The main goal of the current study was to unravel the genetic architecture of popping ability in nuña bean. Thus, popping traits related to changes in the physical structure of seeds have been analysed on the basis of their similarity to popcorn, whose cotyledons also expand when dry grains are heated. Genetic analysis performed indicated that popping ability traits show a polygenic inheritance, making this the first work to report the genetic control of these traits in common bean. Transgressive segregation was observed for popping traits, suggesting that combinations of alleles from both parents have effects in the same direction; in fact, not only PHA1037 but also PMB0225 bear alleles with a positive effect on popping ability, a finding backed up by QTL analyses. Since transgressive segregation relies on additive genetic variation, the extreme phenotypes can be maintained and fixed through artificial selection, providing the potential for improvement of popping ability. Furthermore, the analysis of variance showed that although the genotype x environment interaction affects popping ability, this effect is fairly uniform across all genotypes, and it does not seriously compromise genotypic main effects, making progress from selection feasible.
A comprehensive QTL analysis was performed to detect single-locus QTLs, epistatic QTLs and their environment interactions on a newly created genetic linkage map. This map was constructed for an Andean intra-gene pool cross involving PMB0225 (dry bean) and PHA1037 (popbean) parents. Despite the morphological diversity observed in the Andean intra-gene pool, the low genetic polymorphism existing in this common bean germplasm hinders the development of genetic linkage maps [31, 33, 51, 52]. Our results confirmed a low polymorphism between the Andean parents, thus the overall polymorphism rate detected was 8.3%. Likewise, Blair et al.  screened a total of 700 SSR markers on the Andean parents G21242 and G21078, but only 74 mappable markers were found in that survey resulting in a polymorphism rate of 10.6%, comparable to the level of polymorphism here reported (i.e. 10.2% for SSR markers). However, Cichy et al.  found a moderate SSR polymorphism of 30% between the Andean parents used to generate a G19833 x AND696 RIL mapping population.
Interestingly, the genetic map described in this work shares 55 SSR markers with previously published common bean maps [26, 31–33, 45–50]. In fact, linkage associations have been found in terms of SSR marker mapping in the present map and previous maps, while the collinear order of the commonly mapped SSR loci has been generally observed although some inversions affecting SSR markers located close to one another have been detected. Since these loci were distributed throughout all LGs, they would permit the alignment of homologous LGs between maps and facilitate marker transfer across populations as well as between related species. Hence, these shared markers could be used as anchor points for map merging and syntenic analysis such as Galeano et al.  have recently reported for the consensus Mesoamerican intra-gene pool map.
The genetic linkage map developed herein includes 193 loci (85 AFLP, 95 SSR, and 13 SNP markers) across 12 LGs that cover a genetic distance of 822.1 cM, with an average of 4.3 cM per marker. Prior to this work, two Andean maps have been described for QTL analysis; the map depicted by Cichy et al.  included 167 loci that spanned a total map length of 1105 cM with an average marker density of 6.6 cM per locus. On the other hand, the map constructed by Blair et al.  contained 118 loci with a total map length of 726.0 cM and a mean marker density of 6.2 cM per locus. Therefore, compared to previous Andean maps [31, 33], the genetic map here developed shows a suitable marker density and genome coverage, which has permitted the first identification of popping ability QTLs.
Three closely related popping traits such as PDI, EC, and PUS have been analysed and the reliability of the QTLs associated to these traits has been enhanced by using several software programs, which decreased the risk of detecting false positive and negative QTLs [53–55]. Therefore, single and multi-environment QTL analyses were performed to dissect the genetic architecture of popping ability in nuña bean. In summary, a total of nineteen single-locus QTLs were identified by MapQTL and QTLNetwork. Eleven of the fourteen QTLs identified by QTLNetwork were also detected by MapQTL; thus, the two independent approaches converged on the identification of common single-locus QTLs for PDI (PDI3PP, PDI5PP, PDI6PP, and PDI7PP), EC (EC3PP, EC5PP, and EC7PP), and PUS (PUS3PP, PUS5PP, PUS6PP, and PUS7PP). The percentage of phenotypic variation explained by the single-locus QTLs identified by MapQTL for popping traits was comparatively higher than that of the QTLNetwork. The results of multi-environment analyses showed that genetic main effects were sometimes subject to environmental modification; this could explain why we obtained a lower phenotypic variance using QTLNetwork software. Even so, for multi-environment analyses, the percentage of phenotypic variance attributable to genetic effects was as expected for a complex trait, which is governed by several small effect QTLs/genes located in different genomic regions, and where the environment interactions play an important role. Therefore, the four common single-locus QTLs detected for PDI and PUS together explained 22.2 and 21.8% of the phenotypic variance, respectively. Regarding EC, the three common QTLs explained 11.7% of the phenotypic variance in the RIL population. In addition, it was interesting to find that the common QTLs (detected with both software programs) not only were consistent over environments, but they also co-localized with QTLs for the analysed popping traits.
Overall, significant positive correlations between PDI and EC and negative correlations among PUS, and PDI and EC, together with the detection of co-localized QTLs for PDI, EC, and PUS on LGs 3, 5, 6, and 7, suggested that QTLs for popping ability are not evenly dispersed throughout the genome but rather are clustered in several genomic regions. The QTLs sign values of additive effects corresponded to the significant genotypic correlations observed among the three popping traits. Thus, the co-localized QTLs located on LGs 3, 5 and 6 showed positive (alleles from PHA1037) and negative (alleles from PMB0225) values of additive effects for PDI and EC, and PUS, respectively. Meanwhile, the opposite sign values of additive effects were found for the co-localized QTLs located on LG 7, which indicated that PMB0225 also contributes positively to popping ability. To date, research into popping ability has focused on popcorn. Thus, Babu et al.  detected four QTLs for popping expansion volume, five for flake volume, and five for percentage of unpopped kernels, and revealed QTLs in overlapping or mostly adjoining regions in the same chromosomes affecting two or three popping traits. Likewise, Li et al.  evaluated three important traits for popcorn (i.e. popping volume, flake size, and popping rate), and six chromosome regions were found to control two or three popping traits simultaneously. Hence, as in nuña bean, the detection of co-localized QTLs for popping traits suggested that either pleiotropic QTLs controlled several popping traits, or tightly linked QTLs for different traits are present together in the same genomic regions. The issue of pleiotropy versus tight linkage of QTLs may be resolved in the future through fine mapping of the target genomic regions.
Epistatic effects are often involved in complex traits, but they are difficult to confirm because of their usually small effects and environmental interactions. Genetic models for QTL mapping assuming no epistasis could lead to biased estimation of QTL parameters, and subsequently result in considerable loss of response in MAS. In popcorn, Li et al.  carried out a preliminary epistatic analysis and detected thirteen pairs of digenic interactions for popping ability. In the present work, several epistatic interactions were found involving all of the evaluated popping traits. A total of ten E-QTLs, involved in six epistatic interactions, were detected, and only one epistatic interaction for PUS showed significant E-QE interaction effect. Although the phenotypic variation explained by each epistatic interaction was found to be small, it is interesting to note that the genomic regions located on LGs 3, 5, 6 and 7 not only harbor QTLs that have individual genetic effects, but are also involved in epistatic interactions. Therefore, QTL analysis revealed that popping ability of nuña bean is controlled by several QTLs, which have only individual additive effects, or may also be involved in epistatic or environmental interactions, indicating that popping is inherited as a polygenic trait, and that epistasis could play a key role.
Nowadays, popping of common bean is considered an interesting agronomic trait, since it allows greater diversification of this crop as well as the commercialization of nuña bean as a new snack product. In popcorn, selection for increased expansion coefficient has been successfully achieved given its high heritability value [20, 21]. Similarly, Vorwald and Nienhuis  estimated that the narrow sense heritability values of fully expanded seeds after popping (popping percentage) and expansion coefficient in nuña bean were relatively high, 0.87 ± 0.07 and 0.74 ± 0.09, respectively. The broad sense heritability values calculated in the present work were moderate, suggesting that genetic gain could be obtained for popping ability in this legume species. The introgression of popping and the development of new day-length insensitive popbean cultivars would require genetic tools which facilitate efficient genotyping selection. Conventional phenotype selection methods for popping traits are laborious and time-consuming; consequently, MAS provides an efficient and cost-effective alternative that accelerates the selection of interesting genotypes. However, MAS approaches have been difficult to apply in the case of complex traits such as popping ability, because individual QTLs have small genetic effects which in many cases are also environmentally modulated. Consequently, the identification of potential candidate QTLs for MAS is crucial. Based on the results obtained in our study, the co-localized QTLs located on LGs 3, 5, 6, and 7 are good candidates for MAS, since they showed stability across significantly correlated traits, while also sharing QTLs for more than one trait, and they could be manipulated simultaneously in breeding programs. Breeding of nuña cultivars would require adapting them to temperate regions, and for this purpose it is important to improve their insensitivity to photoperiod. The Ppd gene regulates photoperiod sensitivity and it is located on LG 1 , while popping QTLs are located on LGs 3, 5, 6, and 7. Therefore, the use of QTL marker assisted selection would facilitate the introgression of photoperiod insensitivity without loss of popping ability. QTL pyramiding approach would also permit the combination of QTL alleles with positive effects for popping ability on a day-length insensitive genotype through molecular breeding, thus overcoming the main drawback for the production and commercialization of nuña beans in temperate regions. In this research, some RILs showed popping expansion ability and flowered independently of photoperiod conditions. These lines constitute an interesting breeding goal, and they will hopefully allow researchers to isolate the genes and to understand the molecular and physiological mechanisms underlying agronomic traits which are relevant for the genetic improvement of nuña beans.