A Bayesian optimization R package for multitrait parental selection.

Selecting and mating parents in conventional phenotypic and genomic selection are crucial. Plant breeding programs aim to improve the economic value of crops, considering multiple traits simultaneously. When traits are negatively correlated and/or when there are missing records in some traits, selection becomes more complex. To address this problem, we propose a multitrait selection approach using the Multitrait Parental Selection (MPS) R package-an efficient tool for genetic improvement, precision breeding, and conservation genetics. The package employs Bayesian optimization algorithms and three loss functions (Kullback-Leibler, Energy Score, and Multivariate Asymmetric Loss) to identify parental candidates with desirable traits. The software's functionality includes three main functions-EvalMPS, FastMPS, and ApproxMPS-catering to different data availability scenarios. Through the presented application examples, the MPS R package proves effective in multitrait genomic selection, enabling breeders to make informed decisions and achieve strong performance across multiple traits.

Genetic analyses of tropical maize lines under artificial infestation of fall armyworm and foliar diseases under optimum conditions.

Development and deployment of high-yielding maize varieties with native resistance to Fall armyworm (FAW), turcicum leaf blight (TLB), and gray leaf spot (GLS) infestation is critical for addressing the food insecurity in sub-Saharan Africa. The objectives of this study were to determine the inheritance of resistance for FAW, identity hybrids which in addition to FAW resistance, also show resistance to TLB and GLS, and investigate the usefulness of models based on general combining ability (GCA) and SNP markers in predicting the performance of new untested hybrids. Half-diallel mating scheme was used to generate 105 F1 hybrids from 15 parents and another 55 F1 hybrids from 11 parents. These were evaluated in two experiments, each with commercial checks in multiple locations under FAW artificial infestation and optimum management in Kenya. Under artificial FAW infestation, significant mean squares among hybrids and hybrids x environment were observed for most traits in both experiments, including at least one of the three assessments carried out for foliar damage caused by FAW. Interaction of GCA x environment and specific combining ability (SCA) x environment interactions were significant for all traits under FAW infestation and optimal conditions. Moderate to high heritability estimates were observed for GY under both management conditions. Correlation between GY and two of the three scorings (one and three weeks after infestation) for foliar damage caused by FAW were negative (-0.27 and -0.38) and significant. Positive and significant correlation (0.84) was observed between FAW-inflicted ear damage and the percentage of rotten ears. We identified many superior-performing hybrids compared to the best commercial checks for both GY and FAW resistance associated traits. Inbred lines CML312, CML567, CML488, DTPYC9-F46-1-2-1-2, CKDHL164288, CKDHL166062, and CLRCY039 had significant and positive GCA for GY (positive) and FAW resistance-associated traits (negative). CML567 was a parent in four of the top ten hybrids under optimum and FAW conditions. Both additive and non-additive gene action were important in the inheritance of FAW resistance. Both GCA and marker-based models showed high correlation with field performance, but marker-based models exhibited considerably higher correlation. The best performing hybrids identified in this study could be used as potential single cross testers in the development of three-way FAW resistance hybrids. Overall, our results provide insights that help breeders to design effective breeding strategies to develop FAW resistant hybrids that are high yielding under FAW and optimum conditions.

Bayesian modelling of phosphorus content in wheat grain using hyperspectral reflectance data.

BACKGROUND: As a result of the technological progress, the use of sensors for crop survey has substantially increased, generating valuable information for modelling agricultural data. Plant spectroscopy jointly with statistical modeling can potentially help to assess certain chemical components of interest present in plants, which may be laborious and expensive to obtain by direct measurements. In this research, the phosphorus content in wheat grain is modeled using reflectance information measured by a hyperspectral sensor at different wavelengths. A Bayesian procedure for selecting variables was used to identify the set of the most important spectral bands. Additionally, three different models were evaluated: the first model assumes that the observations are independent, the other two models assume that the observations are spatially correlated: one of the proposed models, assumes spatial dependence using a Conditionally Autoregressive Model (CAR), and the other through an exponential correlogram. The goodness of fit of the models was evaluated by means of the Deviance Information Criterion, and the predictive power is evaluated using cross validation. RESULTS: We have found that CAR was the model that best fits and predicts the data. Additionally, the selection variable procedure in the CAR model reveals which wavelengths in the range of 500-690 nm are the most important. Comparing the vegetative indices with the CAR model, it was observed that the average correlation of the CAR model exceeded that of the vegetative indices by 23.26%, - 1.2% and 22.78% for the year 2010, 2011 and 2012 respectively; therefore, the use of the proposed methodology outperformed the vegetative indices in prediction. CONCLUSIONS: The proposal to predict the phosphorus content in wheat grain using Bayesian approach, reflect with the results as a good alternative.

Platelets and endothelial dysfunction in gestational diabetes mellitus.

The prevalence of gestational diabetes mellitus (GDM) has increased in recent years, along with the higher prevalence of obesity in women of reproductive age. GDM is a pathology associated with vascular dysfunction in the fetoplacental unit. GDM-associated endothelial dysfunction alters the transfer of nutrients to the foetus affecting newborns and pregnant women. Various mechanisms for this vascular dysfunction have been proposed, of which the most studied are metabolic alterations of the vascular endothelium. However, different cell types are involved in GDM-associated endothelial dysfunction, including platelets. Platelets are small, enucleated cell fragments that actively take part in blood haemostasis and thrombus formation. Thus, they play crucial roles in pathologies coursing with endothelial dysfunction, such as atherosclerosis, cardiovascular diseases, and diabetes mellitus. Nevertheless, platelet function in GDM is understudied. Several reports show a potential relationship between platelet volume and mass with GDM; however, platelet roles and signaling mechanisms in GDM-associated endothelial dysfunction are unclear. This review summarizes the reported findings and proposes a link among altered amount, volume, mass, reactivity, and function of platelets and placenta development, resulting in fetoplacental vascular dysfunction in GDM.

Consequences of the exposome to gestational diabetes mellitus.

The exposome is the cumulative measure of environmental influences and associated biological responses throughout the lifespan, including those from the environment, diet, behaviour, and endogenous processes. The exposome concept and the 2030 Agenda for the Sustainable Development Goals (SDGs) from the United Nations are the basis for understanding the aetiology and consequences of non-communicable diseases, including gestational diabetes mellitus (GDM). Pregnancy may be developed in an environment with adverse factors part of the immediate internal medium for fetus development and the external medium to which the pregnant woman is exposed. The placenta is the interface between maternal and fetal compartments and acts as a protective barrier or easing agent to transfer exposome from mother to fetus. Under and over-nutrition in utero, exposure to adverse environmental pollutants such as heavy metals, endocrine-disrupting chemicals, pesticides, drugs, pharmaceuticals, lifestyle, air pollutants, and tobacco smoke plays a determinant role in the development of GDM. This phenomenon is worsened by metabolic stress postnatally, such as obesity which increases the risk of GDM and other diseases. Clinical risk factors for GDM development include its aetiology. It is proposed that knowledge-based interventions to change the potential interdependent ecto-exposome and endo-exposome could avoid the occurrence and consequences of GDM.

Worldwide Selection Footprints for Drought and Heat in Bread Wheat (Triticum aestivum L.).

Genome-environment Associations (GEA) or Environmental Genome-Wide Association scans (EnvGWAS) have been poorly applied for studying the genomics of adaptive traits in bread wheat landraces (Triticum aestivum L.). We analyzed 990 landraces and seven climatic variables (mean temperature, maximum temperature, precipitation, precipitation seasonality, heat index of mean temperature, heat index of maximum temperature, and drought index) in GEA using the FarmCPU approach with GAPIT. Historical temperature and precipitation values were obtained as monthly averages from 1970 to 2000. Based on 26,064 high-quality SNP loci, landraces were classified into ten subpopulations exhibiting high genetic differentiation. The GEA identified 59 SNPs and nearly 89 protein-encoding genes involved in the response processes to abiotic stress. Genes related to biosynthesis and signaling are mainly mediated by auxins, abscisic acid (ABA), ethylene (ET), salicylic acid (SA), and jasmonates (JA), which are known to operate together in modulation responses to heat stress and drought in plants. In addition, we identified some proteins associated with the response and tolerance to stress by high temperatures, water deficit, and cell wall functions. The results provide candidate regions for selection aimed to improve drought and heat tolerance in bread wheat and provide insights into the genetic mechanisms involved in adaptation to extreme environments.

Gestational diabesity and foetoplacental vascular dysfunction.

Gestational diabetes mellitus (GDM) shows a deficiency in the metabolism of D-glucose and other nutrients, thereby negatively affecting the foetoplacental vascular endothelium. Maternal hyperglycaemia and hyperinsulinemia play an important role in the aetiology of GDM. A combination of these and other factors predisposes women to developing GDM with pre-pregnancy normal weight, viz. classic GDM. However, women with GDM and prepregnancy obesity (gestational diabesity, GDty) or overweight (GDMow) show a different metabolic status than women with classic GDM. GDty and GDMow are associated with altered l-arginine/nitric oxide and insulin/adenosine axis signalling in the human foetoplacental microvascular and macrovascular endothelium. These alterations differ from those observed in classic GDM. Here, we have reviewed the consequences of GDty and GDMow in the modulation of foetoplacental endothelial cell function, highlighting studies describing the modulation of intracellular pH homeostasis and the potential implications of NO generation and adenosine signalling in GDty-associated foetal vascular insulin resistance. Moreover, with an increase in the rate of obesity in women of childbearing age worldwide, the prevalence of GDty is expected to increase in the next decades. Therefore, we emphasize that women with GDty and GDMow should be characterized with a different metabolic state from that of women with classic GDM to develop a more specific therapeutic approach for protecting the mother and foetus.

Application of multi-trait Bayesian decision theory for parental genomic selection.

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm.

Arsenic trioxide-increased MDCK cells proliferation requires activator protein 1-mediated increase of the sodium/proton exchanger 1 activity.

The release of protons (H+) occurs via the Na+/H+ exchanger isoform 1 (NHE1) leading to a stable intracellular pH (pHi) in MDCK cells. Chronic intake of arsenic trioxide (ATO), in the drinking water, associated with higher morbidity and mortality in neoplastic tissues. ATO increased NHE1 expression and activity, resulting in intracellular alkalization and higher MDCK cells proliferation. Since the pro-proliferative transcription factor activator protein 1 (AP-1) gets activated by al alkaline intracellular pH, a phenomenon paralleled by higher NHEs activity, we asked whether ATO-increased MDCK cells proliferation involves AP-1-dependent NHE1 activation. Cells were exposed (48 h) to ATO (0.05 µmol/L), SR11302 (1 µmol/L, AP-1 inhibitor), HOE-694 (100 nmol/L, NHE1 inhibitor) and EIPA (50 µmol/L, NHE1/NHE3 inhibitor) in the presence of S3226 (10 µmol/L, NHE3 inhibitor), concanamycin A (0.1 µmol/L, V-ATPases inhibitor), and Schering (10 µmol/L, H+/K+-ATPase inhibitor). [3H]Thymidine incorporation, cell counting, wound healing assay, and AP-1 activity were determined. The pHi was measured in cells pre-loaded (10 min) with 2,7-bicarboxyethyl-5,6-carboxyfluorescein acetoxymethyl ester (12 mmol/L) and exposed to NH4Cl (20 mmol/L). Basal pHi and recovery rate (dpHi/dt), intracellular buffer capacity (ßi) and H+ flux (JH+) were determined. NHE1 protein abundance was measured by Western blotting and immunofluorescence. ATO increased the cell growth (1.5 fold), basal pHi (0.4 pHi units), dpHi/dt (1.8 fold), JH+ (1.4 fold), AP-1 activity and NHE1 protein abundance (1.3 fold). ATO also increased (1.5 fold) the nuclear/perinuclear NHE1 immunosignal. SR11302 and HOE-694 blocked ATO effects. Thus, ATO-increased proliferation resulted from AP-1-dependent NHE1 activation in MDCK cells.

Insulin requires A2B adenosine receptors to modulate the L-arginine/nitric oxide signalling in the human fetoplacental vascular endothelium from late-onset preeclampsia.

Late-onset preeclampsia (LOPE) associates with reduced umbilical vein reactivity and endothelial nitric oxide synthase (eNOS) activity but increased human cationic amino acid (hCAT-1)-mediated L-arginine transport involving A2A adenosine receptor in the fetoplacental unit. This study addresses the A2B adenosine receptor (A2BAR)-mediated response to insulin in the fetoplacental vasculature from LOPE. Umbilical veins and HUVECs were obtained from women with normal (n = 37) or LOPE (n = 35) pregnancies. Umbilical vein rings reactivity to insulin was assayed in the absence or presence of adenosine and MRS-1754 (A2BAR antagonist) in a wire myograph. HUVECs were exposed to insulin, MRS-1754, BAY60-6583 (A2BAR agonist), NECA (general adenosine receptors agonist) or NG-nitro-L-arginine methyl ester (NOS inhibitor). A2BAR, hCAT-1, total and phosphorylated eNOS, Akt and p44/42mapk protein abundance were determined by Western blotting. Insulin receptors A (IR-A) and B (IR-B), eNOS and hCAT-1 mRNA were determined by qPCR. Firefly/Renilla luciferase assay was used to determine -1606 bp SLC7A1 (hCAT-1) promoter activity. L-Citrulline content was measured by HPLC, L-[3H]citrulline formation from L-[3H]arginine by the Citrulline assay, and intracellular cGMP by radioimmunoassay. LOPE-reduced dilation of vein rings to insulin was restored by MRS-1754. HUVECs from LOPE showed higher A2BAR, hCAT-1, and IR-A expression, Akt and p44/42mapk activation, and lower NOS activity. MRS-1754 reversed the LOPE effect on A2BAR, hCAT-1, Akt, and eNOS inhibitory phosphorylation. Insulin reversed the LOPE effect on A2BAR, IR-A and eNOS, but increased hCAT-1-mediated transport. Thus, LOPE alters endothelial function, causing an imbalance in the L-arginine/NO signalling pathway to reduce the umbilical vein dilation to insulin requiring A2BAR activation in HUVECs.

On Hadamard and Kronecker products in covariance structures for genotype × environment interaction.

When including genotype × environment interactions (G × E) in genomic prediction models, Hadamard or Kronecker products have been used to model the covariance structure of interactions. The relation between these two types of modeling has not been made clear in genomic prediction literature. Here, we demonstrate that a certain model based on a Hadamard formulation and another using the Kronecker product lead to exactly the same statistical model. Moreover, we illustrate how a multiplication of entries of covariance matrices is related to modeling locus × environmental-variable interactions explicitly. Finally, we use a wheat and a maize data set to illustrate that the environmental covariance E can be specified easily, also if no information on environmental variables - such as temperature or precipitation - is available. Given that lines have been tested in different environments, the corresponding environmental covariance can simply be estimated from the training set as phenotypic covariance between environments. To achieve a high level of increase in predictive ability, the environmental covariance has to be defined appropriately and records on the performance of the lines of the test set under different environmental conditions have to be included in the training set.

Retrospective Quantitative Genetic Analysis and Genomic Prediction of Global Wheat Yields.

Breeding for grain yield (GY) in bread wheat at the International Maize and Wheat Improvement Center (CIMMYT) involves three-stage testing at Obregon, Mexico in different selection environments (SEs). To understand the efficiency of selection in the SEs, we performed a large retrospective quantitative genetics study using CIMMYT's yield trials evaluated in the SEs (2013-2014 to 2017-2018), the South Asia Bread Wheat Genomic Prediction Yield Trials (SABWGPYTs) evaluated in India, Pakistan, and Bangladesh (2014-2015 to 2017-2018), and the Elite Spring Wheat Yield Trials (ESWYTs) evaluated in several sites globally (2003-2004 to 2016-2017). First, we compared the narrow-sense heritabilities in the Obregon SEs and target sites and observed that the mean heritability in the SEs was 44.2 and 92.3% higher than the mean heritabilities in the SABWGPYT and ESWYT sites, respectively. Second, we observed significant genetic correlations between a SE in Obregon and all the five SABWGPYT sites and 65.1% of the ESWYT sites. Third, we observed high ratios of response to indirect selection in the SEs of Obregon with a mean of 0.80 ± 0.21 and 2.6 ± 5.4 in the SABWGPYT and ESWYT sites, respectively. Furthermore, our results also indicated that for all the SABWGPYT sites and 82% of the ESWYT sites, a response greater than 0.5 can be achieved by indirect selection for GY in Obregon. We also performed genomic prediction for GY in the target sites using the performance of the same lines in the SEs of Obregon and observed moderate mean prediction accuracies of 0.24 ± 0.08 and 0.28 ± 0.08 in the SABWGPYT and ESWYT sites, respectively using the genotype x environment (GxE) model. However, we observed similar accuracies using the baseline model with environment and line effects and no advantage of modeling GxE interactions. Overall, this study provides important insights into the suitability of the Obregon SEs in breeding for GY, while the variable genomic predictabilities of GY and the high year-to-year GY fluctuations reported, highlight the importance of multi-environment testing across time and space to stave off GxE induced uncertainties in varietal yields.

Oxidative stress and mitochondrial dysfunction in early-onset and late-onset preeclampsia.

Preeclampsia is a pregnancy-specific syndrome with multisystem involvement which leads to foetal, neonatal, and maternal morbidity and mortality. This syndrome is characterized by the onset of clinical signs and symptoms and delivery before (early-onset preeclampsia, eoPE), or after (late-onset preeclampsia, loPE), the 34 weeks of gestation. Preeclampsia is a mitochondrial disorder where its differential involvement in eoPE and loPE is unclear. Mitochondria regulate cell metabolism and are a significant source of reactive oxygen species (ROS). The syncytiotrophoblast in eoPE and loPE show altered mitochondrial structure and function resulting in ROS overproduction, oxidative stress, and cell damage and death. Mitochondrial dysfunction in eoPE may result from altered expression of several molecules, including dynamin-related protein 1 and mitofusins, compared with loPE where these factors are either reduced or unaltered. Equally, mitochondrial fusion/fission dynamics seem differentially modulated in eoPE and loPE. It is unclear whether the electron transport chain and oxidative phosphorylation are differentially altered in these two subgroups of preeclampsia. However, the activity of complex IV (cytochrome c oxidase) and the expression of essential proteins involved in the electron transport chain are reduced, leading to lower oxidative phosphorylation and mitochondrial respiration in the preeclamptic placenta. Interventional studies in patients with preeclampsia using the coenzyme Q10, a key molecule in the electron transport chain, suggest that agents that increase the antioxidative capacity of the placenta may be protective against preeclampsia development. In this review, the mitochondrial dysfunction in both eoPE and loPE is summarized. Therapeutic approaches are discussed in the context of contributing to the understanding of mitochondrial dysfunction in eoPE and loPE.

Mitochondrial dysfunction in the fetoplacental unit in gestational diabetes mellitus.

Gestational diabetes mellitus (GDM) is a disease of pregnancy that is associated with d-glucose intolerance and foeto-placental vascular dysfunction. GMD causes mitochondrial dysfunction in the placental endothelium and trophoblast. Additionally, GDM is associated with reduced placental oxidative phosphorylation due to diminished activity of the mitochondrial F0F1-ATP synthase (complex V). This phenomenon may result from a higher generation of reactive superoxide anion and nitric oxide. Placental mitochondrial biogenesis and mitophagy work in concert to maintain cell homeostasis and are vital mechanisms securing the efficient generation of ATP, whose demand is higher in pregnancy, ensuring foetal growth and development. Additional factors disturbing placental ATP synthase activity in GDM include pre-gestational maternal obesity or overweight, intracellular pH, miRNAs, fatty acid oxidation, and foetal (and 'placental') sex. GDM is also associated with maternal and foetal hyperinsulinaemia, altered circulating levels of adiponectin and leptin, and the accumulation of extracellular adenosine. Here, we reviewed the potential interplay between these molecules or metabolic conditions on the mechanisms of mitochondrial dysfunction in the foeto-placental unit in GDM pregnancies.

Hybrid Breeding for MLN Resistance: Heterosis, Combining Ability, and Hybrid Prediction.

Prior knowledge on heterosis and quantitative genetic parameters on maize lethal necrosis (MLN) can help the breeders to develop numerous resistant or tolerant hybrids with optimum resources. Our objectives were to (1) estimate the quantitative genetic parameters for MLN disease severity, (2) investigate the efficiency of the prediction of hybrid performance based on parental per se and general combining ability (GCA) effects, and (3) examine the potential of hybrid prediction for MLN resistance or tolerance based on markers. Fifty elite maize inbred lines were selected based on their response to MLN under artificial inoculation. Crosses were made in a half diallel mating design to produce 307 F1 hybrids. All hybrids were evaluated in MLN quarantine facility in Naivasha, Kenya for two seasons under artificial inoculation. All 50 inbreds were genotyped with genotyping-by-sequencing (GBS) SNPs. The phenotypic variation was significant for all traits and the heritability was moderate to high. We observed that hybrids were superior to the mean performance of the parents for disease severity (-14.57%) and area under disease progress curve (AUDPC) (14.9%). Correlations were significant and moderate between line per se and GCA; and mean of parental value with hybrid performance for both disease severity and AUDPC value. Very low and negative correlation was observed between parental lines marker based genetic distance and heterosis. Nevertheless, the correlation of GCA effects was very high with hybrid performance which can suggests as a good predictor of MLN resistance. Genomic prediction of hybrid performance for MLN is high for both traits. We therefore conclude that there is potential for prediction of hybrid performance for MLN. Overall, the estimated quantitative genetic parameters suggest that through targeted approach, it is possible to develop outstanding lines and hybrids for MLN resistance.

The activity of IKCa and BKCa channels contributes to insulin-mediated NO synthesis and vascular tone regulation in human umbilical vein.

Insulin regulates the l-arginine/nitric oxide (NO) pathway in human umbilical vein endothelial cells (HUVECs), increasing the plasma membrane expression of the l-arginine transporter hCAT-1 and inducing vasodilation in umbilical and placental veins. Placental vascular relaxation induced by insulin is dependent of large conductance calcium-activated potassium channels (BKCa), but the role of KCa channels on l-arginine transport and NO synthesis is still unknown. The aim of this study was to determine the contribution of KCa channels in both insulin-induced l-arginine transport and NO synthesis, and its relationship with placental vascular relaxation. HUVECs, human placental vein endothelial cells (HPVECs) and placental veins were freshly isolated from umbilical cords and placenta from normal pregnancies. Cells or tissue were incubated in absence or presence of insulin and/or tetraethylammonium, 1-[(2-chlorophenyl)diphenylmethyl]-1H-pyrazole, iberiotoxin or NG-nitro-l-arginine methyl ester. l-Arginine uptake, plasma membrane polarity, NO levels, hCAT-1 expression and placenta vascular reactivity were analyzed. The inhibition of intermediate-conductance KCa (IKCa) and BKCa increases l-arginine uptake, which was related with protein abundance of hCAT-1 in HUVECs. IKCa and BKCa activities contribute to NO-synthesis induced by insulin but are not directly involved in insulin-stimulated l-arginine uptake. Long term incubation (8 h) with insulin increases the plasma membrane hyperpolarization and hCAT-1 expression in HUVECs and HPVECs. Insulin-induced relaxation in placental vasculature was reversed by KCa inhibition. The results show that the activity of IKCa and BKCa channels are relevant for both physiological regulations of NO synthesis and vascular tone regulation in the human placenta, acting as a part of negative feedback mechanism for autoregulation of l-arginine transport in HUVECs.

On the approximation of interaction effect models by Hadamard powers of the additive genomic relationship.

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly.