Main SNP Identification of Hanwoo Carcass Weight with Multifactor Dimensionality Reduction(MDR) Method

Multifactor Dimensionality Reduction(MDR)Õ l é

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Õ x íU [ œ U [ œ” ¢ w  > < j í< S" h4 É • ¢| ¡ SNP  ‹ h Ù ^∗

s

] j% ò

¹⁾

^ ” 1 l x^ o =

²⁾

כ

¹ €  • {

9

ì ø Í& h Ü ¼– Ð “  ç ß –_  | 9 # î õ  » ¡ ¤_   â ] j& h “   : £ ¤$ í “ É r 
_  Ä »„        # Œ Q Ä »

„



 _   © œ  ñ Œ •6   xÜ ¼– Ð { 9 # Qè ß – “ ¦ b ” “ ¦ e ”  .   " f ‘ : r ƒ  ½ ¨\ " f  H [ j@ /\  ¦  [ þ v½ + Éà º2 Ÿ ¤

@

/w n Ä »„   _  Ä »„  s  î ß –& ñ & h Ü ¼– Ð µ 1 ÏÒ q t÷ &# Qt “ ¦ > h^ ‰_  l 0 p x& h “   Ä »„  & h  u \  ¦ f ” ] X 

&

h

Ü ¼– Ð Æ Ò& ñ ½ + É Ã º e ”   H single nucleotide polymorphism(SNP)`  ¦ ô  ÇÄ º_   â ] j& h  : £ ¤$ í “  

•

¸^ ‰×  æ(carcass cold weight)\  @ / # Œ — ¸Ã º& h “   ~ ½ ÓZ O “   ANOVAü < q — ¸Ã º& h “   ~ ½ ÓZ O “   multifactor dimensionality reduction(MDR)`  ¦ s 6   x # Œ 
_  Ä »„   _  ´ òõ ü < ¿ º > h _

 Ä »„   _   © œ  ñ Œ •6   x ´ òõ \  ¦ q “ § % i  . ANOVA\ " f  H 
_  Ä »„    SNP1s  • ¸^ ‰

×



æ\  Ä »_ ô  Ç ´ òõ  e ” % 3 “ ¦  © œ  ñ Œ •6   x ´ òõ \ " f  H • ¸^ ‰×  æ\  Ä »_ ô  Ç ´ òõ   H \ O % 3  . MDR

\

" f  H 
_  Ä »„   _  ´ òõ “   SNP1õ  ¿ º > h_  Ä »„   _   © œ  ñ Œ •6   x“   SNP1*SNP2_ 

´

òõ  ( Ž Ü ¼ 9 SNP1õ  SNP1*SNP2\  ¦ q “ §Ù þ ¡`  ¦ r \   H SNP1*SNP2_  ´ òõ   8 ß ¼> 

 z Œ ¤ . s   H > hZ >  SNPÄ »„    ˜ Ð  4 Ÿ ¤½ + Ë SNPÄ »„   _   © œ  ñ Œ •6   xs   â ] j& h “   : £ ¤$ í “  

•

¸^ ‰×  æ\   8 % ò † ¾ Ó`  ¦ ï  r   H  כ `  ¦ · ú ˜ à º e ” % 3  .

Å

Òכ ¹6   x# Q: SNP, ANOVA, MDR, • ¸^ ‰×  æ, CART(classification and regression trees).

1. " V´ * 0

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ç ß –_  | 9 # î ¢ ¸  H » ¡ ¤_   â ] j& h “   : £ ¤$ í \  › ' aô  Ç Ä »„   _  ½ ©" î “ É r Ä »„  † < Æ\ " f B Ä º ×  æכ ¹ ô



Ç › ' ad ”  s  . { 9 ì ø Í& h Ü ¼– Ð “  ç ß –_  | 9 # î õ  » ¡ ¤_   â ] j& h “   : £ ¤$ í “ É r 
_  Ä »„       

#

Œ Q Ä »„   _   © œ  ñ Œ •6   xÜ ¼– Ð { 9 # Qè ß – “ ¦ b ” “ ¦ e ”  . Õ ªA " f s    # Œ Q Ä »„   _   © œ  ñ Œ •6   x

`



¦ “ ¦ 9ô  Ç — ¸+ þ AÜ ¼– Ð ‚  + þ A— ¸+ þ A ° ú  “ É r ³ ðï  r : Ÿ x> & h  — ¸4 S q– Ð  6   xK M ® o . Õ ª Q
 Ä »„   _  à º

´ ú

§`  ¦  â Ä º  © œ  ñ Œ •6   x_  › ¸½ + Ës  ´ ú § t Ù ¼– Ð 7 á x7 á x — ¸Ã º[ þ t_   © œ  ñ Œ •6   x\  @ /ô  Ç K $ 3 õ  — ¸+ þ A`  ¦





& ñ   H  כ s  # Q 9Ö  ¦ à º e ”  . Õ ªo “ ¦ q 2 Ÿ ¤ # Œ Q Ä »„   _   © œ  ñ Œ •6   x\  @ / # Œ — ¸+ þ A o ) a  â Ä

º • ¸ ´ ú §“ É r 0 p xô  Ç _ …s ^  ¦ ! s q\  › ' a8 £ ¤° ú כs  \ O `  ¦ à º• ¸ e ”  . s   â Ä º\  Æ Ò& ñ ° ú כõ  š ¸   8 ß

¼> 
 ± ú ˜ à º e ”   (Hosmerü < Lemeshow, 2000). Õ ªA " f Ä ºo   H # Œ Q Ä »„   \  @ /ô  Ç  © œ  

ñ Œ •6   x`  ¦   & ñ   H ~ ½ ÓZ O Ü ¼– Ð Multifactor Dimensionality Reduction`  ¦ ™ è> hô  Ç (Ritchie 1 p x,

∗

‘:r ƒ½¨H 0lxaË>ÂÒ ‚&ñ â·¡¤ôÇĺ\Oéߖ_ t"é¶(2006)ܼ–Ð ú'Ÿ÷&%36£§.

1) (712-749) “§’$. â·¡¤ âíߖr @/1lx 214-1 %òzŒ™@/†<Ɠ§ :Ÿx>†<Æõ, “§Ãº.

E-mail: [email protected]

2) (712-749) â·¡¤ âíߖr @/1lx 214-1 %òzŒ™@/†<Ɠ§ :Ÿx>†<Æõ, @/†<Æ"é¶, $3.

E-mail: [email protected]

2001). Multifactor Dimensionality Reduction(MDR)“ É r  © œ  ñ Œ •6   x\  @ /ô  Ç " î S X ‰ô  Ç — ¸+ þ A_  

&

ñ

\ O s  q — ¸Ã º& h “   ~ ½ ÓZ O Ü ¼– Ð & h { © œô  Ç high-order à º_  X <s ' – Ð 4 Ÿ ¤¸ ú šô  Ç › ' a> \  ¦ µ 1 ߁ n = à º e

”

 . Õ ªA " f ‘ : r ƒ  ½ ¨\ " f  H ô  ÇÄ º_   â ] j+ þ A| 9 “   • ¸^ ‰×  æ(carcass cold weight)\  › ' aº   ) a Å Òכ ¹ Ä

»„  “   \  ¦ MDR ~ ½ ÓZ O `  ¦ s 6   x # Œ ¹ 1 Ô ˜ Ð 9“ ¦ r • ¸ % i  .

‘ :

r ƒ  ½ ¨_  X <s '   H Korean cattle (Lee 1 p x, 2007)\ " f à º| 9 ÷ &% 3 Ü ¼ 9 0 l xa ž ?×  æ€ © œ r » ¡ ¤> h

|

¾

Ó  Á º™ è\ " f > hµ 1 Ï÷ &% 3 “ ¦ 16 grand-sire half-sibs families– РÒ'  229¿ º_  à º5 Å x t – Ð ½ ¨$ í

÷

&# Q& ’  . • ¸^ ‰×  æ“ É r — ¸Ž  H F1  ’ < HÜ ¼– РÒ'  à º| 9 ÷ &# Q& ’ “ ¦ ô  Dz D G» ¡ ¤í ß –Ó ü t1 p x/ å Ló ø Í& ñ ™ è_  ½ ©  \ 



  8 £ ¤& ñ ÷ &% 3  . @ / Òì  r_  QTL ƒ  ½ ¨  H | 9 é ß –_  ½ ©— ¸ ß ¼ 
 ì ø Í+ þ AB (half-sib)\ " f sire_ 

@

/w n Ä »„    Ä »„  ÷ &  H microsatellite marker\  ¦  6   xô  Ç . Õ ª Q
 QTL ƒ  ½ ¨_    õ [ þ t`  ¦ ‰ & ³



©

œ\  & h 6   x l  F Gy  ] jô  Ç& h s  .  =
 €   l ï  r| 9 é ß –\ " f QTL“ É r  6 £ §[ j@ /– Ð Ä »„  ÷ &# Qt  l

 # Q§ > l  M :ë  Hs  .   " f ´ ú §“ É r [ j@ /\  ¦  [ þ v½ + Éà º2 Ÿ ¤ @ /w n Ä »„   _  Ä »„  s  î ß –& ñ & h Ü ¼– Ð µ 1 Ï Ò

q

t÷ &# Qt “ ¦ > h^ ‰_  l 0 p x& h “   Ä »„  & h  u \  ¦ f ” ] X & h Ü ¼– Ð Æ Ò& ñ ½ + É Ã º e ”   H single nucleotide polymorphism(SNP)`  ¦ ô  ÇÄ º_   â ] j& h  : £ ¤$ í \  @ / # Œ genetic test_  > hµ 1 Ï\  s 6   xô  Ç .

‰

&

³F  t  ™ è\ " f  H • ¸^ ‰+ þ A| 9 (• ¸^ ‰×  æ| ¾ Ó, 1 p xt ~ ½ Ó¿ ºa , 1 p xd ” é ß –€  & h ,   H? /t ~ ½ ӕ ¸)õ  ƒ  › ' as  e

”

  H SNP marker[ þ ts  { 9 ì ø Í» ¡ ¤\ " f ¨ î ÷ &# Qt  
 & h 6   x÷ &“ ¦ e ”   (Barendse 1 p x, 2004;

Page 1 p x, 2004).   " f ‘ : r ƒ  ½ ¨\ " f  H EST-based SNP ƒ  › ' at • ¸ (Snelling 1 p x, 2005)\ 

"

f Kim 1 p x (2003)\  _ K  ½ ©" î ÷ &# Q”   ô  ÇÄ º % i Ò  o^ ‰ 6  \  0 Au ô  Ç candidate QTL“   IL- STS035 microsatellite marker ü < ° ú  “ É r  o \  e ”   H SNP[ þ t ×  æ polymorphisms
 è ß – 31465 446(SNP1), 12273 165(SNP2), AH1-4(SNP3)\  ¦ ‚  µ 1 Ï (Lee 1 p x, 2007) # Œ ² D G Ê ê@ /



Ž

& ñ Ä º 229¿ º\  @ /ô  Ç  â ] j+ þ A| 9 _  • ¸^ ‰×  æ\  @ / # Œ ANOVA(Analysis of variance)‚  + þ A — ¸+ þ A Ü

¼– Ð ì  r$ 3  % i  . Õ ª Q
 · ú ¡\ " f ´ ú ˜ô  Ç  כ õ  ° ú  s   © œ  ñ Œ •6   x_  — ¸+ þ A“ É r — ¸Ã º_   © œ  ñ Œ •6   x\  @ / ô



Ç K $ 3 õ  — ¸+ þ A_    & ñ s  # Q 9Ö  ¦ à º e ”  . Õ ªA " f  © œ  ñ Œ •6   x_  4 Ÿ ¤¸ ú šô  Ç › ' a> \  ¦ µ 1 ߁ n = à º e ”   H MDR ~ ½ ÓZ O `  ¦ & h 6   xK  ˜ Ð 9“ ¦ ô  Ç . s  ƒ  ½ ¨\ " f X <s ' _   â ] j+ þ A| 9 _  • ¸^ ‰×  æs  ƒ  5 Å q+ þ A  « Ñ s

l  M :ë  H\  €  $  X <s '  s _ ç l Z O ×  æ 
“   CART(classification and regression trees)~ ½ Ó Z

O

Ü ¼– Ð case-control– Ð s ì  r o r †   Ê ê\  MDR ~ ½ ÓZ O \  & h 6   xr (   . ‘ : r  7 Hë  H“ É r  6 £ §õ  ° ú   s

 ½ ¨$ í ÷ &% 3  . 2] X \ " f  H · ú ¡\   6   xô  Ç ì  r$ 3 ~ ½ ÓZ O “   MDR\  @ / # Œ ™ è> h\  ¦ “ ¦ 3] X \ " f  H ANOVA, MDR`  ¦ & h 6   xô  Ç   õ \  ¦ ˜ Ð# Œï  r . 4] X \ " f  H ƒ  ½ ¨  õ \  ¦ כ ¹€  • & ñ o  % i  .

2. Multifactor-Dimensionality Reduction(MDR) O , 0; . 㠕 î |q @ è

MDR ~ ½ ÓZ O “ É r { 9 ì ø Í o ) a ‚  + þ A — ¸+ þ A“   „  : Ÿ x& h “   : Ÿ x>  l Z O õ   H ² ú ˜o  # Q‹ "  — ¸Ã º\  @ /ô  Ç Æ Ò

&

ñ

õ  genetic — ¸+ þ A_  & ñ `  ¦ כ ¹½ ¨ t  · ú §  H ( r  ´ ú ˜ €   : £ ¤Z > ô  Ç Ä »„  + þ A| 9  — ¸+ þ A\  @ /ô  Ç 

&

ñ

s  € 9 כ ¹ \ O  ). Ritchie 1 p x (2003)õ  Hahn 1 p x (2003)\  _  €   MDR — ¸+ þ A\ " f % ƒ6 £ §Ü ¼– Ð r

' Ÿ    H  כ “ É r caseü < control`  ¦ 1:1– Ð ç  H+ þ A`  ¦ ´ ú Æ ҍ  H  כ s  .  6 £ § step\ " f case-control\ 

@

/ô  Ç MDR ~ ½ ÓZ O `  ¦ r ' Ÿ    H õ & ñ `  ¦ ˜ Ð# Œï  r .

Step 1. X <s ' \  ¦  ½ ™ ü Ü ¼– Ð 10> h_  ° ú  “ É r ß ¼l – Ð
è  H . Õ ªo “ ¦ Õ ª×  æ 9> h\  ¦ training set Ü ¼

–

Ð 1> h\  ¦ testing setÜ ¼– Ð é  H .

Step 2. — ¸Ž  H SNP– РÒ'  k> h_  SNP› ¸½ + Ë ×  æ 
\  ¦ ‚  × þ ˜ô  Ç .

Step 3. ‚  × þ ˜ ) a SNP› ¸½ + Ë\ " f SNP_  y Œ •y Œ • à ºï  r`  ¦ l œ í– Ð ô  Ç > h^ ‰[ þ t`  ¦ multifactor classes

¢

¸  H cells\  l Õ ü tô  Ç . \ V\  ¦ [ þ t# Q" f k = 2 { 9   â Ä º SNP  H 3> h_  à ºï  rÜ ¼– Ð ÷ &# Qe ”  .



 " f 9> h_  ! s q`  ¦ ”   . y Œ •y Œ • 9> h_  ! s q\  case_  ° ú כõ  control_  ° ú כ`  ¦ & h   H .

Step 4. Caseü < control_  q \  ¦ ½ ¨ # Œ 1˜ Ð  ß ¼ 
 ° ú  Ü ¼€   high-risk, 1˜ Ð   Œ •Ü ¼€   low- risk  ô  Ç . \ V\  ¦ [ þ t€   1' Ÿ  1\ P _   â Ä º caseü < control_  q  1˜ Ð   Œ •Ü ¼€   s  ! s q“ É r low-risks  .

Step 5. K> h_  SNP_  › ¸½ + Ë „   Ò\ " f X <s ' _  9/10“   traing set\ " f ¸ ú ˜3 l w ì  rÀ ӝ ) a q Ö  ¦“   misclassification error(ME)\  ¦ ½ ¨ô  Ç . # Œl " f ¸ ú ˜3 l w ì  rÀ ӝ ) a q Ö  ¦“   ME   H {T otal

high

− Case

high

+Case

low

}/N s  . T otal

high

  H highÕ ªÒ  ¨_  „  ^ ‰ ° ú כs  9 Case

high

  H highÕ ª Ò



¨_  „  ^ ‰ case  â Ä º_  à ºs  9 Case

low

  H lowÕ ªÒ  ¨_  „  ^ ‰ case  â Ä º_  à ºs  . Õ ªo “ ¦ N“ É r „  ^ ‰ X <s ' _  à ºs  . s X O >  ½ ¨ô  Ç ME[ þ t ×  æ\   © œ  Œ •“ É r ° ú כ`  ¦ ‚  × þ ˜ô  Ç .

Step 6. Training set\ " f high-low– Ð
è  H ³ ð\  ¦
 Qt  1/10_  X <s ' “   testing set`  ¦ s 6   x

# Œ ¸ ú ˜3 l w ì  rÀ ӝ ) a q Ö  ¦“   prediction error(PE)\  ¦ Step 5_  & ñ _ ü < ° ú  s  ½ ¨ô  Ç .

Õ

ª  6 £ § 0 A_  õ & ñ _  ì ø Í4 Ÿ ¤\ " f
“ : r 10> h_  MEü < PE_  ¨ î ç  H`  ¦ ½ ¨K  Õ ª ° ú כs   © œ ± ú “ É r

 כ

`  ¦ best n-factors — ¸+ þ AÜ ¼– Ð & ñ ô  Ç  (Bastione 1 p x, 2004). Õ ªo “ ¦ · ú ¡\ " f ½ ¨ô  Ç y Œ •y Œ •_  ME\  ¦ s

6   x # Œ cross validation consistency(CVC)\  ¦ ½ ¨   HX < s  כ “ É r 10  _  cross- validation`  ¦ r

' Ÿ ½ + É M : y Œ • r ' Ÿ \ " f ‚  × þ ˜ ) a best model`  ¦ î  rà Ô   H  כ s  (Chung 1 p x, 2005).   " f MEü < PE_  ¨ î ç  Hs   © œ ± ú “ ¦ CVC  © œ Z  }“ É r ° ú כs  best n-factors — ¸+ þ As  .

3. Í P æB   „ ÄØ þ l 5 æÑ ä

3.1. Í P æB    „ Ä s

 X <s '   H 0 l xa ž ?×  æ€ © œ r » ¡ ¤> h| ¾ Ó  Á º™ è\ " f > hµ 1 Ï÷ &% 3 “ ¦ 16 grand-sire half-sibs fam- ilies– РÒ'  229¿ º_  à º5 Å x t – Ð ½ ¨$ í ÷ &# Q& ’  . • ¸^ ‰×  æ“ É r — ¸Ž  H F1  ’ < HÜ ¼– РÒ'  à º| 9 ÷ &# Q

&

’

“ ¦ ô  Dz D G» ¡ ¤í ß –Ó ü t1 p x/ å Ló ø Í& ñ ™ è_  ½ ©  \     8 £ ¤& ñ ÷ &% 3  . Õ ªo “ ¦ polymorphisms
 è ß – 12273 165(SNP1), 31465 446(SNP2), AH1-4(SNP3)\  ¦ s 6   x % i   (Lee 1 p x, 2007).

3.2. ANOVA˜ Þ 2 c ë à f £ ­ ƒ ¬> u… ¾ Q q 7 1f £ ­ SNP < … ê ø ³ ô



ÇÄ º_  € ª œ& h + þ A| 9 \  @ /ô  Ç Ä »„  ì  r$ 3 \  e ” # Q  © œ l ‘ : rs  ÷ &  H > h¥ Æ “ É r # QÖ ¼ > h^ ‰_  ³ ð‰ & ³+ þ A s

 Õ ª > h^ ‰_  Ä »„   + þ A\  _ ô  Ç ´ òõ ü < ¨ 8 Š â _  ´ òõ \  _  # Œ   & ñ  ) a   H  כ s  . 7 £ ¤, > h^ ‰

\

 @ /ô  Ç ³ ð‰ & ³+ þ A“ É r  6 £ §õ  ° ú  s  ¿ º  Òì  rÜ ¼– Ð
Ð ü t à º e ”  .

P = G + E. (3.1)

#

Œl " f P  H ³ ð‰ & ³+ þ As “ ¦ G  H Ä »„   ´ òõ , E  H ¨ 8 Š â ´ òõ   ô  Ç . Õ ªA " f » ¡ ¤_   â ] j+ þ A

| 9

 ƒ  ½ ¨\ " f  H { 9 ì ø Í& h Ü ¼– Ð  6 £ §õ  ° ú  “ É r : Ÿ x> & h  — ¸4 S q`  ¦  6   xô  Ç .

³

ð 3.1: SNP1, SNP2, SNP3_  Å Ò´ òõ [ þ t\  @ /ô  Ç • ¸^ ‰×  æ_  ¨ î ç  Hõ  ³ ðï  r¼ #  ü < P -value

M arker Genotype numberof Animals x ± s¯

SNP1 AA 16 294.19±26.999

AG 75 303.97±31.227

GG 138 313.61±34.369

signif icance(P−value) 0.020

SNP2 CC 45 305.89±29.071

CT 112 307.70±31.698

TT 72 313.28±38.015

signif icance(P−value) 0.662

SNP3 AA 54 307.74±35.971

AT 118 313.17±33.754

TT 57 301.95±28.786

signif icance(P−value) 0.703

Y

ijkl

= µ + C

i

+ S

j

+ βage + M

k

+ ε

ijkl

, (3.2)

(P ) (E) (G)

i = 1, . . . , c, j = 1, . . . , s, k = 1, . . . , m, l = 1, . . . , n.

#

Œl " f Y

ijkl

  H • ¸^ ‰×  æs “ ¦ C

i

(contemporary)  H • ¸» ¡ ¤> ] X õ   © œ™ è\  ¦ ° ú  s  “ ¦ 9ô  Ç Õ ªÒ  ¨Ü ¼

–

Ð “ ¦& ñ ´ òõ s  9 S

j

  H sire Õ ªÒ  ¨_   ½ ™ ü  ´ òõ , M

k

  H SNP  & _  “ ¦& ñ ´ òõ , ⍠ H
s \  @ / ô



Ç  r) > Ã º, ε

ijkl

  H N (0, σ

²

)“   S X ‰Ò  ¦  à ºs  . Õ ª Q
 Ä ºo  › ' ad ” `  ¦ t   H  Òì  r“ É r • ¸^ ‰

×



æ\  % ò † ¾ Ó`  ¦ Šҍ  H  כ Ü ¼– Ð ¨ 8 Š â ´ òõ ˜ Ð  Ä »„   ´ òõ \  › ' ad ” s  e ”  .   " f Ä »„   ´ òõ “   SNP • ¸^ ‰×  æ\  # Q‹ "  % ò † ¾ Ó`  ¦ Šҍ  Ht \  @ /ô  Ç ANOVA : Ÿ x> & h  — ¸+ þ A“ É r  6 £ §õ  ° ú   .

Y

ijkl

= µ + α

i

+ β

j

+ γ

k

+ (αβ)

ij

+ (αγ)

ik

+ (βγ)

jk

+ ε

ijkl

, (3.3) i = j = k = 1, 2, 3, l = 1, 2, . . . , n.

#

Œl " f Y

ijkl

  H • ¸^ ‰×  æs “ ¦ α

i

  H SNP1, β

j

  H SNP2, γ

k

  H SNP3s   ) a . Õ ªo “ ¦ ε

ijkl

  H N (0, σ

²

)“   S X ‰Ò  ¦  à ºs  . • ¸^ ‰×  æ\  @ /ô  Ç SNP_  % ò † ¾ Ó`  ¦ ˜ Ðl  0 A # Œ 0 A_  ANOVA— ¸+ þ A\ 

&

h

6   xô  Ç   õ   H  A ü < ° ú   .

0

A_  ³ ð 3.1“ É r ² D G Ê ê@ /  Ž & ñ Ä º 229¿ º\  ¦ s 6   x # Œ SNP[ þ t_  Å Ò´ òõ \  @ /ô  Ç • ¸^ ‰×  æ_ 

¨ î

ç  Hõ  ³ ðï  r¼ #  \  ¦ ½ ¨ “ ¦  l \     ANOVA— ¸+ þ A\ " f SNP_  genotypeç ß –\  • ¸^ ‰×  æ_ 

¨ î

ç  H\  s  e ”   Ht \  @ /ô  Ç P -value\  ¦ ½ ¨ô  Ç  כ s “ ¦ ³ ð 3.2  H SNP[ þ t_  2> h_   © œ  ñ Œ •6   x

\

 @ / # Œ ³ ð 3.1õ  ° ú  s  • ¸^ ‰×  æ_  ¨ î ç  Hõ  ³ ðï  r¼ #  \  ¦ ½ ¨ “ ¦  l \     ANOVA— ¸+ þ A

\

" f SNP_  genotypeç ß –\  • ¸^ ‰×  æ_  ¨ î ç  H\  s  e ”   Ht \  @ /ô  Ç P -value\  ¦ ½ ¨ô  Ç  כ s 



.   õ \  ¦ ˜ Ѐ   2> h_   © œ  ñ Œ •6   x\  @ /ô  Ç ´ òõ   H — ¸¿ º : Ÿ x> & h Ü ¼– Ð • ¸^ ‰×  æ\  Ä »_ ô  Ç s 


 
t  · ú §€ Œ ¤Ü ¼ 9 1> h_  Å Ò´ òõ \  @ /ô  Ç  כ “ É r SNP1s  : Ÿ x> & h Ü ¼– Ð • ¸^ ‰×  æ\  Ä »_ ô  Ç  s

(significance = 0.020) e ”  “ ¦ ½ + É Ã º e ”  . genotypes  GG  { 9 { 9   â Ä º   É r  { 9 ˜ Ð 

³

ð 3.2: SNP1, SNP2, SNP3_  2> h_   © œ  ñ´ òõ [ þ t\  @ /ô  Ç • ¸^ ‰×  æ_  ¨ î ç  Hõ  ³ ðï  r¼ #  ü < P - value

M arker Genotype numberof Animals x ± s¯ (SNP1*SNP2) (AA , CC) 5 307.00±25.436

(AA , CT) 6 283.50±27.472

(AA , TT) 5 294.20±27.689

(AG , CC) 15 303.07±32.101

(AG , CT) 35 304.03±30.014

(AG , TT) 25 304.44±33.594

(GG , CC) 25 307.36±28.860

(GG , CT) 71 311.55±32.090

(GG , TT) 42 320.81±40.211

signif icance(P−value) 0.322 (SNP1*SNP3) (AA , AA) 3 292.33±11.015

(AA , AT) 6 297.83±39.163

(AA , TT) 7 291.86±21.965

(AG , AA) 19 296.84±34.012

(AG , AT) 38 312.74±29.431

(AG , TT) 18 293.00±27.903

(GG , AA) 32 315.66±37.044

(GG , AT) 74 314.64±35.502

(GG , TT) 32 309.19±29.205

signif icance(P−value) 0.243 (SNP2*SNP3) (CC , AA) 10 311.10±28.521

(CC , AT) 26 308.73±32.189

(CC , TT) 9 291.89±14.641

(CT , AA) 31 309.39±35.861

(CT , AT) 50 306.78±32.783

(CT , TT) 31 307.48±25.918

(TT , AA) 13 301.23±42.748

(TT , AT) 42 323.52±34.103

(TT , TT) 17 297.18±37.323

signif icance(P−value) 0.135



8 • ¸^ ‰×  æs   H  כ `  ¦ · ú ˜ à º e ”  . t ë ß – Ä ºo   H · ú ¡\ " f  â ] j+ þ A| 9 “   • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ Šҍ  H Ä

»„    > hZ >  SNPÄ »„        # Œ Q> h_  4 Ÿ ¤¸ ú šô  Ç SNPÄ »„   _   © œ  ñ Œ •6   xs   8 % ò † ¾ Ó`  ¦ ï  r



“ ¦ b ” “ ¦ e ” % 3  . Õ ª Q
 ANOVA\  ¦ s 6   xô  Ç ~ ½ ÓZ O \ " f  H • ¸^ ‰×  æ\   © œ  ñ Œ •6   xs  Šҍ  H % ò † ¾ Ó

“ É

r \ O   H  כ Ü ¼– Ð
 z Œ ¤ . ANOVA  H • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ Šҍ  H כ ¹“  `  ¦ 
_  כ ¹“  õ   © œ  ñ Œ • 6

 

xכ ¹“  `  ¦ ô  Ç   \  ° ú  s  & h 6   x   H — ¸+ þ A`  ¦  6   x Ù ¼– Ð 
_  ´ òõ s €   
_  ´ òõ ë ß –,  © œ  

ñ Œ •6   xs €    © œ  ñ Œ •6   x´ òõ ë ß – “ ¦ 9   H ~ ½ ÓZ O “   MDR — ¸+ þ A\  & h 6   x # Œ ˜ Ð ’ x .

3.3. Multifactor Dimensionality Reduction(MDR) • î |q @ èœ Ù ÿ c ë à f £ ­ O , 0; . ã

· ú

¡\ " f ´ ú ˜ô  Ç  כ õ  ° ú  s  # Œ Q > h_  Ä »„   _   © œ  ñ Œ •6   xs   â ] j+ þ A| 9 \   8 % ò † ¾ Ó`  ¦ ï  r “ ¦ ½ + É Ã

º e ”  .   " f # Œ Q  © œ  ñ Œ •6   x\  @ /ô  Ç high-order à º_  X <s ' – Ð 4 Ÿ ¤¸ ú šô  Ç › ' a> \  ¦ µ 1 ߁ n = à º e

”

  H MDR ~ ½ ÓZ O `  ¦ s 6   x # Œ ì  r$ 3 `  ¦ K ˜ Ð . MDR ~ ½ ÓZ O “ É r caseü < control data\ " f # Œ Q Ä »

„



 _   © œ  ñ Œ •6   x`  ¦ ¹ 1 Ô`  ¦ à º e ”  . • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ Šҍ  H SNP[ þ t_   © œ  ñ Œ •6   x`  ¦ · ú ˜ ˜ Ðl  0 A ô



Ç ~ ½ ÓZ O Ü ¼– Ð MDR ~ ½ ÓZ O `  ¦ s 6   xô  Ç . MDR ~ ½ ÓZ O “ É r caseü < control ¿ º  Òì  rÜ ¼– Ð
¾ º# Q4 R 

“ ¦ caseü < controls  1:1– Ð ° ú    ô  Ç . Õ ª Q
 " é ¶ X <s ' \ " f  H • ¸^ ‰×  æ   à º ƒ  5 Å q“   X <

s

' s  . Õ ªA " f Õ ª@ /– Ð MDR ~ ½ ÓZ O \  & h 6   x½ + É Ã º \ O  .   " f ' Í é ß –> \ " f  H • ¸^ ‰×  æ   à º

\



¦ X <s '  s _ ç l Z O  ×  æ CART ~ ½ ÓZ O Ü ¼– Ð case-control– Ð
è  H + ' Ritchie 1 p x (2003)õ  Hahn 1

p

x (2003)_  MDR ~ ½ ÓZ O \  & h 6   xô  Ç .

Step 1. • ¸^ ‰×  æ   à º\  ¦ CART ~ ½ ÓZ O Ü ¼– Ð s ì  r o\  ¦ r †   . Õ ªa Ë > 3.1_  STEP 1`  ¦ ˜ Ѐ   CART ~ ½ ÓZ O \ " f • ¸^ ‰×  æ   à º\  ¦ l ï  rÜ ¼– Ð 1 p x/ å Ls  case(high)ü < control(low)– Ð
 ¾ º

#

Q”   . # Œl " f caseÕ ªÒ  ¨s  54> h controlÕ ªÒ  ¨s  175> h– Ð
¾ º# Qt   HX < s X O > 
¾ º# Q

”



 X <s '   H 1:1s  ÷ &t  · ú §Ü ¼Ù ¼– Ð SPSS clementin10.1`  ¦ s 6   x # Œ case Õ ªÒ  ¨ 175> h\  ¦ l

ï  rÜ ¼– Ð ç  H+ þ A 7 £ x; Ÿ ¤ r †   . s X O >  7 £ x; Ÿ ¤÷ &# Q”   350¿ º\  ¦ s 6   x # Œ  6 £ § Step[ þ t\  & h  6

  xô  Ç .

Step 2. X <s ' \  ¦  ½ ™ ü Ü ¼– Ð 10> h_  ° ú  “ É r ß ¼l – Ð
è  H . Õ ªo “ ¦ Õ ª ×  æ 9> h\  ¦ training set Ü

¼– Ð & ñ “ ¦ 1> h\  ¦ testing setÜ ¼– Ð & ñ ô  Ç .

Step 3. 3> h_  SNP[ þ t– РÒ'  2> h_  SNP› ¸½ + Ë ×  æ 
\  ¦ ‚  × þ ˜ô  Ç .

Step 4. ‚  × þ ˜ ) a SNP› ¸½ + Ë\ " f SNP_  y Œ •y Œ • à ºï  r`  ¦ l œ í– Ð ô  Ç > h^ ‰[ þ t`  ¦ multifactor classes

¢

¸  H cells\  l Õ ü tô  Ç . 0 A_  Õ ªa Ë >_  STEP 4ü < ° ú  s  2> h_  › ¸½ + Ës Ù ¼– Ð 3

²

= 9> h_  ! s q

`



¦ ”   . y Œ •y Œ • 9> h_  ! s q\  case_  • ¸Ã ºü < control_  • ¸Ã º\  ¦ & h   H .

Step 5. Caseü < control_  q \  ¦ ½ ¨ # Œ 1˜ Ð  ß ¼ 
 ° ú  Ü ¼€   high-risk, 1˜ Ð   Œ •Ü ¼€   low- risk  ô  Ç . 0 A_  Õ ªa Ë >\ " f% ƒ! 3  1' Ÿ  1\ P _   â Ä º caseü < control_  q  1.333s Ù ¼– Ð high-risk  ) a .

Step 6. 2> h_  SNP_  › ¸½ + Ë „   Ò\ " f X <s ' _  9/10“   traing set\ " f ¸ ú ˜3 l w ì  rÀ ӝ ) a q Ö  ¦

“



 misclassification error(ME)\  ¦ ½ ¨ô  Ç . 0 A_  Õ ªa Ë >\ " f% ƒ! 3  ME_  ° ú כs   © œ  Œ •“ É r SNP1õ  SNP2_  › ¸½ + Ë`  ¦ ‚  × þ ˜ô  Ç .

Step 7. Training set\ " f high-low– Ð
è  H ³ ð\  ¦
 Qt  1/10_  X <s ' “   testing set`  ¦ s 6   x

# Œ ¸ ú ˜3 l w ì  rÀ ӝ ) a q Ö  ¦“   prediction error(PE)\  ¦ ½ ¨ô  Ç .

s

% ƒ! 3  2> h_  SNP_   © œ  ñ Œ •6   x\  @ / # Œ Step 2∼Step 7_  õ & ñ `  ¦ 10   ì ø Í4 Ÿ ¤K " f
“ : r MEü < PE_  ¨ î ç  Hõ  10  _  ì ø Í4 Ÿ ¤õ & ñ \ " f
“ : r ° ú כ`  ¦ l ï  rÜ ¼– Ð CVC\  ¦ ½ ¨ô  Ç   õ ü < ° ú  “ É r ~ ½ Ó Z

O

Ü ¼– Ð 
_  SNP\  @ /ô  Ç MEü < PE_  ¨ î ç  Hõ  CVC_    õ   H ³ ð 3.3õ  ³ ð 3.4ü < ° ú  s 
 

z Œ ¤ .

Õ

ªa Ë > 3.1: • ¸^ ‰×  æ\  @ / # Œ SNP[ þ t`  ¦ s 6   xô  Ç MDR ~ ½ ÓZ O _  & h 6   xõ & ñ

³

ð 3.3: • ¸^ ‰×  æ\  @ /ô  Ç SNP y Œ •y Œ • › ¸½ + Ë_  average MEü < average PE   õ 

N umberof f actors M arker averageM E averageM E

1 SNP1 0.4299 0.4412

SNP2 0.4478 0.4971

SNP3 0.4322 0.4588

2 SNP1*SNP2 0.3713 0.3853

SNP1*SNP3 0.4131 0.4353 SNP2*SNP3 0.4226 0.4706

0

A_  ³ ð 3.3“ É r MDRõ & ñ `  ¦ 10   ì ø Í4 Ÿ ¤ô  Ç Ê ê y Œ •y Œ •_  SNP › ¸½ + Ë\  @ /ô  Ç MEü < PE_  ¨ î ç  H

`



¦ ½ ¨ô  Ç ° ú כs  . Best model“ É r average MEü < average PE  © œ ± ú “ É r  כ `  ¦ ‚  × þ ˜   HX < 0 A _

 ³ ð\  ¦ ˜ Ѐ   
_  כ ¹“  \  @ /ô  Ç ´ òõ \ " f SNP1_  average ME 0.4299. PE 0.4412– Ð

 © œ ± ú > 
 z Œ ¤“ ¦ ¿ º> h_  כ ¹“  \  @ /ô  Ç ´ òõ \ " f  H SNP1*SNP2_  average ME 0.3713, PE 0.3853Ü ¼– Ð  © œ ± ú “ É r   – Ð
 z Œ ¤ .   " f 
_  כ ¹“  \ " f  H SNP1s  ‚  × þ ˜÷ &% 3 

“

¦ ¿ º > h_  כ ¹“  \ " f  H SNP1*SNP2 ‚  × þ ˜÷ &% 3  . Õ ªo “ ¦ SNP1õ  SNP1*SNP2\  ¦ ˜ Ѐ    © œ  

ñ Œ •6   x ´ òõ “   SNP1*SNP2_  average MEü < PE  8 ± ú “ É r  כ `  ¦ · ú ˜ à º e ”  .   " f 
 _

 כ ¹“  \  @ /ô  Ç ´ òõ ˜ Ð   H  © œ  ñ Œ •6   x\  @ /ô  Ç ´ òõ   8 ´ ú §   H  כ `  ¦ · ú ˜ à º e ”  .  6 £ §Ü ¼– Ð

³

ð 3.4: • ¸^ ‰×  æ\  @ /ô  Ç 
_  Ä »„   ´ òõ ü < ¿ º > h_   © œ  ñ Œ •6   x ´ òõ _  CVC   õ 

Number of factors 1 2

Cross Validation SNP1 SNP2 SNP3 SNP1*SNP2 SNP1*SNP3 SNP2*SNP3

Interval ME ME ME ME ME ME

#1 of 10 0.4299 0.4522 0.4395 0.3599 0.4108 0.4268

#2 of 10 0.4236 0.4459 0.4299 0.3758 0.4204 0.4204

#3 of 10 0.4299 0.4427 0.4331 0.3758 0.4076 0.4045

#4 of 10 0.4236 0.4395 0.4299 0.3694 0.4108 0.4236

#5 of 10 0.4268 0.4459 0.4140 0.3599 0.3949 0.4045

#6 of 10 0.4363 0.4490 0.4236 0.3790 0.4236 0.4236

#7 of 10 0.4427 0.4490 0.4459 0.3694 0.4172 0.4363

#8 of 10 0.4363 0.4682 0.4522 0.3726 0.4076 0.4395

#9 of 10 0.4299 0.4395 0.4268 0.3758 0.4172 0.4236

#10 of 10 0.4204 0.4459 0.4268 0.3758 0.4204 0.4236

count 7 0 3 10 0 0

CVC  õ  (³ ð 3.4)\  ¦ ¶ ú ˜( R˜ Ð .

s

  H 10  _  cross-validation`  ¦ r ' Ÿ ½ + É M : y Œ • r ' Ÿ \ " f ‚  × þ ˜ ) a best model`  ¦ î  rà Ôô  Ç ° ú כ s

 CVC “ ¦ ô  Ç . 0 A_  ³ ð 3.4\  ¦ ˜ Ѐ   #1 of 10_  r ' Ÿ \ " f ME SNP1s  0.4299, SNP2

0.4522, SNP3 0.4395Ü ¼– Ð SNP1s   © œ  Œ •Ü ¼Ù ¼– Ð SNP1\  @ / # Œ count +1`  ¦ ô  Ç . 8 ú x 10  `  ¦ r ' Ÿ  Ù þ ¡`  ¦ M : ³ ð 3.4ü < ° ú  s  SNP1s  y Œ • r ' Ÿ \ " f  © œ a % ~“ É r — ¸+ þ AÜ ¼– Ð ‚  × þ ˜ ) a  כ s  7  s l  M :ë  H\  SNP1_  CVC  H 7s   ) a . SNP1*SNP2 % i r  y Œ • r ' Ÿ \ " f  © œ a % ~“ É r — ¸+ þ A Ü

¼– Ð 10  s  ‚  × þ ˜÷ &% 3 l  M :ë  H\  CVC  H 10s   ) a .   " f ³ ð 3.3õ  ³ ð 3.4\  ¦ ˜ Ѐ   þ j7 á x best model“ É r כ ¹“  s  ô  Ç > h { 9  M :  H average MEü < average PE  © œ ± ú “ ¦ CVC  © œ Z  }“ É r SNP1 set`  ¦ ‚  × þ ˜÷ &“ ¦ כ ¹“  s  ¿ º > h { 9  M :  H average MEü < average PE  © œ ± ú “ ¦ CVC

 © œ Z  }“ É r SNP1*SNP2 sets  þ j7 á x best setÜ ¼– Ð ‚  × þ ˜÷ &% 3  .

4. l 5 æ´ * 0 Ë  ì Œ Ã? ê

Ä

ºo   H 4 Ÿ ¤½ + Ë| 9 # î \  @ /ô  Ç 0 A+ « > ¢ ¸  H » ¡ ¤_   â ] j: £ ¤$ í _  # Œ Q Ä »„   \  › ' aº   ) a polymor- phism_  › ¸½ + Ë`  ¦ s 6   x # Œ — ¸Ã º& h “   ~ ½ ÓZ O “   ANOVAü < q — ¸Ã º& h “   ~ ½ ÓZ O “   MDR`  ¦ ™ è> h 

% i

 . s [ þ t ~ ½ ÓZ O `  ¦ & h 6   x # Œ • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ Šҍ  H SNP[ þ t`  ¦ ½ ©" î  9“ ¦ r • ¸ô  Ç   õ  — ¸Ã º

&

h

“   ~ ½ ÓZ O “   ANOVA\ " f  H SNP1s  • ¸^ ‰×  æ\  Ä »_ ô  Ç s  e ” % 3 “ ¦  © œ  ñ Œ •6   x\  @ /ô  Ç % ò † ¾ Ó

“ É

r \ O   H  כ Ü ¼– Ð
 z Œ ¤ . t ë ß – q — ¸Ã º& h “   ~ ½ ÓZ O “   MDR~ ½ ÓZ O \ " f  H 
_  SNP\ " f  H SNP1s  • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ ´ ú §s  Å Ò% 3 Ü ¼ 9 ¿ º > h_   © œ  ñ Œ •6   x\ " f  H SNP1*SNP2 % ò † ¾ Ó`  ¦ ´ ú § s

 Šҍ  H  כ `  ¦ · ú ˜ à º e ” % 3  . ¢ ¸ô  Ç SNP1õ  SNP1*SNP2_  MEü < PE\  ¦ q “ §ô  Ç   õ  SNP1“  


_  Ä »„   _  ´ òõ  ˜ Ð   H SNP1*SNP2ü < ° ú  s   © œ  ñ Œ •6   x\  _ ô  Ç Ä »„  ´ òõ  • ¸^ ‰×  æ  â ]

j+ þ A| 9 \   8 ´ ú §“ É r % ò † ¾ Ó`  ¦ Šҍ  H “   – Ð µ 1 ß) €& ’  .  Ö  ¦ Q CVC  Ž & ñ   õ \ " f• ¸ SNP1*SNP2

“



  þ j7 á x— ¸+ þ Ae ” s  µ 1 ß) €& ’  .   " f ô  ÇÄ º_  • ¸^ ‰×  æ\  % ò † ¾ Ó`  ¦ Šҍ  H SNP\  ¦ ½ ©" î   H ë  H ]

j\ " f — ¸Ã º& h “   ~ ½ ÓZ O “   ANOVA— ¸+ þ A\ " f
 
t  · ú §“ É r Å Òכ ¹ô  Ç  © œ  ñ Œ •6   x\  › ' a>  ) a “   

 MDR ~ ½ ÓZ O \  _ K  ½ ©" î ÷ &# Q& ’  .

ô



Ǽ #  MDR ~ ½ ÓZ O \ " f ë  H] j& h “ É r X <s '  case-control– Ð s ì  r+ þ As  ÷ &# Q  l  M :ë  H\  ƒ   5

Å

q+ þ A  « э  H  6   x½ + É Ã º \ O    H  כ s  . s    ë  H] j& h `  ¦ K    l  0 AK " f ‘ : r ƒ  ½ ¨\ " f  H • ¸

^

‰×  æ   à ºü < ° ú  “ É r ƒ  5 Å q+ þ A  « э  H · ú ¡ ] X \ " fü < ° ú  s  • ¸^ ‰×  æ   à º\  ¦ CART l Z O Ü ¼– Ð p o  caseü < control– Ð
è  H + '\  MDR\  & h 6   x½ + É Ã º e ” % 3  . Õ ªo “ ¦ ¢ ¸   É r ë  H] j& h Ü ¼– Ð MDR~ ½ Ó Z

O

“ É r  © œ@ /& h Ü ¼– Ð & h “ É r ³ ð‘ : r à º\  ¦ ”    â Ä º\   © œ  ñ Œ •6   x`  ¦ ½ ©" î   H q — ¸Ã º& h “   ~ ½ ÓZ O s l  M

:ë  H\  Ä »„   _  à º ´ ú §`  ¦  â Ä º y Œ • ! s q\  › ' a8 £ ¤° ú כs  \ O   H ‘   ! s qs  Ò q tU  ´ à º e ”  . \ V\  ¦ [ þ t€   SNP Ä »„   _  à º 10> h s  © œ{ 9   â Ä º SNP Ä »„    10> h  © œ  ñ Œ •6   x\ " f_  ´ òõ \  ¦ ˜ Ѐ   “   59049> h_  ! s q– Ð
¾ º# Qt l  M :ë  H\  ´ ú §“ É r ! s q î ß –\  › ' a8 £ ¤° ú כs  \ O   H  â Ä º Ò q t|   . ‘ : r ƒ  ½ ¨\ 

"

f  H SNP Ä »„   _  à º 3> hs l  M :ë  H\  MDR ~ ½ ÓZ O \  & h 6   x½ + É Ã º e ” % 3 Ü ¼
, ´ ú §“ É r SNP Ä »

„



 [ þ t_   â Ä º  © œ  ñ Œ •6   x½ ©" î \  ë  H] j e ” 6 £ §“ É r  8 ƒ  ½ ¨÷ &# Q  ½ + É Â Òì  rs  .

™ Ú

y ”N ù ý  

Barendse, W., Bunch, R., Thomas, M., Armitage, S., Baud, S. and Donaldson, N. (2004).

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Bastione, L., Reilly, M., Rader, D. J. and Foulkes, A. S. (2004). MDR and PRP: A com- parison of methods for high-order genotype-phenotype associations, Human Geredity, 58, 82–92.

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[ 2007¸   6 Z 4 ] X à º, 2007¸   11 Z 4 G × þ ˜ ]

Main SNP Identification of Hanwoo Carcass Weight with Multifactor Dimensionality Reduction(MDR)

Method ^∗

Jea-Young Lee

¹⁾

Dong Chul Kim

²⁾

Abstract

It is commonly believed that disease of human or economic traits of livestock are caused not by single gene acting alone, but by multiple genes interacting with one an- other. This issue is difficult due to the limitations of parametric statistical method like as logistic regression for detection of gene effects that are dependent solely on interac- tions with other genes and with environmental exposures. Multifactor dimensionality reduction (MDR) nonparametric statistical method, to improve the identification of sin- gle nucleotide polymorphism (SNP) associated with the Hanwoo(Korean cattle) carcass cold weight, is applied and compared with ANOVA results.

Keywords: Single nucleotide polymorphism(SNP), multifactor dimensionality reduction(MDR), carcass cold weight.

∗

This research was supported by Gyeongbuk Hanwoo cluster(Ministry of Agriculture and Forestry) Republic of Korea.

1) Corresponding author. Professor, Dept. of Statistics, Yeungnam University, Kyungsan 712-749, Korea.

E-mail: [email protected]

2) Graduate, Dept. of Statistics, Yeungnam University, Kyungsan 712-749, Korea.

E-mail: [email protected]