Abstract Background Stalk lodging is one of the main factors affecting maize (Zea mays L.) yield and limiting mechanized harvesting. Developing maize varieties with high stalk lodging resistance requires exploring the genetic basis of lodging resistance-associated agronomic traits. Stalk strength is an important indicator to evaluate maize lodging and can be evaluated by measuring stalk rind penetrometer resistance (RPR) and stalk buckling strength (SBS). Along with morphological traits of the stalk for the third internodes length (TIL), fourth internode length (FIL), third internode diameter (TID), and the fourth internode diameter (FID) traits are associated with stalk lodging resistance. Results In this study, a natural population containing 248 diverse maize inbred lines genotyped with 83,057 single nucleotide polymorphism (SNP) markers was used for genome-wide association study (GWAS) for six stalk lodging resistance-related traits. The heritability of all traits ranged from 0.59 to 0.72 in the association mapping panel. A total of 85 significant SNPs were identified for the association mapping panel using best linear unbiased prediction (BLUP) values of all traits. Additionally, five candidate genes were associated with stalk strength traits, which were either directly or indirectly associated with cell wall components. Conclusions These findings contribute to our understanding of the genetic basis of maize stalk lodging and provide valuable theoretical guidance for lodging resistance in maize breeding in the future. Supplementary Information The online version contains supplementary material available at 10.1186/s12863-022-01091-5. Keywords: Maize, Stalk lodging resistance, Genome-wide association study, Quantitative trait nucleotides, Candidate gene Background Maize (Zea mays L.) plays an important role in food security, feed provision, and fuel resources. Nevertheless, stalk lodging can lead to 5–20% maize yield loss annually worldwide [[47]1]. Achieving high agricultural yields under different environmental conditions is a major goal of maize breeders. In low-density populations, the yield was improved by selecting taller plants to increase the biomass per plant. In high-density populations, the high yield was obtained by increasing the population density of selected medium height plants through the combination of reasonable panicle height coefficient and lodging resistance. Stable quantitative trait loci (QTLs) are particularly useful in marker-assisted selection [[48]2]. Stalk lodging is a phenomenon whereby plants collapse from the upright state, a complicated and integrated quantitative trait caused by many factors, such as the quality of the stalk itself and the external environmental factors (e.g., climatic and soil conditions, planting density, fertilization and irrigation, pests and diseases) which cause irreversible damage to corn stalks and roots [[49]1, [50]3]. Maize lodging can be divided into three types: root lodging, stem bending, and stem breaking [[51]4]. Stalk lodging usually occurs at or below the ear node, which consequently influences the regular growth of the ear before harvest and the final yield of maize [[52]5, [53]6]. Furthermore, grain yield per unit area is highly correlated to the plant’s adaptability to high crop density, but stalk lodging limits planting density and mechanized harvesting [[54]7, [55]8]. Therefore, improving stalk lodging resistance in maize would benefit future breeding programs and agricultural production. Stalk lodging resistance is correlated with stalk mechanical strength, hence this variable was used to evaluate lodging resistance in maize [[56]9, [57]10]. Common methods to quantify the stalk mechanical strength include rind penetration, bending, breaking, and vertical crushing [[58]4, [59]7, [60]11]. Most studies have found that the stalk rind penetrometer resistance (RPR) and stalk buckling strength (SBS) are important determinants of crop lodging resistance. Furthermore, RPR did not damage the stalk structure [[61]12–[62]14]. Compared with RPR, SBS is more closely correlated to stalk lodging under natural conditions, as stalk lodging happens in case of over-bending [[63]15]. According to previous studies, we found that lodging occurs most frequently at flowering stage or a few weeks after flowering and the third or fourth internode of maize plants is extremely sensitive to stalk lodging in the field [[64]6, [65]8, [66]13, [67]16]. Furthermore, Liu et al. [[68]11] showed that the best period for evaluating stalk strength is the silking phase or stage after silking. The position of the stem lodging mainly occurs between the second and fifth internodes, especially in the third internodes and the fourth internodes above ground (FIAG) were significantly correlated with RPR and SBS [[69]6, [70]8, [71]11, [72]17, [73]18]. In addition, with the increase of plant density, the length of the base nodes increased significantly, the diameter of the stems decreased significantly, and the content of cellulose, hemicellulose and lignin decreased, resulting in a decrease in the mechanical strength of the stems and an increased risk of lodging [[74]19]. QTL mapping has been widely used in the study of various agronomic traits, including yield-related traits, which is a useful tool for analyzing the genetic structure of complex agronomic traits. In crop, QTL mapping on lodging have been gradually applied in sorghum, wheat, rice, especially in maize. For example, a linkage map with 129 SSRs markers was constructed by Hu et al. [[75]6], and two, three, and two QTLs were detected for the maximum load exerted to breaking (F max), the breaking moment (M max) and the critical stress (σ max), respectively. Li et al. [[76]12] identified seven QTLs associated with RPR in two maize recombinant inbred line (RIL) populations using 3072 single nucleotide polymorphisms (SNP) markers. Zhang et al. [[77]17] identified 44 significant QTLs for SD, SBS, and RPR using the IBM Syn10 DH population in three environments. The efficiency and accuracy of QTL mapping depend largely on the marker density, the variation range of phenotypes within the population, as well as the population size and type [[78]20]. Genome-wide association study (GWAS) is a powerful tool for analyzing the genetic basis of complex traits. So far, GWAS has been used to analyze many agronomic traits such as plant height, leaf structure and yield-related traits [[79]21–[80]23], and other characteristics, i.e. In addition, some genetic studies on crop lodging have also been carried out using GWAS. On the contrary, although there are some GWAS reports on stalk lodging [[81]13, [82]24], they are still relatively few, and the molecular mechanism of the variation of corn lodging-related traits is still poorly understood. High-throughput SNP markers have been widely used to identify genes controlling quantitative traits [[83]25–[84]28]. Genotyping by sequencing (GBS) is a relatively inexpensive method to obtain high-density markers for large populations taking the advantage of next-generation sequencing technologies [[85]29–[86]32]. In this study, an association mapping panel was genotyped by GBS. Based on this, association mapping was used to identify SNPs and excavate potential candidate genes on RPR, SBS, and morphological traits associated with stalk lodging resistance. The objectives of this study were to: (1) identify associated loci for RPR, SBS, and morphological traits of the stalk of maize; (2) ascertain stable SNPs and predict potential candidate genes in these regions; (3) dissect the genetic architecture of stalk lodging resistance-related traits. Results Phenotype analysis of the six lodging resistance-related traits The phenotypes of all lodging resistance-related traits in the association mapping panel are shown in Table [87]1. The mean values of RPR, SBS, TID, and FID in the low plant density were higher than those in the high plant density. As for TIL and FIL, the mean values in the high plant density were higher than the mean values in the low plant density. For the six traits mentioned above, the skewness and kurtosis were less than 1, indicating that these traits followed a normal distribution. Furthermore, the coefficients of variation (CV) of these traits in the plant densities examined in this study ranged from 5.78–15.78% and 6.49–17.05%, respectively (Table [88]1). Table 1. Phenotypic performance for related traits of stalk lodging resistance in the association mapping panel Trait ^a Density ^b Mean ± SD Range Skewness Kurtosis CV (%) RPR (N/mm^2) L 42.55 ± 5.70 29.61–60.78 0.43 0.24 13.39 H 41.06 ± 4.68 29.74–54.51 0.15 -0.22 11.40 SBS (N/cm^2) L 429.08 ± 67.72 199,98–634.29 0.17 0.90 15.78 H 354.04 ± 60.36 171.08–547.67 0.16 0.33 17.05 TIL(mm) L 87.40 ± 9.10 65.60–110.39 0.04 -0.36 10.41 H 90.50 ± 9.62 66.01–115.74 -0.03 -0.13 10.63 TID (mm) L 17.55 ± 1.01 15.53–21.47 0.49 1.01 5.78 H 16.73 ± 1.09 14.31–19.75 0.27 -0.07 6.49 FIL (mm) L 103.90 ± 11.49 77.23–133.33 0.08 -0.47 11.06 H 106.99 ± 11.04 79.92–135.88 -0.10 -0.47 10.32 FID (mm) L 17.10 ± 1.00 14.96–20.09 0.39 0.58 5.85 H 16.32 ± 1.08 13.95–19.29 0.22 0.10 6.60 [89]Open in a new tab ^aRPR, SBS, TIL, TID, FIL, and FID stand for rind penetrometer strength, stalk bending strength, third internode length, third internode diameter, fourth internode length, and fourth internode diameter, respectively ^bL stands for low plant density, H stands for high plant density ANOVA showed that the environment effects, density effects, genotype effects and interactive effects between the genotype and environment were both significant for six traits in the association mapping panel (Table [90]2). For the association mapping panel, the broad-sense heritability (h^2[B]) of all traits in low and high plant densities ranged from 0.59 to 0.72 and 0.61 to 0.71, respectively (Table [91]2), suggesting that variations of stalk strength traits were mainly controlled by genetic factors. Table 2. Analysis of variance (ANOVA) for related traits of stalk lodging resistance under two plant densities in the association mapping panel Trait ^a F-value h^2[B] Environment Density Genotype Environment × Genotype Density × Genotype Low plant density High plant density RPR 477.91^** 22.52^** 11.36^** 2.90^** 1.73^** 0.62 0.61 SBS 204.10^** 432.13^** 11.56^** 2.01^** 2.21^** 0.67 0.65 TIL 47.41^** 79.48^** 10.76^** 1.76^** 1.12 0.66 0.70 TID 443.44^** 87.55^** 10.45^** 1.78^** 1.21^* 0.59 0.67 FIL 310.40^** 121.74^** 11.21^** 1.67^** 0.79 0.72 0.71 FID 322.96^** 86.36^** 11.21^** 1.84^** 1.28^* 0.61 0.68 [92]Open in a new tab ^aRPR, SBS, TIL, TID, FIL, and FID stand for rind penetrometer strength, stalk bending strength, third internode length, third internode diameter, fourth internode length, and fourth internode diameter, respectively ^*Significant at P < 0.05 ^**Significant at P < 0.01 The results of the correlation analysis between the six traits of stalk strength at two densities for the maize inbred lines are shown in Fig. [93]1. In the correlation analysis, the consistency of all trait correlations between the two densities highly coincided with the results of GWAS. In addition, there was a strongly significant positive correlation between traits between SBS and RPR, SBS and TID as well as SBS and FID. Fig. 1. [94]Fig. 1 [95]Open in a new tab Correlation analysis of lodging resistance-related traits under two plant densities in the association mapping panel. A and B stand for low plant density and high plant density, respectively. * Significant at P < 0.05. ** Significant at P < 0.01 GWAS for stalk lodging resistance related-traits For RPR, a total of 29 significant SNPs were detected and located on chromosomes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 at all environments, which explained 11.10-16.07% of the phenotypic variation. For SBS, a total of 32 SNPs were detected across all environments, which explained phenotypic variation ranging from 9.29-17.69%. For other lodging resistance traits, the number of SNPs detected for TIL, TID, FIL and FID was 36, 53, 31 and 47, respectively, and accounted for phenotypic variation ranging from 12.31-20.72%, 11.23-18.50%, 13.96-23.59%, and 10.92%-17.44%, respectively (Table S[96]1). In total, 33 SNPs detected of different traits under same environment and density and explained phenotypic variation ranging from 11.23% to 20.70% (Table [97]3). Moreover, 2 significant SNPs for TIL were commonly detected across different environments, among which, Chr1_289271328 were identified in 2015BD, 2016BD and 2016SJZ at under high density and Chr2_54407952 were identified in 2016SJZ under low density and high density, with explanation of phenotypic variation range from is 14.97% to 18.14%. Moreover, one SNP, Chr2_233691764, was collocated for SBS, TID and FID on chromosomes 2 (Table [98]3). Table 3. Important SNPs detected of different traits under same environment and density Environment Density^a Traits SNP Chr Position (bp) ^b P-value Allele bin PVE (%) 2015BD L SBS Chr2_233691764 2 233,691,764 1.23E-05 C/G 2.09 13.55 TID Chr2_233691764 2 233,691,764 2.10E-05 C/G 2.09 16.43 FID Chr2_233691764 2 233,691,764 5.34E-05 C/G 2.09 14.90 TID Chr2_101115591 2 101,115,591 5.37E-05 A/G 2.05 15.25 RPR Chr6_113876033 6 113,876,033 4.13E-05 G/T 6.04 11.98 TID Chr6_129298262 6 129,298,262 4.52E-05 C/T 6.05 15.80 TID Chr6_129298294 6 129,298,294 4.67E-05 A/C 6.05 15.86 FID Chr6_129298262 6 129,298,262 2.86E-05 C/T 6.05 15.55 FID Chr6_129298294 6 129,298,294 3.58E-05 A/C 6.05 15.57 H TIL Chr1_289271328 1 289,271,328 1.58E-05 C/T 1.11 18.14 TID Chr2_101115591 2 101,115,591 3.06E-05 A/G 2.05 16.94 TIL Chr2_157483756 2 157,483,756 5.14E-05 C/T 2.06 17.00 FIL Chr2_157483756 2 157,483,756 7.13E-06 C/T 2.06 20.70 TID Chr2_11053123 2 11,053,123 9.32E-05 A/G 2.02 15.54 FID Chr2_11053123 2 11,053,123 9.69E-05 A/G 2.02 14.53 RPR Chr6_113876033 6 113,876,033 4.24E-05 G/T 6.04 11.84 TIL Chr9_26826507 9 26,826,507 5.79E-06 C/T 9.03 19.48 FIL Chr9_26826507 9 26,826,507 4.94E-05 C/T 9.03 18.65 2015SJZ L TID Chr1_159420156 1 159,420,156 3.03E-05 C/T 1.05 15.68 FID Chr1_159420166 1 159,420,166 4.18E-05 C/T 1.05 16.59 H TID Chr1_251713297 1 251,713,297 3.36E-05 G/T 1.09 17.43 FID Chr1_251713297 1 251,713,297 9.44E-05 G/T 1.09 15.62 TID Chr2_209021682 2 209,021,682 4.15E-05 C/T 2.08 17.47 FID Chr2_209021682 2 209,021,682 9.88E-05 C/T 2.08 15.83 TID Chr2_4671519 2 4,671,519 9.11E-05 C/T 2.02 16.75 FID Chr2_4671519 2 4,671,519 3.25E-05 C/T 2.02 17.32 TID Chr4_79001631 4 79,001,631 5.25E-05 G/T 4.05 17.53 FID Chr4_79001631 4 79,001,631 7.59E-05 G/T 4.05 16.45 2016BD L TID Chr1_256791485 1 256,791,485 4.71E-05 A/G 1.09 14.17 FID Chr1_256791485 1 256,791,485 1.82E-05 A/G 1.09 13.16 TID Chr4_175218919 4 175,218,919 7.09E-05 A/G 4.07 14.51 FID Chr4_175218919 4 175,218,919 7.45E-05 A/G 4.07 12.32 FIL Chr6_98760375 6 98,760,375 3.80E-05 C/T 6.03 15.70 H TIL Chr1_289271328 1 289,271,328 1.58E-05 C/T 1.11 18.14 FIL Chr6_98760375 6 98,760,375 4.00E-05 C/T 6.03 16.05 TIL Chr6_147922112 6 147,922,112 1.22E-05 C/T 6.05 17.33 FIL Chr6_147922112 6 147,922,112 6.47E-05 C/T 6.05 15.17 2016SJZ L TID Chr1_148452951 1 148,452,951 2.91E-05 G/T 1.05 15.33 FID Chr1_148452951 1 148,452,951 7.54E-06 G/T 1.05 16.33 TID Chr1_148452943 1 148,452,943 5.60E-05 C/G 1.05 15.29 FID Chr1_148452943 1 148,452,943 4.91E-05 C/G 1.05 14.89 TID Chr2_54407952 2 54,407,952 3.00E-05 C/T 2.05 15.50 TIL Chr2_216932638 2 216,932,638 3.76E-05 A/G 2.08 16.81 FIL Chr2_216932638 2 216,932,638 3.15E-05 A/G 2.08 16.12 TIL Chr2_216932653 2 216,932,653 6.35E-05 A/C 2.08 15.93 FIL Chr2_216932653 2 216,932,653 2.51E-05 A/C 2.08 16.09 TID Chr2_45966977 2 45,966,977 4.37E-05 C/G 2.04 15.39 FID Chr2_45966977 2 45,966,977 4.88E-05 C/G 2.04 14.68 TID Chr3_191764915 3 191,764,915 8.68E-06 A/C 3.07 16.38 FID Chr3_191764915 3 191,764,915 1.06E-05 A/C 3.07 15.49 TID Chr4_235448449 4 235,448,449 7.48E-05 A/G 4.09 14.25 FID Chr4_235448449 4 235,448,449 4.44E-05 A/G 4.09 14.24 H TIL Chr1_289271328 1 289,271,328 7.74E-05 C/T 1.11 16.66 TID Chr2_54407952 2 54,407,952 2.19E-06 C/T 2.04 16.10 FID Chr2_54407952 2 54,407,952 1.57E-06 C/T 2.04 14.97 TID Chr2_54407976 2 54,407,976 4.52E-06 C/T 2.04 15.48 FID Chr2_54407976 2 54,407,976 5.07E-06 C/T 2.04 14.76 TID Chr2_12921336 2 12,921,336 5.30E-05 A/C 2.02 11.99 FID Chr2_12921336 2 12,921,336 3.41E-05 A/C 2.02 12.37 TID Chr2_12921363 2 12,921,363 9.33E-05 C/T 2.02 11.23 FID Chr2_12921363 2 12,921,363 4.23E-05 C/T 2.02 12.00 TID Chr3_8597909 3 8,597,909 5.23E-05 A/G 3.02 11.91 FID Chr3_8597909 3 8,597,909 4.64E-05 A/G 3.02 11.93 TIL Chr5_10438064 5 10,438,064 8.53E-05 C/T 5.02 16.56 FIL Chr5_10438064 5 10,438,064 7.21E-05 C/T 5.02 14.30 TID Chr5_125087688 5 125,087,688 4.98E-05 A/G 5.04 12.19 FID Chr5_125087688 5 125,087,688 4.32E-05 A/G 5.04 11.67 [99]Open in a new tab To minimize the effect of environmental variation, the BLUP values were used to examine associations. In total, we identified the number of SNP for each trait by BLUP data, 6 for RPR, 3 for SBS, 10 for TIL, 8 for TID, 8 for FIL, 7 for FID at low plant density and 5 for RPR, 9 for SBS, 7 for TIL, 5 for TID, 7 for FIL, 6 for FID at high plant density (Fig. [100]2 and Table S[101]2). The percentage of phenotypic variation explained by the identified SNPs (R^2) for six traits ranged from 13.30 to 21.13% and from 10.10 to 21.01% at low and high plant densities, respectively (Table S[102]2). The Manhattan plots and Quantile–quantile (Q-Q) plots between the six related traits of stalk strength at two densities are shown in Figs. [103]3 and [104]4. In addition, 14 important SNPs was detected of different traits at same density by BLUP value, which were located on chromosomes 2, 3, 4, 5, 8, 9 and 10 (Table [105]4). Fig. 2. [106]Fig. 2 [107]Open in a new tab Stable SNPs were repeatedly detected in the two planting densities and the BLUP model, which were associated with six stalk lodging resistance-related traits. The significance threshold is –log10 (P-value) = 4.0. LD represent low plant density, HD represent high plant density, respectively. Purple represents third internodes length, Red represents fourth internode length, Blue represents third internode diameter, Orange represents fourth internode diameter, Yellow represents rind penetrometer resistance and Green represents stalk buckling strength, respectively Fig. 3. Fig. 3 [108]Open in a new tab Manhattan plots and QQ plots for the six traits at the low plant density. A Rind penetrometer strength. B Stalk bending strength. C Third internode length. D Third internode diameter. E Fourth internode length. F Fourth internode diameter Fig. 4. Fig. 4 [109]Open in a new tab Manhattan plots and QQ plots for the six traits at the high plant density. A Rind penetrometer strength. B Stalk bending strength. C Third internode length. D Third internode diameter. E Fourth internode length. F Fourth internode diameter Table 4. Important SNPs detected of different traits by BLUP value Number SNP Traits Density ^a Chr Position(bp)^b Allele bin P-value PVE (%) 1 Chr4_66017316 RPR L 4 66,017,316 C/T 4.05 3.52E-05 16.10% RPR H 4 66,017,316 C/T 4.05 8.47E-05 16.90% 2 Chr2_231360274 TIL L 2 231,360,274 C/G 2.09 5.95E-05 19.56% FIL L 2 231,360,274 C/G 2.09 2.27E-05 20.46% 3 Chr3_99647159 TID H 3 99,647,159 A/G 3.04 4.86E-05 16.51% FID H 3 99,647,159 A/G 3.04 3.19E-05 15.67% 4 Chr4_16211307 TID L 4 16,211,307 A/G 4.03 6.74E-05 18.06% FID L 4 16,211,307 A/G 4.03 2.05E-05 18.00% TID H 4 16,211,307 A/G 4.03 2.51E-05 17.60% FID H 4 16,211,307 A/G 4.03 1.45E-05 16.94% 5 Chr4_199957809 TIL L 4 199,957,809 A/T 4.08 6.93E-05 19.26% FIL L 4 199,957,809 A/T 4.08 6.35E-05 18.22% 6 Chr4_203233149 TID L 4 203,233,149 A/C 4.08 3.66E-05 18.41% FID L 4 203,233,149 A/C 4.08 3.39E-05 17.16% TID H 4 203,233,149 A/C 4.08 3.56E-05 16.97% FID H 4 203,233,149 A/C 4.08 2.03E-05 16.31% 7 Chr4_236385528 TID L 4 236,385,528 G/T 4.09 2.25E-05 19.25% FID L 4 236,385,528 G/T 4.09 1.29E-05 18.54% FID H 4 236,385,528 G/T 4.09 5.61E-05 15.46% 8 Chr5_48630086 TIL H 5 48,630,086 C/T 5.03 4.05E-05 20.21% FIL H 5 48,630,086 C/T 5.03 6.16E-05 18.07% 9 Chr5_48630116 TIL H 5 48,630,116 A/G 5.03 4.05E-05 20.21% FIL H 5 48,630,116 A/G 5.03 6.16E-05 18.07% 10 Chr5_174286151 TIL H 5 174,286,151 C/T 5.05 1.64E-05 20.70% FIL H 5 174,286,151 C/T 5.05 7.84E-05 17.30% 11 Chr8_67356036 TID L 8 67,356,036 C/T 8.03 2.08E-05 19.89% FID L 8 67,356,036 C/T 8.03 6.39E-05 17.34% 12 Chr8_130686461 TID L 8 130,686,461 C/T 8.05 1.11E-05 20.19% FID L 8 130,686,461 C/T 8.05 1.46E-05 18.59% TID H 8 130,686,461 C/T 8.05 1.17E-05 18.64% FID H 8 130,686,461 C/T 8.05 6.09E-05 15.52% 13 Chr9_133921410 TIL H 9 133,921,410 C/G 9.05 4.81E-05 21.01% FIL H 9 133,921,410 C/G 9.05 5.93E-05 19.14% 14 Chr10_148095509 FIL L 10 148,095,509 A/T 10.07 2.66E-05 19.75% TIL H 10 148,095,509 A/T 10.07 9.83E-05 20.05% [110]Open in a new tab ^aL means low plant density, H means high plant density ^bphysical position of the SNP loci according to B73 RefGen_v2 Candidate genes associated with significant SNPs The physical locations of the SNPs were recorded using the B73 RefGen_v2 ([111]www.maizesequence.org) based on the LD decay distance. A total of 346 candidate genes with gene descriptions were found (Table S[112]3). The number of candidate genes involved in the six stalk lodging resistance related-traits of RPR, SBS, TIL, TID, FIL, and FID were 55, 78, 117, 37, 51, and eight, respectively. From the GO analysis results of the candidate genes in biological processes are mainly concentrated in the metabolic and cellular process, those influencing cellular component are mainly found in the intracellular and cellular anatomical entity, and those influencing molecular functions are mainly found in catalytic activity and binding (Fig. [113]5). As for the KEGG analysis of the candidate genes, a total of 13 pathways were identified (Fig. [114]6). These pathways included the carbon metabolism, ubiquitin mediated proteolysis, starch and sucrose metabolism, beta-alanine metabolism, pyrimidine metabolism, etc., which could be related to the stalk lodging. Among them, the pathway with the largest number of genes is the metabolic pathways, which have 36 candidate genes. Furthermore, we identified seven candidate genes to be associated with stalk lodging resistance (Table [115]5). Annotation information suggested that these candidate genes may control multiple traits during maize growth and development. Fig. 5. [116]Fig. 5 [117]Open in a new tab GO-second class of candidate gene Fig. 6. [118]Fig. 6 [119]Open in a new tab Analysis of KEGG pathway based on candidate genes (The figure was created by R version 3.6.1 based on KEGG pathway database www. kegg. jp/ kegg/ kegg1. html) Table 5. Putative candidate gene of stalk lodging resistance-related traits Trait SNP Bin Candidate gene Gene ID RefGen_v2 Annotated Gene description RPR Chr6_158343036 6.06 GRMZM2G074792 103,630,593 probable xyloglucan glycosyltransferase SBS Chr1_272576164 1.1 GRMZM2G300412 109,942,298 UDP-glucuronic acid decarboxylase SBS Chr7_160255239, Chr7_160255241 7.04 GRMZM2G072526 100,282,931 glucan endo-1,3-beta-glucosidase TIL Chr5_15958677 5.03 GRMZM2G111344 100,381,816 UDP-glycosyltransferase TIL Chr10_139852648 10.06 GRMZM2G007899 541,747 MYB transcription factor GRMZM2G311059 FIL Chr2_233691559 2.09 GRMZM2G021051 100,217,010 gibberellin 20-oxidase FID Chr3_212705423 3.08 GRMZM2G408462 103,651,407 WRKY transcription factor [120]Open in a new tab Discussion Phenotypic variation, heritability, and correlations of traits In general, obtaining an accurate measurement of phenotypic traits is essential to obtain reliable association results. The six traits investigated in this study exhibited large phenotypic variations with a normal distribution. A previous study showed that relatively high heritability will determine the power of QTL detection [[121]33]. Our genetic analysis shows that the heritability of RPR and SBS ranged from 0.61 to 0.80. It was much higher than the range of 0.08–0.34 in a nested association population of maize [[122]1]. The relatively high heritability in this study shows the predominant role of genetic factors for these traits. There were significant correlations between each pair of stalk lodging resistance-related traits in this study, for instance: between RPR and SBS, which is consistent with previous results [[123]13, [124]17]. Our study showed that the stalk strength traits decreased gradually with increasing density, which was consistent with previous findings [[125]11, [126]34]. In the association mapping panel, a significant correlation was detected between SBS, TID, and FID. By contrast, the correlation between SBS, TIL and FIL was significantly negative, indicating that stalk strength traits are negatively associated with internode length and width at the population level. The above results suggest that some genetic factors were shared among these stalk lodging resistance-related traits. Mapping analysis Compared with traditional QTL mapping, GWAS covers a wide range of genetic diversity and more allelic polymorphisms, which could exploit the short linkage disequilibrium distance and help to pinpoint the functional genes of target traits using high-density molecular markers. Hu et al. [[127]8] detected ten QTLs for RPR and three QTLs for Internode diameter (InD) by applying the RIL population. In this study, we used GWAS to identify some RPR-related SNPs, among which Chr7_163048364 (bin7.04) and Chr8_88680106 (bin8.03) were located in the chromosomal region with Hu et al. [[128]8]. In addition, Chr4_203233149 (bin4.08) and Chr8_67356036 (bin8.03) for TID and FID identified by the GWAS analysis locates exactly in the interval of the InD QTLs detected by Hu et al. [[129]8]. Liu et al. [[130]11] identified pleiotropic QTL, pQTL6-2, was association with RPR, whose confidence interval encompassed 16 QTLs, its genomic region is coincided with the physical position Chr6_158343036 (158 Mb) in this study. In addition, the SNP Chr1_272576164 (272 Mb) was detected association with SBS in this study also have same physical position with Liu et al. study. The remaining SNPs in this study were first reported to be associated with lodging resistance-related traits in maize. Co-localization of SNPs for stalk lodging resistance traits The SNP repeatedly detected in multiple environments is generally considered a stable SNP. Stably expressed SNPs detected in this study, five co-localized SNPs (Chr4_66017316, Chr4_16211307, Chr4_203233149, Chr4_236385528 and Chr8_130686461) were simultaneously identified under two plant densities. These stable SNPs were insensitive to the external environment and were hence considered to be important loci for the improvement of stalk lodging traits, as such, they can provide references for further gene cloning. Meanwhile, some specific SNPs were