Thinking on Breeding of Fecundity Genes in Guizhou Black Goats Through Cost-benefit Analysis of Mutton Sheep by SAS Multivariate Stepwise Regression

Qingmeng LONG Min YAO Ping LI Shengli XIONG Ying SHI Yan WANG Di ZHOU

Abstract The total output value of mutton in Northwestern China has accounted for more than 60% of the total output value of animal husbandry over the years. It can be seen that the mutton industry in Northwest China not only plays a pivotal role in animal husbandry， but also plays an important role in Chinese agriculture. In this study， based on cost accounting theory， income-related theories and total factor productivity theory， using basic knowledge of statistics and economics， drawing on existing research results at home and abroad， and adopting a combination of qualitative analysis and quantitative analysis of SAS multiple stepwise regression， the changing trends of cost-benefit of mutton sheep breeding in Northwest agricultural and pastoral areas and influencing factors of production costs and production efficiency were investigated， aiming to provide reference for saving mutton sheep feeding material resources， reducing mutton sheep breeding costs， and improving mutton sheep breeding benefits.

Key words Lamb costs and benefits; Stepwise regression; Guizhou black goats; Selection and breeding thinking

Received： February 23， 2021  Accepted： May 3， 2021

Supported by Guizhou Agricultural Research Project （QKH[2019]2279）; Construction of Guizhou Breeding Livestock and Poultry Genetic Resources Testing Platform （QKZYD[2018]4015）; Scientific and Technological Innovation Talent Team of Major Livestock and Poultry Genome Big Data Analysis and Application Research in Guizhou Province （QKHPTRC[2019]5615）.

Qingmeng LONG （1973-）， female， P. R. China， senior veterinarian， master， devoted to research about livestock and poultry breeding management， disease prevention and control， molecular breeding， genetic resource collection， production preservation and development and utilization.

*Corresponding author. E-mail： 250161818@qq.com.

The development of animal husbandry plays an important role in the realization of agricultural industrialization and the acceleration of the increase of farmers income in China. The seven provinces and cities in Northwest China are Chinas five major pastoral areas， and they are also major beef and mutton producing provinces. However， since 2006， due to the decline in sheep stocks in Northwest China， the decline in mutton sheep production and the decrease in market supply， the price of mutton has been rising. However， problems such as high cost， low benefit， high risk， and contradiction between livestock and grass have become the main reasons for many farmers to withdraw from the breeding industry. The breeding industry faces the grim reality of slow growth of farmers income and low efficiency of livestock production[1].

Research Progress and Existing Problems of Guizhou Black Goats

The black horse sheep population and a small number of intersex sheep are naturally differentiated from Guizhou black goats. In order to explore the molecular mechanism of Guizhou black goats with or without horns and intersex phenotype and realize early detection of intersex sheep， Peng et al.[2] designed specific primers PIS1 U/D and PIS-outU/D， established a PCR technology suitable for detection of PIS locus in Guizhou black goat genome， and determined the sequences of large PIS fragments by chromosome walking technology. The results showed that the early detection of horned sheep， hornless sheep and intersex sheep in Guizhou black goat population can be realized by PCR technology; and combined with chromosome walking technology， it was proved that the PIS locus in the genome of Guizhou horned sheep is complete， the PIS locus in the genome of hornless sheep is single deletion， and the PIS locus in the genome of intersex sheep is double deletion. It shows that the PIS locus in the Guizhou black goat genome has a large variation， and the occurrence of the intersex sheep in the Guizhou black goat population is caused by the deletion of the PIS locus in the genome. Li et al.[2] established three different mixed models to calculate the genetic parameters of the growth traits of Guizhou black goats. The expectation maximum-average information restricted maximum likelihood （EM-AI REML） method was used to estimate the heritability of the birth weight， 3-month-old body weight， 12-month-old body weight and 24-month-old body weight in Guizhou black goats， and the Akaike information criterion （AIC） was used to verify each model finally. The results showed that different models had different estimates of heritability. When only the additive effect was set as a random effect in the model， the model could most accurately estimate the heritability of the 12-month-old body weight and the 24-month-old body weight of Guizhou black goats; and when the additive effects and maternal genetic effects were random effects， the model could most accurately estimate the heritability of birth weight and 3-month-old weight. It showed that the newborn weight and 3-month-old body weight of Guizhou black goats were greatly affected by maternal genetic effects， while the 12-month-old body weight and 24-month-old body weight were less affected by maternal genetic effects; and the growth traits of Guizhou black goats belonged to medium-heritability traits. However， The exploration and breeding of fecundity genes in Guizhou black goats requires a certain population， while the breeding of Guizhou black goats suffers from problems such as high cost， low benefit， high risk， conflicts between livestock and grass， and severe practical impacts of slow growth and low production efficiency of livestock products， leading to insufficient populations for the exploration and breeding of fecundity genes in Guizhou black goats. Therefore， we systematically and comprehensively explored the production factors of mutton， and analyzed the in-depth influencing factors that affect the total cost and net profit of mutton， aiming to facilitate the provision of breeding populations for the exploration and breeding of fecundity genes of black goats in Guizhou Province and provide a reference for the improvement project of Guizhou mutton sheep industry. This study of great significance for developing Guizhous mutton sheep industry， consolidating the results of poverty alleviation and boosting rural revitalization.

Composition of livestock product cost

According to Compilation of National Agricultural Product Cost and Benefit Data-2020， the cost composition of livestock products is shown in Fig. 1.

Introduction to Stepwise Regression Analysis

Regression analysis is a commonly used method. When there is not only one independent variable related to a certain dependent variable （y）， probably more than one independent variables， and the independent variables are set as x x2，…， x（p）， the amount of calculation is large and it is inconvenient to operate when the number of the independent variables is large.  On the other hand， the equation may contain variables that are not significant to the dependent variable （y）， which leads to instability of the equation and inaccurate prediction results. Many methods of variable selection have been proposed. When a regression model is transformed into another model， it is often only discussed to add a variable to or delete a variable from a subset of the regression variables. These methods are roughly forward selection methods， backward elimination methods， and there is an amendment to the forward selection methods called stepwise regression analysis[4].

The basic idea of stepwise regression analysis： When considering the independent variables x x2，…， x（p）， variables with large significant influences are selected according to the significance of their effects on the independent variable （y） （i.e.， sum of squares of partial regression and the value）; after introducing variables one by one， a regression equation containing these variables is established， and meanwhile， after each variable is introduced， the selected variables must be tested one by one; and when an originally introduced variable becomes no longer significant due to the introduction of subsequent variables， it is deleted.  Introducing a variable or removing a variable from the regression equation is a step of stepwise regression， and F-test is performed at each step to ensure that only significant variables are included in the regression equation before introducing new variables[5]. When it is calculated that there are no variables to choose from and to delete， the regression equation is the "optimal" regression equation.

Stepwise Regression Calculation Steps

The specific calculation steps of the stepwise regression method[6]：

The first step is to find the correlation coefficient matrix R.

The second step is to give the critical value of the test. When it is estimated that the number of independent variables entering the regression equation is p， generally， Fintrodcutionα=Fdeletion， α=Fα（ n-1-p）= Fα.

The third step is introducing a variable. If the stepwise regression work is completed to the mth step， then the （m+1）th step of calculation will be performed on the mth step matrix R（m）=（r（m）ij）. For variable xi（i=k， j= 2，…，l ）， the sum of squares of the partial regression is calculated： V（m）i=（riy（m））2/（rii（m））， V（m）ki=max{V（m）i}， and then for whether the independent variable xkt should be introduced， a significance test is performed. The test statistic is Fkt-introduction=V（m）kt （n-1-l）/r（m）yy-V（m）kt， and if Fkt-introduction>Fα， the independent variable xkt can be introduced in the （m+1） step.

The fourth step is to determine whether a variable in the regression equation should be eliminated. When introducing variables， the elimination of variables should be considered also. When considering whether variable xks should be eliminated， a significance test is performed on it. The test statistic is Fks-elimination=V（m）ks（n-1-l）/r（m）yy， and if Fks≤Fα， the independent variable xks can be eliminated， and R（m+1） can be obtained through inverse compact transformation. If Fks>Fα， the independent variable xks can be reserved， and introducing variables can be continued.

The fifth step it to repeat the process of introducing and removing variables. When the selection of independent variables in the regression equation has been carried out until there is no variable to be screened， the stepwise regression analysis ends and the final result is given， including standard regression coefficients：

b′ki=r（m）kiy， i=  … ，

standard residual sum of squares： Q（m）=r（m）yy， residual sum of squares： Q=Q（m） Lyy=r（m）yy Lyy， sum of squares of regression： U=Lyy-Q， multiple correlation coefficient： R =1-r（m）yy，

regression equation： y^= b0+∑bixki.

The sixth step is to perform a significance test on the regression equation.

Data Processing

The data comes from the website of the Ministry of Agriculture and Rural Affairs of the Peoples Republic of China （http：//zdscxx.moa.gov.cn） and the National Development and Reform Commission. The specific data are shown in Table 1.

It can be seen from Table 1 that the consumption of each cost item of raising a mutton sheep in the pastoral areas of Ningxia and Xinjiang had a greater impact on the production cost than the price of each cost item. The consumption of fee for green and coarse fodder per sheep （or one hundred sheep）， labor price per sheep （or one hundred sheep）， feed processing fee per sheep （or one hundred sheep）， other direct costs and depreciation of fixed assets per sheep （or one hundred sheep） had greater impacts on the production cost， and the change trend of labor cost was consistent with the change trend of the consumption of each expense item， indicating that the consumption of each expense item had a greater impact on the production cost than the price of each expense item.

Qingmeng LONG et al. Thinking on Breeding of Fecundity Genes in Guizhou Black Goats Through Cost-benefit Analysis of Mutton Sheep by SAS Multivariate Stepwise Regression

Table 1 Mutton production cost and profit list in 2017-2018

CityQuantity ofconcentratedfeed∥kgDepreciation offixed assetsper sheep （orone hundredsheep）∥yuanLabor priceper sheep （orone hundredsheep）∥yuanIndirect costper sheep （orone hundredsheep）∥yuanFee for greenand coarsefodder per sheep（or one hundredsheep）∥yuanWater feeper sheep（or onehundredsheep）∥yuanWater feeper sheep （orone hundredsheep）yuanFeed processingfee per sheep（or onehundredsheep）∥yuanMain productoutput persheep （orone hundredsheep）∥kgCost-profitratio persheep （orone hundredsheep）∥%Net profitper sheep（or onehundredsheep）∥yuan

Stepwise Regression Analysis

Matrix generation

The mutton production cost factors （11 factors） such as the quantity of concentrated feed were respectively represented by a matrix （x x x3， x4…x11）， where x1 represents quantity of concentrated feed and x2 represents depreciation of fixed assets per sheep （or one hundred sheep）， …x11 represents net profit per sheep （or one hundred sheep）.

Drawing

① Line charts were drawn to observe the changing trend of each production factor. In order to keep the data of each production factor at a uniform level， part of the data were converted， such as dividing labor price per sheep （or one hundred sheep） by 10， and dividing the net profit per sheep （or one hundred sheep） by 100， and then charts were drawn， as shown in Fig. 2. ② Pie charts were also drawn to observe national average proportions of mutton production factors， as shown in Fig. 3 and Fig 4.

It can be seen from Table 1 and Fig. 2 that the changing trends of concentrate cost， fee for green and coarse fodder and labor cost for raising a mutton sheep in the agricultural areas of the 7 provinces were consistent with the changing trends of the consumption of various expense items， indicating that the consumption of each expense item had a greater impact on the production cost than the price of each expense item， and the prices of various expense items or labor cost were on the increase.

Results and Analysis

The program ran for seven steps， at each of which was gradually introduced a variable， and the model was continuously optimized， striving to achieve the significance of each variable introduced. In step 3， x1 was introduced， but it was removed in step 6， indicating that x1 （the amount of concentrate） was not the optimal variable. During the seven-step operation， the F value was constantly adjusted. For example， the F value of x8 （feed processing fee per sheep （or one hundred sheep）） was 20.19 in the second step， and the final optimization result was 72.17. The running results are shown in Table 2.

Model building

The predicted values of the independent variables are shown in Table 3. It can be seen that the regression relationship between the dependent variable mutton production cost and profit y and various production factor was：

YMutton production cost and profit=-4.38 X2（Depreciation offixed assets per sheep （or onehundred sheep））+1.90 X4（Indirect cost per sheep （or one hundred sheep））-0.23 X5（Fee forgreen and coarse fodder per sheep （or one hundred sheep））+5.28 X8 （Feed processing fee per sheep（or one hundred sheep））+11.52 X10 （Cost-profit ratio per sheep （or one hundred sheep））

It can be seen from the regression equation that the coefficients of x x8 and x10 were relatively large， indicating that the production factors in the mutton production process， such as depreciation of fixed assets per sheep （or one hundred sheep）， feed processing fee per sheep （or one hundred sheep） and cost-profit ratio per sheep （or one hundred sheep） had greater impacts on the profit of mutton. It can be seen from Table 1 that for production efficiency of mutton sheep breeding in Heilongjiang and Hebei pastoral areas， the mutton price， material and service costs and labor cost per one or one hundred sheep， had greater impacts on the net profit of mutton per sheep or one hundred sheep than the consumption of material and service costs of mutton per sheep or one hundred sheep. The increase in the net profit due to the increase in the price of material and service costs was greater than the increase due to the increase in the consumption of mutton material and services.

proc stepwise;

model y=x1-x10;

run;

Table 2 Summary table of stepwise regression results

Analysis stepIntroduced variableF valuePr>FConclusionNote

Step1x10 （Cost-profit ratio per sheep （or one hundred sheep））343.16<0.001Extremely significantAs shown in Fig. 5

Step2x8 （Feed processing fee per sheep （or one hundred sheep））20.190.006Extremely significantAs shown in Fig. 6

Step3x1 （Quantity of concentrated feed）6.490.025 6SignificantAs shown in Fig. 7

Step4x4 （Indirect cost per sheep （or one hundred sheep））9.570.010 2SignificantAs shown in Fig. 8

Step5x2 （Depreciation of fixed assets per sheep （or one hundred sheep））4.560.058 5SignificantAs shown in Fig. 9

Step6Remove x1---As shown in Fig. 10

Step7x5 （Fee for green and coarse fodder per sheep （or one hundred sheep））4.270.065 7SignificantAs shown in Fig. 11

Total resultsx2 （Depreciation of fixed assets per sheep （or one hundred sheep） （yuan））31.090.000 2Extremely significantAs shown in Fig. 12

x4 （Indirect cost per sheep （or one hundred sheep））28.380.000 3Extremely significant

x5 （Fee for green and coarse fodder per sheep （or one hundred sheep））4.270.065 7Significant

x8 （Feed processing fee per sheep （or one hundred sheep））72.17<0.000 1Extremely significant

x10 （Cost-profit ratio per sheep （or one hundred sheep））2 495.86<0.000 1Extremely significant

Significance level of stepwise regression： α=0.15.

The exploration and breeding of fecundity genes in Guizhou black goats requires a certain population， while the breeding of Guizhou black goats suffers from problems such as high cost， low benefit， high risk， conflicts between livestock and grass， and severe practical impacts of slow growth and low production efficiency of livestock products， leading to insufficient populations for the exploration and breeding of fecundity genes in Guizhou black goats. Therefore， systematically and comprehensively understanding the production factors of mutton and analyzing the in-depth influencing factors that affect the total cost and net profit of mutton can provide theoretical guidance for the breeding of Guizhou black goats， and provide breeding populations for the exploration and breeding of fecundity genes in Guizhou black goats. Furthermore， it can provide a scientific basis for Guizhou Province to consolidate the results of poverty alleviation and vigorously develop the mountain ecological mutton sheep industry and for Guizhou mutton sheep breeding enterprises to improve the effective breeding cost and economic benefit estimates， and has important guiding significance to promotion of rural revitalization.

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