A mathematical model for the feed utilization of Japanese quail

A general mathematical description of the feed utilization was aimed in this study. Three different plumage colour lines of Japanese quail were raised to collect their growth and feed consumption data at three-day intervals up to 48 days of age. The model equation is in the linear fashion with two parameters, which of both have biological meanings. The regression coeffi cient is the measure of the net feed need to produce one unit live quail weight while the intercept coeffi cient is the measure of the net feed need just for supporting the daily activities of quail. The regression coeffi cient values have ranged from 0.7430 to 1.1327 g feed/g liveweight gain. The regression coeffi cient for brown quail differs from the one for wild quail. The intercept coeffi cient has ranged from 0.1238 to 0.1342 g feed/g quail weight/day. The proposed linear model can be used together with the growth model to perform the computer simulation of quail raising for developing economic farming practices.


INTRODUCTION
The Japanese quail, Coturnix coturnix japonica, is a migratory, gallineous, ground dwelling game bird native to east Asia and Japan.Japanese quail is an interesting domesticated economic species for commercial egg and meat production besides chicken because it has fast growth, early sexual maturity, high rate of egg production, short generation interval and short incubation period (Ernst, 2000).Nutrition is one of the most important factors required to maintain quails in good physical condition and to obtain normal growth and egg production (Shim and Vohra, 1984).The selection of the quail genotypes with high growth rate, high fi nal body weight together with less feed consumption has been studied by Marks (1978Marks ( , 1991)), Anthony et al. (1996) and Hyánková et al. (1997Hyánková et al. ( , 2001)).These studies provided more general measures such as feed conversion ratio (total feed consumption/total weight gain) between two consecutive sampling points or between the beginning and the end of growth experiments.They reported the decrease of feed conversion ratio over time and the change of feed conversion ratio among the lines.These results are not in the form of a mathematical equation describing the feed utilization of quails, which can be used for the computer simulation of quail farming/raising.The objective of this study was to develop a general mathematical equation having biologically meaningful and distinct parameters for describing the feed consumption data of three plumage colour lines of Japanese quails.

MATERIAL AND METHODS
The growth experiments were conducted at the Gaziosmanpasa University Quail Breeding Unit.Three plumage colour lines of Japanese quail were used.One of the lines was wild-type European-originated.The other two lines are the extended brown and dotted-white mutant quails generated from the hatching collected from commercial hatcheries and the Quail Breeding Unit.The dotted white quail shows white plumage with a small coloured spot on the head and/ or back and an autosomal recessive gene controls this plumage colour (Tsudzuki et al., 1992).Extended brown is incompletely dominant to wild-type.Homozygous brown individuals have uniformly dark brown plumage with a small area of white feathers around the beak.The lines hereafter are referred as wild, white and brown.Before the study was started, the lines were maintained as folks constituted 60 females and 20 males and reared at this unit for 12 generations without selection for any productive traits but taking special care to avoid inbreeding.
All birds used in this study were hatched at the same day.When the chickens hatched (day 0) they were weighted, labelled with wing-rings and placed in the quail battery brooders by line at a stocking density of 70 cm 2 /chick.At 6 days of age quails randomly divided into 8 replicates by line (10 quails per replicate) and stocking density raised to 250 cm 2 /bird.Thereafter, feed consumption of the groups was recorded.Because of the diffi culties of sex determination in chickens especially within colour types, groups were also formed randomly according to the sex.All birds and the feed available to the groups were weighted at 3-day intervals up to 48 days of age with a 0.01 g sensitivity electronic balance.The adjustments of temperature, lighting regime and feeding were applied as common practice in the industry.The temperature started at 36°C and every week temperature were decreased 3°C and fi xed at 24°C after four weeks of age.Birds were housed for the fi rst three weeks at 24 h lighting, following weeks at 16:8 light:dark cycle.Birds were allowed to ad libitum access to feed and water.They were fed with 24% crude protein (CP) and 3200 kcal ME/kg starter diet for 21 days, 19% CP and 3000 kcal ME/kg grower diet between 21 and 35 days of age and thereafter 17% CP and 2750 kcal ME/kg breeder diet.

Model development
The mathematical models for the feed consumption of animals range from simple allometric equations (Nagy, 1987) to a set of equations describing simultaneously various metabolic activities (Emmans, 1997).The complexity of any biological model increases the amount of experimental and/or theoretical work that should be performed to calibrate the model parameters.On the other hand, pure curve-fi tting does not shed any light on the mechanism of biological processes (France and Thornley, 1984;Haefner, 1996).Therefore, complex models can be preferred to enhance the fundamental knowledge about the biological process while curve-fi tted equations can be preferred to summarize the extensive experimental data and to perform optimization studies.The mathematical model developed for the feed consumption of both cell cultures (Doran, 1999) and animals (Woodward, 1998) was modifi ed to describe the feed consumption rate of quails.The mathematical equation is as follows: where SFCR is the specifi c feed consumption rate (g feed consumption/g quail weight/day); SGR is the specifi c growth rate (1/day);Y F is the real weight yield coeffi cient (g quail weight gain/g feed consumption); SPFR Y P is the specifi c product formation rate (g product formation/g quail weight/day); is the product yield coeffi cient (g product formation/g feed consumption); and m F is the maintenance coeffi cient (g feed consumption/g quail weight/day).In this study, the term for production formation in equation 1 was omitted since the growth period considered in this study covered the pre-laying period.Then, equation one was rewritten as follows:

Parameter estimation
The growth and feed consumption data were numerically differentiated to get the growth rates and feed consumption rates over time (Mathews, 1992).The values of SFCR were linearly related to the values of SGR to estimate the intercept and the slope of equation 2. As shown in equation 2, its intercept is equal to maintenance coeffi cient while its slope is equal to the inverse of weight yield coeffi cient.The curve fi tting process including the estimation of parameters, the analysis of variance for the linear model and t-tests for the signifi cance of model parameters was performed by using SigmaPlot software (SigmaPlot, 1995).In addition, the parameters of linear equations for the quail lines were compared with each other as described in the literature (Zar, 1996).

RESULTS AND DISCUSSION
The mean liveweight changes over time of three plumage colour quail lines are presented in Figure 1 while their cumulative feed consumption data are presented in Figure 2. Liveweight shows initially rapid increase and slow increase later in time.However, cumulative feed consumption constantly increases in time.This result indicates the existence of a complex relationship between feed consumption and liveweight change.Therefore, simple feed conversion ratio used in the literature are not suffi cient for the thorough mathematical description of the feed utilization of the quail lines.For this reason, the relationship between specifi c feed consumption rate (SFCR) and specifi c growth rate (SGR) were investigated to develop a simpler and more meaningful correlation between growth and feed consumption.The plots of SFCR over SGR for white, brown and wild quail lines were given in Figures 3, 4 and 5, respectively.
The linear equation for white quail fi tted to the experimental data is as follows: SFCR = 0.1325+0.9155x SGR (R 2 = 0.930 and P-value < 0.0001) The model predictions stay within the experimental data as shown in Figure 3.
The linear equation for brown quail line is as follows: SFCR + 0.1238 + 1.1327 x SGR (R 2 = 0.824 and P-value < 0.00001) (4) The model predictions do not show consistent deviations from the experimental data as shown in Figure 4.The linear equation for wild quail line is as follows: SFCR + 0.1342 + 0.743 x SGR (R 2 = 0.780 and P-value < 0.00001) (5) The last equation has the lowest coeffi cient of determination value (R 2 =0.780), but its predictions do not show consistent deviation from the experimental data, either as shown in Figure 5.
The model separates the feed consumption into two main metabolic activities: liveweight gain and daily maintenance.This approach explained 78 (for wild) to 83% (for white) of variation in specifi c feed consumption rate.The unexplained part of the variation can be minimized by accounting the egg production in the models to consider some unexpected early laid-eggs and/or by using unique model parameter values for each bird diets used during the growth experiments.
Two different statistical analyses were performed over the model parameters.The fi rst statistical test has shown that the slope and intercepts values of all three equations differ from zero (Table 1.)All model parameters differ from zero (P<0.01).Therefore, the omission of any model parameter reduces the prediction accuracy of a future computer simulation.
The second statistical test was to compare the parameter values with each other (Table 2).The only slopes of equations 4 and 5 differ from each other (P<0.05).The slope of equation 3 does not differ from the slopes of equations 4 and 5 (P>0.05).The intercepts of these three equations do not differ from each other (P>0.05).The weight yield coeffi cients calculated are 1.092, 0.883 and 1.346 g quail weight gain/g feed consumption, respectively for white, brown and wild lines.The weight yield coeffi cients can be used to select the quail lines, which are Figure 5. Plot of specifi c product formulation rate (SCFR) over specifi c growth rate (SGR) for wild quail line effi cient meat producers for commercial practices.For instance, the brown quails converted feed to body weight less effi ciently than the wild quails.The comparisons of model parameters revealed that the brown quails should consume 52.4% more feed than the wild quails to gain 1 g liveweight.The quails also need 0.1238 to 0.1342 g feed per their liveweight per day to sustain their life as symbolized by maintenance coeffi cients.The maintenance need of quails did not vary among the lines.The quails must be supplied with feed more than maintenance coeffi cients to increase their liveweight.On the contrary, if the quails consume less feed than the amount equal to the multiplication of maintenance coeffi cients by their liveweights, they can be said under the condition of feed starvation.This situation may cause weight loss and stress in quails.Therefore, the maintenance coeffi cients can guide the development of feeding management.
The models developed in this study can also be used to explain the results reported in the previous literature (Hyánkova et al., 1997(Hyánkova et al., , 2001)).It was reported that the feed conversion ratios decreased as growth went into retardation.During the early phase of the growth, the quails utilize the big portion of feed consump- tion to weight gain as associated with higher specifi c growth rates.During the late phase of the growth, the quails have very low specifi c growth rates, which reduce the portion of feed consumption to weight gain while the heavier quail weights increase the maintenance need of quails to sustain their life.Heavier quail weight need more feed for managing daily routines of the life under reduced growth conditions like the late phase of growth.All these changes can be easily followed by the model because of its comprehensive formulation.
The computer simulation of feed consumption can be done to manage optimally quail meat production by using the model suggested in this study.However, the specifi c growth production rates over time are needed to run the simulation.These values can be obtained by using the growth models previously developed for following the quail growth (Hyánková et al., 1997(Hyánková et al., , 2001;;Aggrey, 2003).Furthermore, it is expected that this model study on quails may be considered as preliminary for the studies on the other farm animals (for example, chickens) that has long reproductive cycle since common results may apply to them.

CONCLUSIONS
The model is in a linear fashion and has two biologically meaningful parameters (the inverse of true weight yield coeffi cient and maintenance coeffi cient).The proposed linear model can be used together with the growth model to perform the computer simulation for quail selection and the development of good feeding management.It may also be adapted to the other farm animals.

Figure 1 .
Figure 1.Mean growth data of three plumage colour quail lines over time

Figure 2 .Figure 4 .
Figure 2. Feed consumption data of three plumage colour quail lines over time

TABLE 2
The results of the statistical comparison of model parameters (t 0.05/2,204 =1.972)

TABLE 1
The results of curve fi tting process