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 . 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. Non-environmentally specific QTLs are particularly useful in marker-assisted selection . 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 [1, 3]. Maize lodging can be divided into three types: root lodging, stem bending, and stem breaking . 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 [5, 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 [7, 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 crops [9, 10]. Common methods to quantify the stalk mechanical strength include rind penetration, bending, breaking, and vertical crushing [4, 7, 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 [12–14]. Compared with RPR, SBS is more closely correlated to stalk lodging under natural conditions, as stalk lodging happens in case of over-bending . 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 [6, 8, 13, 16]. Furthermore, Liu et al.  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 [6, 8, 11, 17, 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 .
Quantitative trait loci (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. A linkage map with 129 SSRs markers was constructed by Hu et al. , 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.  identified seven QTLs associated with RPR in two maize recombinant inbred line (RIL) populations using 3072 single nucleotide polymorphisms (SNP) markers. Zhang et al.  44 significant QTLs were identified for SD, SBS, and RPR using the IBM Syn10 DH population in three environments QTLs.
The efficiency and accuracy of QTL mapping depend largely on the gene marker density, the variation range of phenotypes within the population, as well as the population size and type . 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 [21–23], 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 [13, 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 [25–28]. 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 [29–32].
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 of the stalk for the third internodes length (TIL), fourth internode length (FIL), third internode diameter (TID), and the fourth internode diameter (FID) 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.