藏猪体重非线性生长曲线分析

藏猪是我国青藏高原特有的高原型地方猪种,本研究用logistic、Gompertz和Richards模型拟合了藏猪体重生长曲线,并以成华猪为对照分析了藏猪的生长规律。结果表明logistic、Gompertz和Richards模型均适宜拟合藏猪和成华猪的生长曲线,其中Richards模型最好,Gompertz模型优于logistic模型。Richards模型拟合的藏猪极限体重为71.91kg,生长拐点为9.45月龄,最大生长速度为180.0g;说明藏猪存在体重小、生长速度慢、生长拐点迟等特点。     

藏鸡和低地鸡种的生长曲线拟合与杂种优势分析

本试验测定了饲养在北京的藏鸡(T)、寿光鸡(S)、藏鸡×寿光鸡(TS)、矮小隐性白(D)和藏鸡×矮小隐性白(TD)5组鸡早期体重生长数据,用Brody、logistic、Gompertz、vonBertalanffy、Richards和多项式6种模型拟合其生长曲线。通过拟合优度(R2)和残差平方和(E)的比较,发现Gompertz和Richards模型拟合效果较佳。进一步比较不同组间Gompertz模型的拟合参数。结果表明,藏鸡与低地鸡种相比,有较低的初始体重、极限体重、成熟速度、初始生长速度和拐点体重,较高的生长拐点年龄。TD的极限体重、拐点体重、成熟速度、初始生长速度、绝对增重速度和相对生长率比藏鸡都有很大幅度的提高,拐点时间也有提前,存在明显的杂交优势。     

内江猪生长曲线拟合及体重预测模型构建

为研究内江猪生长发育规律,本研究测定了346头内江猪的体重,并使用Logistic、Gompertz和Von Bertalanffy这3种非线性生长曲线模型对其进行生长曲线拟合,使用最佳的生长曲线模型计算相对生长量(R)和绝对生长量(G)。对114头内江猪的体重和体尺进行相关性分析,进一步构建体重预测模型。结果表明：Gompertz模型对内江猪体重具有最佳的拟合效果,该模型估计的拐点日龄为156.74 d,拐点体重为64.41 kg。通过对内江猪生长发育规律分析,发现内江猪在180日龄时生长速度达到最大,之后随日龄的增加逐渐下降,体重与体尺性状间呈正相关关系。雌性内江猪的最佳体重预测模型为：BW=20.1+0.644BH+0.304BL+0.472CC,R²=0.645;雄性内江猪的最佳体重预测模型为：BW=2.7+0.884BH+0.477BL+0.260CC,R²=0.777。内江猪体重拟合效果最好的模型是Gompertz模型。以上结果可为内江猪饲养管理和生长发育的相关研究提供一定的理论基础。     

高海拔地区隐性白羽肉鸡生长曲线的拟合与分析

试验测定了隐性白羽肉鸡在高海拔饲养环境中2～20周龄的体重和胫长,用logistic、Gompertz模型拟合了生长曲线。结果表明隐性白羽肉鸡体重和胫长生长受高海拔环境抑制,logistic和Gompertz模型都适宜拟合隐性白羽肉鸡在高海拔体重和胫长的生长过程,拟合度高,其中logistic模型优于Gompertz模型。隐性白羽公鸡比母鸡有较高的成年体重、拐点体重、绝对生长速度和相对生长速度。     

甘肃合作猪的生长曲线分析和拟合研究

利用Logistic、Gompertz和Richards三种曲线拟合甘肃合作猪的生长模型。结果表明,三种模型中,Gompertz模型拟合效果最理想（R^2=0.9995）;合作猪公、母猪在150日龄前生长基本一致,150日龄后母猪的生长速度明显快于公猪;公、母猪的生长拐点分别为118.32日龄和146.75日龄,母猪的成年体重明显大于公猪,但达到生长拐点的日龄较公猪迟。     

崇仁麻鸡肉用品系生长曲线的拟合与分析

为了解崇仁麻鸡肉用品系的生长发育规律,运用Logistic、Gompertz和Bertalanffy 3种非线性模型分别对崇仁麻鸡肉用品系公、母鸡0～12周龄体重生长数据进行曲线拟合和分析.结果表明:3种模型均能很好地模拟崇仁麻鸡肉用品系公、母鸡的生长曲线,但Gompertz模型和Bertalanffy拟合效果更佳;进一步分析模型拟合参数和理论值与实测值,认为公鸡以Bertallanffy模型拟合较好,拐点周龄为8.272周,拐点体重为1 025.668 g;母鸡以Gompertz模型拟合较好,拐点周龄为6.188周,拐点体重为619.991 g.3种模型估计的公鸡拐点体重、最大周增重均高于母鸡,拐点周龄均晚于母鸡.     

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。     

舍饲型合作猪生长曲线拟合研究

以舍饲型合作猪为研究对象,对其生长发育进行了研究,并运用Gompertz、Richards和Logistic三种非线性模型拟合了体重变化规律。结果表明：舍饲型合作猪体重与占初生重倍数随日龄增加而逐渐增大,相对生长率随日龄增加逐渐下降,90-120日龄日增重最大,为242.5 g;Gompertz模型拟合效果最理想（R^2=0.9995）,用此模型拟合成年公猪体重为47.02 kg,成年母猪体重为59.86 kg;公、母猪生长拐点分别在118.32 d和146.75 d。     

舍饲型合作猪生长曲线拟合研究

以舍饲型合作猪为研究对象,对其生长发育进行了研究,并运用Gompertz、Richards和Logistic三种非线性模型拟合了体重变化规律。结果表明：舍饲型合作猪体重与占初生重倍数随日龄增加而逐渐增大,相对生长率随日龄增加逐渐下降,90-120日龄日增重最大,为242.5 g;Gompertz模型拟合效果最理想（R^2=0.9995）,用此模型拟合成年公猪体重为47.02 kg,成年母猪体重为59.86 kg;公、母猪生长拐点分别在118.32 d和146.75 d。     

苏淮猪体重和背膘生长曲线的拟合与分析

文内运用混合线性模型(Nlmixed)及Logistic、Von Bertalanffy、Gompertz 4种非线性生长模型对苏淮猪0~200日龄之间的体重、背膘进行生长曲线拟合和分析。结果表明,4种模型均能够很好地模拟苏淮猪的生长曲线,R2均达到了0.95以上。其中,Nlmixed模型拟合度较低,实际值与预测值相差较大,相较于其他模型不适于模拟苏淮猪生长曲线。而Gompertz模型更适于模拟苏淮猪的体重生长规律,其极限体重为204.48 kg,拐点日龄为158.81 d,拐点体重为75.22 kg,具有生长快、成熟早的特点,有助于提高出栏率。混合线性模型(Nlmixed)模拟苏淮猪背膘生长规律中,实际值与预测值相差不大,故该模型适于模拟苏淮猪背膘的生长规律。     

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.     

浙东白鹅生长曲线及拟合分析

运用Logistic、Gompertz和Von Bertalanffy 3种非线性模型对浙东白鹅0~8周龄的生长曲线进行分析及拟合比较。结果表明,浙东白鹅公、母鹅在3周龄前生长曲线基本一致,之后一直到8周龄公鹅明显高于母鹅;3种曲线模型拟合度均达到0.99以上,其中Gompertz曲线模型在拟合度和预测极限生长量拐点周龄和最大周增重等方面相对较好。进一步分析结果表明,浙东白鹅公鹅的拐点体重高于母鹅,拐点周龄性别间差异不大。本研究对不同性别浙东白鹅的生长模式及其对营养环境的需求进行了初步探讨,为开展浙东白鹅的规模化养殖提供参考。     

半番鸭及其亲本生长曲线拟合与杂种优势分析

实验测定了樱桃谷鸭、白羽番鸭、苏牧麻鸭、白羽番鸭♂×樱桃谷鸭♀(樱番鸭)、白羽番鸭♂×苏牧麻鸭♀(苏番鸭)早期体重数据,发现樱番鸭杂种优势率为12.8%,苏番鸭为22.04%。用Logistic、Von Bertalanffy和Gompertz3种非线性生长模型拟合其生长曲线,通过比较拟合优度、复相关指数和进行适合性χ2检验,发现Gompertz模型拟合效果最好。比较5组鸭Gompertz模型拟合参数,结果表明:在亲本鸭组中白羽番鸭初始重较樱桃谷鸭和苏牧麻鸭高,初始生长速度、最大周增重较这2个亲本组低,拐点时间也比其晚。2个杂交组最大周增重、成熟速度、极限体重、拐点体重、初始重和拐点时间都有很大提高,存在明显的杂种优势。     

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.     

Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs

Success of pig production depends on maximizing return over feed costs and addressing potential nutrient pollution to the environment. Mathematical modeling has been used to describe many important aspects of inputs and outputs of pork production. This study was undertaken to compare 4 mathematical functions for the best fit in terms of describing specific data sets on pig growth and, in a separate experiment, to compare these 4 functions for describing of P utilization for growth. Two data sets with growth data were used to conduct growth analysis and another data set was used for P efficiency analysis. All data sets were constructed from independent trials that measured BW, age, and intake. Four growth functions representing diminishing returns (monomolecular), sigmoidal with a fixed point of inflection (Gompertz), and sigmoidal with a variable point of inflection (Richards and von Bertalanffy) were used. Meta-analysis of the data was conducted to identify the most appropriate functions for growth and P utilization. Based on Bayesian information criteria, the Richards equation described the BW vs. age data best. The additional parameter of the Richards equation was necessary because the data required a lower point of inflection (138 d) than the Gompertz, with a fixed point of inflexion at 1/e times the final BW (189 d), could accommodate. Lack of flexibility in the Gompertz equation was a limitation to accurate prediction. The monomolecular equation was best at determining efficiencies of P utilization for BW gain compared with the sigmoidal functions. The parameter estimate for the rate constant in all functions decreased as available P intake increased. Average efficiencies during different stages of growth were calculated and offer insight into targeting stages where high feed (nutrient) input is required and when adjustments are needed to accommodate the loss of efficiency and the reduction of potential pollution problems. It is recommended that the Richards and monomolecular equations be included in future growth and nutrient efficiency analyses.     

皮特兰猪生长发育规律及其生长曲线拟合分析

试验旨在研究皮特兰猪的生长发育规律并对其生长曲线进行拟合。利用奥斯本测定系统,导出皮特兰猪（122头公猪和129头母猪）从出生到210 d的7个时间点的生长发育数据,并以此数据为基础分别利用Logistic、Bertalanffy、Gompertz 模型进行生长曲线拟合。结果显示,皮特兰猪体重增长符合S型生长曲线,110~150日龄为快速增长期,出生后越早期相对生长强度越大,之后随着日龄增加逐渐降低。3种拟合模型均获得较理想效果,其中Logistic模型对皮特兰猪拟合度最高（R²=0.9815,母猪）,拟合结果最接近真实情况;其他两种模型也相对较高,为0.9589（母猪）和0.9698（母猪）,均高于0.95。因此Logistic模型最适合法系皮特兰猪的生长发育过程,对方程进行求导,可得公、母猪最大日增重分别为1.051和0.983 kg/d。在其拟合生长曲线中,皮特兰公、母猪拐点日龄分别为114.72和114.89 d,体重分别为65.30和63.00 kg。     

A Growth Performance and Nonlinear Growth Curve Functions of Large- and Normal-Sized Japanese Quail (Coturnix japonica)

This study aimed to evaluate the differences between the growth patterns of large- and normal-sized Japanese quail strains and their F₁ progeny, by fitting their growth parameter values to five nonlinear regression growth models (Weibull, Logistic, Gompertz, Richards, and Brody). The Richards model presented the best fit for both sexes of the large-sized quail strain, whereas the Gompertz model presented the best fit for both sexes of the normal-sized quail strain, based on goodness-of-fit criteria (higher adjusted R² and lower Akaike and Bayesian information criteria). Both sexes of F₁ birds derived from the cross between normal-sized females and large-sized males were best fitted by the Richards model. In contrast, growth parameters of the F₁ birds derived from the cross between large-sized females and normal-sized males were best fitted to the Gompertz model. The data could be fitted nearly as well to the Weibull and Logistic models as to the Richards and Gompertz models. The Brody model presented the poorest fit for the growth parameter values. The results indicated that the Richards and Gompertz models could best describe the growth characteristics of both large- and normal-sized quails. Moreover, the observed growth pattern of the F₁ birds was likely inherited from the male parental strain. To the best of our knowledge, this is the first study comparing the growth curves of the reciprocal F₁ generations with their parental strains in quails.