A total of 273 spinach genotypes, including 265 accessions of the USDA spinach germplasm collection and 8 commercial cultivars, were used for the association analysis of leaf spot resistance (Supplementary Table S1). The 273 spinach genotypes were collected originally from 30 countries, with a majority from eight countries: Turkey, United States (US), Serbia, Afghanistan, England, Iran, China, and Belgium for 80, 32, 22, 22, 16, 15, 12, and 11 accessions or cultivars, respectively. These comprised 76.6% of the spinach genotypes tested (Supplementary Table S1). All seeds of USDA germplasm accessions were kindly provided by the USDA- ARS North Central Regional Plant Introduction Station at Iowa State University, Ames, IA. The seeds of “Symphonie” was from Gautier.Graines; “Space” and “Springfield” from Gowan Seed Co; “Whale” from Rijk. Zwaan; and “Polka”, “Seven R”, “Unipack 12”, and “Unipack 277” from Seminis.

Leaf spot disease evaluation was conducted at the Agricultural Research Station of the USDA in Salinas, CA [16] . The 265 accessions of the USDA spinach germplasm collection plus 8 commercial cultivars were screened for Stemphylium leaf spot resistance in a greenhouse. The experimental design was a randomized complete block (RCB) with two replications/genotype. In each replication, eight seeds from each genotype were planted in a plastic pot (10 cm × 10 cm × 10 cm) filled with Sunshine Mix #1 (Sun Gro Horticulture Canada Ltd., Seba Beach, Canada) and seedlings were thinned to 5 plants per pot after emergence.

An isolate of S. botryosum obtained from infected plants of the spinach cultivar Cheetah grown in Arizona was maintained for 4 weeks on plates of V8 juice agar under a 12 h/12 h light/dark regime. A conidial suspension (approximately 10⁵ conidia per ml) was prepared in water and applied using a hand-held mister onto leaves of each genotype five weeks after seeding (four- to six-true-leaf stage). Inoculated plants were incubated in a humidity chamber maintained at 100% relative humidity for 72 h, and then maintained in a greenhouse at 14˚C /27˚C (night/day cycle). Three weeks after inoculation, the plants in each pot were evaluated for severity (percent of leaf area with symptoms) of Stemphylium leaf spot symptoms. Re-isolations for S. botryosum were conducted to confirm the presence of the pathogen in association with the leaf spots.

Disease severity data were subjected to analysis of variance (ANOVA) using the general linear models (GLM) procedure of JMP Genomics 7 (SAS Institute, Cary, NC). Genotype was considered a fixed effect, and replication was considered a random effect. For comparisons among genotypes, least significant differences (LSDs) were calculated with a Type I (α) error rate of P = 0.05. The disease severity data also were analyzed using Microsoft (MS) Excel 2013 for the average, range, standard deviation (SD), standard error (SE), and coefficient of variation (CV).

Genomic DNA was extracted from leaves of spinach plants using the CTAB (hexadecyltrimethyl ammonium bromide) method [27] . A DNA library was prepared using the restriction enzyme ApeKI following the GBS protocol described by Elshire et al. (2011) [20] . The 90 bp, double-end sequencing was performed on each spinach accession/cultivar using the GBS protocol by an Illumina HiSeq 2000 machine at the Beijing Genomics Institute (BGI) in Hong Kong. GBS data assembly, mapping and SNP discovery were done using SOAP family software (http://soap.genomics.org.cn/) by the bioinformatics team at BGI. The GBS data provided by BGI averaged 3.26 M with 90 bp, short-read nucleotides for each spinach sample. The short reads of the GBS data were first aligned to the spinach reference genome Viroflay-1.0.1 with the AYZV01 project (http://www.ncbi.nlm.nih.gov/Traces/wgs/?val=AYZV01) using SOAPaligner/soap2 (http://soap.genomics.org.cn/). After the Spinach-1.0.3 spinach genome reference was released on July 22, 2015, the AYZV01 series of contig accessions were changed to the AYZV02 accessions (http://www.ncbi.nlm.nih.gov/Traces/wgs/?val=AYZV02), and all SNP information was updated to the AYZV02 version. The SOAPsnp v 1.05 was used for SNP calling [28] [29] . Approximately a half-million SNPs were discovered from the GBS data among the 273 spinach germplasm accessions, as provided by BGI. The spinach accessions and SNPs were filtered before conducting genetic diversity and association analyses. If a spinach accession had >20% missing SNP data and the heterozygous SNP genotype was >30%, the spinach genotype was removed from the panel. The SNP data was filtered for minor allele frequency (MLF) >2%, missing data <7%, and heterozygous genotype <25%. After filtering, 787 SNPs for 273 spinach accessions were used for genetic diversity and association analysis.

The model-based program STUCTURE 2.3.4 [30] was used to assess the population structure of the 273 spinach accessions/cultivars based on 787 SNP loci. In order to identify the number of populations (K) making up the structure of the data, the burn-in period was set at 10,000 with the Markov Chain Monte Carlo iterations and the run length set at 20,000 in an admixture model. The analysis then correlated allele frequencies independently for each run [31] . Ten runs were performed for each simulated value of K, which ranged from 1 to 11. For each simulated K, the statistical value delta K was calculated using the formula described by Evanno et al. (2005) [32] . The optimal K was determined using STRUCTURE HARVESTER [33] (http://taylor0.biology.ucla.edu/structureHarvester/). After the optimal K was determined, a Q-matrix was obtained and used in Tassel 5 for association analysis. Each spinach accession was then assigned to a cluster (Q) based on the probability determined by the software that the genotype belonged in the cluster. The cut-off probability for assignment to a cluster was 0.55 for only two clusters (structure populations), or 0.50 for three or more clusters. Based on the optimum K, a Bar plot with ‘Sort by Q’ was obtained to show the population structure among the 273 spinach accessions.

Genetic diversity of the 273 spinach accessions was also assessed, and the phylogeny trees were drawn using MEGA 6 [34] based on the Maximum Likelihood tree method with the following parameters. Test of phylogeny: bootstrap method with 500 bootstrap replications. Model/Method: General time reversible model. Rates among sites: Gamma distributed with invariant sites (G + I). Number of discrete gamma categories: 4. Gaps/missing data treatment: use of all sites. ML heuristic method: Subtree-pruning-regrafting-extensive (SPR level 5). Initial tree for ML: make initial tree automatically (Neighbor Joining). Branch swap filter: moderate. In order to compare results from the two software programs during the drawing of phylogeny trees using MEGA, the color, shape and branch of each spinach genotype was drawn using the same color located at the cluster (Q) from STRUCTUR. For the sub-tree of each Q (cluster), the shape of ‘Node/Subtree Marker’ and the ‘Branch Line’ was drawn with the same color as the bar plot of population clusters from the STRUCTURE analysis.

Association analysis was performed using TASSEL 5 software, in which the single marker regression (SMR) model without structure and without kinship, the regression linear model (GLM), and the mixed linear model (MLM) methods were used as described by Bradbury et al. (2007) [35] (http://www.maizegenetics.net/tassel). Two workflows of regression linear models, GLM (Q) and GLM (PCA), and two workflows of mixed linear models, MLM (Q + K) and MLM (PCA + K), were used in Tassel 5 for association analysis of SNP markers. Population structure (Q) was estimated using STUCTURE 2.3.4 [30] ; principal component analysis (PCA) was estimated by the tool PCA with covariance and three components; and Kinship (K) was estimated by the tool Kinship with Scald_IBS method in Tassel 5.

Stemphylium leaf spot severity varied among the 273 spinach genotypes tested, ranging from 0.2% to 23.5%, and averaged 4.6% with a standard deviation of 3.8, and with a standard error of 0.23%, indicating significant genetic differences in Stemphylium leaf spot resistance among the accessions (Supplementary Table S1). The distribution of Stemphylium leaf spot resistance was skewed to low disease severity and near normal after transformation by square root (Figure 1), indicating that Stemphylium leaf spot resistance is quantitative and probably controlled by multiple minor genes.

The population structure of the 273 spinach accessions and cultivars was initially inferred using STRUCTURE 2.3.4 [30] . The peak delta K was observed at K = 2, indicating the presence of two main population clusters, Q1 and Q2, in the spinach panel (Figure 2(a) and Figure 2(b)). The classification of accessions into populations or clusters based on the model-based structure from STRUCTURE 2.3.4 is shown in Figure 2(b) and Supplementary Table S1. A Q-value = 0.55 was used to divide the clusters, i.e., if a spinach genotype had a Q1 >= 0.55, the genotype was placed into Cluster Q1; if a spinach had a Q2 ≥ 0.55, it was placed into Cluster Q2; and the remaining genotypes (0.45 < Q1 < 0.55 or 0.45 < Q2 < 0.55) were placed into Q1Q2 of the admixture. In total, 252 of the 273 accessions or cultivars (92.3%) were assigned to one of the two populations or clusters. Q1 and Q2 consisted of 115 (42.1%) and 137 (50.2%) accessions and cultivars, respectively. The remaining 21 accessions (7.7%) were categorized as having admixed ancestry between Q1 and Q2, called Q1Q2 (Supplementary Table S1).

The genetic diversity among spinach accessions or cultivars was also assessed using the Maximum Likelihood (ML) method in MEGA 6 [34] , with phylogenetic trees drawn based on the results. Q1 and Q2 were defined as the two main clusters or populations (see above), with the same colors as the population structure Q1 (red) and Q2 (green) from the STRUCTURE 2.3.4 analysis (Figure 2(b)) to draw subtrees of the phylogenetic tree (Figure 2(c)). Q1 is denoted with a red color and round shape, Q2 with a green color and square shape, and the admixture Q1Q2 with black, empty squares. Four phylogenetic trees were included: (1) without taxon names assigned in order to compare the populations from STRUCTURE (Figure 2(c)); (2) with two formats of the traditional rectangular phylogenetic tree (Supplementary Figure S1-1 and Figure S1-2); and (3) the circular phylogenetic trees (Supplementary Figure S2-1 and Figure S2-2, which represent a different format of Figure S1-1). The phylogenetic trees from MEGA 6 (Figure 2(c) and Supplementary Figure S1-1, Figure S1-2, Figure S2-1, and Figure S2-2), were not fully consistent with the structure populations Q1 and Q2 developing in STRUCTURE 2.3.4 (Figure 2(a) and Figure 2(b)), indicating there were two differentiated genetic populations and admixtures in the spinach panel, which was not divided distinctly into two clusters.

Besides the two structured populations inferred using the STRUCTURE analysis, the second highest peak of delta K was observed at K = 5 using Structure Harvester, indicating the presence of five sub-population clusters

(Q1 to Q5) within the 273 spinach accessions or cultivars (Figure 3(a)). Figure 3(b) shows the bar plot drawn in STRUCTURE to visualize the five populations, where Q1 is red; Q2 is green; Q3 is blue; Q4 is yellow; Q5 is purple; and the admixture of the five populations is represented by black empty squares. The classification of accessions into populations based on the model-based structure developed in STRUCTURE 2.3.4 is shown in Figure 3(b) and Supplementary Table S1. Each spinach accession was also assigned to one of the five populations based on probabilities calculated in STRUCTURE (Supplementary Table S1). A Q value = 0.5 was used to divide the five clusters and the admixture. In total, 230 accessions or cultivars (84.2%) were assigned to one of the five populations, Q1 to Q5. Q1 to Q5 consisted of 49 (17.9%), 7 (2.6%), 24 (8.8%), 32 (11.7%), and 118 (43.2%) accessions/cultivars, respectively. The remaining 43 accessions (15.8%) were categorized as having admixed ancestry between Q1 to Q5 (Supplementary Table S1).

The genetic diversity of the 273 spinach accessions also was analyzed using the ML method in MEGA 6 by combining the five structured populations, Q1 to Q5, from STRUCTURE as done for the two structured populations above. The five clusters shown in Figure 3(c) were divided according to the five structured populations, Q1 to Q5, with same colors as in Figure 3(b), indicating five differentiated genetic populations and admixtures among the 273 accessions. The same approaches and methods were also used to analyze genetic diversity of the five structured populations using MEGA 6. The four phylogenetic trees drawn were consistent with the structure populations Q1 to Q5 from STRUCTURE 2.3.4, indicating that there were five differentiated genetic subpopulations and admixtures in the spinach panel. However, the five structured subpopulations were not very clear (Supplementary Figure S3-1, Figure S3-2, Figure S4-1 and Figure S4-2).

Based on the genetic diversity analysis from STRUCTURE and MEGA, and the phylogenetic trees from Figure 2 and Figure 3, as well as Supplementary Figure S1-1, Figure S1-2, Figure S2-1, Figure S2-2, Figure S3-1, Figure S3-2, Figure S4-1, and Figure S4-2, the 273 spinach accessions/cultivars were organized into two

or five structured populations, as described above. Therefore, we used both the Q matrix with two structures and the matrix with five structures for association mapping in TASSEL. In total, nine models were used in TASSEL to do association analysis of Stemphylium leaf spot resistance: a single marker regression (SMR) model; two workflows with linear regression models, GLM (Q) and GLM (PCA); two workflows with mixed linear models, MLM (Q + K) and MLM (PCA + K); two Q-matrices, with 2 vectors and 5 vectors; and two PCA-matrices, with 2 and 5 vectors. First, we screen SNP markers using a Log of the Odds (LOD) (or likely LOD =~ (−LOG(P), where P is the P value). Based on the suggestion by Lander and Botstein (1989) [36] , a typical LOD threshold should be between 2 and 3 in order to detect at 5% level for a QTL [37] . The LOD value of 2.5 was used as the threshold to screen associated SNP markers. For each SNP, if a LOD value ≥ 2.5 was observed in one of the nine models, the SNP was selected for further identification, as listed in Supplementary Table S2.

Among the 16 SNPs selected (Table S2), different LOD values were observed from different models, SMR gave the largest LOD values, GLM (GLM (Q) and GLM (PCA)) second, and the MLM (MLM (Q + K) and MLM (PCA + K)) the smallest. Of the SNPs with an LOD ≥ 2.5, there were 13 SNPs in the SMR model; 14 SNPs in GLM (Q) under both two-structured and five-structured populations; 13 and 8 SNPs in the GLM (PCA); 7 and 4 SNPs in the MLM (Q + K), 6 and 5 SNPs in the MLM (PCA + K) under the two-structured and five- structured populations, respectively (Table S2). The two-structured populations based Q-matrix and PCA provided more SNP markers with significant association with Stemphylium leaf spot resistance, which was consistent with the population structure analysis by STRUCTURE where the peak delta K was observed at K = 2.

The SNP markers listed in Table S2 were further identified based on five models from TASSEL under the two-structured populations in order to identify and confirm the SNP markers with stable results because different models can give different results. It was assumed that if significant associations were calculated using models for a particular SNP, the SNP marker should be robust for association mapping. If a SNP had an LOD ≥ 2.5 or close to 2.5 in the five models, SMR, GLM (Q), GLM (PCA), MLM (Q + K), and MLM (Q + PCA), the SNP marker was identified as relevant for association mapping. Using these selection criteria, eight SNP markers were identified as being strongly associated with Stemphylium leaf spot resistance (Table 1).