For each trait examined in the current study, considerable variation was observed for the entry means or adjusted entry means Mi (Table ). The total number of marker alleles detected for rapeseed, potato, sugar beet, maize, and Arabidopsis was 331, 158, 176, 1106, and 1752, respectively. The average allele frequency ranged from 0.18 for potato to 0.50 for maize and Arabidopsis.
The model-based approach of STRUCTURE revealed z + 1 = two, two, two, five, and six sub-populations for rapeseed, potato, sugar beet, maize, and Arabidopsis, respectively, when using the ad-hoc criterion ΔK. In contrast, based on SBC, the number of sub-populations revealed by STRUCTURE was 11, 15, 10, 15, and 5. For rapeseed, potato, sugar beet, maize, and Arabidopsis, the minimum number of principal components p explaining simultaneously 25% of the variance was 4, 5, 4, 13, and 8, respectively.
The MSD between observed and expected P values of the K approach ranged from 0.0002 (maize, ED) to 0.0604 (potato, PM) and was considerably lower than that of the ANOVA approach ranging from 0.0004 (Arabidopsis, FRI) to 0.1928 (potato, GPR) (Table ). For the Q1K and Q2K methods, the MSD values were of similar size and varied between 0.0002 (maize, DPS) and 0.0389 (potato, PM). The MSD value of the PK method ranged from 0.0002 (maize, DPS) to 0.0422 (potato, PM).
Mean of squared differences (MSD) between observed and expected P values for various association mapping methods in five plant species.
For all plant species, traits, and mixed-model approaches examined, considerably different values of REML-based deviance as well as MSD were observed for the examined levels of T
(Additional file 3
). The optimum threshold Topt
, identified based on deviance profiles, ranged from 0.450 to 0.925 (Table ). By comparison, the threshold Topt
, identified based on MSD profiles, ranged from 0.275 to 0.975. The correlation between the Topt
values identified using these two criteria was 0.83 (Additional file 4
). The MSD values observed for the mixed- model approaches, which were based on the
matrix, were lower than that observed for the approaches which were based on the K
matrix (Table ; Table ; Fig. ).
T values for which the lowest deviance or the lowest mean of squared differences between observed and expected P values were found for various association mapping methods in five plant species.
Figure 1 Plot of observed vs. expected P values for the nine different association mapping methods. For maize, every fifth, and for Arabidopsis, every eigth P value was plotted to increase the clarity of the plot. For each of the five plant species, the result (more ...)
The 95% quantile of differences in MSD calculated for the five pairs of association methods Q1
K/PK, and Q1
was highest for potato and ranged from 0.0041 to 0.0114 (Additional file 5
). For Arabidopsis, the 95% quantile of differences in MSD was lowest and varied from 0.0001 to 0.0004.
The slopes of the power curve were flat for small as well as large genetic effects, whereas for genetic effects of medium size the slope was steep (Fig. ). For most traits under consideration, the adjusted power of the
methods was slightly higher across all examined sizes of genetic effects than those of the Q1
K, and PK methods. In comparison with the other association mapping methods, the ANOVA method showed the lowest adjusted power to detect QTL across all examined sizes of genetic effects for all traits and plant species except potato (PIR).
Figure 2 Adjusted power to detect quantitative trait loci (QTL) for the nine different association mapping methods depending on the size of the QTL effect Gr. The percentage of phenotypic variation explained by a QTL was calculated for the average allele frequency (more ...)
The Pearson correlation coefficient between the observed P
values of all examined association mapping methods ranged from -0.05 to 0.99 (Additional file 6