Table S3 The genotype and genotype effect of marker and QTL for combining ability and heterosis with multiple alleles at each locus in DH
population
MM
mm
Genotype in DH population
MMQQ
MMqq
mmQQ
mmqq
Genotype effect in DH population
 a
 a
 a
 a
Genotype frequency
population
1
(1  r )
2
1
r
2
1
r
2
1
(1  r )
2
*Genotype in TC population
MMQ1Q
MMQ1q
mmQ1Q
mmQ1q
*Genotype effect in TC population
  g1
  g1'
  g1
  g1'
1
(1  r )
2
1
g1  (2  a1  a)
2
1
1
( g1  g1 )  (G  G )
2
2
1
r
2
1
r
2
1
g1  (2   a1  a )
2
1
1
 ( g1  g1 )  (G  G)
2
2
1
g1  (2  a1  a)
2
1
1
( g1  g1 )  (G  G )
2
2
1
(1  r )
2
1
g1  (2   a1  a )
2
1
1
 ( g1  g1 )  (G  G)
2
2
…
…
…
…
…
#Genotype in TC population
MMQk Q
MMQk q
mmQk Q
mmQk q
#Genotype effect in TC population
d
 a
d
 a
*Genotype
population
frequency
in
in
DH
TC
*Genotype effect in Hmp data set
*Genotype effect in Sca data set
#Genotype
population
frequency
in
TC
#Genotype effect in Hmp data set
#Genotype effect in Sca data set
#Genotype effect in Gca data set
1
(1  r )
2
1
g k  (2  ak  a )
2
1
1
( g k  g k  )  (G  G )
2
2
1
(G  G )
2
1
r
2
1
r
2
1
g k   (2   ak  a )
2
1
1
 ( g k  g k  )  (G  G)
2
2
1
 (G  G )
2
1
g k  (2  ak  a )
2
1
1
( g k  g k  )  (G  G )
2
2
1
(G  G )
2
1
(1  r )
2
1
g k   (2   ak  a )
2
1
1
 ( g k  g k  )  (G  G)
2
2
1
 (G  G )
2
MM and mm denote the two different genotype of molecular marker M; Q and q denote two alleles of QTL in DH population, Qi (i=1~k) represents the multiple
alleles of QTL in tester; r represents the recombinant value between molecular marker M and QTL in DH population; μidenotes the overall mean value. a, a1 and ak
denote the additive effect of different allele; gi and gi’ (1~k) denote the genotypic value of the homozygote and heterozygote of QTL, respectively. G 
G 
1 k
 gi . For the RI population, the expectations were similar to those in the DH population except for r, which was replaced by
k i 1
respectively. The
rm
and
rm were
 /(1 2 r ')
2 rm
m
and
1 k
 gi ，
k i 1
4 rm /(16 rm )
recombinant values for two RI populations (selfing population and sib-mating population), respectively(Hu et al. 2002).
*When the genotype of QTL is Q1Q1 in tester
# When the genotype of QTL is QkQk in tester
,