中国荷斯坦奶牛泌乳曲线的数学模型及其遗传特性研究
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摘要
奶牛泌乳过程中的泌乳量是随着时间而呈现规律性变化的，泌乳曲线及其数学模型是描
述这一变化规律及趋势的有效方法之一。通过研究奶牛泌乳曲线及其数学模型，对奶牛遗传
育种、饲养管理等都具有非常积极的意义。本文利用Wood于1967年提出的泌乳曲线数学模
型比较全面、系统地研究了不同分组、抽样的中国荷斯坦奶牛泌乳量资料拟合泌乳曲线模型
的效果，估计、分析了决定Wood模型特征的参数的遗传力、遗传相关表型相关、影响因素，
以及不同模型对奶牛305天和各泌乳月泌乳量的预测效果。主要结果如下：
1.利用Wood模型拟合奶牛的泌乳曲线，不同数据资料具有不同的效果。利用完整资料
（10个泌乳月泌乳量资料）对泌乳曲线的拟合分析表明，对个体水平的拟合效果不理想，拟
合度在0.90以上的个体数仅占总个体数的5.82％（测定日模型）、42.80％（月平均模型），并
有非正常泌乳曲线出现；对群体水平的拟合效果较理想，测定日模型和月平均模型分别可以
描述96.13％和96.75％的泌乳量变异；在按公牛家系、胎次、产犊年份、产犊季节、牛舍、305
天泌乳量、高峰泌乳量等各分组模型中，测定日模型和月平均模型的拟合度分别为
0.9068～0.9764和0.9237～0.98，具有较好的拟合效果，明显优于由个体平均形成的群体平均
的拟合效果，模型参数间大多没有差异。利用部分资料（前4个泌乳月泌乳量资料）对泌乳
曲线的拟合分析表明，各分组的月平均模型显示了较好的拟合效果，其拟合度为
0.8876～0.9950，而测定日模型的拟合效果和稳定性均相对较差，其拟合度为0.5195～0.9957，模型参数间存在一定的差异。
2.除了产犊年份对参数A外，胎次、公牛家系、产犊季节、产犊年份、牛舍均对完整
资料的测定日模型的参数A、b、c存在显著的影响（p<0.05），除了胎次、产犊季节、产犊年
份对参数A，产犊年份对参数c外，其它因子对月平均模型参数A、b、c有显著影响（p<0.05）。
因子间的互作效应对模型参数的影响普遍较小，对于测定日模型，仅有胎次和公牛的互作对
参数b、c；胎次和产犊季节、公牛和牛舍、产犊季节和产犊年份、牛舍和产犊季节和产犊年
份、胎次和公牛和产犊季节和产犊年份等的互作效应对参数b有显著影响（p<0.05）；对于月
平均模型，仅有胎次和公牛的互作对参数b，胎次和产犊年份的互作对于A，胎次和产犊季
节、公牛和牛舍的互作对参数b有显著影响（p<0.05），其它互作效应对参数的影响均没有达
到显著水平。测定日模型比月平均模型更易受各因子的影响。
3.利用完整资料估计的测定日、月平均模型的参数的遗传力普遍较低，测定日模型参数A、b、c、PT、P、PM的遗传力分别为0.1125、0.1094、0.1718、0.0976、0.1589、0.596，
仅有参数c的遗传力达到显著水平（p<0.05）；月平均模型参数的遗传力分别为0.1403、0.0751、
0.1573、0.1581、0.1825、0.0775，均没有达到显著水平。遗传和表型相关分析表明，对于测
定日模型，参数A与b、P具有显著的遗传相关，其中与b呈负相关，b与c、c与P、PT与
PM呈现显著的正邀传相关，C与p、PM、PT与于具有显著的负邀传相关，表型相关除了
A与b、r与PM外，其它均达到显著水平，遗传和表型相关系数的正负号基本一致；对于
月平均模型，除了参戮A与b、r与PM的表型相关关系没有达到显著外，其它均达到显著
水平，系数的方向也基本一致。月平均模型参数似乎比测定日模型具有更高的邀传能力。
4.利用部分资料的测定日模型和月平均模型预测整个群体奶牛的305天平均泌乳量，
其相对误差分别为吕.00％和4.04％，而完鳖资料相应模型的估值的相对误差分别为0.038％和
0.03％，完整资料模型和月平均模型预测效果比部分资料模型和测定日模型好。均方根分析
表明，部分资料模型和完整资料模型的平均均方根分别为92.48和86.46千克，两者差异不明
显，均具有较低的均方根，预测效果较好。各分组模型对305天泌乳量估计的平均预测偏差，
其偏差由小到大的各分组方法顺序排列为：高峰泌乳量、产犊季节、胎次、公牛家系、305
天泌乳量，完整资料模型和部分资料模型的变化趋势基本一致；完整资料模型的预测效果明
显要优于部分资料模型，月平均模型比测定日模型的估计效果好，但没有明显差异。不同分
组模型的均方根分布除了公牛家系组别的预测效果不稳定外，其它效果都比较好，其均方根
由小到大的各分组方法顺序排列为：高峰泌乳量、胎次、产犊季节、305天泌乳量；测定日
与月平均模型的均方根变化趋势基本一致，相互间没有明显的差异，但部分模型的均方根均
大于完整模型。
5.利用部分、完整资料的测定日、月平均模型预测整个群体10个泌乳月平均泌乳量，
其平均预测偏差随着泌乳月份的增加，四类模型的预测偏差均呈逐渐增?
Lactation curves and mathematical models of dairy cattle are one of effective methods
accurately to describe rules of milk yield against time. Research in lactation curves and
mathematical models is of great importance in genetics and breeding,feeding and management etc.
of dairy cattle.The fitting effect of Wood model that was tabled by Wood in 1967 was studied by the
numbers used different grouping and sampling data of Chinese Holstein Cattle,.Heritaility, genetic
correlation, phenotypic correlation and influencing factors of parameters of Wood model were
estimated and analyzed, and the effect of 305-day milk yield and monthly milk yield were forecast
according to different Wood models. The main results of the present study were as following:
1.There has different fitting effect of Wood models using different lactation data. The analysis
of fitting lactation curves using entirely lactation data (1～10 months milk yield data) indicate that, it
is not good fitting effect for individual, the percent of lactations of R2≥0.90 are just 5.82%(test-day
models) and 42.80% (month mean models), and there have several atypical lactation curves;It is
better fitting effect for herds,R2 of test-da models and month mean models are 96.13% and
96.75% respectively; There also have better fitting effect for grouping models,R2 of test-day models
and month mean models are 0.9068～0.9764 and 0.9237～0.98 respectively in grouped by bull
families, parities, years of freshing seasons of freshing, houses, 305-day milk yield and peak milk
yield. but there are no significant difference in parameters of models. The analysis of fitting effect of
lactation curves using part lactation data (1～4 months milk yield data) indicate that the grouping
month mean models (R2: 0.8876～0.9950) are more better fitting effect than test-day models(R2:
0.5195～0.9957), and R2 of test-da models are very instability and there are significant difference
in parameters of models.
2. There are significant affect in bull families, parities, yeare of freshing, seasons of freshing,
houses to parametere A, b, c of test-da tnodels besides mp of bohing tO A, and in all bo tO tO
parameters A, b, c of month mean modeis besideS parities, years of heshing, seasons of fhahiDg to
A and M of freshing tO c. The the of bo boons to modls parambo are gewtly
SInailer sighfiCan de are jUSt in ~esx bull families interactions tO b, c, Paritiesx seasons of
bohing, bul families X hoUSeS, years Of ffe~x seasons of ffeshing, howt X seasons of eq
x years of beshing, Parities x buIl bolies x seasons of ffeshing x years of wtng intendons to
b in teSttw models, and in Parihesxbull families, parities Xseasons of ffeshing, bull familiesx
houses, interaCtions tO b, parities X yearS of bohing interaCtions to A in month mean models. The
Wt deN of M models are more than month mean models.
3. The heritability of parameters of teSt~ and month mean models in complete herds are
genetally lowef, the heritaility of A, b, c, PT P, PM of test-day models are 0.l l25, 0.l094, 0.l718,
0.0976, 0.l589, 0.0596 reSPeCtively, jUSt c is signifiCan (P<0.05). The heritability of pmbo of
month mean modls are 0.l403, 0.075l, 0.l573, 0.l581, 0.l525, 0.0775 res~vely, bot there has
no swifiCan in ParameteI'S. The twis of poeters of genetic cormlation and PhenOtyPic
cormlallon indibe that, for hav sighfiCan genedc cormlation foreen A and b, P; b and c; c and
v, rr PM; pp tal P; anu ail pnenotwic cormlation boiaes A anu b; rv nd PM in test'ar mwtls.
Thot are all signifiCan cormlation besides pboic correlation between A and b; PT and PM, the
posthe and wt Symbol of the coefficient of genetic the phenOtyPic corrlallon are basically
same. The p-- of mOnth mean models seem more heritability than testday models.
4. The 305wi milk yields Of herds have been foreCaS using testtw and month mean modls
of COmlete and pat ha The relboly MPE are 8.00O/ and 4.04% of Part bo and 0.038O/o and
0.03l% of Wlere data, the M Of models of comlete h
述这一变化规律及趋势的有效方法之一。通过研究奶牛泌乳曲线及其数学模型，对奶牛遗传
育种、饲养管理等都具有非常积极的意义。本文利用Wood于1967年提出的泌乳曲线数学模
型比较全面、系统地研究了不同分组、抽样的中国荷斯坦奶牛泌乳量资料拟合泌乳曲线模型
的效果，估计、分析了决定Wood模型特征的参数的遗传力、遗传相关表型相关、影响因素，
以及不同模型对奶牛305天和各泌乳月泌乳量的预测效果。主要结果如下：
1.利用Wood模型拟合奶牛的泌乳曲线，不同数据资料具有不同的效果。利用完整资料
（10个泌乳月泌乳量资料）对泌乳曲线的拟合分析表明，对个体水平的拟合效果不理想，拟
合度在0.90以上的个体数仅占总个体数的5.82％（测定日模型）、42.80％（月平均模型），并
有非正常泌乳曲线出现；对群体水平的拟合效果较理想，测定日模型和月平均模型分别可以
描述96.13％和96.75％的泌乳量变异；在按公牛家系、胎次、产犊年份、产犊季节、牛舍、305
天泌乳量、高峰泌乳量等各分组模型中，测定日模型和月平均模型的拟合度分别为
0.9068～0.9764和0.9237～0.98，具有较好的拟合效果，明显优于由个体平均形成的群体平均
的拟合效果，模型参数间大多没有差异。利用部分资料（前4个泌乳月泌乳量资料）对泌乳
曲线的拟合分析表明，各分组的月平均模型显示了较好的拟合效果，其拟合度为
0.8876～0.9950，而测定日模型的拟合效果和稳定性均相对较差，其拟合度为0.5195～0.9957，模型参数间存在一定的差异。
2.除了产犊年份对参数A外，胎次、公牛家系、产犊季节、产犊年份、牛舍均对完整
资料的测定日模型的参数A、b、c存在显著的影响（p<0.05），除了胎次、产犊季节、产犊年
份对参数A，产犊年份对参数c外，其它因子对月平均模型参数A、b、c有显著影响（p<0.05）。
因子间的互作效应对模型参数的影响普遍较小，对于测定日模型，仅有胎次和公牛的互作对
参数b、c；胎次和产犊季节、公牛和牛舍、产犊季节和产犊年份、牛舍和产犊季节和产犊年
份、胎次和公牛和产犊季节和产犊年份等的互作效应对参数b有显著影响（p<0.05）；对于月
平均模型，仅有胎次和公牛的互作对参数b，胎次和产犊年份的互作对于A，胎次和产犊季
节、公牛和牛舍的互作对参数b有显著影响（p<0.05），其它互作效应对参数的影响均没有达
到显著水平。测定日模型比月平均模型更易受各因子的影响。
3.利用完整资料估计的测定日、月平均模型的参数的遗传力普遍较低，测定日模型参数A、b、c、PT、P、PM的遗传力分别为0.1125、0.1094、0.1718、0.0976、0.1589、0.596，
仅有参数c的遗传力达到显著水平（p<0.05）；月平均模型参数的遗传力分别为0.1403、0.0751、
0.1573、0.1581、0.1825、0.0775，均没有达到显著水平。遗传和表型相关分析表明，对于测
定日模型，参数A与b、P具有显著的遗传相关，其中与b呈负相关，b与c、c与P、PT与
PM呈现显著的正邀传相关，C与p、PM、PT与于具有显著的负邀传相关，表型相关除了
A与b、r与PM外，其它均达到显著水平，遗传和表型相关系数的正负号基本一致；对于
月平均模型，除了参戮A与b、r与PM的表型相关关系没有达到显著外，其它均达到显著
水平，系数的方向也基本一致。月平均模型参数似乎比测定日模型具有更高的邀传能力。
4.利用部分资料的测定日模型和月平均模型预测整个群体奶牛的305天平均泌乳量，
其相对误差分别为吕.00％和4.04％，而完鳖资料相应模型的估值的相对误差分别为0.038％和
0.03％，完整资料模型和月平均模型预测效果比部分资料模型和测定日模型好。均方根分析
表明，部分资料模型和完整资料模型的平均均方根分别为92.48和86.46千克，两者差异不明
显，均具有较低的均方根，预测效果较好。各分组模型对305天泌乳量估计的平均预测偏差，
其偏差由小到大的各分组方法顺序排列为：高峰泌乳量、产犊季节、胎次、公牛家系、305
天泌乳量，完整资料模型和部分资料模型的变化趋势基本一致；完整资料模型的预测效果明
显要优于部分资料模型，月平均模型比测定日模型的估计效果好，但没有明显差异。不同分
组模型的均方根分布除了公牛家系组别的预测效果不稳定外，其它效果都比较好，其均方根
由小到大的各分组方法顺序排列为：高峰泌乳量、胎次、产犊季节、305天泌乳量；测定日
与月平均模型的均方根变化趋势基本一致，相互间没有明显的差异，但部分模型的均方根均
大于完整模型。
5.利用部分、完整资料的测定日、月平均模型预测整个群体10个泌乳月平均泌乳量，
其平均预测偏差随着泌乳月份的增加，四类模型的预测偏差均呈逐渐增?
Lactation curves and mathematical models of dairy cattle are one of effective methods
accurately to describe rules of milk yield against time. Research in lactation curves and
mathematical models is of great importance in genetics and breeding,feeding and management etc.
of dairy cattle.The fitting effect of Wood model that was tabled by Wood in 1967 was studied by the
numbers used different grouping and sampling data of Chinese Holstein Cattle,.Heritaility, genetic
correlation, phenotypic correlation and influencing factors of parameters of Wood model were
estimated and analyzed, and the effect of 305-day milk yield and monthly milk yield were forecast
according to different Wood models. The main results of the present study were as following:
1.There has different fitting effect of Wood models using different lactation data. The analysis
of fitting lactation curves using entirely lactation data (1～10 months milk yield data) indicate that, it
is not good fitting effect for individual, the percent of lactations of R2≥0.90 are just 5.82%(test-day
models) and 42.80% (month mean models), and there have several atypical lactation curves;It is
better fitting effect for herds,R2 of test-da models and month mean models are 96.13% and
96.75% respectively; There also have better fitting effect for grouping models,R2 of test-day models
and month mean models are 0.9068～0.9764 and 0.9237～0.98 respectively in grouped by bull
families, parities, years of freshing seasons of freshing, houses, 305-day milk yield and peak milk
yield. but there are no significant difference in parameters of models. The analysis of fitting effect of
lactation curves using part lactation data (1～4 months milk yield data) indicate that the grouping
month mean models (R2: 0.8876～0.9950) are more better fitting effect than test-day models(R2:
0.5195～0.9957), and R2 of test-da models are very instability and there are significant difference
in parameters of models.
2. There are significant affect in bull families, parities, yeare of freshing, seasons of freshing,
houses to parametere A, b, c of test-da tnodels besides mp of bohing tO A, and in all bo tO tO
parameters A, b, c of month mean modeis besideS parities, years of heshing, seasons of fhahiDg to
A and M of freshing tO c. The the of bo boons to modls parambo are gewtly
SInailer sighfiCan de are jUSt in ~esx bull families interactions tO b, c, Paritiesx seasons of
bohing, bul families X hoUSeS, years Of ffe~x seasons of ffeshing, howt X seasons of eq
x years of beshing, Parities x buIl bolies x seasons of ffeshing x years of wtng intendons to
b in teSttw models, and in Parihesxbull families, parities Xseasons of ffeshing, bull familiesx
houses, interaCtions tO b, parities X yearS of bohing interaCtions to A in month mean models. The
Wt deN of M models are more than month mean models.
3. The heritability of parameters of teSt~ and month mean models in complete herds are
genetally lowef, the heritaility of A, b, c, PT P, PM of test-day models are 0.l l25, 0.l094, 0.l718,
0.0976, 0.l589, 0.0596 reSPeCtively, jUSt c is signifiCan (P<0.05). The heritability of pmbo of
month mean modls are 0.l403, 0.075l, 0.l573, 0.l581, 0.l525, 0.0775 res~vely, bot there has
no swifiCan in ParameteI'S. The twis of poeters of genetic cormlation and PhenOtyPic
cormlallon indibe that, for hav sighfiCan genedc cormlation foreen A and b, P; b and c; c and
v, rr PM; pp tal P; anu ail pnenotwic cormlation boiaes A anu b; rv nd PM in test'ar mwtls.
Thot are all signifiCan cormlation besides pboic correlation between A and b; PT and PM, the
posthe and wt Symbol of the coefficient of genetic the phenOtyPic corrlallon are basically
same. The p-- of mOnth mean models seem more heritability than testday models.
4. The 305wi milk yields Of herds have been foreCaS using testtw and month mean modls
of COmlete and pat ha The relboly MPE are 8.00O/ and 4.04% of Part bo and 0.038O/o and
0.03l% of Wlere data, the M Of models of comlete h
引文
王加启，米军祥，1995，奶牛氨基浓缩料的研究和应用，中国奶牛，2：40
王光国，张家贞，1993，建立估测奶牛产奶量多元回归数学模型的研究，中国奶牛，2：18
王治华，吴常信，1995，奶牛泌乳曲线参数最小二乘均值的估计，中国奶牛，2：38
王治华，1992，奶牛泌乳曲线数学模型的起源、发展和应用，安徽农业技术师范学院学报，21(2)：49
王治华，1993，泌乳曲线数学模型的研究进展，中国奶牛，4：44
王治华，张斌，徐慧如，1994a，黑白花奶牛泌乳曲线参数的方差组分和遗传特性分析，畜牧兽医学报，25(5)：417
王治华，吴常信，张斌，1994b，公牛家系泌乳曲线的研究，黄牛杂志，20(2)：8
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