### INTRODUCTION

*FASN*gene, which is closely related to C18:1 as an important factor influencing the beef flavor, may play an important role in improving beef quality.

*FASN*gene influencing C18:1, MUFAs, CWT, and MS in Hanwoo (Korean native cattle). The

*FASN*gene is significantly related to FAC and carcass traits [7,11]. The first important point is that most traits of economic importance in livestock are multifactorial in nature, and are thus influenced by multiple genes and their interactions with environmental factors. Enhancing the accuracy of genetic analysis necessitates a statistical model that excludes environmental effects. Therefore, this study proposes an analysis of covariance (ANCOVA) model that includes environmental and genetic factors influencing the phenotype of Hanwoo and uses a new adjusted model that eliminates the estimated values of environmental factors. In addition, the study employs the multifactor dimensionality reduction (MDR) method to test the main and interaction effects of multiple SNPs on the meat quality of Hanwoo and compares the analysis accuracy between the adjusted and unadjusted models. Finally, the study explores superior genotype groups based on interactions between SNPs in exons of the

*FASN*gene.

### MATERIALS AND METHODS

### Phenotypes and SNP genotyping

*FASN*gene in GenBank (Accession no. AF285607) were genotyped, according to our previous study [7]. We previously examined the genetic relationships between the FAC of beef and multiple nucleotide sequence variants in the

*FASN*gene, and five variants, namely g.12870 T>C, g.13126 T>C, g.15532 C>A, g.16907 T>C, and g.17924 G>A in exon regions 23, 24, 34, 37, and 39, respectively, were found to be associated with the composition of unsaturated fatty acids [7].

### A statistical ANCOVA model of the economic traits of Hanwoo

*FASN*gene, calving farms and age as factors. The relationship between economic traits and factors can be expressed as the following ANCOVA model:

*Y*

*indicates the economic traits of Hanwoo*

_{k}*k*,

*μ*is the overall mean,

*A*

*the covariate for age in days at slaughter,*

_{k}*Ā*the mean of

*A*

*,*

_{k}*α*

*the covariate effect,*

_{0}*F*

*an indicator variable for calving farm*

_{ik}*i*(17 classes),

*α*

*the fixed effect of*

_{i}*F*

*,*

_{ik}*G*

*the genotype*

_{jk}*j*,

*β*

*the fixed effect of*

_{j}*G*

*, and*

_{jk}*ε*

*a random residual assumed to have an independent and identical normal distribution. In a statistical model, if a qualitative (categorical) variable has more than two classes (17 calving farms), we require additional indicator variables in the model [14]. Since the calving farm variable has 17 classes, we require 16 indicator variables.*

_{k}*F*

*as follows:*

_{ik}*Y*matrix, and environmental and genetic factors, as the

*E*and

*G*matrices, respectively:

**,**

*Z***,**

*Y***are**

*α̂***).**

*Z*### Multifactor dimensionality reduction analysis

Step 1. Data were randomly divided into 10 equal parts: one testing set and nine training sets as part of the cross-validation procedure.

Step 2. A set of

*n*SNPs was selected from the pool of all SNPs.Step 3. Based on the observed level of each

*n*, steers were partitioned into classes referred to as cells. If*n*= 2, then a set of two SNPs was selected, and because one SNP had three genotypes, there were 3^{2}= 9 possible cells. Case-control ratios were calculated for each cell.Step 4. The case-control ratio of total data was used as the threshold such that a cell with a higher case-control ratio than the threshold was labeled as high and the remainder, as low.

Step 5. The MDR model with the smallest test data error was chosen among all two-factor combinations.

Step 6. To evaluate the predictive ability of the model, the test data error was estimated using a 10-fold cross-validation method.

*n*. The model with the minimum test data error was selected as the best model. However, statistical significance was not determined by the test data error for the selected best model. Therefore, t-tests were conducted, and Cohen’s d was calculated to determine empirical significance thresholds by applying the same MDR method.