Genetic (co)variances and breeding value estimation of Gompertz growth curve parameters in Finnish Yorkshire boars, gilts and barrows.

This paper's objectives were to estimate the genetic (co)variance components of the Gompertz growth curve parameters and to evaluate the relationship of estimated breeding values (EBV) based on average daily gain (ADG) and Gompertz growth curves. Finnish Yorkshire central test station performance data was obtained from the Faba Breeding (Vantaa, Finland). The final data set included 121,488 weight records from 10,111 pigs. Heritability estimates for the Gompertz growth parameters mature weight (alpha), logarithm of mature weight to birth weight ratio (beta) and maturation rate (kappa) were 0.44, 0.55 and 0.31, respectively. Genotypic and phenotypic correlations between the growth curve parameters were high and mainly negative. The only positive relationship was found between alpha and beta. Pearson and Spearman rank correlation coefficients between EBV for ADG and daily gain calculated from Gompertz growth curves were 0.79. The Spearman rank correlation between the sire EBV for ADG and Gompertz growth curve parameter-based ADG for all sires with at least 15 progeny was 0.86. Growth curves differ significantly between individuals and this information could be utilized for selection purposes when improving growth rate in pigs.     

禽类三种常用生长曲线浅析

生长曲线的分析和拟合是研究畜禽生长发育规律的主要方法之一,它在实践中可用于生长速率的预测和生长过程的遗传分析。本文对Logistic,Bertanlanffy和Gompertz三种禽类常用生长曲线加以探讨,并以丝羽鸟骨鸡资料为实例进行了分析,结果表明,Logistic模型,Bertanlanffy模型和Gompertz模型对丝羽乌骨鸡的拟合度都很好,其中Gompertz模型在预测早期生长发育方面更具有优越性。     

连城白鸭肉用新品系早期生长规律及生长曲线拟合的研究

对0～9周龄的连城白鸭肉用新品系早期生长发育情况进行了测定和分析,并运用Gompertz模型对其生长曲线进行拟合与分析。结果表明:Gompertz模型能很好地模拟连城白鸭肉用新品系生长曲线,拟合度(R2)高(公鸭:R2=0.9998,母鸭:R2=0.9997),进一步对拟合参数分析,发现连城白鸭肉用新品系公鸭极限体重为2423.6g,拐点体重为891.7g,拐点周龄为3.5周;母鸭极限体重为2099.2g,拐点体重为772.3g,拐点周龄为3.2周。     

湘西黄牛母牛生长曲线的探讨

本研究分别利用Logistic和Gompertz方程对562头湘西黄牛母牛的生长曲线进行了拟合。结果表明,Logistic和Gompertz方程均能很好地拟合湘西黄牛母牛的生长过程(P<0.0001),拟合优度R2分别为0.9940和0.9961。综合拟合优度和预测能力来看,Gompertz方程更适合于湘西黄牛母牛的生长曲线研究,因此用Gompertz方程更为合适。Logistic和Gom-pertz方程生长曲线的拐点分别为(11.38,166.33)和(6.78,124.5)。本研究结论对湘西黄牛的保种、选育、杂交利用及饲养管理具有指导意义。     

A genetic investigation of various growth models to describe growth of lambs of two contrasting breeds

This study compared the use of various models to describe growth in lambs of 2 contrasting breeds from birth to slaughter. Live BW records (n = 7559) from 240 Texel and 231 Scottish Blackface (SBF) lambs weighed at 2-wk intervals were modeled. Biologically relevant variables were estimated for each lamb from modified versions of the logistic, Gompertz, Richards, and exponential models, and from linear regression. In both breeds, all nonlinear models fitted the data well, with an average coefficient of determination (R2) of > 0.98. The linear model had a lower average R2 than any of the nonlinear models (< 0.94). The variables used to describe the best 3 models (logistic, Gompertz, and Richards) included estimated final BW (A); maximum ADG (B); age at maximum ADG (C); position of point of inflection in relation to A (D, for Richards only). The Richards and Gompertz models provided the best fit (average R2 = 0.986 to 0.989) in both breeds. Richards estimated an extra variable, allowing increased flexibility in describing individual growth patterns, but the Akaike's information criteria value (which weighs log-likelihood by number of parameters estimated) was similar to that of the Gompertz model. Variables A, B, C, and D were moderately to highly heritable in Texel lambs (h2 = 0.33 to 0.87), and genetic correlations between variables within-model ranged from -0.80 to 0.89, suggesting some flexibility to change the shape of the growth curve when selecting for different variables. In SBF lambs, only variables from the logistic and Gompertz models had moderate heritabilities (0.17 to 0.56), but with high genetic correlations between variables within each model (< -0.88 or > 0.92). Selection on growth variables seems promising (in Texel more than SBF), but high genetic correlations between variables may restrict the possibilities to change the growth curve shape. A random regression model was also fitted to the data to allow predictions of growth rates at relevant time points. Heritabilities for growth rates differed markedly at various stages of growth and between the 2 breeds (Texel: 0.14 to 0.74; SBF: 0.07 to 0.34), with negative correlations between growth rate at 60 d of age and growth rate at finishing. Following these results, future studies should investigate genetic relationships between relevant growth curve variables and other important production traits, such as carcass composition and meat quality.     

麻旺鸭生长曲线拟合分析

本文对麻旺公母鸭体重随日龄增长应用Logistic和Gompertz模型进行生长曲线拟合分析,建立麻旺鸭公、母鸭的拟合曲线方程及求出拐点体重、拐点日龄。结果表明:两种模型均能很好地拟合公、母鸭生长规律,Logistic和Gompertz模型拟合公鸭的拟合度分别为R2=0.983,R2=0.986,母鸭R2=0.989,R2=0.990,两种模型相比,Gompertz拟合效果更好。     

新疆褐牛种公牛体重生长发育曲线拟合

为探究新疆褐牛种公牛生长发育规律,利用SAS 8.1软件中的Logistic、Gompertz、Brody和Bertallanffy 4种常用的生长曲线模型对344头次新疆褐牛种公牛体重生长曲线进行拟合。结果表明,4种模型均能较好的拟合新疆褐牛种公牛体重生长,拟合度R²分别为 0.9217、0.9263、0.9176和0.9261,其中Gompertz模型对新疆褐牛种公牛体重生长发育的拟合效果较好,Logistic、Gompertz和Bertallanffy模型生长曲线的拐点分别为(0.4937岁、502.10 kg)、(1.3168岁、379.54 kg)和(1.0477岁、311.25 kg)。本研究对实际生产具有一定的参考价值。     

高邮鸭生长发育与曲线拟合研究

为了研究高邮鸭的早期生长发育规律,本试验运用Gompertz、Logistic和Von Bertalanffy 3种非线性生长模型对高邮鸭1~10周龄生长情况进行了分析和曲线拟合。结果表明,高邮鸭早期生长迅速,3周龄时体重增加最大;3种模型均能较好地拟合高邮鸭早期生长,其中Gompertz曲线模型的拟合度为0.99902,拟合估计值与实际观测值最接近,拟合效果最佳,更适合早期生长发育较快的高邮鸭。     

西藏藏鸡生长曲线拟合及分析

为探究西藏藏鸡早期的生长发育规律,本研究采用Logistic、Bertalanffy和Gompertz非线性模型对公、母鸡从出生到24周龄的体重进行拟合分析。结果显示:3种生长曲线模型的拟合度均能达到0.99以上;进一步从统计和生物学意义角度评价3种模型发现,Gompertz模型拟合效果最好;Gompertz方程拟合公鸡和母鸡的生长拐点周龄分别为10.28周和10.65周;公鸡的拐点体重、最大周增重和最大体重分别为577.20、80.81、1569 g,母鸡分别为465.80、55.90、1266.18 g。研究表明3种模型对西藏藏鸡生长曲线的拟合和分析是可行的,可为管理藏鸡生长发育关键点提供参考。     

不同羽色儋州鸡生长曲线拟合与分析研究

为研究儋州鸡生长发育规律和各阶段的生长速度,本试验采用Gompertz、Logistic和Bertalanffy 3种非线性模型对黑色羽系和麻花色羽系儋州鸡0~18周龄体重生长数据进行拟合和分析,选取黑色羽系、麻花色羽系儋州鸡各200只（公、母各半）,分别于0、2、4、6、8、10、12、14、16和18周龄晨饲前空腹称重并记录,并利用3种非线性模型对儋州鸡生长曲线进行拟合比较分析。结果显示,2种羽色儋州鸡实测生长曲线基本一致,接近于"S"型,符合正常生长发育规律,2种不同羽色儋州鸡母鸡0~18周龄的体重实测值差异不显著（P>0.05）,公鸡0~16周龄的体重实测值差异不显著（P>0.05）,而16~18周龄麻花色羽系公鸡体重显著高于黑色羽系公鸡（P<0.05）。3种非曲线模型拟合度（R²）均在0.992以上,均能较好地拟合2个羽系儋州鸡的生长曲线,且模型的预测曲线与实际观测曲线基本吻合,但Gompertz模型曲线吻合度高于Logistic和Bertalanffy模型曲线,且母鸡比公鸡拟合效果好。本研究结果初步揭示了儋州鸡的生长发育规律和各阶段的生长特征,可为儋州鸡选育、生产和产业化发展提供科学依据。     

马岗鹅早期生长及体尺性状发育规律的研究

为揭示马岗鹅的生长发育规律,挖掘马岗鹅的生长潜力,本研究通过测定马岗鹅0~12周龄的体重和体尺性状,并用Logistics、Von Bertalanffy和Gompertz 3种模型进行生长曲线拟合。结果表明:马岗鹅体重生长曲线最佳模型为Gompertz模型(R2=0.999),拐点周龄是4.31周龄,拐点体重是1459.01g,2~8周龄的周增重都在320 g以上,相对生长率都在16%以上,8周龄前为马岗鹅体重迅速增长时期。胸深、龙骨长、颈长的最佳拟合模型为Gompertz,拐点周龄分别为0.65、3.71、2.28周龄;体斜长、半潜水长的最佳拟合模型为Von Bertalanffy,拐点周龄分别为0.53、0.47周龄;胸宽、骨盆宽、胫长、胫围的最佳拟合模型为Logistic,拐点周龄分别为3.81、1.39、0.91、0.51周龄;7周龄前为马岗鹅体尺性状迅速增长时期。本研究结果可为马岗鹅的生产和饲养管理提供理论指导。     

渝东白山羊与波尔山羊杂交F1生长发育规律研究

采用Logistic、Von Bertalanffy和Gompertz 3种典型非线性生长模型分别对渝东白山羊与波尔山羊F1 0~6月龄体重数据进行曲线拟合分析。结果表明,Logistic、Von Bertalanffy和Gompertz 3种模型均能很好地拟合杂交F1生长曲线,但Von Bertalanffy在拟合效果和预测体重效果方面更佳。分析Von Bertalanffy模型拟合参数,发现拐点体重为6.501 kg,拐点月龄为1.292月,最大月增重为2.955 kg,成熟体重为21.994 kg。     

渝东白山羊与波尔山羊杂交F1生长发育规律研究

采用Logistic、Von Bertalanffy和Gompertz 3种典型非线性生长模型分别对渝东白山羊与波尔山羊F,0-6月龄体重数据进行曲线拟合分析。结果表明,Logistic、Von Bertalanffy和Gompertz3种模型均能很好地拟合杂交F．生长曲线,但VonBertalanffy在拟合效果和预测体重效果方面更佳。分析Yon Bertalanffy模型拟合参数,发现拐点体重为6．501kg,拐点月龄为1．292月,最大月增重为2．955kg,成熟体重为21．994kg。     

Evaluation of non-linear growth curve models in the Vietnamese indigenous Mia chicken

Understanding of animal growth is important for the improvement of management and feeding practices; however, little is known about the growth curve in Vietnamese indigenous chicken. This study was performed to determine the most appropriate models for describing the growth curve of Vietnamese Mia chicken. The study evaluated the performances of the Logistic, Gompertz, Richards, and Bridges models of body weights in 224 Mia chickens. Models were fitted using minpack.lm package in R software and Akaike’s information criterion and Bayesian information criterion were used for model comparison. Based on these criteria, the Gompertz and Bridges were the best models for males and females, respectively. Estimated asymmetric weights (α) were ranged from 2,241.91 ± 14.74 (g) (Logistic) to 2,623.86 ± 30.23 (g) (Gompertz) for males and from 1,537.36 ± 10.97 (g) (Logistic) and 1,958.36 ± 72.92 (g) (Bridges) for females, respectively. The age at the inflection point was estimated from 9.32 to 10.5 weeks and from 8.51 to 9.86 weeks for males and females, respectively. In conclusion, the Gompertz model is the most suitable model for describing the growth curve of Mia chicken. The parameters obtained from growth models could help define feeding programs to meet nutritional needs from hatching to the age of maximum growth, reproduction programs, and marketing strategies.     

新美系大约克猪的生长规律及上市屠宰体重的优化

以66头2005年底引进的新美系大约克猪纯繁一代为对象,分析了从初生到120 kg体重间不同性别不同体重阶段的增重、耗料情况和饲料报酬,进行了Logistic方程、Gompertz方程和Polynomials函数的生长曲线拟合。不同性别间生长规律差异分析表明,母猪成熟体重稍大,达到拐点的日龄和体重也最大,公猪次之,阉猪则最早达到生长拐点。利用经济学平衡原理,分析出其新美系大约克猪的最佳上市体重为125 kg,最佳上市日龄为193.6 d。     

海兰褐蛋鸡和京粉2号蛋鸡的生长发育规律及初产蛋品质比较研究

[目的]研究相同饲养条件下海兰褐蛋鸡苗和京粉2号蛋鸡苗的生长发育规律,评价其初产蛋品质.[方法]选取1日龄海兰褐蛋鸡苗和京粉2号蛋鸡苗各500只,在相同条件下饲养,每周随机挑选60只个体测量体重,直到13周龄试验结束.采用Logistic、Gompertz和Von Bertalanffy 3种曲线模型对2种鸡苗的生长发...     

湖羊生长发育曲线模型预测及趋势分析

本试验旨在研究湖羊的生长发育状况,初步探讨湖羊的生长发育曲线模型并作出趋势分析,并根据此模型建立的生长曲线为湖羊的选育和改善饲养管理提供依据,从而找出湖羊养殖的最佳生长点和上市点.选用木板高床饲养的湖羊31只,测定了初生重、7日龄、14日龄、1～12月龄的体重.采用Logistic、Gompertz和Von Bertalanffy 3种生长曲线模型对湖羊的生长曲线进行拟合.结果发现,Logistic和Gompertz模型对湖羊生长发育的拟合效果较好,其值均高于0.97,其中以Gompertz为最优.利用最优拟合模型进一步分析模型拟合参数,湖羊在2月龄时出现生长拐点.     

Comparison on accuracy of different nonlinear models in predicting growth of Podolica bulls

Animal growth does not follow a linear pattern, being explained mathematically by functions that have parameters with biological meaning. These parameters are used to estimate the expected weight of animals at specific ages. Several nonlinear models have been used to describe growth. This study was carried out to estimate the parameters of logistic, Gompertz, Richards and von Bertalanffy growth curve models in a sample of Podolica young bulls to determine the goodness of fit. Animals were weighed every 3 months from birth to 810 days of age. The results indicate that all the growth models used were easily fitted to the observed data with Gompertz and logistic functions presenting less computational difficulty in terms of number of iterations to achieve convergence. Moreover, logistic and Richards equations provided the best overall fit being useful to describe the growth of Podolica bulls. Considering that the literature lacks information on growth curves in Podolica breed, the study of a mathematical model for growth describing the developmental pattern of a specific population within a peculiar environment is a useful tool to improve Podolica breed production.     

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co)variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand's check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co)variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.     

罗曼肉鸡生长发育规律研究

对1～9周龄的罗曼肉鸡体重进行了测量,计算了绝对生长、相对生长指标,运用Logistic、Gom-pertz和von Bertalanffy三种非线性模型对其累积生长情况进行了拟合与分析。结果表明：罗曼肉鸡在4周龄前生长缓慢,4周龄后逐渐加快;Gompertz模型和von Bertalanffy模型均能很好地拟合罗曼肉鸡的生长曲线（R2分别为0.9989和0.9998）,尤其是von Bertalanffy模型效果更佳,此模型拟合的生长曲线拐点日龄为39.23d,拐点体重为1512.09g。