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

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

Method Statistical model Population structure matrix D Kinship matrix K
ANOVA M i = μ + α X i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSIaemyzau2aaSbaaSqaaiabdMgaPbqabaaaaa@3A64@ - -
K M i = μ + α X i + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSIaem4zaC2aa0baaSqaaiabdMgaPbqaaiabgEHiQaaakiabgUcaRiabdwgaLnaaBaaaleaacqWGPbqAaeqaaaaa@3F1E@ - SPAGeDi
Q1K M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ STRUCTURE; ΔK criterion SPAGeDi
Q2K M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ STRUCTURE; Log likelihood SPAGeDi
PK M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ Principal components; explaining simultaneously 25% of the variance SPAGeDi
K T M i = μ + α X i + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSIaem4zaC2aa0baaSqaaiabdMgaPbqaaiabgEHiQaaakiabgUcaRiabdwgaLnaaBaaaleaacqWGPbqAaeqaaaaa@3F1E@ - K T i j = S i j 1 1 T + 1 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4saS0aaSbaaSqaaiabdsfaujabdMgaPjabdQgaQbqabaGccqGH9aqpjuaGdaWcaaqaaiabdofatnaaBaaabaGaemyAaKMaemOAaOgabeaacqGHsislcqaIXaqmaeaacqaIXaqmcqGHsislcqWGubavaaGccqGHRaWkcqaIXaqmaaa@3D86@ ;
T = 0,0.025, ..., 0.975
Q1K T M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ STRUCTURE; ΔK criterion T = 0,0.025, ..., 0.975
Q2K T M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ STRUCTURE; Log likelihood T = 0,0.025, ..., 0.975
PK T M i = μ + α X i + u = 1 z D i u v u + g i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSYaaabmaeaacqWGebardaWgaaWcbaGaemyAaKMaemyDauhabeaakiabdAha2naaBaaaleaacqWG1bqDaeqaaOGaey4kaScaleaacqWG1bqDcqGH9aqpcqaIXaqmaeaacqWG6bGEa0GaeyyeIuoakiabdEgaNnaaDaaaleaacqWGPbqAaeaacqGHxiIkaaGccqGHRaWkcqWGLbqzdaWgaaWcbaGaemyAaKgabeaaaaa@4E25@ Principal components; explaining simultaneously 25% of the variance T = 0,0.025, ..., 0.975
  1. For a detailed definition of the statistical models and description of the different methods see Materials and Methods.