Table 1.

Description of the association mapping models.

Model	Description
General linear model (GLM)	GLM induces the simplest structure for single-locus analysis with population structure (Q) as fixed effect, whereas no random effect component is involved in the model; principal components are used as covariates in such a model to reduce the false positives
Mixed linear model (MLM)	MLM includes the kinship matrix (K) as an additional random effect component; hence it is also called the Q + K model
Multiple loci MLM (MLMM)	MLMM is designed for multiple locus analysis, is an improvement over MLM which incorporates multiple markers simultaneously as covariates in order to partially remove the confounding between testing markers and kinship. Gapit uses forward and backward stepwise linear mixed-model regression to include the markers as covariates
Compressed MLM (CMLM)	In CMLM the similar individuals are assigned into groups through cluster analysis and then groups are used as elements of reduced kinship matrix for random effect structure. The model has improved statistical power compared to regular MLM methods due to grouping or clustering
Enriched CMLM (ECMLM)	ECMLM calculates kinship using different algorithms and then chooses the best combination between kinship algorithms and grouping algorithms
Fixed and random model circulating probability unification (FarmCPU)	This is an iterative approach which iteratively fits both fixed and random effect model to eliminate the models overfitting problem while using stepwise regression in MLMM. To control the false positives, kinship derived from associated markers is used
Settlement of MLM under progressively exclusive relationship (SUPER)	The SUPER model uses the associated genetic markers (pseudo Quantitative Trait Nucleotides) to derive the kinship matrix, instead of all the markers. Whenever a pseudo QTN is correlated with the testing marker, it is excluded from those used to derive kinship. The method has higher statistical power than regular MLM