Table 1.

Methods used for association mapping and the corresponding statistical models.

Method	Statistical model	Population structure matrix D	Kinship matrix K
ANOVA	$M_i=\mu +{\alpha }^{\prime }{X}_i+e_i$	-	-
K	$M_i=\mu +{\alpha }^{\prime }{X}_i+g_i^{\ast }+e_i$	-	SPAGeDi
Q1K	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	STRUCTURE; ΔK criterion	SPAGeDi
Q2K	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	STRUCTURE; Log likelihood	SPAGeDi
PK	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	Principal components; explaining simultaneously 25% of the variance	SPAGeDi
KT	$M_i=\mu +{\alpha }^{\prime }{X}_i+g_i^{\ast }+e_i$	-	$K_{Tij}=\frac{S_{ij}-1}{1-T}+1$; T = 0,0.025, ..., 0.975
Q1KT	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	STRUCTURE; ΔK criterion	T = 0,0.025, ..., 0.975
Q2KT	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	STRUCTURE; Log likelihood	T = 0,0.025, ..., 0.975
PKT	$M_i=\mu +{\alpha }^{\prime }{X}_i+{\displaystyle {\sum }_{u=1}^z{D}_{iu}{v}_u+}{g}_i^{\ast }+e_i$	Principal components; explaining simultaneously 25% of the variance	T = 0,0.025, ..., 0.975

For a detailed definition of the statistical models and description of the different methods see Materials and Methods.