Genomic prediction has greatly improved animal and plant breeding (Hickey et al., 2017) and has the potential to improve genetic gain even in crops with complex genomes (Voss-Fels et al., 2021). In the past, predictions based on linear mixed models used relatedness to borrow information on target phenotypes of relatives. Henderson (1975) derived this relationship from pedigrees via the numerator relationship matrix with the expectation that each parent contributes exactly 50% of its genome to its offspring. With the advance of sequencing technology nowadays, genomic data is used to replace the pedigree relationship with realized relationships calculated from dense marker maps. Furthermore, with the inclusion of genetic markers, information about linkage disequilibrium and cosegregation is available for genomic prediction (Habier et al., 2013). Today, individuals in breeding populations of major crops can be sequenced with high quality at low costs, enabling the identification of millions of genome-wide single nucleotide polymorphism (SNP) markers that can be easily screened in large populations using high-throughput genotyping technologies. Together with phenotype measurements, genome-wide marker profiles can be used to predict breeding values of non-phenotyped individuals (Lande and Thompson, 1990; Bernardo, 1994; Meuwissen et al., 2001; VanRaden, 2008). This can assist breeders in the accurate identification of superior genotypes within their breeding material without the need for additional phenotyping. Moreover, it can facilitate the decision-making process for selecting which genotypes should undergo phenotyping, leading to reduced phenotyping costs and improved accuracy in estimating breeding values. Hence, genomic selection has the potential to considerably increase genetic gain and profit in many crops (Voss-Fels et al., 2021).

There are a variety of statistical methods for genome-based predictions (e.g. VanRaden, 2008; de los Campos et al., 2009; Zhang et al., 2010; Gianola, 2013; Hofheinz and Frisch, 2014; Werner et al., 2018a; Millet et al., 2019), differing in their assumptions of variance components, marker effects or marker modes of action. Examples for genomic prediction models are ridge regression BLUP, GBLUP (Bernardo, 1994; Meuwissen et al., 2001; VanRaden, 2008), Reproducing Kernel Hilbert Space Regression (RKHS) (de los Campos et al., 2009), as well as Bayesian models like Bayesian LASSO (Park and Casella, 2008) or Bayesian ridge regression (Pérez and de los Campos, 2014).

However, biallelic SNPs are sometimes unable to identify all variants and allelic combinations of genes that contribute to a particular trait, since most genes carry multiple sequence polymorphisms. Furthermore, accurate genomic prediction is often obtained based on close relatives (VanRaden, 2008; Hayes et al., 2009) while this accuracy decreases as the validation individuals get more unrelated (Habier et al., 2010; Wolc et al., 2011). This implies that SNPs are not necessarily in LD with causal QTL and the prediction accuracy is at least partly driven by implicitly capturing relationship among individuals. Hence, one strategy to improve predictions is increasing marker density. With the advance of whole genome sequencing technologies, increasingly large and dense marker datasets can today be generated for most major crops (Edwards and Batley, 2010; Yu et al., 2011). However, increasing marker density does not consistently improve prediction accuracies (Solberg et al., 2008; Druet et al., 2014; Hayes et al., 2014; Norman et al., 2018) and often improvements are only observed following pre-selection of markers (van Binsbergen et al., 2015; Ni et al., 2017; Raymond et al., 2018). Furthermore, prediction accuracy is influenced by trait heritability (Zhang et al., 2017) and the number of genotypes with phenotypic records available for genomic selection. Hence, another approach to enhance prediction accuracy is by increasing the number of phenotyped lines used for model training (VanRaden et al., 2009; Combs and Bernardo, 2013). However, due to the high costs associated with phenotyping, this may not always be feasible, particularly when sparse testing methods (Jarquin et al., 2020; Crespo-Herrera et al., 2021; Atanda et al., 2022; Terraillon et al., 2022) are not applicable. Hence, one strategy to address low prediction accuracy could be to identify more informative variants for predictions without necessarily increasing the marker density per se.

Loci along the genome are usually inherited in a block-like structure, with only few recombination hotspots (Daly et al., 2001; Jeffreys et al., 2001; Reich et al., 2001) defining the so-called haplotype blocks. There are several ways to define a haplotype block, for example as a fixed window of adjacent markers, as a fixed window of adjacent base pairs, or based on a statistical measure of LD. While the first two are straightforward and simple, they may not represent haplotype blocks in a true biological sense. More sophisticated approaches may model the true haplotype blocks better. Commonly, LD based measures like D´ or r² are used for construction of haplotype blocks (Devlin and Risch, 1995). Furthermore, prior information of interaction between adjacent markers may help model local epistasis (Liu et al., 2019), however, difficulties in computing higher order interactions limits the size of haplotype blocks of that type. Haplotype blocks are assumed to be in higher linkage disequilibrium with QTL, and it was proven that haplotype blocks are able to capture local epistasis of markers in close proximity (Jiang et al., 2018). Furthermore, it has been suggested that the problem of apparent or phantom epistasis, which occurs between markers and QTL in incomplete LD, can be overcome with haplotype blocks (Wood et al., 2014; de los Campos et al., 2019). Hence it can be assumed, that haplotype blocks may improve genomic prediction.

In genomic selection, there is evidence that markers grouped to haplotype blocks can improve genomic prediction (Cuyabano et al., 2014; Jiang et al., 2018; Ballesta et al., 2019), while other studies delivered evidence against improving predictions (Solberg et al., 2008). Even with the methods described above for construction of haplotype blocks, it is always necessary to set appropriate hyperparameters like window size or an LD threshold to define block boundaries. Most previous studies in this area investigated a small range of LD thresholds, adjacent markers or window sizes in association studies and genomic prediction (Cuyabano et al., 2014; Hess et al., 2017; Maldonado et al., 2019). However, in terms of genomic prediction for plant breeding the huge variety of options and hyperparameters possible to construct haplotype blocks were not assessed in detail. Hence, the present study sought to investigate the following questions: 1.) How does the method of building haplotype blocks and its parameters affect the number of haplotypes? 2.) Are haplotype block predictions different from SNP predictions in terms of prediction accuracy? 3.) Is there a preferable haplotype construction method to improve genomic prediction?

These questions were addressed by employing various methods for constructing haplotypes, which are commonly discussed in the literature. The methods range from simple approaches such as marker adjacency (Villumsen and Janss, 2009; Villumsen et al., 2009; Jiang et al., 2018; Liang et al., 2020) and physical distances (Hess et al., 2017; Liang et al., 2020) to more sophisticated methods based on LD thresholds (Cuyabano et al., 2014; Voss-Fels et al., 2019; Bayer et al., 2021; Li et al., 2022) the confidence intervals of D´ method described by Gabriel et al. (2002), the Four-gamete Rule method described by Wang et al. (2002) the Solid Spine of LD method (Barrett et al., 2005) and “HaploBlocker” (Pook et al., 2019), using four example datasets from canola, maize, wheat and soybean. To assess prediction accuracy, genomic prediction was performed using GBLUP, Bayesian LASSO, EGBLUP and RKHS models.

Using datasets from four diverse crops and haplotype blocks constructed using a broad range of construction parameters, we show how haplotype blocks change in size and influence the effective number of predictors for genomic prediction. While haplotype blocks sometimes drastically change the number of predictors, genomic prediction accuracy was only marginally affected with no consistent improvement for any method and trait.

Haplotype blocks were built based on LD (r² ), fixed window sizes of adjacent marker or base pairs as well as the three algorithms implemented in the software “Haploview” and the method “Haploblocker”. The r² measurement of LD between markers (Hill and Robertson, 1968; Hill, 1981) is highly correlated to D´ (VanLiere and Rosenberg, 2008), which is more commonly used in tagSNP methods where it showed superior performance to other measures (Carlson et al., 2004; de Bakker et al., 2005). According to Cuyabano et al. (2014), r² and D´ show no difference in terms of prediction accuracy in genomic prediction. The high resolution of haplotype blocking methods and construction parameters allowed an examination of a wide range of haplotype block sizes that are normally not considered in genomic prediction. Most studies in this regard only include single or few construction methods or parameters (Lorenz et al., 2010; Ballesta et al., 2019; Maldonado et al., 2019), although our results show that the method of haplotype construction can potentially impact prediction quality. We included haplotype blocks of relatively large sizes, such as a LD threshold of 0.01 and whole chromosome blocks, which may initially seem unrealistic. However, we included these large blocks to account for scenarios in which traits are controlled by large chromosome segments (Voss-Fels et al., 2019), possibly resulting from introgression breeding with suppressed recombination (Hao et al., 2020).

Here, in three datasets the number of haplotypes could be increased substantially compared to the number of SNPs. The number of haplotypes we observed in the four examined datasets was lower than observed in cattle (Cuyabano et al., 2014; Cuyabano et al., 2015; Li et al., 2021; Li et al., 2022) and human (Liang et al., 2020) but similar to previous reports in plants including Eucalyptus globulus (Ballesta et al., 2019), maize (Matias et al., 2017) and rice (Matias et al., 2017). These variations may arise from differences in population diversity, marker density, and sequencing technology. The haplotype number detected in maize by Matias et al. (2017) was comparable to that observed in our analysis using around ten times fewer SNP markers, indicating that haplotype number is not (solely) dependent on marker density. However, as expected there is a relationship between the population size and haplotype number, with more (diverse) genotypes causing more haplotypes. The number of haplotypes we detected corresponded to the population size used for each crop, with wheat having the fewest haplotypes and soybean the most, independent of the method. Nevertheless, an effect of genetic diversity within a species or population cannot be discounted without comparative within-species analyses of alternative populations. Some authors argue that use of haplotype blocks can help to reduce dimensionality (Kim et al., 2019; Pook et al., 2019). However, depending on the methods and parameters for haplotype construction the number of haplotypes was sometimes higher in the examined datasets than the number of SNPs. This may reflect lower marker numbers and different methods compared to Kim et al. (2019). Dimensionality can certainly be decreased if rare haplotypes would be excluded (Hess et al., 2017; Li et al., 2022). The method “HaploBlocker” described by Pook et al. (2019) decreased the dimensionality in every examined dataset. In all cases, the major drawback of the large number of additional variants is the very low frequency at which the haplotypes occur. However, low frequency variants are often assumed to be in higher LD with recent causal mutations (Bloom et al., 2019; Wainschtein et al., 2022), implying that their detection and use for predictions could be beneficial. However, caution is needed when considering all haplotypes, especially rare ones. In genomic predictions. effect estimation of rare variants require large populations to be estimated accurately (Meuwissen et al., 2001; Goddard and Hayes, 2007). In large populations, rare variants can be observed at higher frequencies which enables a more accurate estimation of their trait effects. In SNP based prediction markers are commonly excluded if they have a minor allele frequency ≤ 0.05 (Technow et al., 2012; Crossa et al., 2013; Jan et al., 2016; Werner et al., 2018a; Zhang et al., 2018). With large populations, filtering could be shifted from frequencies to allele counts, potentially leading to more reliable effect estimates of rare haplotypes. However, increasing the population could again increases the number of rare new haplotypes. In all four datasets, the number of unblocked SNPs decreased with increasing block size. With LD based haplotype blocks, increasing the LD threshold resulted in an increase of unblocked SNPs.

Genomic prediction was conducted using four models: GBLUP, EGBLUP, Bayesian LASSO, and RKHS regression, with the latter two implemented within a Bayesian framework. GBLUP, being the golds standard of genomic prediction, is a widely employed prediction models in breeding, hence we included it in the analysis. However, GBLUP assumes that all markers or haplotypes contribute to the trait (through relationship), prompting the inclusion of Bayesian LASSO, which allows for marker or haplotype-specific shrinkage of effects towards zero. This is beneficial in scenarios where not all markers or haplotypes have an impact on the trait. Given the assumption that haplotypes capture local epistatic effects (Jiang et al., 2018), EGBLUP and RKHS regression were employed to assess whether considering global epistasis between haplotype blocks could yield a substantial improvement in genomic prediction. Although haplotype blocks are typically fewer in number compared to SNPs, the number of haplotypes used for prediction was often comparable to or even greater than the number of SNPs. Therefore, we selected prediction models capable of handling the challenges posed by the large p small n scenario, opting not to explore machine learning models. Furthermore, the application of machine learning methods would have required extensive hyperparameter optimization, which would have significantly exceeded the computational time required for the four prediction models employed in this study. Lastly, the objective of this study was to compare various haplotype blocking methods and parameters, rather than comparing different prediction models.

Generally, genomic prediction accuracies based on SNPs were similar to those reported in the literature across all datasets. In the canola dataset, accuracies closely matched Jan et al. (2016), with a small improvement likely due to the higher number of markers remaining after filtering. Trait prediction accuracies in canola/rapeseed were mostly consistent with previous reports, with minor variations observed for field emergence, and glucosinolate content (Würschum et al., 2014; Jan et al., 2016; Werner et al., 2018a; Werner et al., 2018b). Also in the maize dataset, SNP-based genomic prediction accuracy roughly matched the original publication (Lehermeier et al., 2014), with expected differences due to varying cross-validation schemes. Maize hybrids exhibited high prediction accuracies as previously reported (Technow et al., 2012; Crossa et al., 2014; Millet et al., 2019). In wheat, prediction accuracies based on SNPs for seed yield and yield components were on a very high level ( Table S1 ) compared to many previously published reports (Lado et al., 2013; Zhao et al., 2013; Crossa et al., 2014; Daetwyler et al., 2014; Crossa et al., 2016; Edwards et al., 2019). Furthermore, prediction accuracies based on SNPs for stripe rust resistance, despite population differences, showed a similar level than observed by Daetwyler et al. (2014). Whereas protein content had a higher prediction accuracy compared to Crossa et al. (2016), sedimentation value was predicted equally well. In soybean, prediction accuracies based solely on SNPs were comparable to levels reported by Jarquin et al. (2016) for oil content and protein content, despite considerable differences in the cross-validation and modeling schemes. The lack of differences in prediction accuracies may be explained by the narrow genetic diversity in soybean breeding material due to genetic bottlenecks (Hyten et al., 2006).

Genomic prediction with LD-based haplotype blocks in canola resulted in the highest accuracy improvements for most model/trait combinations. Variation in prediction accuracy across LD thresholds was minimal. The optimal threshold varied significantly by trait and model, ranging from very low (0.01) to high (0.89). In wheat, LD-based haplotype blocks were superior to the other haplotyping methods for 20 out of 60 model/trait combinations, but accuracy didn’t always improve compared to SNP-based prediction. Similar low variation across LD thresholds was observed in soybean. For soybean’s oil content, the ideal LD threshold for accuracy estimates across all models was 0.24-0.26. In maize, only the Bayesian LASSO and RKHS models achieved the highest improvements with LD based haplotype blocks with a threshold of 1, effectively removing redundant information. In this scenario, only markers in complete LD were grouped into a block, effectively removing redundant information. This process, is similar to LD pruning, which has been demonstrated to enhance prediction accuracy (Ye et al., 2019). Intriguing patterns were observed with LD-based haplotypes in maize, the two models implemented in a Bayesian framework (Bayesian LASSO and RKHS) behaved in an opposite direction to the other (frequentist) models, potentially due to different estimation procedures. In contrast to Cuyabano et al. (2014), we generally did not find an ideal LD threshold or even an ideal threshold specific to each dataset and mostly not even an ideal threshold within one trait. The prediction accuracy variation along LD thresholds reported in cattle (Cuyabano et al., 2014; Li et al., 2021; Li et al., 2022) was similar to the variation observed in our analyses. This suggests that any LD threshold is reasonable for genomic prediction due to low variation of prediction accuracy. We propose that even with extreme LD thresholds, reasonably accurate haplotype blocks are constructed, which explains the low variation observed across LD thresholds in all datasets. Additionally, in all datasets, the correlation between relationship coefficients obtained from markers and haplotypes was consistently high, with little variation across LD thresholds. This suggests that relationship representation remains consistent when using LD-based haplotype blocks.

The use of small fixed window blocks led to prediction accuracies comparable to those achieved with individual SNPs. Additionally, in maize, our findings aligned with those of Jiang et al. (2018) in Flint material, showing similar prediction accuracy patterns for frequentist models using small fixed window size haplotype blocks (2-5 markers). Interestingly, in maize, prediction accuracy eroded with the two frequentist models and increasing block size based on fixed windows, whereas for two Bayesian models the prediction accuracy was low across all parameters. Except for the wheat dataset, using excessively large fixed windows to build haplotype blocks considerably reduced prediction accuracy, as observed in previous studies with cattle (Hess et al., 2017). Unrealistically large blocks likely obscure the effects of true QTL within them. Furthermore, these larger blocks are generally more prone to errors in genotyping, and imputation, which accumulate in large blocks and limit prediction accuracy of genomic prediction models utilizing these blocks. These errors can also introduce false rare haplotypes, exacerbating issues related to rare variants. Additionally, as block size increases, haplotypes become more specific to genotypes or subpopulations, resulting in the absence of certain haplotypes in the training set but presence in the validation set. This lack of overlap leads to inaccurate estimation of the effects for those haplotypes, thus decreasing prediction accuracy due to the limited shared haplotypes between the training and validation sets. In the case of wheat, however, using very large blocks, such as whole chromosomes, resulted in considerable improvements in prediction accuracy. Mentionable improvements were observed for traits such as wheat stripe rust resistance, powdery mildew resistance, and kernel spike^-1. This improvement can likely be attributed to introgression breeding in wheat, where large chromosome segments are introgressed and preserved due to restricted recombination (Hao et al., 2020). Furthermore, the wheat D-subgenome exhibits large LD haplotype blocks that are important for yield and biomass-related traits (Voss-Fels et al., 2019). However, it should be noted that these improvements were observed in cases where the model performance was initially at a very low level with SNPs. The correlation between relationship coefficients obtained from markers and haplotypes was high for small fixed window blocks but decreased as block size increased. This suggests that crucial relationship information is lost or encoded within large haplotype blocks, which cannot be accessed for accurate prediction. As a result, the prediction accuracy in canola, maize, and soybean is reduced. However, it is important to highlight that large blocks can potentially introduce additional trait information, as demonstrated by their impact in some of the wheat traits.

The widely used algorithms implemented in “Haploview” did not exhibit superiority in terms of prediction accuracy compared to other methods. Although the method proposed by Gabriel et al. (2002) showed a slight improvement, particularly in maize DMY, these gains remained modest when compared to SNP-based prediction. In contrast to the findings of Matias et al. (2017), our analysis generally revealed a decrease in prediction accuracy rather than a benefit from haplotypes based on “Haploview” in the maize dataset. This discrepancy could be attributed to differences in the plant materials studied. While Matias et al. (2017) examined a diverse collection of tropical maize lines, our analyses focused on European dent material characterized by a relatively strong population structure (Lehermeier et al., 2014). Moreover, the population studied by Matias et al. (2017) was nearly twice the size of our investigation, potentially leading to increased recombination events between loci and reducing the potential size of haplotype blocks. Another contributing factor may be the limited representation of relationship captured by those haplotypes, as evidenced by the intermediate correlation between relationship coefficients obtained from markers and haplotypes. In contrast, canola, wheat, and soybean exhibited a high correlation in this regard. Unlike the findings of Ma et al. (2016) suggest, our study did not observe improved prediction accuracies in soybean using the method proposed by Gabriel et al. (2002). This discrepancy could be attributed to several factors, including differences in the traits under examination, as well as substantial variations in population size and marker density. It is worth noting that the method proposed by Gabriel et al. (2002) shares similarities with the LD-based method described earlier, implying that haplotype blocks formed using this method may already be represented using a specific LD threshold.

The “HaploBlocker” method (Pook et al., 2020) has the advantage of constructing subgroup-specific haplotype blocks and was implemented to address this aspect. However, this approach did not improve prediction accuracy and even led to a decrease of prediction accuracy in some cases. In canola and soybean, haplotype blocks from “HaploBlocker” effectively captured the genomic relationship represented by SNPs. In wheat, the representation was reasonable, but in maize, it was notably inadequate. Similar to the large fixed windows, haplotypes generated by this method are specific to genotypes or subpopulations. Consequently, haplotypes present in the validation set may not be observed in the training set, resulting in the inability to estimate their effects accurately and leading to decreased prediction accuracy due to the limited number of shared haplotypes between the training and validation sets. Particularly in the maize population, which exhibited strong population structure, the “HaploBlocker” method resulted in comparatively low prediction accuracies. This was pronounced with the family-wise cross validation, where the accuracies were diminished to nearly zero. In this scenario, even when using SNPs, the number of shared alleles or haplotypes between the training and validation sets will be minimized. This effect will be particularly prominent when employing a method that constructs subgroup-specific blocks.

In general, with the exception of wheat, prediction accuracies based on haplotype blocks using GBLUP and EGBLUP followed the correlation observed between relationship coefficients obtained from SNPs and haplotype blocks. This suggests that a portion of the prediction accuracy achieved with haplotypes is derived from reinterpreting the SNP information. However, in the case of wheat, this pattern did not hold true, even when using large fixed window blocks. Furthermore, considerable prediction accuracy differences were observed across models for wheat traits, but these differences were consistently compensated for by utilizing haplotype blocks with varying methods and parameters. This indicates that additional information beyond genetic relatedness contributes to the prediction accuracy when using haplotype blocks. One possible explanation is that haplotype blocks are generally considered to exhibit higher LD with QTL compared to individual markers (Jiang et al., 2018).

Multiple factors contribute to the accuracy of genomic prediction. One crucial factor is the relationship among genotypes, which is overlooked in random cross-validation approaches. In such cases, closely related genotypes may be included in both the training and validation sets, leading to higher prediction accuracies for related individuals (Massman et al., 2013; Hickey et al., 2014; Werner et al., 2020). Consequently, the prediction accuracies obtained from random cross-validation are population-specific and cannot be readily adopted to all breeding populations (Werner et al., 2020). To address this issue, we conducted a family-wise cross-validation in the maize dataset to assess the predictive performance of haplotype blocks for less related individuals. As expected from Werner et al. (2020), we observed a decrease in prediction accuracy compared to random cross-validation. However, the relative ranking of haplotype block methods and parameters remained consistent with that of the random cross-validation, indicating no added benefit from haplotypes in predicting the breeding values of genetically distinct materials.

Moreover, GBLUP models trained with small haplotype blocks exhibited very similar prediction accuracies to models trained with SNPs. This is expected since haplotype effects can be partially defined as the sum of individual marker effects within their respective block. Another advantage of haplotype effects is their ability to capture local epistasis, as demonstrated by Jiang et al. (2018). However, it is worth noting that purely additive models, especially in prediction methods like GBLUP where marker effects are estimated simultaneously, already implicitly capture local epistasis among markers in complete LD.

The use of haplotypes has been proposed as a means to address the challenges associated with apparent or phantom epistasis (Wood et al., 2014). Apparent or phantom epistasis can occur when two markers are in incomplete LD with QTL, resulting in statistically significant marker interactions in association studies and enhanced prediction accuracies in genomic prediction with models considering epistasis (Wood et al., 2014; de los Campos et al., 2019; Schrauf et al., 2020). This effect may be particularly pronounced in the wheat dataset, which had a significantly lower marker density compared to the other three datasets. Consequently, the use of haplotype blocks sometimes led to considerable improvements in prediction accuracy.

There is a multitude of factors affecting the accurate assembly of haplotype blocks and their respective haplotypes. Especially in complex plant genomes like the allopolyploids canola and wheat, SNP array markers can potentially be non-specific in terms of physical position, representing different homoeologous loci in different individuals (Mason et al., 2017; Makhoul et al., 2020). Furthermore, all methods to build haplotype blocks rely on known marker positions along the genome. These positions are obtained from a reference genome and are not necessarily the same in every population or even genotype. Especially if the reference genome is only distantly related. In such cases, a lack of precision in assembled haplotype blocks and their corresponding haplotypes may limit their potential in genomic prediction. Furthermore, haplotype block borders are not necessarily the same across populations and generations. Even though, Gabriel et al. (2002) showed high harmony of block structure across different human populations, however in plant breeding, with selection favoring positive alleles or haplotypes, this could ultimately change. Especially LD based haplotype blocks may only be useful for very few generations, since initially defined blocks will rapidly be disrupted by recombination or extended due to selection in later generations as the breeding program progresses. Indeed, an important goal of breeding is to accumulate favorable alleles through selection and recombination. This underlines the need for constant updating of both, the haplotype block assignment and the prediction model. Furthermore, besides the two fixed window approaches, all of the methods tested are only capable of identifying a proxy to true chromosomal recombination breakpoints. Even though crossovers tends to aggregate in recombination hotspots (Li and Stephens, 2003; Myers et al., 2006), haplotype blocking methods with limited marker density and population size may not necessarily be able to detect these hotspots. Therefore, there is a need to develop enhanced haplotype blocking pipelines that can effectively capture natural recombination patterns and address challenges associated with polyploidy, structural variations, and chromosomal rearrangements commonly observed in crop plants (Mason et al., 2017; Schiessl et al., 2019). Consequently, ongoing efforts focus on the development of innovative methods to capture local epistatic effects (Pook et al., 2020).

Unfortunately, we could not identify a single optimal haplotype blocking method that suits all datasets. Therefore, it is important to consider haplotype block construction methods and parameters as hyperparameters that require careful optimization, rather than fixed biological parameters. A breeding program that adopts haplotype block-based genomic selection should explore multiple haplotype blocking methods with different parameter settings. In general, the selected method should effectively capture relationships among individuals. Additionally, it is worth examining blocks of large size, as, in the case of the wheat dataset, larger blocks proved beneficial in improving prediction accuracy. The wheat dataset, which had the lowest marker density, generally showed the greatest improvements. This suggests that haplotype block-based genomic selection could be particularly valuable for breeding programs lacking access to high-density SNP arrays. However, further investigation is required in other datasets with varying SNP densities to validate these findings.

Although we observed only marginal beneficial effects of haplotype blocks in the canola, maize and soybean datasets on genomic prediction, they can still have a beneficial effect when used in other contexts. For example, haplotype blocks can help to identify regions of interest for the identification of candidate genes near significant marker-trait associations, or to compare different genotype groups at such loci (Clark, 2004; Li et al., 2017; Vollrath et al., 2021). Moreover, even if the majority of SNP markers exhibit intermediate minor allele frequency in a population, specific combinations of alleles represented as haplotypes may not be common in a population. Therefore, haplotypes can assist in identifying rare variants that have a potential impact on phenotypic traits. (Bloom et al., 2019; Wainschtein et al., 2022; Wang et al., 2023). Furthermore, especially in highly quantitative traits like yield where markers tend to have very small effects on traits, haplotype blocks can identify positive or negative chromosomal segments. This information can be implemented for cross designs to recombine haplotypes with positive effects (Bernardo and Thompson, 2016; Werner et al., 2018a). This can be considerably easier than selecting for single positive SNPs, as their positive effect can be obscured by deleterious SNPs in proximity that are only rarely separated by recombination in subsequent generations.

As anticipated based on numerous previous reports, our study confirms that haplotype blocks have the potential to enhance genomic selection, although the magnitude of improvement is sometimes only marginal. Haplotype blocks can particularly compensate for model differences when there is considerable variation in model performance across different prediction models. The extent of improvement with haplotypes compared to SNP-based predictions seem to be highly dependent on factors such as population, population structure, trait, and model. for a multitude of different traits from different crop species with different genome properties and breeding schemes, we were unable to identify optimal methods or parameters for constructing haplotype blocks in terms of prediction accuracy. Approaches based on LD resulted in improved prediction accuracies across various traits and demonstrated robustness in LD-threshold selection. However, the greatest improvements were observed with haplotype blocks consisting of entire chromosomes. Therefore, we recommend treating haplotype block definition as a tunable hyperparameter when employing genomic selection, taking into account extremely large haplotype blocks.

Publicly available datasets were analyzed in this study. This data can be found here: Please refer to the original publications of the four datasets.

SW and RS designed the study. SW conceived the analysis, MF developed the software for Linkage Disequilibrium (LD) based haplotyping. KV-F and MF supervised the statistical analysis. SW wrote the manuscript. RS and KV-F revised the manuscript. All authors contributed to the article and approved the submitted version.