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Linkage disequilibrium (LD) decay in the pea-Aphanomyces collection. Coloured curves represent the estimated LD decay for each linkage group (LG). Dashed horizontal lines represent half of the maximum LD value (LD threshold=0.5). Arrows represent the LD decay rate, as the estimated genetic distance (cM) to drop to the LD threshold on each LG. (PDF 157 kb)

Clustered heatmap of correlation coefficients between disease resistance, earliness and height variables data. Variables are coded as described in Additional file 4. Only correlations with a p-value < 0.05 are shown. Colours represent level of correlation, coded as follow: dark red: r < −0.8; medium red: −0.8 < r < −0.5; light red: −0.5 < r < −0.2; white: −0.2 < r < 0.2 or p-value > 0.05; light green: 0.2 < r < 0.5; medium green: 0.5 < r < 0.8; dark green: r > 0.8. Clustering is based on the UPGMA method. (PDF 48 kb)

Frequency distribution of least square means obtained for Aphanomyces resistance, earliness and plant height in the pea-Aphanomyces collection. Least square means were obtained from analysis of variance for three Aphanomyces resistance traits (Root Rot Index, first and second Aerial Decline Indexes, coded RRI, ADI1 and ADI2, respectively), three earliness traits (dates to 50 % bloom, 100 % bloom and 100 % dried plants, coded FLO1, FLO2 and RIPE, respectively) and plant height (HT). Aphanomyces resistance traits were assessed over nine infested field environments and against two reference strains of A. euteiches (RB84 and Ae109) in controlled conditions. Earliness and height were assessed in two healthy environments. n: total number of pea lines assessed; m: mean ± standard deviation of the pea-Aphanomyces collection; h2: mean-based heritability. (PDF 38 kb)

Clustered heatmap of the Kinship matrix. Kinship matrix from the GAPIT R package [75] based on 2937 SNP markers. Clustering is based on the UPGMA method. Colours represent the degree of relationship between two given lines. Pea line information is described as in Additional file 1. Lines sharing same pedigree or end use or sowing type are well clustered thus the Kinship matrix efficiently represents the relationships between individuals. (PDF 1253 kb)

Example of MLMM R package plot outputs for analysis of the MFA.Dim.1 variable. (A): Bonferroni correction of the highest marker p-value for each step of the forward and backward analysis. Optimal step (dashed blue vertical line) is determined as the largest stepwise mixed model regression in which all cofactors have –log10(p-value) above the mBonf threshold (dashed black horizontal line). (B): QQ-plot at the optimal step. (C): Partition of variance for each forward and backward step. Variance explained by population structure (PCA; grey); all markers used as cofactors (blue); Kinship matrix (green) and unexplained variance (= missing heritability; red). The dashed blue vertical line represents the optimal step according to mBonf threshold. (D) Genome-wide Manhattan plot without marker cofactors. The dotted line represents the multiple-Bonferroni threshold above which markers are considered as significant. (E): Genome-wide Manhattan plot at the optimal step with marker cofactors (4 red dots). The dotted line represents the multiple-Bonferroni threshold above which markers are considered as significant. (PDF 148 kb)