Comparison of mixed-model approaches for association mapping in rapeseed, potato, sugar beet, maize, and Arabidopsis

Table 1 Methods used for association mapping and the corresponding statistical models.

Method	Statistical model	Population structure matrix D	Kinship matrix K
ANOVA	$M_{i} = μ + α^{'} X_{i} + e_{i}$	-	-
K	$M_{i} = μ + α^{'} X_{i} + g_{i}^{*} + e_{i}$	-	SPAGeDi
Q₁K	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	STRUCTURE; ΔK criterion	SPAGeDi
Q₂K	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	STRUCTURE; Log likelihood	SPAGeDi
PK	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	Principal components; explaining simultaneously 25% of the variance	SPAGeDi
K_T	$M_{i} = μ + α^{'} X_{i} + g_{i}^{*} + e_{i}$	-	$K_{T i j} = \frac{S_{i j} - 1}{1 - T} + 1$ ; T = 0,0.025, ..., 0.975
Q₁K_T	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	STRUCTURE; ΔK criterion	T = 0,0.025, ..., 0.975
Q₂K_T	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	STRUCTURE; Log likelihood	T = 0,0.025, ..., 0.975
PK_T	$M_{i} = μ + α^{'} X_{i} + \sum_{u = 1}^{z} D_{i u} v_{u} + g_{i}^{*} + e_{i}$	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.

ISSN: 1471-2164