Information Technology Reference
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35
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Locus
Fig. 1. Simulated heatmap of activation probabilities for main effect and epistatic effects. Activa-
tion probabilities along the diagonal correspond to main effects and off diagonal correspond to
epistatic effects.
determined which needed to be reflected in the analysis. For the i th observation and
locus l j this information can be coded into X ij as:
1 , allele l j is from parent A
X ij =
1 , allele l j is from parent B
0 , allele l j is undetermined
(1)
Here the X ij correspond to the main effects. For the epistatic effects (two-way interac-
tion) this produces the interaction between loci l j and l k as:
1 , alleles l j and l k from same parent
X ij X ik =
1 , alleles l j and l k from different parents
0 , allele l j or l k is undetermined
(2)
Using a traditional first order model with a two-way multiplicative interaction terms the
model is defined as:
p
β j X ij I P c ( l j )+
k<j
y i = μ +
β jk X ij X ik I P c ( l j ) I P c ( l k )+ i .
(3)
j =1
N (0 c ) , P c is the set of loci l j in model M c ,and I P c
where i
is an indicator
function that takes the value 1 if l j
P c and 0 otherwise. Here β j corresponds to the
main effect of locus l j and β jk is the epistatic effect between loci l j and l k .
 
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