### INTRODUCTION

_{1}generation. “Relative” means that it is dependent on the unit of phenotypes. Thus, it was recalibrated by the maximum value. The predicted value of the selection coefficient could be the actual value if selection were performed only using breeding values of a given trait and selection followed Fisher’s theorem.

### MATERIALS AND METHODS

### Materials

### Prediction of SNP effects for milk production traits

*Gu*) and e~MVN(0,R) where MVN are denoted as multivariate normal distribution. The SNP effects were calculated using single nucleotide polymorphism-genomic best linear unbiased prediction (SNP-GBLUP) using the SNP-SNP relationship matrix (Lee et al., 2014). This SNP-SNP relationship matrix (SSRM) is based on the genomic relationship matrix (GRM) (Goddard et al., 2011). SSRM was denoted as G

_{u}and GRM as G. The SSRM (G

_{u}) can be calculated using the relationship, G

*= (*

_{u}*Z*

^{T}*G*

^{−1}

*Z*)

^{−1}(Lee et al., 2014). The fixed effect was season. The R package, “rrBLUP” was used for the analysis (Endelman, 2011).

### Estimation of expected current relative selection coefficient

*w*

*,*

_{AA}*w*

_{AA}_{′},

*w*

_{A}_{′}

_{A}_{′}) = (1-s, 1-s/2, 1) and s is the selection coefficient symbol.

##### (3)

^{th}individual, j represents j

^{th}marker or SNPs, Z

_{ij}represents the i

^{th}individuals and j

^{th}SNPs’ 0, 1, 2 coding. u

_{j}represents the SNP effect. The additive genetic variance calculation is a data-driven method which uses the Z matrix, directly.

*s*

^{2}= 4

*u*

^{2}according to var(

*Z*

*) = 2*

_{i}*pq*. If we pay heed on the expected relationship of the sign between selection coefficient s and SNP effect u, we can derive that

*s*= 2

*u*.

### Characterization of candidate genes under selection regions

### RESULTS AND DISCUSSION

### SNP-GBLUP method results and highly selective SNPs

_{1}generation’s expected allele frequency change under linear additive model. It demonstrates that allele frequency can be predicted via the SNP effect. Table 2 shows highly selective SNPs and the genes containing them (any p-value <0.001; nearly top 0.1% SNPs). The genes containing very highly selective SNPs with p-value <0.01 (nearly top 1% SNPs) in all traits and p-value <0.001 (nearly top 0.1%) in any traits were phosphodiesterase 4B (PDE4B), serine/threonine kinase 40 (STK40), collagen, type XI, alpha 1 (COL11A1), ephrin-A1 (EFNA1), netrin 4 (NTN4), neuron specific gene family member 1 (NSG1), estrogen receptor 1 (ESR1), neurexin 3 (NRXN3), spectrin, beta, non-erythrocytic 1 (SPTBN1), ADP-ribosylation factor interacting protein 1 (ARFIP1), mutL homolog 1 (MLH1), transmembrane channel-like 7 (TMC7), carboxypeptidase X, member 2 (CPXM2), and ADAM metallopeptidase domain 12 (ADAM12). We inferred the sign of relative selection coefficient from the SNP effect information in Table 1. The positive sign of SNP effect represents that of the selection coefficient and vice versa.