Hexaploid triticale (X Triticosecale Wittmack) is a hybrid of tetraploid wheat and diploid rye with genome composition AA, BB and RR. It is cultivated in Poland mainly as a fodder cereal, and its area of cultivation doubled during the last 10 years [1]. Triticale is frequently grown on acid soils in the presence of excessive toxic aluminum ions that inhibit root growth and seed yields [2]. The development of tolerant cultivars, including triticale, is an important breeding objective.

Tolerant plants can be identified by physiological tests [3–9]. This robust approach is inexpensive and generally provides a reliable measure of tolerance [4]. It relies on morphological traits that may not be directly related to the expression of Al-tolerant genes in response to environmental factors. More direct methods based on DNA markers [10–13] and saturated genetic maps or, preferentially, consensus maps of the species are needed to overcome these issues.

One of the most promising marker platforms for such studies is Diversity Arrays Technology (DArT) [14], which enables the identification of thousands of highly reliable markers in a single run [15–17]. DArT performs well in many species in which several markers can be assigned to individual chromosomes [15, 18]. This system is also available for triticale and the first genetic map saturated with DArTs was recently published [19]. Moreover, AFLPs and SSR markers can be used for such studies [20–22].

There are at least two approaches to the identification of markers useful for marker-assisted selection (MAS). The first one is based on biparental mapping populations and it allows the identification of QTLs and linked markers [23, 24], while the second method involves the study of "non-Mendelian" populations and is called association mapping [25, 26]. The "Mendelian" approach enables only the identification of loci segregating in tested samples of a given cross. Thus, many different mapping populations may be needed to represent the allelic diversity of the genes contributing to the character under study in the tested species. Moreover, alleles present in some crosses may not always be expressed with major effects in other crosses within the species or may not be present there at all [27, 28]. In contrast, the association mapping approach allows for the identification of many loci and alleles among all the individuals of the population [26]. This type of analysis was done in maize, lettuce, barley, wheat, oat and soybean [29–36]. However, in the absence of genetic maps, markers obtained through association mapping cannot be assigned to the respective chromosomes.

Additional sets of markers useful for MAS could be derived from markers representing genomic regions under putative selection pressure [37]. Genomic regions under positive selection pressure may be bound to adaptation traits in breeding materials [38, 39]. Such markers would be of special value if mapped in the region of known QTLs.

The initial attempts to identify the chromosomal location of the Al-tolerant QTLs were performed on the wheat-triticale substitution lines [40–42]. The rye chromosomes number 3, 4, and 6 seem to contain major Al tolerance-related genes [40–42]. Aluminum tolerance also appeared to be controlled by certain wheat genes, but their location on chromosomes in triticale is unknown [43]. Little is known about the genes coding for this trait in triticale [41]. Nevertheless, studies performed in several octoploid triticale genotypes demonstrated that Al tolerance was associated with a high level of citrate exudation from roots [43], which is mediated by a transporter encoded by a Multidrug and Toxin Efflux (MATE) family gene mapped to 4BL in wheat [11]. In addition, studies in wheat suggested that Aluminum-Activated Malate Transporter (ALMT) family genes located on 4DL may participate in the trait [44]. A gene belonging to the same family was also identified in rye on the 7RS chromosome [45]. DNA markers based on the sequences of such genes may be used by breeders for MAS in triticale, although the causal link between these genes and Al resistance remains to be established.

The present study aimed to identify molecular markers associated with Al tolerance among plants randomly selected from advanced triticale breeding materials. The association mapping approach was applied, using General (GLM) and Multiple Linear (MLM) Models, as well as Statistical Machine Learning (SML). The chromosomal location of the markers was determined based on available genetic maps of triticale and rye.

Several factors need to be controlled when performing association mapping. First, the plant material must be properly selected and properly phenotyped. Then, after sample profiling with a carefully selected molecular marker system, redundant data and missing markers should be preferentially eliminated, genetic structure should be evaluated and statistical analyses can then be performed.

The plant material itself is possibly the most important factor [46, 47]. For association studies, the most diverse or elite inbred lines [32, 48, 49], cultivars [33, 50, 51], and land races in the case of rice [52, 53] should be used. Prior studies were based on 57 [54] to 577 [52] plants with the most common number ranging from 70 to 150 plants [26]. In this context, our mapping population consisting of 232 advanced breeding forms of triticale was quite large and above the lower limits used by others. Considering that triticale is predominantly a self-pollinated species and some of the forms that originated from double haploids were developed via anther culture, the plant material used is appropriate for association mapping studies with dominant marker platforms [14, 55].

Another factor of importance for association studies is the careful phenotyping of plant materials to eliminate false associations between trait and markers [56]. In our experiments, we used a well described and widely explored test for Al tolerance [7]. Although the test is based on root regrowth, which is an indirect approach to the identification of tolerant plants, it is usually assumed to correlate well with the trait [57]. Nevertheless, it is obvious that Al tolerance is multigenic and a physiological test is not necessarily the best choice for screening plant material [58]. Another important issue is the use of relative rather than direct measures of a trait to enable comparison between different experiments [59]. The ratio between the root regrowth of a given plant and the longest root regrowth measured within the analyzed population is a possible measure. The ratios underwent arcsine transformation [59] and aluminum tolerance values were rescaled to new values to fulfill the statistical requirements of quantitative traits.

The DArT platform proved to be useful in association mapping performed on wheat [29, 33], barley [34] and oat [31], and was a reasonable choice for our studies on advanced breeding forms of triticale, which identified several markers assigned to different chromosomes. However, it should be stressed that even using DArT markers it is practically impossible to avoid missing data that may appear at a level lower than 5% in the case of DArTs. Moreover, due to the high sensitivity of the approach, numerous rare markers with low frequencies were identified. Because such markers may influence linkage disequilibrium, they had to be removed from the analysis [60, 61]. Similarly, identical markers or tightly linked ones (redundancy) may reduce the sensitivity of association mapping. Our approach nearly entirely eliminated or significantly reduced missing markers without involving mclust R-CRAN packages that are insensitive to such data [61]. Elimination of redundancy did not affect the information on markers that could be alternatives for the associated ones. Nevertheless, by using this approach, the advanced breeding forms used in each chromosomal set were reduced due to the merging of identical forms following the removal of missing and merging redundant markers. In some cases, the number of forms used dropped from 232 to 141. However, the chromosomal sets remained sufficiently large and exceeded the lower limits used by other studies [54].

The presence of population structure may result in spurious associations that could lead to numerous false positives [55, 56]. To avoid such a problem, we used the agglomeration analysis implemented in the PAST software [62] and Bayesian statistics implemented in the Structure program [56]. Both methods indicated the presence of data structuring without separating winter and spring forms. Interestingly, while agglomeration and Bayesian approaches were capable of identifying data structuring, only the latter approach grouped individuals according to their known Al tolerance and was thus selected for routine use. Although calculations performed in the Structure software are time consuming due to the requirement for many burning periods, iterations and repetitions for each K value tested, they deliver information on the average genetic structure of the chromosomal sets required for association mapping in TASSEL [63], which is the most widely used software for association studies in plants [12, 26, 30, 35]. It was used in similar studies on wheat and allowed for the identification of markers associated with traits such as response to stem rust, leaf rust, yellow rust, powdery mildew, grain field, heading date, flowering time, etc. [29, 33].

Association mapping using both the GLM and MLM methods resulted in congruent results. However, the MLM approach usually provided higher r ² values and a stronger association for the same markers than GLM. This confirms that the involvement of data structuring and relationships among analyzed forms improves the resolution of association mapping. An alternative approach based on Statistical Machine Learning (SML) to identify associated markers [64] was also applied. This approach has numerous advantages over the Bayesian method and it does not require time consuming analyses of population structure, as calculations are performed relatively fast [64]. It allowed identification of Al tolerance-associated markers that mostly, but not always, corresponded with those obtained in TASSEL. The discrepancies were possibly due to the fact that the whole data set rather than the chromosomal sets was used for calculations. Another possible explanation is the effect of structure on the results of association analysis. It will be interesting to compare the results with those of an SML algorithm that corrects for "structure", as this version has been developed recently (DArT PL, unpublished). In general, the smaller number of associated markers detected by SML is consistent with the more conservative (and likely more realistic) performance of this method when compared to several other techniques, as reported by Bedo et al. [64].

Based on known assignments of DArTs, Al-tolerant associated markers were localized to 3R, 4R, 6R and 7R chromosomes independently of the mapping approach used. No association was detected on the wheat genome. Our results are in agreement with several prior reports [40–42, 65], indicating that Al-tolerant genes crucial for the expression of the trait in triticale are located on rye chromosomes rather than on wheat chromosomes. Considering that the strongest associations were in the 3R and 7R chromosomes, our results are congruent with those presented earlier [41, 65, 66] and our own results on several biparential triticale mapping populations (in preparation). Keeping in mind that most of our Al tolerance-associated markers have redundant counterparts, we succeeded in identifying as many as 52 candidate markers (46 via mapping in TASSEL and 14 following the SML approach, including eight markers identified via both methods).

Although association mapping may provide valuable information on associated markers and comparison with known DArTs may suggest their chromosomal assignments, their precise location is difficult to determine if saturated consensus genetic maps are not available. Unfortunately, such maps do not exist in triticale. However, a recently published report generated triticale and rye genetic maps using DArT markers [15, 19]. Although rearrangements of rye chromosomes in the triticale genome in comparison to the rye genome may occur [67], changes in the distance between markers within several cM should not be a frequent occurrence. Thus, both maps could be used to verify whether associated markers assigned to the same chromosome fall within the same region or not. Such information proved to be valuable in estimating the putative location and the number of QTLs at least in the 4R and 6R chromosomes, where markers associated with the trait were located within a very short distance, which indicated the presence of two QTLs. Although few markers associated with Al tolerance were mapped to 3R, they were highly associated with the trait, indicating that a single QTL is present on the 3R chromosome. Similarly, at least two QTLs of different significance are present on 4R. The data for the 6R chromosome suggest that there might be as many as three QTLs, but only one seems to be highly significant. Finally, it is suggested that a single QTL represented by highly associated markers is also located on 7R, which is in agreement with previously published reports. Prior studies reported one QTL located on 3RS [41, 42], 4RL [40, 68] and 7RS [65]. Gallego and Benito [69] identified two isozyme loci linked to the rye Alt1 gene on chromosome 6R. This gene is probably the same as that located on chromosome arm 6RS (Alt1) by Anioł and Gustafson [40]. These results reported in the literature suggest that our QTLs may be located on the same arms of the chromosomes mentioned above. However, this localization is difficult to verify because prior studies used wheat-rye addition lines.

Genome regions under selection pressure for a given trait are likely to be involved in the expression of the trait [37]. Positive selection is considered to be responsible for adaptive traits [39]. The forms used in this study were selected for aluminum tolerance via many generative cycles; therefore, the identification of genomic regions under selection pressure (via markers called outliers), could be the method of choice to identify linked markers. Unfortunately, outliers reflecting genomic regions under positive selection located in the vicinity of markers highly associated with Al tolerance (ca 9 cM apart) were only present in the 4R linkage group. Moreover, some outliers under balancing selection were also within the same genomic region. Interestingly, all outliers indirectly mapped to the fourth chromosome covered the same region, extending over approximately 20 cM. In addition, the possibility that a single marker under positive selection could be close to the group of markers highly associated with the trait on 6R cannot be excluded. However, with the currently available rye and triticale maps (including possible discrepancies in synteny/colinearity between these genomes due to genome rearrangements), such a hypothesis is difficult to test. Similarly, another outlier under positive selection could be located in the proximity of the associated marker on 3R (ca 50 cM apart), while the other one did not appear to be linked to the second Al-associated marker. Our data confirm that outliers reflecting genomic regions under positive selection may be linked to the trait of interest, at least in the material used in this study. Nevertheless, it is evident that markers identified via analysis of outliers need independent confirmation of their value for MAS purposes.

The DArT approach was used to generate numerous polymorphic markers for association mapping and to support the chromosomal location of the markers. Association mapping using GML, MLM and SML resulted in comparable results, although data obtained by SML differed to some extent from those derived by GLM and MLM. Involvement of genetic maps of rye and triticale allowed the grouping of markers according to their chromosomal positions and the identification of specific genomic regions (possibly QTLs) that could be involved in the expression of the trait. Outliers related to positive selection could be useful as additional candidate markers linked to the trait of interest.