At the beginning of the formation of quantitative genetics theory, a large number of studies have confirmed that the genetic basis of quantitative traits is still genes that follow Mendelian inheritance laws. Due to the large number of genes affecting the quantitative traits, their respective effects could not be identified under the prevailing conditions, so that there was a well-known microscopic polygenic theory (Nilsson-Ehle 1909). Although this doctrine makes a rather simplistic assumption about the genetic basis of quantitative traits, it is still a good foundation under the theoretical and technical conditions at that time. The main technical system of quantitative genetics was established on this basis. . However, because this theory does not understand the genetic background of quantitative traits, and does not know the position and transmission of genes controlling quantitative traits on chromosomes, it is impossible to accurately estimate the effect values, and it is impossible to separate and control quantitative traits. The genetic, genetic manipulation of quantitative traits at the molecular level. So for a long time, the genes of quantitative traits have been an elusive abstract unit. For the study of quantitative traits, quantitative genetics can only be used for induction and analysis. In 1923, K.Sax located several quantitative traits of Phaseolus vulgaris by controlling the linkage between the loci of quantitative trait loci and Mendelian loci (1). But until about 1960, his method was limited to Drosophila because it was difficult to find enough or typical morphological or luster markings like kidney beans in other plants and animals. With advances in biochemical genetic experiments, especially molecular biology techniques, molecular genetics (such as DNA markers), molecular biology (such as nuclear transplantation), statistics (such as assessment methods) and computer science and other disciplines and quantitative genetics In combination, geneticists may return to explore the molecular genetic basis of quantitative traits, the quantitative trait loci (QTL). A QTL is a specific chromosome fragment that is a single gene or a cluster of small, multi-genes that have a deterministic effect on a quantitative trait. In theory, any locus that can observable phenotypic traits can find a linked DNA marker in the linkage map. Therefore, the analysis of QTLs for important economic traits of livestock and poultry in the genome and its contribution to phenotype mainly depend on genetic linkage maps. The rapid progress in the construction of genetic linkage maps for animal polymorphic markers has made it possible for the system to search for QTLs affecting economically important forms. The approach is: based on a certain experimental design, (1) record phenotypic values ​​of quantitative traits; (2) determine polymorphic genetic marker genotypes at known locations; (3) perform phenotypic and marker alleles Statistical correlation analysis; (4) If a linkage relationship is found, statistical methods are used to infer and label nearby QTL positions, effect size, and frequency of QTL alleles. Once a QTL is found within the marker interval, the next step is to isolate and identify the QTL itself, that is, to screen candidate genes by comparison of map studies and tissue-specific cDNA libraries. 1 Current Status of QTL Mapping for Livestock At present, the focus of gene mapping for quantitative traits in livestock is milk production, milk protein content, milk fat content, mastitis resistance, and ease of delivery; beef cattle is the growth rate; pigs are litter size and growth. Rate, back-thickness and disease resistance. Genes or regions have been found in dairy cows with milk production [2], milk fat percentage and milk protein rate, somatic cell number and production lifespan [3]; pig back fat thickness and abdominal fat rate [4,5], pig carcass composition , Meat quality, lipid storage capacity, stress response, head weight, early growth rate, live weight and feed conversion rate, etc. [6], pig's spine count, number of nipples, and 4-week-old body weight [7]. Arranzl et al. (1998) demonstrated a QTL affecting milk production on chromosome 20 of dairy cows (8). In 1995, Taylor et al. of A&M University in Texas, USA, used Angus, Brahman and their hybrid cattle populations to study carcass traits and mapped several QTLs with large effects. These traits are: meat quality, marble, Warner-Bratzler cutting force, slaughter weight, enthalpy weight, slaughter rate, longissimus dorsi muscle cholesterol, saturated and unsaturated fatty acid content [9]. 2 Statistical methods for QTL mapping in livestock There are two ways to look for QTL, one is the candidate gene method, and the other is the QTL mapping using markers to locate the QTL. The candidate gene method has low cost and simple operation, and is convenient for application in MAS. However, the candidate gene method also has its serious defects. Its initial cost is high and it is easily interfered by non-candidate genes. It is difficult to determine whether the candidate gene is QTL. The QTL mapping statistical method can use the information provided by the marker covering the entire genome, so the QTL can always be found and the success rate is high. Statistical methods for QTL mapping can be classified from different perspectives. According to the type of QTL parameter estimation, it is divided into the method of estimating the substitution effect of QTL and the method of estimating the variance component of QTL. 2.1 Methods for locating QTLs by estimating QTL substitution effects, including analysis of variance (ANOVA) or simple linear regression; multiple linear regression; maximum likelihood interval mapping ( Maximum likelihood interval mapping) and composite interval mapping. However, there are certain flaws in this type of method: 1) Because the QTL effect is treated as a fixed effect, the estimation of the effect value is higher than the true value; 2) These methods are mainly for inbreed line crossings. Designed, it is not suitable for complex pedigree structures, unknown parental linkages, low heterozygosity on markers and QTLs (especially for QTLs with large effect values ​​due to selection making them fixed in the population), markers | QTL linkage phase There are large differences in livestock populations between families. The QTL is positioned as a fixed effect, and an example on livestock is Andersson et al. (1994). The materials used were the F2 hybrids of European wild boar and Great White pig, using 105 genetic markers distributed on 15 autosomes. The method is the least squares method of QTL positioning established by Haley & Knott et al. (1994) [10]. Results QTLs with greater effects on growth, small intestine length, and fat deposition were detected on chromosome 4, and QTLs affecting early growth were detected on chromosome 13. The main results are shown in Table 1. Table 1 Significant QTLs for porcine growth and fat deposition traits and effect traits F value locations (cM) Dominant additive effects accounted for F2 variance (%) Number 4 chromosomes for primary birth ~70 kg daily gain (g/d) 11.8 58 -23.54.9 0.77.3 11.9 Intestinal length (m) 11.1 27 -0.870.18 0.030.27 11.3 Average back fat thickness (mm) 18.0 3 2.300.42 1.470.65 17.6 Abdominal fat percentage (%) 19.4 7 0.380.06 0.150.10 18.7 Chromosome 13 - 30 kg daily gain (g/d) 7.6 53 -13.53.6 6.05.2 7.5 From data [4]. 2.2 QTL mapping by estimating the QTL variance components in livestock populations due to: 1) unknown parental QTL genotypes; 2) unknown exact QTL allele numbers in the population; 3) family-based marker-based genotypes The frequency of QTL genotypes is different. Given these complexities, the effect of QTL is more realistic as a random effect. When using a stochastic model, it does not necessarily require knowledge of the true genetic pattern of the QTL. Considering the effect of QTL as a random effect, not only can the QTL effect and location be estimated, but also the QTL's variance contribution can be estimated. Such methods include BLUP method, Bayesian linkage analysis method, and ML method based on mixed linear model and REML method. Grignola (1996) used the QTL as a random effect and adopted the REML method based on the mixed linear model. Using the information of multiple linkage markers and the interval mapping method, the QTL mapping for the granddaughter design (GDD) population was studied.[11] ]. The heritability of the traits (h2), QTL alleles were obtained for the three QTL models, ie, two QTLs, multiple (10) alleles, and QTL effects that were normally distributed in the population. The contribution of the variance to the total additive genetic variance (σ2v/σ2a), the position of the QTL (dQ) and the residual variance (σ2e) are accurately estimated. 3 The QTL positioning random effects model is used for QTL parameter estimation and QTL mapping. BLUP, which combines traits and marker information, is called TM-BLUP. The stochastic model adopted by the TM-BLUP method has two forms. One is the random game effect model proposed by Fernando & Grossman (1989) [12] and the other is the random QTL effect model adopted by Goldgar [13]. Goddard [14] & Van Arendonk et al. [15] modified the random game effect model of Fernando & Grossman to enable them to handle multiple marker linked QTLs. Goddard's model applies to multiple linkage markers, with one QTL per marker interval; Van Arendonk's model considers multiple non-linked markers, each linked to a QTL. In the model proposed by Fernando & Grossman, the marker genotypes of each individual in the population are known, and some methods developed later allow individuals with no marker information to be included in the model; there are also people using the reduced animal model, or several The sum of the effects of non-linked markers QTL reduces the number of equations and simplifies the calculation. The probability of an IBD (identical by descend) of QTLs based on marker information is necessary for the solution of mixed linear model equations (MME) in TM-BLUP. The IBD value can be estimated from the information provided by a sigle marker or a flanking marker. 4 QTL positioning Prospects The statistical method of QTL positioning has great potential for application. In particular, the presence of abundant DNA polymorphism provides a reliable guarantee for the application of this method. In QTL analysis, relatively simple methods can be used first, such as pre-analysis using Least Squares method, preliminary determination of the interval where QTL is located, and then maximum likelihood based on mixed linear model. The law or the constrained maximum likelihood method makes a more accurate estimate of the parameters and position of the QTL. With the construction of saturated genetic linkage maps and the emergence of efficient statistical analysis methods, marker-assisted selection of livestock and poultry is expected to be applied at the end of this century. The genetic manipulation of quantitative traits will eventually be realized.