, Iran.
4 Department of Ostrich, Special Domestic Animals Institute, Research Institute of Zabol, Zabol, Iran.
چکیده [English]

Growth traits (such as body weights at different ages) in most of the birds have been often considered in most of the poultry breeding programs. Changes in growth pattern can be evaluated through measuring body weight traits at regular intervals and using mathematical functions (growth curve functions). For this purpose, data from 1182 wild (including 905 female and 277 male) and 674 Italian speckled (including 499 female and 175 male) quails were utilized. Accordingly, after body weight at hatch, body weights of the birds were recorded through 45 days in a 5-day interval manner. Gompertz, Logistic, Lopez, Richards, and von Bertalanffy were used to estimate growth curve parameters. To evaluate/ rank the goodness of fit for functions, the BIC, AIC, MSE, and  were used. Based on results, Richards’ function for both studied populations (wild and Italian speckled quails) and for both genders (females and males) were the best fitted model. The relatively same growth pattern and same function for describing growth pattern in these two quail strains refer to the same growth traits, therefore simultaneous production of them can be achieved under same management practices. Moreover, comparing results of the current studies with other researches, by comparing other studies with this study’s results, it can be concluded that increasing the number of records and shortening the weighing intervals can be effective in determining the appropriate function.

کلیدواژه‌ها [English]

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

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.

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