Nig. J. Anim. Prod. 2017 44(1):61 - 75 © Nigerian Society for Animal Production Nigerian Journal of Animal Production Mathematical Modelling of Egg Production Curves of Shikabrown® Parents 1 Ahmadu, A., 1Kabir, M., 2Iyiola-Tunji, A. O., 1Akinsola, O. M. and 3Igbadun, H. 1 Department of Animal Science, Ahmadu Bello University (ABU) Zaria, Kaduna State, Nigeria. 2 Department of Fisheries and Livestock, National Agricultural Extension and Liaison Services , Ahmadu Bello University (ABU) Zaria, Kaduna State, Nigeria. 3 Department of Soil and Water Engineering, Faculty of Agricultural Engineering, Ahmadu Bello University (ABU) Zaria, Kaduna State, Nigeria. Abstract This study was conducted to evaluate egg production curves of Shikabrown® parents, using mathematical models. A total of 200 birds: 100 from each of the two strains of Shikabrown® parents (sire and dam) lines at the Breeding Unit of Poultry Research Programme, National Animal Production Research Institute (NAPRI) were used for the study. The birds were obtained from the selected lines (sire and dam) and were denoted as Strain A and Strain B, respectively. Body weight (BWT), age at sexual maturity (ASM), egg number (EGGNO), and egg weight (EWT) were examined. Four non-linear models (Logistic, Richard, Gompertz, and Exponential) and a linear model were used to predict the efficiency of weekly bodyweight and egg production traits. The adequacies of the models were fitted using R Package, version 3.0.3. High coefficients of determination for BWT (R2 = 0.84 - 0.93) were recorded in the models for both Strains. Strain A had higher R2 (0.93) for BWT in Richard, Gompertz and Exponential models while Strain B recorded (R2 = 0.89) in Logistic, Richard and Gomprtz models. High coefficient of determination was obtained in a reproductive trait; egg number; 2 2 in which almost all the models gave (R = 0.70). Exponential model recorded a higher R 2 (0.93) for EGGNO in strain A. EWT in strain A recorded higher R (0.96) coefficient of 2 determination across the four nonlinear models except linear model with (R = 0.95) for egg weight. Significant differences (P<0.05) were observed in the birds' performance for BWT and EWT, with strain B having a higher BWT (1.59±0.01) and Strain A having a higher EWT (48.75±0.17). Similarly, age of birds in lay had a concomitant significant differences (P<0.05) in their BWT as well as their EWT. The birds performed better for BWT and EWT in week 26 and 27 for both Strains. It was concluded that Strain significantly (P<0.05) had effect on BWT and EWT of Shikabrown® parent with Stain B performing better than Strain A in the former trait and strain A better than strain B in the latter trait. R2 identified differences between Strains in predicting egg production traits. Strain B was adjudged good and profitable because the Strain had the highest mean values in body weight and egg number ® and it is being recommended as one of the lines for future improvement of Shikabrown . Keywords: Mathematical models, Egg Production Curves, Body weight, ASM, Egg Number, Egg weight Introduction Egg production is the single most important phenotype for evaluating the productivity of laying birds. It helps in evaluating the efficiency of management and optimum managerial practices that will sustain gain at optimum level (Aboul-Seoud, 2008). Egg production is known to be a complex quantitative trait; it depicts a considerable variation over time within the production 61 Egg production curves of Shikabrown® parents cycle of a hen. Several methods of expressing egg production and its component characters have been studied (Dogan et al., 2010). Despite the application of different forms of analysis of variance, however, it remained difficult to give a clear explanation of the variation in egg production over time (Dogan et al., 2010). However, studies by Oni (1997) have shown that when egg production in chickens is summarized on a weekly, biweekly or monthly basis, it gradually increases, attained peak and persist and then gradually decline. Peak in lay is usually attained a month after first egg is laid. Although variations to this exist among breeds, strains and lines. This regularity, though not a steady process over time, is generally denoted as egg production curve in poultry. Egg production curves are useful tools representing the evolution of egg production changes and of particular importance in both breeding and management. Fairfull and Gowe (1990) reported that mathematical models can be used to forecast income and flock performance to evaluate theoretical expectations or to predict whole record performance based on part record of egg production. Therefore, a mathematical model describing such a curve would enable poultry breeders and commercial egg producers to analyze egg production process as well as to predict annual production from part records (Fairfull and Gowe 1990; Oni, 1997). Shikabrown® chickens had been tested and certified as a good stock of chicken in the six geopolitical zones of Nigeria. However, the institutional evaluation of the production pattern of the chicken was last done in 1997 (Oni, 1997). Change of climatic elements and its effect on livestock had been documented to fit broadly into one of two categories: loss of productivity and increasing cost of production (Adesiji et al., 2013; The Poultry Site, 2009). Evaluation of egg production patterns of Shikabrown® parents after the last one that was done at about 20 years ago is necessary. This study was therefore aimed at evaluation of egg ® production curves of Shikabrown parents using mathematical models. Materials and methods Experimental Site The research was conducted at the Poultry Unit of the National Animal Production Research Institute (NAPRI) Shika, Zaria. The institute is located in Northern Guinea Savannah zone of Nigeria on latitude 11o12´16.78´´N and longitude o 7 33´39.18´´E with an elevation of 691 metres above sea level (Ovimaps, 2015). Experimental Birds A population of 100 birds each of two strains of Shikabrown® Parents (sire and dam) housed at the Breeding Unit of Poultry Research Programme of National Animal Production Research Institute (NAPRI) were used for the study. The birds were obtained from the selected lines (sire and dam lines) and were denoted as Strain A and Strain B, respectively. Strain A was identified with a gold plumage while Strain B with a silver plumage. Management Practices Populations of 100 birds each of two strains ® of Shikabrown parents were used for the study. The birds were obtained from the selected lines (sire and dam lines) and were denoted as Strain A and Strain B, respectively. Strain A was identified with a gold plumage while strain B with a silver plumage. Production traits measured were Body weight (BWT) (Kg): Was measured on weekly basis using top-loading weighing scale. Age at Sexual Maturity (ASM): Was obtained on the day each pullet laid the first egg, recorded in days. Egg 62 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun number (EGGNO): Counted as the number of eggs laid by a hen in a week from point of lay to 12th week. Egg weight (EWT) (g): Measured using sensitive electronic balance scale on weekly basis from point of th lay to 12 week. Data Collection At 20 weeks of age, 100 each of the two Strains were randomly picked and transferred to individual battery cage in order to monitor egg production. Eggs collected were recorded in daily egg record book and summarized at the end of every month. Records of body weight at 20 to 32 weeks of age were taken on weekly basis. For each bird, egg production was standardized into 28 days period, (Gavora et al., 1982; Oni, 1997; Orunmuyi, 2007), starting from the day the pullet laid the first nd egg which was recorded up to 92 day of egg production. Analysis of variance Data obtained on egg production traits (BWT, ASM, EGGNO and EWT) were analyzed using General Linear Model and Pearson Correlation Procedure of SAS (SAS, 2004). Models Fitted Each mathematical model was fitted independently to data collected on each strain of breeder hens. Denoting egg production in the 28-day period starting from the day of 1st egg by Y., the following models were studied: 1. Logistic yt= C [1 + Exp[- a * (weeks – b)] Where: a = growth rate b = inflection point c= asymptote 2. Richard yt= [d – c] c + [1 + Exp[- a * (weeks – b)]]f Where: a= growth rate b = inflection point c = asymptote 1 d= asymptote 2 f= power 3. Gompertz yt= a * Exp [ - Exp [ -b * [weeks – c]]] Where: a = asymptote b = growth rate c = inflection Point 4. Linear yt= a + b * weeks – c Where: a = intercept b = slope 5. Exponential yt= a + b * Exp [ c * [weeks ] Where: a=asymptote b= scale c= growth rate In all the models fitted, y represents the body weight in Kilograms, egg number or egg weight in grams respectively; t = is the age of hen or its productive cycle, in weeks or months. Similarly, the constants, a, b, c, d, and f represent the model parameters as defined by the above equations and have their specific significance in each model. Also the authors referred to the parameters in the model as constants to be evaluated and did not attribute any biological meaning to them, Narinc et al. (2014). Statistical Criteria to Evaluate the Fitted Curves The adequacy of fit of each model was evaluated by Akaike's Information 63 Egg production curves of Shikabrown® parents R2 = [Ssmodel] SStotal Where: SSmodel = is the sum of the squares of the model SStotal= is the total sum of the squares. Graphical evaluation of curve fitting Data used for the fitted curve was evaluated using R Statistical Software, version 3.0.3 (2013). Criterion (AIC), Mean square error, MSE Coefficient 2 of determination (R ) and graphical evaluation. Akaike's information criterion (AIC) Akaike's information criterion (Akaike, 1974), that can be approximated to the least mean square method (Motulsky and Christopoulos, 2003), was calculated as follows: AIC = n. In [SSError] + 2.k n Where: n is the number of data points, k is the number of parameters in the model, and SSError is the sum of the squared error. Results Tables 1 and 2 shows the descriptive statistics for egg production characteristics as affected by strains and age of production. In Table 1, significant (P<0.05) difference existed for BWT and EWT except for ASM and EGGNO. Coefficient of variation ranged from low (9.13%) for EWT to high for EGGNO (28.46 %). BWT was better (P<0.05) in Strain B with a higher value of (1.59±0.01) compared to (1.55±0.10) for Strain A. EWT in Strain A had higher value (P<0.05) (48.75±0.17) than its counterpart (47.92±0.17). EGGNO and ASM were not affected by strain. EWT was significantly (P<0.05) affected by Strain at 24, 26, 27 and 28 weeks of production. BWT attained higher growth (P<0.05) at 27 and 28 weeks of production. Decline in BWT especially for Strain A and EWT in Strain B were recorded at week 28 and week 29, respectively. Mean square error (MSE) The Mean Square Error was calculated as follows: MSE = ∑ni=1∑mi=1(yit – yit)2 nm - p Where: yit – yit Are the observed and predicted weeklyegg production rates, respectively, of hen i at week t of laying, n is the total number of hens, m is the total number of weeks of egg laying evaluated, nm is the total number of observed values in the data set, and p is the number of model parameters. 2 Coefficient of determination (R ) 2 The R was calculated as follows: Table 1: Effect of Strain on egg production traits Strain A ` Strain B Traits Mean±SE Mean±SE CV (%) b a BWT (Kg) 1.55±0.10 1.59±0.01 18.26% ASM (days) 158.30±1.50 154.24±1.50 16.67 EGGNO(g) 14.33±0.24 14.48±0.24 28.46 EWT(g) 48.75±0.17a 47.92±0.17b 9.13 Traits: BWT: Body weight, ASM: Age at Sexual Maturity, EGGNO: Egg number, EWT: Egg weight ab Means with different superscripts on the same row are significantly different (P<0.05) 64 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun Table 2: Effect of Age on body weight and egg weight BWT EWT Weeks Mean±SE N Mean±SE 21 1.48±0.02e 200 48.00±0.46bcd 22 1.57±0.02bcd 200 48.73±0.41bc bcd 23 1.57±0.02 200 49.29±0.42ab ab 24 1.61±0.02 200 49.68±0.41a 25 1.61±0.02ab 196 49.63±0.39a a 26 1.63±0.02 196 49.89±0.40a 27 1.64±0.02a 196 49.90±0.40a 28 1.64±0.02cde 196 48.02±0.38bcd de 29 1.54±0.02 196 46.19±0.45e 30 1.59±0.02abc 194 46.76±0.44de 31 1.54±0.02cde 194 47.96±0.45cd cde 32 1.54±0.02 194 45.96±0.48e Traits: BWT: Body weight, ASM: Age at Sexual Mat urity, EGGNO: Egg number, EWT: Egg weight, N: Number, abcdeMeans with different superscripts on the same row are significantly different (P<0.05). bodyweight over the duration of the study. At 32 weeks, Strain A was significantly (P<0.05) higher in bodyweight than Strain B. As the birds advanced in age, their body weights also increased unlike strain B where there were periods of rising and falling in bodyweights of birds irrespective of age. Figure 4 shows the effect of age on body ® weight of Shikabrown parent. The curve showed that Strain B attained a mature bodyweight earlier, but showed little increase in body weight over the duration of the study. Strain A on the other hand, attained mature bodyweight late, but showed relatively steady increase in ® Figure1: Effect of Strain on Body Weight of Shikabrown Parent 65 Egg production curves of Shikabrown® parents th Figure 2 shows the effect of age on egg ® weight of Shikabrown parent. Similar trend was also observed in both Strains for egg weight as did for body weight. Strain A showed a rapid rise in egg weight within st nd 21 and 22 weeks of age. The rate of increase in egg weight in the subsequent 22nd and 31st weeks of age although significant and steady, it was less rapid than st nd between 21 and 22 weeks and between the st nd 31 and 32 week. Strain B showed an increased egg weight at an earlier age than Strain A, but increase significantly over st th time (21 to 27 week). The egg weight th st declined subsequently from 28 to 31 weeks of age. The egg weight of Strain A was less than the egg weight of Strain B in the first five weeks of the study, however it was less than the egg weight of Strain A in the subsequent seventh weeks, with the egg weight of Strain A being significantly (P<0.05) bigger at the 12 week of the study. Strain B roughly showed a pleateau trend, meaning there was no significant (P>0.05) increase in egg weight over time. Figure 3 shows the variation in egg number over the duration of study (March, April and May). In March, Strain B laid higher number of eggs than Strain A. Both strains performed well in the month of April with Strain B having an edge over Strain A. In May, there was a significant (P<0.05) distinction between the performance of Strain A, and Strain B, in egg number. Strain A performed appreciably better than Strain B with a decisively higher record of eggs laid in May. Generally, there was a steady increase in number of eggs laid by Strain A over the duration of the study, with the highest number of eggs laid in May. On the other hand, the number of eggs laid by Strain B increased from March to April, when it peaked, but declined in May. ® Figure 2: Effect of Age on Egg Weight of Shikabrown Parent 66 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun ® Figure 3: Variation in Egg Number of Shikabrown Over Time 2 Tables 3 and 4 showed the values estimated for egg production traits in Strain A and B. It shows the relationship between model parameters and egg production traits. In both Strains, Exponential and Gompertz models recorded higher weight changes (a) for body weight. Exponential model had higher value in Strain A as compared to B (3062.09 and 2227.35) while Gompertz model also recorded similar pattern (2621.33 and 2132.02). Significant differences are recorded within models for the egg production traits studied. Egg weight in Strain A recorded the best 2 prediction accuracy (R = 0.96) across the four nonlinear models with the exception of linear model with (R2 = 0.95) for egg weight. This is followed by body weight with the range of 0.92-0.93 for the prediction accuracy recorded in the models. Coefficient of determination of (R = 0.70) was obtained in a reproductive trait; egg number, in which similar value was recorded for Richard, Gompertz, Logistic and linear models. Exponential model 2 recorded a higher R of (0.93) for egg number in Strain A. Also within egg production traits of interest in strain B, body weight also recorded a higher R2 value of 0.89 each in Strain A for Logistic, Richard 2 and Gompertz models, followed by R 2 value of (R = 0.70) in linear model, the least 2 2 R was (R = 0.84) recorded for body weight in Exponential model. In Strain B also, similar value of (R2 = 0.70) was recorded for egg number as was the case in Strain A. Egg 2 weight was (R = 0.83) for linear models in Strain B. 67 Table 3: Traits Comparism within Models for Strain A Model Trait Parametric Estimates Goodness of Fit Validation a b c d f RMSE R2 AIC AIC Wt Logistic BWT 0.09 19.86 2624.96 48.11 0.92 12421.03 1.47 EGGNO 0.75 3.66 29.04 2.30 0.70 10.37.90 0.19 EWT 0.13 16.57 63.25 1.21 0.96 48.89 0.13 Richard BWT 0.02 -2.16.33 4384.30 3341.06 -67.66 47.60 0.93 12395.60 0.75 EGGNO 1.12 3.82 5.51 25.51 1.03 2.32 0.70 1042.10 0.02 EWT 0.04 -140.64 81.03 69.31 -1599.26 1.30 0.96 62.77 0.00 Gompertz BWT 2621.33 0.10 15.64 47.86 0.93 12421.03 0.00 EGGNO 35.33 0.41 3.37 2.30 0.70 1037.90 0.19 EWT 64.57 0.11 13.86 1.19 0.96 48.45 0.16 Linear BWT 592.19 48.72 48.15 0.92 1242.88 1.47 EGGNO -4.45 5.17 2.30 0.70 1036.90 0.42 EWT 12.08 1.40 1.24 0.95 46.09 0.51 Exponential BWT 3062.09 -3534.24 -0.03 47.59 0.93 12395.58 0.75 EGGNO 73.70 -81.85 -0.01 47.59 0.93 12395.58 0.75 EWT 66.52 -145.43 -0.10 1.16 0.96 47.96 0.20 BWT: Body weight, EGGNO: Egg Number, EWT: Egg Weight, RMSE = Root Mean Square Error, R 2 = Coefficient of determination, AIC (Model efficiency) = Akaike Information Criterion, AIC Wt (Model ranking) = Akaike Information Criterion, a= Growth rate, b = Inflection point, c = Asymptote 1, d = Asymptote 2, f = Power Egg production curves of Shikabrown® parents 68 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun Figure 4: Growth curves of strain A birds, estimated by Logistic, Richard, Gompertz, ® Linear and Exponential models for Shikabrown Parent Figure 5: Growth curves of strain B birds, estimated by Logistic, Richard, Gompertz, ® Linear and Exponential models for Shikabrown Parent. 69 Table 4: Traits Comparism within Models for Strain B Model Trait Parametric Estimates Goodness of Fit Validation A b c d f RMSE R2 AIC Logistic BWT 0.13 18.09 2072.48 64.17 0.89 13096.78 EGGNO 0.65 3.83 30.91 2.30 0.70 1037.90 EWT 0.13 16.38 63.29 2.02 0.84 2782.43 Richard BWT 0.02 -74.92 2505.54 2462.66 -21.73 63.15 0.89 13079.45 EGGNO 1.70 3.94 9.28 23.11 1.04 2.32 0.70 1037.90 EWT 0.01 34.31 67.62 67.62 -10.95 2.00 0.84 2774.05 Gompertz BWT 2132.02 0.10 15.05 63.70 0.89 13079.45 EGGNO 39.61 0.34 3.64 2.30 0.70 1036.30 EWT 64.62 0.10 13.62 2.00 0.84 1776.79 Linear BWT -4.45 5.17 2.30 0.70 1036.90 EGGNO -3.12 4.85 2.30 0.70 1036.30 EWT 12.68 1.38 2.06 0.83 2807.04 Exponential BWT 2227.35 -4922.58 -0.00 1.99 0.84 2770.79 EGGNO 152.37 -156.77 -0.04 2.30 0.70 1037.90 EWT 66.59 -139.47 -0.08 1.99 0.84 2770.79 BWT: Body weight, EGGNO: Egg Number, EWT: Egg Weight, RMSE = Root Mean Square Error, R 2 = Coefficient of determination, AIC (Model efficiency) = Akaike Information Criterion, AIC Wt (Model ranking) = Akaike Information Criterion, a= Growth rate, b = Inflection point, c = Asymptote 1, d = Asymptote 2, f = Power AIC Wt 8.94 0.19 0.00 5.05 0.19 0.16 5.05 0.42 0.04 0.42 0.42 1.07 0.80 0.42 0.80 Egg production curves of Shikabrown® parents 70 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun development. Omeje and Nwosu (1986) opined that these relationships could be utilized in the genetic improvement of growth through selection. The rising and falling in egg weight followed the trend observed for body weight. Such effects could be attributed to climatic effects, heat stress, as well as, on the health and feed consumption of layers (Hani et al., 2011). ® The growth curves of the Shikabrown parent as presented by the models for both strains are presented in Figures 1 and 2. Goodness of fit criteria was generally high for most of the models (R2 = 0.84 - 0.96) for BWT and EWT. This is in line but numerically lower than the results of Narinc et al. (2010) who reported higher R2 values of (R2 = 0.98 - 0.99) and also DarmaniKuhi et al. (2003), who also reported a range of 2 = (R 98.87 - 99.99%) in chicken. The high 2 R values in the present study indicate that the models adequately described the ® observed Shikabrown data on egg production traits. Forni et al., (2008) observed that model goodness of fit is generally evaluated by using Root Mean Square Error and Coefficient of Determination. The effect of strain on model parameter showed that the constant 'a' (growth rate/maximum potential for egg production per strain) for EGGNO was significantly (P<0.05) higher (152.37) for strain B (dam line) than (73.70) for strain A (sire line). This agrees with the report of (Oni, 1997), who reported maximum egg per period for strain B. This is not surprising since selection to improve number of eggs is concentrated on the female line, while the emphasis on the male line is to improve BWT and EWT. The high coefficient of determination obtained from Richard and Gompertz, agrees with the results of these writers (Ricklefs, 1985; Aggrey, 2002; Anthony et al., 1991 and). The Richard and Gompertz Discussions Differences in age at sexual maturity are subject to genetic variation. However it is not clear whether age at sexual maturity is inherited independently of body size (Agaviezorb et al., 2011).Variation observed in ASM which is higher in strain A (158 days) as compared to strain B (154 days), could be as a result of different (P<0.05) body weight at maturity of the strains considered. This is in agreement with Charles and Tucker (1993), who found that layers of light strain consumed comparable little feed as opposed to heavy strains which consumed more feed. Similarly, Sowunmi et al. (1998) reported that the body weight at first egg depends to a large extent upon age. Those that mature when relatively young weigh less than those that do not begin laying until they are somewhat older. In this present study, individual egg production was expressed in 28-d periods from the day the birds laid the first egg. Consequently, summation of such records in strain egg production data was free of the influence of sexual maturity (Oni, 1997). The curve trend revealed that the two strains differed significantly (P<0.05) in body and egg weights (Figures 1 and 2). Strain B had the highest body weight (1.59±0.01 Kg) and strain A had the highest egg weight (48.75±0.17Kg). Generally, body weight increased with age of the birds in each strain. This result compares with the findings of Crawford (1990), Hossain and Ahmed (1993). Giordani et al. (1992) and Ebangi and Ibe (1994) all reported differences in growth rate of chickens as a result of genotype and age. Similarly, increase in body weight of each strain as they advanced in age, in this study is in line with the reports of Ojedapo et al. (2008) and Pingel et al. (1990) that age is a major determinant of growth and physiological 71 Egg production curves of Shikabrown® parents (2621.33), Linear (592.19), Logistic (0.09) and then Richard model (0.02). This is in agreement with the report of Kucuk and Eyduran (2009) that compared Monomolecular, Gompertz and Logistic models and ranked the Monomolecular first and Logistic last in terms of asymptote body weight. However the result contrasted with the results reported by Aggrey (2002), who ranked the Richards ahead of Gompertz and Logistic. And also Narinc et al. (2010), ranked Gompertz first, Richards next and Logistic last. Similar R2 value of (0.70) obtained for egg number; a reproductive trait, in almost all the models used for the two strains suggests that the strains had similar age at sexual maturity as buttressed in (Table 1). Also this implies that the birds' genetic potential can be further exploited for more genetic gain. The estimation and analysis of the asymptotic weight is essential and project the flock efficiency, as underweight animals have delayed onset of sexual maturity and tend to lay fewer eggs (Kirikci et al., 2007). models have been shown to give good descriptions of growth in species such as cattle, chicken, ostrich, turkey, quails and emus (Ersoyet al., 2005). The Gompertz growth model has been cited as the model of choice for chicken data based on its overall fit and biological meaning of model parameters. In addition, it has good fitting for weight information whose inflection points occur, when approximately 35-40 % of growth has been achieved (Braccini, 1993). This is in agreement with the findings of Narushin and Takma (2003). They reported Gompertz and Richards models as the best models to predict growth patterns. In this study, the Richards equation provided a better fit than the Gompertz equation. This is in agreement with the report by DarmaniKuhiet al. (2003) and Faridi et al. (2011) they found Richards equation to be a better model for describing growth data in broilers than the Gompertz equation. This could be due to the higher number of model parameters in Richard model: which has five (5) model parameters than in Gompertz which has three (3) model parameters. As far as the goodness of fit is concerned, the best value (the lowest) of the AIC gives the closest representation of data (Marc, 2007). However, the suitability of the model for egg production curves depends not only on its general goodness of fits but also on the ability of describing the asymptotic phase of the curve (Macciotta et al., 2011). In this study, the asymptotic phases were recorded for Richard, logistic, Gompertz and Exponential models except for linear model. Brown et al. (1976) had earlier reported that 'a' parameter values offer the best opportunity to make direct comparisons among models. Comparisons of asymptotic weight obtained with the different models showed as earlier stated that Exponential model had the highest value (3062.09) followed by Gompertz Conclusions Body weight of Strain B (1.59±0.01Kg) was significantly superior to that of strain A (1.55±0.10Kg). Egg weight of Strain A (48.75±0.17g) was significantly superior to strain B (47.92±0.17g). The genetic makeup for egg number seems to be similar for the two strains. Values for egg number for strain A (14.33±0.24) and strain B (14.48±0.24) were statistically similar. In strain A, Richard model outperformed the other models in modeling body weight and 2 egg weight with R values of 0.89 and 0.93, respectively. The RMSE generated for Richard model for the two traits were 63.70 and 47.60, respectively. Egg number of strain A was best modeled by Exponential 2 model with R value of 0.93 and RMSE of 47.59. 72 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun pp 89. Brown, J. E., Fitzhugh, H. A. and Cartwright, T. C. 1976. A comparison of nonlinear models for describing weight-age relationships in cattle. Journal of Animal Science, 42(8): 10-818. Charles, D.R. and Tucker, S. 1993. Light intensity, intermittent lighting and feeding regimen during rearing as affected egg production and egg quality. British Poultry Science, 34: 255-266. Crawford, R.D. 1990. Poultry genetic resources: evolution, diversity and conservation. In: Poultry Breeding and Genetics. In: Crawford, R.D. (Editor). Elsevier Science Publishers, Amsterdam. DarmaniKuhi, H., E. Kebreab, E., Lopez, S. and France, J. 2003. An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken. Poultry Science, 82: 1536–1543. Dogan, N. Emre, K., Mehmet, Z.F. and Tulin, A. 2010. Comparison of Non-linear growth models to describe the growth in Japanese quail. Journal of Animal and Veterinary Advances, 9(14): 19611966. Duncan, D.B. 1955. Multiple Range and Multiple F Tests. Biometrics, 11: 142. Ebangi, A.L. and Ibe, S.N. 1994. Heritabilities and genetic correlations between some growth traits in Nigeria local chickens. Nigerian Journal of Animal Production, 21: 19-24. Ersoy, E., Mendes, M., and Aktan, S. 2005. Growth curve establishment for American Bronze turkeys. References Aboul-Seoud, D. I. M. 2008. Divergent Selection for Growth and Egg Production Traits in Japanese quail. Unpublished PhD Thesis, Department of Animal Production, Faculty of Agriculture Al-Azhar University, Egypt. Adesiji, G. B., Baba, S. T. and Tyabo, I. S. 2013. Effects of climate change on poultry production in Ondo State, Nigeria. Russian Journal of Agricultural and Socio-Economic Sciences, 2(14): 55-60. Agaviezor,B.O.,Ajayi, F.O., Adebambo, O.A. and Gunn, H.H. 2011. Nigerian Indigenous vs. Exotic Hens: the Correlation Factor in B o d y We i g h t a n d L a y i n g Performance. An International Multi-Disciplinary Journal,5(1): 405-413. Aggrey, S.E. 2002. Comparison of three nonlinear and spline regression models for describing chicken growth curves. Poultry Science, 81: 1782–1788. Akaike, H. 1974. A new look at the statistical model identification. Institute of Electrical Electronics Engineers (IEEC) Translation Automatic Contribution, 19: 716723. Anthony, N.B., Emmerson, D.A., Nestor, K.E., Bacon, W.L., Siegel, P.B. and Dunnington, E.A. 1991. Comparison of growth curves of weight selected populations of turkeys, quail and chickens. Poultry Science, 70: 13–19. Braccini, N.J. 1993. Genetic study of growth curves of laying birds (Unpublished) dissertation. Pelotas (RS): Federal University of Pelotas. 73 Egg production curves of Shikabrown® parents Science, 6: 604-607. Hossain, M.J. and Ahmed, S. 1993. Body weight of indigenous Rhode Island Red and Barred Plymouth Rock c h i c k e n . A n i m a l B re e d i n g Abstract, 93: 61. Kirikçi, K., Günlü, A., Çetin, O. and Garip, M. 2007. Effect of hen weight on egg production and some egg quality characteristics in the partridge (Alectorisgraeca). Poultry Science, 86: 1380-1383. Kucuk, M. and Eyduran, E. 2009. The determination of the best growth model for Akkaraman and German Black headed Mutton x Akkaraman B1 cross bred lambs. Bulgarian Journal of Agricultural Science, 15: 90-92. Macciotta, N.P.P., Corrado, D., Salvatore, P.G., Roberto, S. and G l u s e p p e , P. 2 0 1 1 . T h e Mathemetical description of lactation curves in dairy cattle. Italian Journal of Animal Science, 10: 51. Marc, J.M. 2007. Making sense out of Akaike's Information Criterion (AIC): Its use and interpretation in model selection and inference from ecological data. http://www.theses.ulaval.ca/2004/ 21842/apa.html. Assessed 9/10/2015. Motulsky, H. and Christopoulos A. 2003. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting. Graph Pad Software Incorporation, San Diego, CA. Narinc, D., Karaman, E., Firat, M. Z. and Aksoy, T. 2010. Comparison of non-linear growth models to describe the growth in Japanese quail. Journal of Animal and ArchivTierzuchtDummerstorf, 49: 293-299. Fairfull, R.W., and Gowe, R.S 1990. Genetics of egg population in chickens. In: Poultry Breeding and Genetics, Crawford, R.D. (Editor). Elsevier, 29: 705-759. Faridi, A., Mottaghitalab, M., Rezaee, F. and France, J. 2011. NarushinTakama models as flexible alternatives for describing economic traits in broiler breeder flocks. Poultry Science, 90: 507–515. Forni, S., Piles, M., Blasco, A.,Varona, L., Oliveira, H.N., Lôbo, R.B. and A l b u q u e rq u e , L . G . 2 0 0 8 . Comparison of different nonlinear functions to describe Nelore cattle growth. Journal of Animal Science, 87: 496-506. Gavora, J.S., Liljedahl, L.E., McMillan, I. and Ahlen, K. 1982. Comparison of three mathematical models of egg production. British Poultry Science, 23: 339–348. Giordani, G.A., Meluzi, C. and Calin, F. 1992. Study on the performance and Adiposity of modern broiler comparison among strains. Animal Breeding Abstract, 6: 581. Hani, N.H., Kamarn, A.A., Aram, M.A., Tahir R., Al-Khatib, Shayma, M.A. and Dastan, A.H. 2011. Effect of genetic lines and season on body weights of chicks. Recent Advances in Biomedical and Chemical Engineering and Materials Science, ISBN: 978-161804-223-1. Haruna, U., Jibril, S.A., Kalla, D.J.U. and Suleiman, H. 2007. Evaluation of egg production in Jos North Local Government Area, Plateau State, Nigeria. International Journal of Poultry 74 Ahmadu, Kabir, Iyiola-Tunji, Akinsola and Igbadun Orunmuyi, M. 2007.Genetic Evaluation of Plasma Alkaline Phosphatase activity in two strains of Rhode Island chickens. (Unpublished) Ph.D. Thesis, Department of Animal Science, Faculty of Agriculture, Ahmadu Bello University Zaria, Nigeria. Pingel, H., Schneider, K.H. and Birla, M. 1990. Factors affecting meat quality in Broilers. Animal Breeding Abstract, 59: 1991. Ricklefs, R.E. 1985. Modification of growth and development of muscles of poultry. Poultry Science 64: 1563-1576. Sowunmi, I.O., Ikeobi, C.O.N. and Adebambo, O.A. 1998. Effect of body weight at caging on pre-peak production performance of white feather Yaafa layers: Egg number and Egg size. NSAP silver anniversary conference/WASAP inaugural conference. Topo, Badagry, March 21-26, pp 21–26. Statistical Analysis System, SAS, 2004. th SAS Users Guide. Statistics, 8 Edition, SAS Institute Cary, NC, USA. The Poultry Site. 2009. Poultry site News: http://'poultry newsdesk.com. Veterinary Advances, 9(14): 19611966. Narinc, D., Uckardes, F. and Aslan, E. 2014. Egg production curve analyses in poultry science. World's Poultry Science Journal, 70: 817828. Narushin, V.G. and Takma, C. 2003. Sigmoid model for the evaluation of growth and production curves in laying hens. Biosystems Engineering, 84: 343-348. Ojedapo, L.O., Akinokun, O., Adedeji, T.A., Olayeni, T.B., Ameen, S.A., Ige, A.O. and Amao, S.R. 2008. Evaluation of Growth Traits and Short-Term Laying Performance of Three Different Strains of Chicken in the Derived Savannah Zone of Nigeria. International Journal of Poultry Science, 7(1): 92-96. Omeje, S.S. and Nwosu, C.C. 1986. Growth and egg production evaluation of F2 and backcross progeny chicks from Nigeria by gold-link crosses. Proceedings of 3rd World Congress. Genetic of Applied Livestock Production, 16th to 22nd July, Lincoln, Nebraska, USA. 10: 304-310. Oni, O.O. 1997. Evaluation of models for egg production in chickens. (Unpublished) Ph.D. Thesis, Department of Animal Science, Faculty of Agriculture, Ahmadu Bello University Zaria, Nigeria. 135 pp. Received: 25th August, 2016 Accepted: 12th March, 2017 75