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

Method Statistical model Population structure matrix D Kinship matrix K
ANOVA $M i = μ + α ′ X i + e i MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaemyta00aaSbaaSqaaiabdMgaPbqabaGccqGH9aqpcqaH8oqBcqGHRaWkiiWacuWFXoqygaqbaiabhIfaynaaBaaaleaacqWGPbqAaeqaaOGaey4kaSIaemyzau2aaSbaaSqaaiabdMgaPbqabaaaaa@3A64@$ - -
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.