PRODUCTION, MODELING, AND EDUCATION. Investigation of nonlinear models to describe long-term egg production in Japanese quail

PRODUCTION, MODELING, AND EDUCATION Investigation of nonlinear models to describe long-term egg production in Japanese quail Dogan Narinc, Emre Karaman, Tulin Aksoy, 1 and Mehmet Ziya Firat Faculty of Agriculture, Department of Animal Science, Akdeniz University, Antalya, 07100, Turkey ABSTRACT In this study, long-term egg production was monitored in a Japanese quail flock, which had not undergone any genetic improvement, for 52 wk as of the age of sexual maturity. The study aimed to detect some traits with respect to egg production, to determine the cumulative hen-housed egg numbers, and to compare goodness of fit of different nonlinear models for the percentage of hen-day egg production. The mean age at first egg was 38.9 d and the age at 50% egg production was 45.3 d. The quail reached peak production at 15 wk of age (wk 9 of egg production period) when the percentage of hen-day egg production was found to be 94%. The cumulative hen-housed egg number for 52 wk as of the age of sexual maturity was 253.08. The monomolecular function, a nonsigmoid model, was used INTRODUCTION 2013 Poultry Science Association Inc. Received June 4, 2012. Accepted February 2, 2013. 1 Corresponding author: zootekni@akdeniz.edu.tr in the nonlinear regression analysis of the cumulative egg numbers. Parameters a, b, and c of the monomolecular model were estimated to be 461.70, 473.31, and 0.065, respectively. Gamma, McNally, Adams-Bell, and modified compartmental models, widely used in hens previously, were used in the nonlinear regression analysis of the percentages of hen-day egg production. The goodness of fit for these models was compared using the values of pseudo-r 2, Akaike s information criterion, and Bayesian information criterion. It was determined that all the models are adequate but that the Adams- Bell model displayed a slightly better fit for the percentage of hen-day egg production in Japanese quail than others. Key words: egg production curve, nonlinear model, Japanese quail 2013 Poultry Science 92 :1676 1682 http://dx.doi.org/10.3382/ps.2012-02511 The most important economic traits of Japanese quail are their egg and meat production, which are influenced by a complex genetic structure and environmental factors. The majority of the studies on quail concern meat production (Baumgartner, 1994; Marks, 1996; Oğuz et al., 1996; Hyánková et al., 2001; Aggrey et al., 2003) in which growth, feed efficiency, and slaughter traits are generally considered. In some studies on egg production, selection was performed to increase production (Nestor et al., 1983; Maeda et al., 1999), the effect of feeding on egg production was investigated (Sahin et al., 2002; İpek et al., 2007), and flock management was investigated (Nagarajan et al., 1991). Long-term egg production in quail was examined in a small number of studies (Minvielle et al., 2000a,b). In Japanese quail, egg production starts with the age of sexual maturity, rapidly reaches the level of peak production, and decreases over time. Various researchers have reported that the age of sexual maturity ranged from 35 to 45 d in Japanese quail (Thomas and Ahuja, 1988; Minvielle et al., 2000b; Camcı et al., 2002; Reddish et al., 2003; Sezer et al., 2006; Karabağ et al., 2010). In some studies, it was found that peak production in quail occurred at 3 mo of age (Minvielle et al., 2000b) and that peak egg production ranged from 88 to 98% (Nestor and Bacon, 1982; Minvielle et al., 2000b). It has been reported that annual egg number ranged from 250 to 300 in quail, although varying with flock management and the level of genetic improvement of birds (Baumgartner, 1994; Minvielle, 1998; Minvielle et al., 2000b). There are many studies in the literature on fitting nonlinear regression models to growth data of Japanese quail and examination of the resultant parameter estimates (Anthony et al., 1986; Akbaş and Oğuz, 1998; Akbaş and Yaylak, 2000; Hyánková et al., 2001; Narinc et al., 2010). However, there are very few studies on the modeling of egg production in quail (Minvielle et al., 2000b, 2006; Mignon-Grasteau and Minvielle, 2003). There is no study on issues such as the comparison of fit of different egg production curve models or the interpretation of model parameters for genetic improvement for lines and genetic groups of Japanese quail. 1676

MODELING LONG-TERM EGG PRODUCTION IN JAPANESE QUAIL Egg production curves resemble lactation curves, and models such as Wood are also used to model lactation production (Gavora et al., 1982). Nonlinear regression, multi-phase modeling, and artificial intelligence methods are used to model egg production (Yang et al., 1989; Grossman et al., 2000; Koops and Grossman, 1992; Minvielle et al., 2006; Alvarez and Hocking, 2007). Fitting a curve to visualize the time-dependent and nonlinear changes in egg production generally requires the estimation of 3 to 5 parameter values. The models widely used in studies are gamma, McMillan, McNally, compartmental, Adams-Bell, logistics, Wood (gamma), and Gloor equations (McMillan, 1981; Mc- Millan et al., 1986; Yang et al., 1989; Cason, 1991; Gloor, 1997; Savegnago et al., 2011). Most the studies on modeling egg production belong to laying hens. Gavora et al. (1982) compared the gamma, compartmental, and postpeak linear function and reported that the compartmental model had the best fit. Cason and Britton (1988) compared the McMillan, Adams-Bell, and compartmental models for laying hens in different flocks and reported that the Adams-Bell model was accurate in predicting the total production based on 24 wk of records. Cason (1990) reported that the Adams-Bell model fitted better to the weekly egg production data from 47 molted commercial flocks than the compartmental or modified compartmental models. Mielenz and Müller (1991) fitted linear, exponential, Adams-Bell, and McMillan models for 450-d egg yield and reported that all models fit equally well to the data. This study aims to reveal some traits regarding egg production in a flock of randombred Japanese quail that did not undergo any genetic improvement study. To examine the cumulative hen-housed egg numbers, the monomolecular model was used. The goodness of fit of the most widely used nonlinear regression models (gamma, McNally, Adams-Bell, and modified compartmental) for the percentages of hen-day egg production is also discussed. MATERIALS AND METHODS 1677 The research was carried out in a poultry house in the Research-Application Unit at the Department of Animal Science, Faculty of Agriculture, Akdeniz University, Turkey. Japanese quail obtained from randombred parents and that had not undergone any genetic improvement were used in the study. After the chicks had been taken out of the incubator, wing numbers were attached and they were placed into the chick growing cages. The quail were provided with feed containing 24% CP and 2,850 kcal/kg of ME for the first 4 wk. One hundred female quail randomly selected after being separated by sex at 4 wk of age were placed into individual egg cages. The quail were provided with feed containing 21% CP and 2,900 kcal/kg of ME ad libitum from the fourth week to the end of the experiment. A 16-h lighting program was applied in the egg production period. The eggs were recorded every morning between 0900 and 1200 h for 52 wk as of the age at first egg. Egg production was calculated cumulatively according to the hen-housed principle and proportionally according to the hen-day principle. Age at first egg was recorded in quail and the age at 50% egg production and peak production were calculated. An average curve that represents long-term egg production was fitted for practical purposes. Such a curve provides clear information not only for a flock but also for the long-term productivity of individuals. For this aim, nonlinear monomolecular model given by the equation EN = a be ( ct) was fitted to the cumulative henhoused egg number. In the equation, EN denotes the cumulative egg number, a denotes the asymptotic total egg number, b denotes the scale parameter concerning the initial egg production, c denotes the relative rate representing the change in increase in the cumulative egg number, and t denotes the number of weeks as of the first laying age. Gamma, McNally, Adams-Bell, and modified compartmental models were used in the nonlinear regression analysis of the percentages of hen-day egg production. These functions are presented in Table 1, where y t is the percentage of hen-day egg production, and a, b, c, d, e, f, g, h, i, j, k, l, and m are the parameters to be estimated. The gamma model was proposed by Wood (1967), where a is the initial production, b is the rate of increase to the peak, and c is the rate of decrease from the peak. The week of peak production (b/c) and persistency of peak production [ (b + 1)ln c] were derived from the model parameters. The McNally model is a modified version of the gamma model developed by McNally (1971) with the addition of an extra parameter, d, proportional to the square root of time. The modified compartmental model was developed by Yang et al. (1989), where e is the scale parameter, f is the rate of decrease of egg laying, 1/g is an indicator of variation in sexual maturity, and h is the mean number of weeks in test until sexual maturity. The Adams-Bell model (Adams and Bell, 1980) modeled the laying period as a sum of a logistic function that describes the initial rise to peak and a linear function for decrease in egg production postpeak. The authors also referred to the parameters in the model (i, j, k, l, and m) as constants to be evaluated and did not attribute any biological meaning. The Adams-Bell model is mostly used to predict total production from early records (Cason and Britton, 1988). Statistical analyses were performed by SAS 9.2 software using MEANS, SURVEYSELECT, and NLIN procedures (SAS Institute Inc., 2009). In modeling the percentages of hen-day egg production, the data from 91 quail were split into an estimation data set (EDS) consisting of data from 60 randomly selected quail and a validation data set consisting of data from the remaining 31 quail using SURVEYSELECT procedure (An and Watts, 1998). Model parameters were estimated in NLIN procedure using EDS, and the goodness of

1678 Narinc et al. Table 1. Expressions of the nonlinear functions used in the study Function Expression 1 b Gamma y= t at exp( ct) b 0.5 McNally y= t at exp( ct + dt ) Adam and Bell 1 y= t k( t l) t j 0.01 + im Modified compartmental e exp( ft) y t= 1+ exp g( t h) 1 y t is the percentage of hen-day egg production at time t (week); exp is the exponential function; a: the initial production (%); b: the rate of increase to the peak; c: the rate of decrease from the peak; d: proportional to the square root of time; e: the scale parameter; f: the rate of decrease of egg laying; 1/g: an indicator of variation in sexual maturity; h: the mean number of weeks in test until sexual maturity; i, j, k, l, m: constants to be evaluated. fit statistics (Table 2) were calculated for validation data set by using the parameter estimates obtained with EDS. This process was repeated 100 times and both the estimated parameters and the goodness of fit statistics were averaged. For the cumulative hen-housed egg numbers, a single estimation procedure was performed in NLIN procedure. The Levenberg-Marquardt algorithm was chosen as the fitting algorithm in the model estimation stage where the iterations were said to have converged if the [(SSE i 1 SSE i )/(SSE i + 10 6 )] < 10 8 criterion was met. Here SSE denotes the sum of squared errors. Pseudo-R 2, which is analogous to the coefficient of determination in linear regression analysis, was used to assess the model accuracy. Akaike s information criterion (AIC) and Bayesian information criterion (BIC) were also used to compare the models and to determine the most appropriate model for the data (Table 2). The AIC and BIC are both methods of assessing model fit penalized for the number of estimated parameters and given a set of competitive models, the preferred model is the one with the minimum AIC and BIC values. RESULTS The mean age at first egg was 38.9 d and the mean age at 50% egg production was 45.3 d. Figure 1 displays the weekly actual hen-day percentage of egg production. It can be seen from the figure that peak production occurred at wk 9 of the production period and that the hen-day egg production during this week was 94%. Mortality was 9% in the egg production period monitored for 12 mo as of the age at first egg. The 24-, 32-, 40-, and 52-wk averages of cumulative hen-housed egg numbers were determined as 139.02, 180.78, 216.31, and 253.08 eggs, respectively (Table 3). As a result of the nonlinear regression analysis of the cumulative egg numbers using the monomolecular model, parameter a, the asymptotic total egg number was estimated to be 461.70, whereas the scale parameter (b) was estimated to be 473.31 and the parameter of Figure 1. Actual hen-day percentages of egg production. relative rate (c) denoting the change in the increase in the cumulative egg numbers was estimated to be 0.065. The pseudo-r 2 for the monomolecular nonlinear regression model was calculated as 0.9992. Actual values and predictions obtained by fitting the monomolecular model are plotted in Figure 2. Predicted hen-day percentages over 52 wk from fitting 4 different models are plotted in Figure 3 for 100 replicates. Resulting parameter estimates of fitting the gamma, McNally, Adams-Bell, and modified compartmental models to the percentages of hen-day egg production data are presented in Table 4, with the goodness of fit statistics of the models. In each estimation process, the estimated parameters are asymptotically valid at the significance level of 0.05. The pseudo-r 2 values for gamma (0.9110), McNally (0.9111), and Adams-Bell (0.9270) are high, implying that the models have a good fit to the data, whereas pseudo-r 2 for the modified compartmental model (0.8768) is slightly smaller. A comparison among the aforementioned models, on the basis of AIC, showed that the Adams-Bell model had the lowest value ( 307.47) among those calculated at 301.43, 299.56, and 282.51 for the gamma, McNally, and modified compartmental models, respectively. A similar ranking was obtained in terms of the BIC values. The Adams-Bell model was followed by the gamma, McNally, and modified compartmental models ( 297.71, 295.57, 291.75, and 274.71, respectively). Table 2. Formulas of model fit statistics Criterion Formula 1 Pseudo-R 2 Pseudo-R 1 SSE SSTC Akaike s information criterion (AIC) AIC = nln( SSE n)+ 2k Bayesian information criterion (BIC) BIC = nln( SSE n)+ kln( n) 2 = ( ) 1 n: the number of observations; k: the number of parameters. ln: natural logarithm; SSE: sum of squared errors; SST C : corrected total sum of squares.

MODELING LONG-TERM EGG PRODUCTION IN JAPANESE QUAIL 1679 Table 3. Descriptive statistics of monthly cumulative egg numbers Week n Mean SD Minimum Maximum 4 100 20.41 3.55 10 28 8 97 45.68 3.91 32 54 12 96 70.72 4.43 56 81 16 94 93.79 5.27 79 106 20 93 116.66 6.34 97 130 24 93 139.02 7.88 116 154 28 92 160.50 9.38 138 180 32 92 180.78 11.33 147 205 36 92 199.30 13.96 151 230 40 92 216.31 16.10 158 252 44 91 231.11 18.56 162 273 48 91 243.20 21.53 166 293 52 91 253.08 24.42 170 311 DISCUSSION The present study, which aimed to determine the age of sexual maturity in Japanese quail, recorded the age at first egg, the age at 5% egg production, and the age at 50% egg production (Nagarajan et al., 1991). The age of sexual maturity (38.9 d) was in agreement with the results of Minvielle et al. (2000b) who reported that the age at first egg ranged from 36.9 to 44.1 d in 8 genetic groups. Likewise, the age of sexual maturity was reported to range from 41.7 to 42.6 d in the randombred control line by Reddish et al. (2003), from 40.6 to 42.3 d by İpek et al. (2007), and 39.7 d in a randombred control line by Karabağ et al. (2010). In this study, the age at 50% egg production was 45.3 d. This finding is in agreement with the results of 44.9 d found in an unselected control group of quail by Camcı et al. (2002) and of 45.82 d reported by Sezer et al. (2006). The results obtained for the age of sexual maturity in the present study were lower than the value of 65.6 d reported by Sachdev and Ahuja (1986) and the values of 48.9 to 49.6 d reported by Thomas and Ahuja (1988). In this study, it was determined that the level of henday peak production was 94% and that the age when peak production was observed was wk 9 of the production period. Nestor and Bacon (1982) reported a peak production level of 90%. Likewise, Minvielle et al. (2000b) reported that peak production ranged from 88 to 98% in 8 genetic groups and that this production was observed at about 3 mo of age. In studies of longevity in Japanese quail, it is reported that mortality increases greatly after 2 yr of age. In a study by Minvielle et al. (2000b), mortality ranged from 39.7 to 78.5% at the end of a 21-mo period in 8 genetic groups and from 13.8 to 26.2% at the end of a 13-mo egg production period. The 9% mortality in a 12-mo production period in our study is significantly lower than for other studies. Figure 2. Actual and predicted hen-housed cumulative egg numbers over 52 wk.

1680 Narinc et al. Table 4. Estimates of model parameters and goodness of fit statistics of each model Function Parameter 1 Estimate Pseudo-R 2 AIC 2 BIC 3 Gamma a 58.463 0.9110 301.43 295.57 b 0.3338 c 0.0324 McNally a 58.528 0.9111 299.56 291.75 b 0.3343 c 0.0323 d 0.0005 Modified compartmental e 116.32 0.8768 282.51 274.71 f 0.0181 g 0.5041 h 1.2785 Adams-Bell i 0.997 0.9270 307.47 297.71 j 9.12 k 0.012 l 7,820 m 0.605 1 a: the initial production (%); b: the rate of increase to the peak; c: the rate of decrease from the peak; d: proportional to the square root of time; e: the scale parameter; f: the rate of decrease of egg laying; 1/g: an indicator of variation in sexual maturity; h: the mean number of weeks in test until sexual maturity; i, j, k, l, m: constants to be evaluated. 2 AIC = Akaike s information criterion. 3 BIC = Bayesian information criterion. Egg production in Japanese quail was monitored for a short period in almost all studies that were performed to determine egg production, to apply selection according to egg production, or to examine the effect of different environmental elements on egg production (Nestor and Bacon, 1982; Nestor et al., 1983; Thomas and Ahuja, 1988; Camcı et al., 2002; Karabağ et al., 2010). In one of the long-term studies, Minvielle et al. (2000a) reported that the 13-mo cumulative egg numbers ranged from 247 to 327 eggs in 6 genetic groups, and another study (Minvielle et al., 2000b) reported that 13-mo egg numbers ranged from 245 to 322 in 8 genetic groups, with 12-mo egg numbers ranging from 222 to 310 eggs. The 12-mo cumulative egg numbers determined in our study (253.08 eggs) are in agreement with those studies in which long-term egg production was monitored. Nestor and Bacon (1982) and Nestor et al. (1983) reported 120-d egg numbers of 107 to 118 and 109 to 113 eggs, respectively. Thomas and Ahuja (1988) reported 18-wk numbers of 55.0 to 64.9 eggs; Camcı et al. (2002) reported 24-wk numbers of 107.0 to 113.3 eggs; and Karabağ et al. (2010) reported 195- Figure 3. Predicted hen-day percentages (circles) for 100 replicates and the mean predictions (lines) of the models.

MODELING LONG-TERM EGG PRODUCTION IN JAPANESE QUAIL d numbers of 144.1 eggs. Our findings were lower than the values determined by Nestor and Bacon (1982) and Nestor et al. (1983), but higher than the values stated by Thomas and Ahuja (1988), Camcı et al. (2002), and Karabağ et al. (2010). The relationship between the partial change in the egg number and the total egg number is in the form of a descending line. Due to the structure of the data of cumulative egg numbers, it was not considered appropriate to use sigmoid functions with an inflection point in their modeling. Consequently, the monomolecular model with no inflection point was used in analysis. The only study describing egg production in Japanese quail with nonlinear regression equations was performed by Minvielle et al. (2000b). These authors analyzed the 21-mo cumulative hen-housed egg numbers in 8 different genetic groups by using the monomolecular model. The asymptotic egg number parameter (a) of the monomolecular model was reported to range from 317.90 to 581.10, and these findings were found to be in agreement with the estimate of parameter a (461.70) obtained in our study. Minvielle et al. (2000b) reported that the values of scale parameter and relative rate of change parameter ranged from 327.0 to 607.4 and from 0.062 to 0.125, respectively. These values are in agreement with the findings of the present study. As a result of the analysis of hen-day percentage of egg production data with the gamma and McNally models in our study, close values were estimated for parameters a, b, and c (Table 4). The estimated parameter that stands for initial production, a, was 58.463 for the gamma model and 58.528 for the McNally model. The rate of increase to the peak (parameter b) was estimated as 0.3338 for the gamma model and 0.3343 for the McNally model. Similarly, parameter c, the rate of decrease from the peak, was estimated to be 0.0324 for the gamma model and 0.0323 for the Mc- Nally model. This is due to the fact that the McNally model is a slight modification of the gamma model and the parameters that symbolized with the same letter also have the same meaning. Estimated peak production was around wk 10 (10.3) and persistency of peak production was 5 wk (4.57) from the gamma model. In a study by Minvielle et al. (2002), egg production in Japanese quail was analyzed with the Wood (gamma) model. Model parameters a, b, and c were estimated to be 20.77, 0.493, and 0.112, respectively. Egg percentages were not used in their study, whereas egg numbers were used. As a result, it is to be expected that the parameter values were rather different from those in our study (Table 4). The only report found in the literature for the nonlinear regression analysis of the percentages of hen-day egg production in Japanese quail is that of Minvielle et al. (2000b) with the modified compartmental model. Analysis of the percentages of hen-day egg production determined for up to 14 mo of age by Minvielle et al. (2000b) with the modified compartmental model, parameters e, f, g, and h ranged from 99.24 to 111.39, from 0.019 to 0.054, from 4.34 to 8.60, and from 0.80 to 0.94, respectively. Except for parameter g, the reciprocal indicator of the variation in sexual maturity, these parameter values were found to be in agreement with the values obtained in our study. It is considered that the difference between results was due to the difference in the variable of time (t) in both studies. According to a comparison of the models in terms of goodness of fit, the Adams-Bell model has a slightly better fit to the data (Table 4). Similarly, Cason and Britton (1988) and Cason (1990, 1991) reported that the Adams-Bell model has the best fit to hen-day percentage of egg production data in laying hens. However, there is no clear meaning that may be attributable to its parameters, which is the main issue of the problem. In this respect, one can conclude that nonlinear models with biologically interpretable parameters that also have good fit to the birds hen-day percentage of egg production data with relatively fewer parameters, such as gamma and McNally, can also be used without loss of information. Short-term egg numbers were used in the previous genetic improvement studies performed for egg production in Japanese quail. In contrast, in this study, 52- wk egg production and characteristics of egg production in Japanese quail were monitored. 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