Metal-organic frameworks (MOFs) have garnered multidisciplinary attention due to their structural tailorability, controlled pore size, and physicochemical functions, and their inherent properties can be exploited by applying them as precursors and/or templates for fabricating derived hollow porous nanomaterials. The fascinating, functional properties and applications of MOF-derived hollow porous materials primarily lie in their chemical composition, hollow character, and unique porous structure. Herein, a comprehensive overview of the synthetic strategies and emerging applications of hollow porous materials derived from MOF-based templates and/or precursors is given. Based on the role of MOFs in the preparation of hollow porous materials, the synthetic strategies are described in detail, including (1) MOFs as removable templates, (2) MOF nanocrystals as both self-sacrificing templates and precursors, (3) MOF@secondary-component core-shell composites as precursors, and (4) hollow MOF nanocrystals and their composites as precursors. Subsequently, the applications of these hollow porous materials for chemical catalysis, electrocatalysis, energy storage and conversion, and environmental management are presented. Finally, a perspective on the research challenges and future opportunities and prospects for MOF-derived hollow materials is provided.  •MOFs have garnered multi-disciplinary attention due to their unique inherent properties•Various synthetic strategies of MOFs-derived hollow porous materials are summarized•Emerging applications of MOFs-derived hollow porous materials are reviewed MOF-derived porous nanomaterials have also played a significant role in photocatalysis, energy storage and conversion, and particularly electrocatalysis, owing to their superior attributes, such as large specific surface area, micro- or mesoporosity for efficient electron and mass transport during the reaction, inherited structural versatility, high tolerance to acid/alkaline environments, and electrical conductivity, as well as diverse chemical components.2 derived from a secondary constituent of MOF@shell composite, (2) hollow porous carbon materials derived from the organic components of the MOF and its shell or guest molecules, and (3) hollow metal oxides, sulfides, carbides, supported MNPs, etc., derived from the metallic components of the MOF or MOF composite. Traditional synthetic methods for HPMs require a hard template, for example, SiO2, and polystyrene (PS), while a significant drawback is that harsh conditions are required for template removal. Compared with the traditional hard template method, the conditions of preparing hollow porous materials from MOFs as a template and precursor system are mild, and there is no need to remove the template. Furthermore, in contrast to the traditional molecular sieve and amorphous porous materials, hollow nanomaterials derived from MOFs demonstrate numerous advantages, including uniform hollow morphology and chemical constituents, tunable distribution of chemical and structural compositions, and tunable porosity. Benefiting from these attributes, MOF-derived hollow nanomaterials exhibit excellent performance in chemical catalysis, electrocatalysis, energy storage and conversion, and other applications.Among these MOF-derived hollow nanomaterials, discrete, hollow structures have garnered considerable attention. In most cases, the synthesis of MOF-derived HPMs essentially relies on a decomposition of the MOF or its composites under a certain condition or chemical reaction with desirable reagents: (1) hollow SiOAlthough several reviews have summarized the MOF-derived hollow nanomaterials and their potential applications,For this part, we will provide various detailed synthetic strategies for fabricating HPMs, such as hollow porous carbons and their composites, hollow layered double hydroxides, hollow metal-based compounds, and their composites .2-based hollow nanocrystals with tunable components.2 was uniformly coated on ZIF nanocrystals from a soluble TEOS precursor through the Stöber method. This produces a ZIF-8@SiO2 core-shell material. Subsequently, hollow SiO2-based materials were obtained from the ZIF-8@SiO2 core-shell composite by different ways of treatment: (1) a ZnO@SiO2 yolk-shell composite was formed by calcination in the air or (2) a ZnO@SiO2 yolk-shell composite and a hollow SiO2 polyhedron were formed by thermal treatment in acidic solution at 100°C for 2 and 24 h, respectively. Inspired by the above research, we proposed a route to prepare hollow TiO2 using ZIF nanocrystals as a removable template and gave rare examples of hollow cubic and polyhedral morphologies  as templates, the Pt NPs were successfully encapsulated into the hollow TiO2 cubes.Usually, the sacrificial template controls the size and morphology of the hollow inorganic nanostructures. He and co-workers proposed a synthetic route for SiOhologies B. It wasTaken together, when an MOF is used as a template to fabricate hollow materials, the shape and size of the obtained hollow structures are controlled by the sacrificial MOF template. And the other advantage is that the MOF template can be completely and rapidly eliminated without affecting the integrity of the hollow shells.,2+-Co3+ LDH,2Co-Mn1-OH, Ni1Co-Mn2-OH, NiCoMn-OH-AD, CoMn-OH, and FeOOH@Ni(OH)2.,in situ technical characterization: etching of the NPs and growth of LDHs on the NP surfaces.in situ transmission electron microscopy (TEM). Conversion of ZIF-67@ZIF-8 core-shells into “shell-in-shell” LDH nanocages is demonstrated in In addition to the removable templates, MOF nanocrystals can be used as both self-sacrificing templates and precursors for fabricating hollow nanostructures. Many approaches have been developed to synthesize MOF derivatives, for instance, hollow metal hydroxides, metal sulfides, metal oxides, metal phosphides, hollow carbon matrixes, and so on.3O4 tetrahedrons were successfully synthesized through the thermolysis of [Co3L2(TPT)2·xG]n (G = guest molecules) at 773 K for 4 h in the air.2O3 nanostructures with an octahedron and a yolk-shell octahedron by calcinating MIL-53 (Fe) in the air for 2 and 6 h, respectively 2. Subsequently, the Co3O4@NiCo2O4 core-shell structure nanocages were formed from ZIF-67/Ni-Co LDH by thermal treatment under air conditions.xCo3−xO4−y nanocages,2O4 dodecahedrons,2O4 hollow core-shell nanocages,x/Co3O4.The metal components of the MOF template are known to be converted into metal oxide by oxidation and pyrolysis in an air atmosphere. Thus, MOF nanomaterials are very suitable as sacrificial templates and precursors for producing various hollow metal oxides. Hollow Coectively D.21 Othe2,2O3,2O5E.26 The 2 atmosphere, and metal species will experience evaporation and/or subsequent leaching in the pyrolysis process. For example, Zhang et al. utilized ZIF-8 as a sacrificial template and precursor for fabricating a hollow carbon matrix 4/3(H2O)2]6[H3PMo12O40] nanocrystals and then pyrolyzed this sample at 1,073 K to prepare MoCx-Cu through an in situ carbonization process involving the Cu-MOF host framework and the guest H3PMo12O40 components. FeCl3 solution is used to selectively etch the Cu species to generate hollow MoCx octahedrons  or Ni(II) could be realized by facilely immersing ZIF-8@K-TA in a methanolic solution of Co(NO3)2 or Ni(NO3)2, respectively. Subsequently, monometallic Co or Ni NPs encapsulated in N-HPC capsules could be achieved by heating ZIF-8@Co-TA or ZIF-8@Ni-TA, respectively, under an Ar atmosphere. We further extended this strategy to synthesize supported multicomponent metal NPs. The heating of ZIF-8/Pt@M-TA or ZIF-8/Pt@Mmix-TA results in N-HPC capsules with Pt-based alloyed NPs embedded in the capsule walls. This approach can be extended to prepare NPs composed of four different metals.x-C, H-Co-Nx-C, H-FeCo-Nx-C, H-FeNi-Nx-C, H-FeCoNi-Nx-C, etc.The growth of MOF@secondary-component core-shell structures is very popular for fabricating MOF-derived hollow porous materials. Hu et al. utilized phenolic acids as surface functionalization and etching reagents to prepare hollow MOFs A.37 MetaSimilarly, the synthetic route toward an N, P, S-co-doped carbon shell (NPS-HCS) was reported.2 atmosphere and subsequent etching treatment, double-shelled NC@Co-NGC nanocages with surface-anchored carbon nanotubes (CNTs) were obtained. It should be noted that the formation of hollow nanostructures can be attributed to surface-stabilized shrinkage of core-shell ZIF-8@ZIF-67 nanocrystals at high temperatures. Similarly, Pan and colleagues used core-shell ZIF-8@ZIF-67 composites to prepare hollow composites of CoP NPs embedded in N-doped CNTs through a continuous pyrolysis-oxidation-phosphorylation process.Moreover, Liu et al. fabricated NC@Co-NGC nanocages via pyrolysis of a ZIF-8@ZIF-67 core-shell composite.,In addition, various hollow carbon2 gas environment resulted in Ni/graphene core-shell composites. After further annealing treatment under air, the final sample NiO/Ni/graphene composites were acquired.x/Ni@C composites,3O4/C-4, and Z9-Co3O4/C-42 hollow prisms by using ZIF-67 as a precursor ) possessed lower conversion efficiency. A similar conclusion was obtained when void@HKUST-1/Pd@ZIF-8 was used as a hydrogenation reaction catalyst.III-MOF-5,Hollow MOF composites with noble metals possess remarkable selectivity in hydrogenation reactions. Tsung and co-workers fabricated Pd on ZIF-8, yolk-shell Pd@ZIF-8, and core-shell Pd@ZIF-8 by utilizing Pd nanocrystals and hollow ZIF-8.3O4 polyhedrons exhibited superior catalytic performance and excellent stability, and the complete conversion was up to 100% for toluene oxidation.2 conversion. Dai and co-workers fabricated hierarchical hollow Ni@C spheres derived from Ni-MOFs, which exhibited superior catalytic performance and enhanced stability for CO2 reduction reaction  the porous MOF shell can serve as a host matrix to prevent NP aggregation and (2) be applied to realize selective catalysis, and (3) the presence of porosity allows for promoting mass transport of chemical species. It is noteworthy that the thickness of the shell has a certain degree of influence on the catalytic performance.Fuel cells and metal-air batteries have garnered extensive attention owing to their being a possible solution to the fossil energy shortage and increasing environmental pollution.,,3), which showed excellent ORR property with Eonset and E1/2 reaching 1.03 and 0.92 V (versus RHE), respectively, in alkaline medium. In real ADMFC, carbonized Fe NPs possessed high output power density and were evenly 1.7 times higher than the 20% Pt/C.3O4@core@bishell NPs derived from MOFs into a highly ordered porous CM to prepare the catalyst Co@Co3O4@C-CM used for ORR.2 and electrolytes, making the NPs hard to detach from the porous CM support. It was found that, in alkaline medium, Co@Co3O4@C-CM displayed almost identical catalytic performance but enhanced stability and better methanol tolerance for ORR relative to the 20% Pt/C.Among the studied non-noble metals, Fe and Co are the most active metal species for ORR.2)-650-C) with enhanced surface area and dense Fe-N4 sites (2)-650-C has the special properties of additional mesoporosity, high surface area, and high exposure to Fe-N4 active-site density -650-C achieved a superior performance of 129 mA cm−2 at 0.8 ViR-free under 1 bar H2-air and a Pmax of 1.18 W cm−2 under 2.5 bar H2-O2. This was better than the performance reported in most of the literature (3 molecules (3Fe-CoN3 in 1/2 (0.863 V versus RHE) and enhanced stability compared with 20% Pt/C, individual Fe SAs/NC, and Co SAs/NC   have also demonstrated supernormal electrocatalytic performance for ORR and have attracted widespread attention.N4 sites A.79 Furt density B and S3Cterature D. Li andolecules E. Multipo SAs/NC G and S3Ho SAs/NC I. Recento SAs/NC A.80 Due in PEMFC B. The Crin PEMFC C. In addin PEMFC D.81 XAS C (4/O6) E and S4Fatalysts G and S4H−2 for PEMFCs and Zn-air batteries, respectively. Interestingly, Fe sites do not contribute to ORR activity  of Fe (N-HPC) was synthesized. Such N-HPCs feature a hollow and hierarchically porous architecture, which shows excellent ORR activity and durability.activity A–6C. Furactivity D–6F.FiguOER plays an essential role in energy conversion technologies. To reduce the expensive cost of OER, extensive efforts have been devoted to exploiting high-performance and inexpensive OER electrocatalysts, with MOF-derived hollow materials being one of them .94−2, and enhanced stability of 96.5% of the initial current is retained after 10 h (3O4/C (Z67-Co3O4/C-4 and Z9-Co3O4/C-4) via carbonized and then oxidized ZIF-67 and ZIF-9 precursors.3O4/C-4 and Z9-Co3O4/C-4 exhibited excellent activity for OER. This is because the unique hollow porous carbon structure improves the electron transfer rate, and vast oxygen vacancies in hollow Co3O4/C can improve the adsorption of water molecules to promote OER activity. Apart from MOF-derived metal oxides, MOF-derived CoSe2 with a hollow structure was also synthesized as an OER electrocatalyst with improved performance.2-450 microspheres displayed 10 mA cm−2 at η = 330 mV with a small Tafel slope of 79 mV dec−1, better than the reference catalysts. This is due to the hollow structure and uniformly distributed active sites, which facilitate a fast mass and electron transport rate. Integration of MOF-derived materials with metallic oxide proved to be a facile and effective strategy to design high-activity OER catalysts.According to numerous reports, MOF-derived bimetal or metal oxide NPs  are beneficial to OER catalysis.ter 10 h B and 7C.dl value compared with the single shelled ones  were prepared through confined carburization in an MOF.x nano-octahedrons showed outstanding catalytic performance for HER in acidic medium and alkaline conditions. Moreover, on repeated potential sweeps, the MoCx nano-octahedrons exhibited promising durability in acidic and alkaline media  and, benefiting from the synergistic effects of the bimetallic alloy components, the Pt3Co@NCNT catalyst showed remarkably enhanced HER performance in both acidic and alkaline media. The exquisite porous carbon shell structure host prevents the ultrasmall Pt3Co NPs from aggregating, thus ensuring long-term durability.xCo3−xS4, M = Zn, Ni, and C) polyhedrals by using MOFs as self-templates. Zn0.30Co2.70S4 exhibited outstanding electrocatalytic HER activity over a wide pH range, with overpotentials of 80, 90, and 85 mV at 10 mA cm−2 and 129, 144, and 136 mV at 100 mA cm−2 in 0.5 M H2SO4, 0.1 M phosphate buffer, and 1 M KOH, respectively. Zn0.30Co2.70S4 further exhibited photocatalytic HER activity when working with an organic photosensitizer (Eosin Y) or semiconductors (TiO2 and C3N4). This study provides a reference for the synthesis of transition metal sulfides used for HER.Like the OER, HER is an essential reaction for water splitting. Although the overpotential of HER is much lower than OER, electrocatalysts are still needed to improve the HER reaction.ne media A. Stabilironment B. The HEElectrocatalysis, as an important process in energy conversion, usually involves more than one process. Specifically, water splitting includes HER and OER, and metal-air batteries involve ORR and OER. The ORR is also the fundamental electrochemical reaction for fuel cells. The design of bifunctional electrocatalysts is significant for the electrochemical process and puts forward higher requirements on the componential tuning and morphological control of the catalyst. MOF-derived hollow structure materials are considered high-efficiency electrocatalysts due to their unique advantages, such as tailorable composition and multilevel porosity.−2, and under alkaline conditions, the overpotential is 310 mV for OER. Hollow heterojunctions derived from MOFs can also be used as outstanding bifunctional electrocatalysts. For instance, hollow Co3S4@MoS2 heterostructuresx@MoS2 microcubes3S4/CoSx and MoS2.Transition metals doped with heteroatoms are considered to be highly efficient electrocatalysts. Pan et al. proposed the preparation of CoP/NCNHP by a successive pyrolysis-oxidation-phosphatization process applied to core-shell-structured ZIF-8@ZIF-67 as the precursor.1/2, with 0.87 V, for ORR than the 20% Pt/C electrocatalyst with 0.84 V (−2 at 1.60 V (versus RHE), which compared favorably with reported nanocarbon-based catalysts and was lower by ∼180 mV than the 20% Pt/C . The advantageous traits of NCNTFs, such as hierarchical shells of interconnected crystalline NCNT, optimum graphitic degree, and N-doping level, are the source of the excellent electrocatalytic activity of both ORR and OER.Heteroatom-doped carbon nanomaterials are considered to be promising electrocatalysts for the electrocatalytic reaction process. Direct formation of NCNTFs C and 8D h 0.84 V E and posIn summary, MOF-derived hollow nanostructures are promising candidates for applications in electrocatalytic reactions owing to their hierarchical porous structures, accessible active sites, high chemical stability, and good electron conductivity. Electrocatalytic reactions such as ORR, HER, and OER are crucial reaction steps in energy conversion and require catalysts to accelerate their slow kinetics. The performance of the catalyst plays an important role in energy conversion efficiency. Although MOF-derived catalysts have made great achievements in electrocatalytic applications, several problems and challenges still exist, such as device durability, stability, cost issues, catalytic performance, structure-activity relationships, etc. Therefore, the above issues should be considered when designing electrocatalysts.,MOF-derived hollow nanostructures with extremely porous structures, low density, robust architecture, large surface area, and rich redox reactions of metal ions have verified their unique capabilities and exhibited improved energy storage and conversion performance.,3O4,,,,xCo3-xO4,4/Co3O4,3O4/TiO2,3O4,2O4/C,2O4/NiO,2O3,9S8,3O4@Co3V2O8 hollow structures were prepared and applied for LIBs.3O4@Co3V2O8 shows superior rate capability, cycling stability, and reversible capacity. Moreover, after a long charge and discharge cycle, the complex hollow structure of Co3O4@Co3V2O8 is almost unchanged, indicating the stability of the hollow structure in LIBs. In addition to LIBs, MOF-derived hollow structures, i.e., VN-NBs,xSy,Various novel MOF-derived hollow structures, such as CuO,5/HNPC) with an optimal Ni-N5 active moiety, which acted as an ideal host for a sulfur cathode under the guidance of theoretical simulations.x/C structure (x = 3–5) with the highest cathode performance was selected by first-principles calculation. The energy calculation results of the reaction step indicated that the Ni-N5/C structure is the best cathode candidate. Therefore, they fabricated Ni-N5/HNPC with Ni-N5 active sites using MOFs as self-sacrificing templates. As cathode of Li-S batteries, Ni-N5/HNPC exhibited outstanding rate performance and long-term cycling stability.The sluggishness of the LiPSs redox reactions is a great challenge in the large-scale practical application of Li-S cells.,,3S2/Co9S8/N-doped carbon composites via carbonization and sulfurization of binary Ni/Co MOFs (Ni-Co-MOF).3S2 and Co9S8 NPs (∼7 nm), hollow porous structure, and an ultrathin N-doped carbon coating, the final composite material exhibited excellent performance when used as an anode in SIBs. Experiments showed that a reversible specific capacity of 419.9 mAh g−1 was achieved after 100 cycles at 0.1 A g−1, and a superior capacity retention rate of 98.6% was achieved. In addition, excellent rate performance was observed: at a current density of 2 A g−1, an average capacity of 323.2 mAh g−1 can be reached. The formation of metal sulfide and N-doped carbon layers provides larger capacity and enhanced conductive surface coating. With these virtues, Ni3S2/Co9S8/N-doped carbon composite materials possess fast sodium storage kinetics and high conductivity, thereby achieving high rate properties.Recently, SIBs have been proposed as a potential alternative to LIBs due to the advantage of the high abundance and low cost of the sodium source, high system safety, and wide distribution, as well as storage mechanisms and components similar to those of lithium.2Se3@C composite with a hierarchical nanodot-in-nanofiber structure in which antimony selenide (Sb2Se3) nanocrystallites are confined by both 0D and 1D carbon layers.2Se3@C composite anode achieved enhanced capacity and exceptional cycle lifespan for over 10,000 cycles at 2.0 A g−1 @MXene composite manifests distinguished electrochemistry performance when used as electrode material for all of the LIBs, SIBs, and PIBs, which benefit from the synergistic effect of the components  with outstanding performance in supercapacitors.9S8.Supercapacitors have become an ideal choice of energy storage device for their various advantages such as low internal resistance, high power density, and excellent cycle life.3C2TX/ZIF-67/CoV2O6) by in situ growth of MOFs and subsequent ion exchange.3C2TX/ZIF-67/CoV2O6 overcomes the disadvantage of poor conductivity of traditional MOFs.,3C2TX/ZIF-67/CoV2O6 electrode demonstrated excellent performance with a high specific capacitance of 253.8 F g−1 at 5 A g−1 and a high coulombic efficiency of 94.4% after 4,000 GCD cycles at 3 A g−1.Pang and co-workers proposed a general approach for preparing hollow 3D Mxene/MOF composites  of Ce-MOF/Au@SiO2 (0.71 min−1) is higher than that of Au@SiO2 . Moreover, the catalytic activity was decreased by only ∼17.6% after five successive cycles, indicating that the CeO2/Au@SiO2 catalyst has superior stability and reusability. The outstanding catalytic performance was attributable to the unique and small size of the Au NPs, as well as the strong synergistic effect between the CeO2 and the Au NPs.3O4/carbon as an effective activator of PMPS and achieved the degradation of BPA.Environmental pollution has become a critical issue in human health and environmental protection.1-xCoxFe2O4 microcubes as adsorbents for efficient removal of nitrophenol. The equilibrium quantity of Ni1-xCoxFe2O4 for nitrophenol was 47 mg g−1 of ferrite accomplished in 7 min. High specific surface area and mesoporous nature are the keys to the excellent adsorption performance of Ni1-xCoxFe2O4 on nitrophenol.Adsorption technology is widely used to purify environmental pollutants due to its advantages of simple operation, simple regeneration, and large-scale applications.2+2 was the definite active site  are a robust system to degrade refractor organic pollutants in environmental pollution management. MOF-derived SACs have been widely used due to the maximum utilization of metal atoms and the unique electronic properties of metal sites and ultralow metal loads.ive site A. 1O2 was 98.89% B and 9C.,,,2O4 hollow nanocages and used them as a sensing material for gas sensors. It demonstrated an improved response to acetone (25.8) with a detection limit of 1 ppm.−1) and sustained stability.In addition to the above-mentioned emerging applications, the unique properties of MOF-derived hollow structures enable their applications in gas storage/separation,x-C-R in uranium extraction from seawater and demonstrated considerable results.x-C-R has a superior uranium extraction capacity of ∼1.2 mg g−1 in 24 h. Interestingly, we found that the isolated Fe-Nx site first reduced UO22+ to UO2+, and then oxidized U(V) to U(VI) in the presence of Na+, finally obtaining the product Na2O(UO3·H2O)x (2O(UO3·H2O)x) in uranium extraction from seawater by an adsorption-electrocatalysis system. We further demonstrated that an amidoxime-functionalized indium-nitrogen-carbon catalyst (In-Nx-C-R) offers a 5-fold higher uranium extraction capacity in seawater compared with our aforementioned Fe-Nx-C-R system. X-ray absorption spectroscopy and in situ Raman spectroscopy allowed the relationship between the In-Nx-C-R structure and the adsorption-electrocatalytic mechanism for uranium extraction from seawater to be understood.Recently, our group applied the MOF-derived adsorption-electrocatalyst Fe-NO3·H2O)x D and 9E.2 RR. For example, Ma et al.2@TiO2 nanohybrids with MOFs as precursors through a simple hydrothermal method. The optimal material showed prominent catalytic activity for HER with a high hydrogen production rate of 10,046 μmol h−1 g−1 under visible light. The catalyst obtained also displayed excellent electrocatalytic activity. The extensive and close contact interface and synergistic effect of different components are regarded as the source of enhanced catalytic activity. Moreover, a novel ZnO@C-N-Co core-shell nanocomposite was also reported as a highly efficient photocatalyst for pollutant photodegradation.2 toward the generation of valuable chemicals is one of the important strategies to achieve the dual carbon goal.,2 RR toward the direct production of formic acid.2 RR benefited from the carbon protective layer preventing the reductive corrosion of indium oxide and the carbon layer, optimizing the adsorption of reaction intermediates.In addition to the above applications, MOF-derived porous hollow materials also exhibited excellent performance in photocatalytic and electrocatalytic COWe have systematically summarized the design strategies of MOFs as precursors and/or soft templates in the fabrication of hollow porous materials, including hollow carbon, metals, metal oxides, metal carbides, metal sulfides, metal hydroxides, and their hybrid composites. Due to various favorable structural features, MOF-derived hollow nanomaterials are considered promising candidates for multifield applications: an enhanced surface area, low density, mesoporous structure, higher loading capacity, and shortened transport distance for mass and charge. Here, the promising applications of MOF-derived hollow structures for chemical catalysis, electrocatalysis, energy storage and conversion, environmental applications, and so on have been summarized.Despite the intriguing progress and great achievements that have occurred in the synthesis and extensive application of various MOF-derived HPMs, the study is at a burgeoning stage, and more effort is needed to deal with the issues that will be encountered in the future development process. Here, we propose several challenges and research directions that MOF-derived hollow materials may face in future development: (1) more effort should be focused on controllably synthesizing complex structures and regulating components of hollow MOFs and derivatives according to the needs of specific applications; (2) combination with other functional nanomaterials, for example, NPs, clusters, CNTs, and GO, etc., is an economical and facile strategy to regulate the properties of hollow MOFs and their derivatives; (3) the design of hollow MOFs or their derivatives with different sizes and geometrical structures will greatly enrich the storage of HPMs and ultimately affect their internal properties; (4) realizing the large-scale yield of hollow MOFs or derivatives is significant in practical applications; (5) strengthening the deep understanding of structure-activity relationships of hollow material structures is important; particularly, the mechanisms of various MOF-derived hollow materials in electrochemistry have not been thoroughly investigated; and (6) future work should combine experimental and computational methods to explore the interior reaction mechanisms, revealing the influence of structure-property-function and their synergistic interactions.


The correlation study identified a positive association between shoot dry weight and root dry weight. The genome-wide association study was conducted on root traits of 14 and 28 days with 2 million single-nucleotide polymorphisms (SNPs) using an efficient mixed model. QTLs over a significant threshold of p < 0.0001 and a 10% false discovery rate were selected to identify genes involved in root growth related to root architecture and nutrient acquisition from 97 QTLs. Candidate genes under these QTLs were explored. On chromosome 4, around 30 Mbp are two important peptide transporters (PTR5 and PTR6) involved in mobilizing nitrogen in the root during the early vegetative stage. In addition, several P transporters and expansin genes with superior haplotypes are discussed. A novel QTL from 21.12 to 21.46 Mb on chromosome 7 with two linkage disequilibrium (LD) blocks governing root length at 14 days were identified. The QTLs/candidate genes with superior haplotype for early root vigor reported here could be explored further to develop genotypes for DSR conditions.Water and land resources have been aggressively exploited in the recent decades to meet the growing demands for food. The changing climate has prompted rice scientists and farmers of the tropics and subtropics to adopt the direct seeded rice (DSR) system. DSR system of rice cultivation significantly reduces freshwater consumption and labor requirements, while increasing system productivity, resource use efficiency, and reducing greenhouse gas emissions. Early root vigor is an essential trait required in an ideal DSR system of rice cultivation to ensure a good crop stand, adequate uptake of water, nutrients and compete with weeds. The  Oryza sativa L.), is grown in a variety of environments, covering a wide range of latitudes, altitudes, and hydrologies. It feeds more than half of the world’s population, especially in Asia where it serves as the main source of carbohydrates. The consumption is as high as 510.6 million tons (estimated) worldwide in the crop year 2020-2021.1 This data illustrate the high demand for the crop and the ongoing intensive production system. Because of its high-water usage  and substantial emissions of the greenhouse gas methane, the traditional transplanted technique of rice farming has prompted particular environmental concerns. This system also carries a high labor cost. A recent UN report in 2021 has stressed the need to move toward a more sustainable approach that can address the ongoing faulty agricultural practices and global climate change by smart planning and coordination of sustainable farming practices (Rice (ractices . In ordeDirect seeded rice (DSR) is one such approach that has the potential to reduce water consumption and labor requirements significantly, while increasing system productivity, resource use efficiency, and checking greenhouse gas emissions . In thisAus, a diverse group that evolved from the annuals Oryza nivara found in Bangladesh, Northern Myanmar, and NE India  from the surface soil. For instance, phosphorus (P) is an element highly required for root growth; plants start transporting P from the second day of germination  and, in seedling  and withseedling , RLCKs , for the discovery of new markers to be used in marker-assisted selection (MAS). Earlier, studies exploiting GWAS have mainly reported QTLs linked to shoot traits influencing seedling vigor. Thus, our objective was to dissect root vigor traits using high-density single-nucleotide polymorphisms (SNPs) between QTLs governing early root and shoot traits and their candidate genes under limited nitrogen conditions in DSR. These SNPs can aid in the identification of superior haplotypes that can be utilized in haplotype-assisted breeding for DSR conditions.aus landraces ] have been utilized in the present study to identify the underlying QTLs and construct haplotypes governing root vigor traits for GWASs.A total of 298 representatives from the Bengal and Assam Aus Panel (BAAP) developed by andraces , 19 of tandraces  plus somandraces . The ∼2 aus population was screened under low N (low soil N levels) at ICAR-National Rice Research Institute, Cuttack  during two consecutive seasons of 2018 Kharif (wet season) and 2019 Rabi (dry season) in the upland situation, i.e., non-saturated aerobic condition with supplemental surface irrigation. The sandy clay loam soil of our experimental plot recorded 0.53% organic carbon, 220 kg/ha of N, 26.3 kg/ha of P, 164.05 K kg/ha, 51.6% sand, 18% silt, and 30.4% clay with a bulk density of 1.41 g/cm3. To assess the early root growth parameters under limited nutrient DSR conditions, N fertilizer was not applied for the entire experimental period of 28 days, while, recommended 100% P (40 kg) and 50% K (20 kg) fertilizer was applied as basal. The subsurface soil compaction was measured using a penetrometer, the resistance ranged between 11 Kpa (15 mm) and 2,148 Kpa (600 mm). In the 2018 wet season, on average the plants received 33.4°C during the day, 25.5°C at night, and sunshine for 3.2 h per day with total rainfall of 190 mm. In the 2019 dry season, plants received an average temperature of 28.15°C during the day, 12.86°C at night, and sunshine for 4.54 h per day with nil rainfall days during the observation period. Four to five seeds of each genotype were sown per hill manually in 3 rows of 1.5 m long, with a spacing of 20 cm between rows and 15 cm between plants in two replicates by following a randomized block experimental design. Weed growth was checked by spraying the pre-emergence herbicide Pendimethalin (at the recommended dose) within 24 h of irrigation. Further hand weeding was done on 15 days after sowing (DAS) to keep the field weed free.The mapping panel of Different vegetative traits concerning root growth were undertaken to assess root vigor (RV) on 14 and 28 DAS. Six rice plants in the middle row from each genotype were selected to study different root and shoot traits. For this, the border plants of the middle rows were excluded, and three consecutive hills were harvested each for 14 and 28 DAS leaving one hill in between the two samples. To have maximum roots during the excavation of plants for observation, the experimental plot was flooded on the day before uprooting. The uprooted seedlings from the field were carefully washed in running tap water to remove soil for measuring root-related parameters such as root length (cm), number of crown roots, and root dry weight (g) on both 14 and 28 DAS. The average root length was measured from the crown of the root to the tip of the root. Shoot weight was also recorded to study the relation between root trait manifestation and shoot biomass accumulation. To observe the dry weight of the shoot and root, the samples were dried in an air-forced oven at 60°C for 5–6 days until the samples were completely dried. These observations were recorded for two seasons as mentioned before.Box plot was deployed to derive the various initial descriptive statistics that included mean, SD, minimum and maximum values, coefficient of variation (%), skewness, kurtosis, and distribution pattern. Absolute growth rate (AGR), crop growth rate (CGR), and relative growth rate (RGR) were calculated for the root traits.Absolute growth rate defines the rate in change of root length and was calculated as follows:1 and L2 are the root length at times t1 (14th  day) and t2 (28th  day), respectively.where L–2 day–1.CGR measures the root dry weight of a particular ground area at a regular interval of time divided by land area and represented as g m1 and W2 are the root dry weights at times t1 (14th  day) and t2 (28th  day), respectively, P = spacing (m2).where W–1 day–1.RGR defines the rate of change in logarithmic root dry weight as follows in mg g1 and W2 are the root dry weights at times t1 (14th  day) and t2 (28th  day), respectively.where WThe variability in traits related to root vigor was described using a PCA. PCA analysis was carried out using the FactoMine R package  in R 3.6p < 0.0001 to identify significant SNPs. Benjamini–Hochberg adjusted probabilities were calculated using the false discovery rate (FDR) of detected associations. The significance threshold of FDR was maintained at 10% to identify putative SNP associations (10(P) < 4 were examined to group the SNPs into QTLs. SNPs that were closer than the genome average linkage disequilibrium (LD) decay value (of 243 Kbp) were assumed to be of the same locus.The BAAP population was subjected to GWA mapping using the PIQUE pipeline in order to preprocess the genotype and phenotype data  for subsciations  and werer2-values were calculated for every SNP with p < 0.0001 and the surrounding SNPs were within the range of 243 kb and also had a p < 0.0001. Any two such SNPs that met these criteria along with an r2 ≥ 0.3 were clumped into bins. Binning was performed for each experiment and trait studied. SNPs that did not meet the above criteria were considered singleton. The QTLs were reported only when they harbored at least one significant SNP (p > 0.0001) with a 10% FDR.Based on the decay of LD, a sliding window was defined to bin together the significant SNPs into peaks, using PLINK  with par3, release 7. The genes with annotations such as “(retro) transposon” and “hypothetical” were excluded from the identification of candidate gene analysis. To understand the gene function and ontology, the RGAP website was used. Additionally, all the available research reports and other online resources were searched exhaustively for any information regarding the genes in the LD block. Any gene that currently has a function related to root vigor including growth, development, or regulation of root metabolic activities was taken into account. Then, the level of expression of these shortlisted genes in the roots was checked from the Rice Expression Profile Database (RiceXpro) database. The RiceXpro repository provides tissue-specific profiles of expression for every gene in the reference cultivar Nipponbare. Only those genes that were expressed in the roots and had a definitive role in the traits related to root vigor and also present in the same LD block as that of the peak SNP were selected as candidate genes. QTLs were identified across traits and/or seasons to be associated with various root traits significantly and the LD heatmap surrounding the peaks of these QTLs was constructed using the “LDheatmap,” an R package that uses squared Pearson’s correlation coefficient (r2). The SNPs that were significantly associated with the root traits studied were extracted using PLINK. The non-synonymous and synonymous SNPs within the exon regions of the candidate genes were identified on the Nipponbare reference genome from the snp-seek.irri.org database. These SNPs in the exon regions were used to group the population into haplotypes and the phenotypic mean performance of each haplotype was determined.For each QTL, the LD decay value of 243 kbp was considered around the peak SNP and all the genes present in this stretch were annotated using the Rice Genome Annotation Project (RGAP)–1 while in the dry season it was 0.001 g day–1. The mean shoot dry weight at 28 days however recorded the same value of 0.63 g both in dry and wet seasons. Correlation studies done in the population revealed a highly positive correlation between the root dry weight (28 days) with RGR (0.78), and CGR (0.97) in the dry season  and CGR had one of the highest coefficients in both dimensions 1 and 2. PC1 showed greater expression for traits like crown root number, root length, root dry weight at 28 days, RGR, AGR, and CGR in the wet season. PC2 showed positive values for the traits root dry weight at 28 days, RGR, AGR, and CGR in the dry season  in the roots were selected for haplotype analysis. These QTLs were distributed across chromosomes, one for crown root number in chromosome 6, two for root dry weight in chromosome 3, two for root length in chromosome 7, and one for AGR in chromosome 4.Genome-wide association mapping conducted on the BAAP population highlighted significant genomic loci, associated QTLs, and genes that regulate various root vigor-related traits at the early seedling stage of rice in DSR conditions under low nitrogen soil status. A total of 97 QTLs associated with at least one of the studied root traits were identified across seasons . Few of 34 genes , 2 were OsGlpT2 (LOC_Os06g08170), a glycerol-3-phosphate transporter 2 gene was selected as the candidate gene for the haplotype study as there was a previous report of this gene’s role in Pi influx in plants , 3,950,213 bp (T/C polymorphism), 3,960,275 (G/A polymorphism), and 3,962,787 (T/A polymorphism) that resulted in the amino acid substitution from Arg (R) to Cys (C), Cys (C) to Arg (R), Gly (G) to Ser (S), and Ser (S) to Thr (T), respectively. The genotypes in this study were grouped into three haplotypes; hap A (n = 3), hap B (n = 153), and hap C (n = 43) for the above-mentioned SNPs. Even though the distinct superiority of haplotype A can be visualized, its reliability is rather less due to the lower number of representatives. However, hap B (12.31) and hap C (14.72) were significantly different than each other and the latter had a better proliferation of crown roots.A QTL on chromosome 6, centered around 4.02 Mb was significantly associated with crown root number at 28 days (wet season). The pairwise LD correlations have highlighted a region from 3.71 Mb to 4.20 Mb as the length of this QTL . Taking n plants . They arOsEXPA12), LOC_Os03g06010 (OsEXPA25), LOC_Os03g06020 (OsEXPA15), LOC_Os03g06040 (OsEXPA18), and LOC_Os03g06060 (OsEXPA20). These genes have been reported to be root-specific and help in the development of outer cell layers (n = 13), hap B (n = 169), and hap C (n = 20) (OsPht 1:2) was chosen as the candidate gene for the haplotype study. It is reported to be a phosphate transporter expressed at the highest levels in the roots during the vegetative stage (RiceXpro database). In total, 53 SNPs were present in this region recognized in the BAAP 2 million SNP database. Of these, 11 SNPs were in the exon region of which 5 SNPs were responsible for non-synonymous changes. These were localized at 2,811,922 bp (G/A polymorphism), 2,812,729 bp (T/A polymorphism), 2,816,130 bp (T/C polymorphism), 2,816,550 bp (G/C polymorphism), and 2,816,770 bp (C/T polymorphism). These resulted in the following amino acid changes: Asp (D) to Asn (N), Phe (F) to Tyr (Y), Leu (L) to Pro (P), Cys (C) to Ser (S), and Leu (L) to Phe (F). Besides these, six synonymous mutations were occurring in this region. The studied cultivars formed three haplotypes based on the above-mentioned SNP; hap A (n = 60), hap B (n = 20), and hap C (n = 119) . The pairwise LD correlations  have higl layers . There w(n = 20) . The hap(n = 20) . Anothern = 119) . The hapn = 119) .PTR5) and LOC_Os04g50950 (PTR6). Both of these genes are reported to be contributing to plant growth by increasing nitrogen uptake (RiceXpro database). A total of 37 SNPs have been identified in the BAAP 2 million SNP database from this QTL region of which only three were located in the exon region. One of them was a non-synonymous change in SNP; 30,161,942 bp (LOC_Os04g50950) with A/G polymorphism leading to a change in amino acid; Ile (I) to Val (V). There were two synonymous SNPs located in this region. The cultivars were grouped into two haplotypes, hap A (n = 125) and hap B (n = 126). Haplotype A (0.00103) was superior to haplotype B (0.00131).Another QTL on chromosome 4, stretched across a region from 29.99 to 30.16 Mb was significantly associated with absolute root growth (dry season) . This ren uptake , and alsRLCK family genes that had significant roles in influencing root traits under DSR. The major ones were OsRLCK234 (LOC_Os07g35280) and OsRLCK235 (LOC_Os07g35390). All of these genes have been reported to be having high levels of expression at the vegetative stage in the roots in the RiceXpro database. As this was a large segment of the chromosome, only the significant SNPs were considered for haplotype mapping. This included the following non-synonymous SNPs in the exon region: 21,116,858 bp (T/G polymorphism) in LOC_Os07g35280, 21,141,586 bp (A/G polymorphism) in LOC_Os07g35330, and 21,121,651 bp (T/A polymorphism) in LOC_Os07g35920 leading to changes in amino acids; Ser (S) to Ala (A), Asp (D) to Gly (G), and Val (V) to Glu (E), respectively. These SNPs grouped the studied haplotypes into three haplotypes; Hap A (n = 69), Hap B (n = 52), and Hap C (n = 132). The haplotype A (6.15 cm) was superior and significantly different than the lowest mean Haplotype B (5.42 cm) and C (6.07 cm). Another candidate gene associated with root length (at 14 days) was identified in the next LD block at 21.46 Mb. This region harbored LOC_Os07g35860 (UCL22) associated significantly with root length at 14 days. The significant SNPs were identified for the haplotype study out of which two were non-synonymous in the exon region located at 21,359,776 bp (C/G polymorphism) and 21,378,144 bp (T/C polymorphism) that led to changes in amino acids such as Pro (P) to Ala (A) and Ser (S) to Pro (P), respectively. These SNPs have grouped the cultivars in this study into the four haplotypes; Hap A (n = 7), Hap B (n = 15), Hap C (n = 57), and Hap D (n = 174). Hap D (6.09 cm) was the superior group with a high mean significantly different than the low mean group; Hap A (4.74 cm).A QTL associated with root length at 14 days (dry season) was identified on chromosome 7 centered around 21.27 Mb having two LD blocks (21.12–21.30 and 21.35–21.46 Mb) . The firAMT1; an ammonium transporter , NRT2.2 (LOC_Os02g02190), NPF6.5 (LOC_Os10g40600), NPF7.4 (LOC_Os04g50940), and PTR6 (LOC_Os04g50950) were expressed in the dry season whereas transporters like AMT1.2 (LOC_Os02g40730), AMT1.3 (LOC_Os02g40710), and AMT3.2 (LOC_Os03g62200) were significant in the wet season. Another important aspect of the experiment was the field maintained under nitrogen-deficient conditions. In the DSR system, the weed menace is a major problem, and to address this situation, there have been suggestions to avoid the basal dose of nitrogen. Instead of the basal dose, it is recommended to apply nitrogen at a later stage (preferably at 14 DAS) which gives the crop a head start against the weeds , OsPht1;1 (LOC_Os03g05620), GLPT2 (LOC_Os06g08170), and OsMYB30 (LOC_Os02g41510) among many others. We can put forward the idea that these genes and transporters may play a pivotal role in the initial root development and nutrient uptake even in nitrogen-deficient soil. The BAAP population under study displayed a wide range of variability for all the root morphological characters and a clear significant difference between the two different soil conditions in the dry and wet seasons. The dry season had high mean values for all the root traits that include root number, length, and dry weight at both 14 and 28 days. This reflects the need of the plant for better root proliferation under moisture stress in the dry season as compared to the wet season. A locus LOC_Os02g50350 encoding the gene OsDHODH1 was found to be significantly associated with root vigor trait in the GWAS study specifically in the dry season. The overexpression of OsDHODH1 is related to drought stress response in rice and could serve as a potential candidate gene for drought tolerance in rice (OsGRAS23) (OsAKT1)  (OsAHP1)   (OsNAC1) (OsERF107), and LOC_Os04g46220 (OsERF1) . This difference not only alters the root extensions but also the transporters operating at the cellular level. In such a soil environment, it is crucial to realize the importance of both genes and the transporters involved in root development. At the nutrient level, this study highlights the importance of nitrogen in the soil maintained under deficient conditions. For instance, transporters like nsporter  is activr family  is functhe weeds . Nitrogehe weeds  because he weeds . It is ahe weeds , an impohe weeds . The res in rice , especia in rice . Other dsGRAS23) , LOC_Os0 uptake) , LOC_Os0(OsAHP1) , LOC_Os0sPIP2;5)   , LOC_Os0sTIP4;1)  in the d(OsNAC1) , LOC_Os0(OsERF1)  in the wZIP4) (ZIP7) (YSL2) (YSL15) (CASP1) (TOM1) (TOM2)  (GLPT2) (OsPT2)  LOC_Os06g21950 , (PAP1B) (OsHAK16) (OsHAK18) (NRT2.1) (NRT2.2) (OsIPT4), LOC_Os04g50940 (PTR5), LOC_Os04g50950 (PTR6), LOC_Os12g43440 (TOND1) (OsAMT1.3), LOC_Os02g40730 (OsAMT1.2) (OsAMT3.2)  , LOC_Os0) (ZIP7) , LOC_Os1) (YSL2) , LOC_Os0 (YSL15) , LOC_Os0 (CASP1) , LOC_Os1) (TOM1) , and LOC) (TOM2)  that enh) (TOM2) , LOC_Os0sPHO1;2) , LOC_Os0 (GLPT2) , LOC_Os0 (OsPT2) , LOC_Os0ht1;10), , and LOC (PAP1B)  in relatOsHAK16) , LOC_Os0OsHAK16) , LOC_Os0OsHAK18) , LOC_Os0(NRT2.1) , LOC_Os0(NRT2.2) , LOC_Os0 (TOND1) , LOC_Os0sAMT1.2) , and LOCsAMT3.2)  for nitrsAMT3.2)  in the dsAMT3.2) , LOC_Os0sAMT3.2) , and LOCsAMT3.2)  in wet sexudates . This caERF3) (ERF107) (OsRR2) (OsARD2) (OsCRL5) (OsCRL6) . There was a significant interaction between the genotypes and seasons for the crown root number at 28 days. Some of the important QTL regions that harbored genes controlling the development of crown root were found in association with root traits in this study, few important ones were LOC_Os01g58420 (ERF3) , LOC_Os0(ERF107) , LOC_Os0 (OsRR2) , LOC_Os0(OsARD2) , LOC_Os0(OsCRL5) , and LOC(OsCRL6) . This hiOsEXPA12) (OsRLCK234), LOC_Os07g35390 (OsRLCK235) (OsRAA1)  , LOC_Os0RLCK235) , and LOC(OsRAA1) . CultivaThe main aim of the study was to visualize the phenotypic variations of the root and then associate them with the variations at the SNP level, candidate genes regulating them, study their functional annotations, and the diverse haplotypes that they form in the BAAP population. Many such QTLs controlling root vigor are already identified pertaining to seedling establishment, root growth, and nutrient uptake. In this study, we found a total of 97 QTL regions strongly associated with different root traits controlling, nutrient, hormonal and growth dynamics. Few of the QTL regions were expressed repeatedly; the QTL region 3.00–3.09 Mb of chromosome 3 was associated with root dry weight 28 days that possessed two candidate genic regions (expansin genes and phosphate transporters). Few of these were already reported while few other regions identified in this study have not been previously reported, for instance, the two haplotype regions (which can be considered as two LD blocks) associated with root length at 14 days from the region of 21.11 to 21.37 Mb on chromosome 7.Pht and EXPA. The haplotype for phosphate transporters included LOC_Os03g05620 (OsPhT1) and LOC_Os03g05640 (OsPhT2). Among these genes, OsPhT1, a high-affinity phosphate transporter is constitutively expressed and involved in the transport of Pi across plasma membrane at the soil root interface while OsPhT2, a low-affinity phosphate transporter involved in Pi transport between subcellular components is induced due to Pi deficiency in the roots (Nipponbare) at all the five SNP positions with the lowest mean root dry weight present in the highest number of aus cultivars. The haplotype A was significantly different having the highest mean and the mutant SNPs at three positions were for LOC_Os03g05640 (OsPhT2), these changes were from Leucine to Proline, Cysteine to Serine, and leucine to phenyl alanine. However, these three changes were similar to that of Haplotype C, but the difference existed in the initial two SNPs representing the locus LOC_Os03g05630 (expressed protein). The substitution here was Aspartic Acid to Asparagine and Phenylalanine to Tyrosine at the positions 2,813,584 and 2,811,999 bp, respectively. Thus, the loci need to be further studied for their putative role in root growth. The QTL region strongly associated with root dry weight harboring expansin genes was overlapping with the above-discussed region. This region represented the candidate genes such as LOC_Os03g06000 (EXPA12), LOC_Os03g06010 (EXPA25), LOC_Os03g06020 (EXPA15), LOC_Os03g06040 (EXPA18), and LOC_Os03g06060 (EXPA20). The expansin proteins help in root cell wall expansion by loosening the cell wall and expansion of epidermal cells to form long coleorhiza hairs. Of the three non-synonymous substitutions in this region, two are in the EXPA25 exon region and one is in the EXPA20 exon region. These three SNPs have grouped the aus cultivars into three different haplotypes. The most superior group with high mean root dry weight is Haplotype A with mutations in the SNP positions; 3,004,023 and 3,004,206 bp, one in each of the two genes mentioned above while the third position 3,037,443 bp resembled the wild-type. This led to a change in amino acids from Leucine to Phenylalanine in both positions. The gene EXPA20 is highly expressed in the roots, especially in the early vegetative stages as suggested by the transcriptome analysis using microarray in the RiceXPro database. Crown root number at 28 days had a strong association with a QTL on chromosome 6 with a high peak centered around the region 4.02 Mb. LOC_Os06g08170 (GLPT2) was chosen as the candidate gene coding for a Glycerol-3-Phosphate transporter involved in the Pi release from the vacuoles to the cytoplasm and helps to adapt to low-Pi stress, this, in turn, modulates the root development. A receptor-like-protein kinase and a protein phosphatase were also present in this region within the QTL. Of the four non-synonymous SNPs, one  was in the GLPT2 exon region, two  in the protein phosphatase gene, and one  in the receptor-like-protein kinase locus, leading to amino acid substitutions; Arginine to Cysteine, Cysteine to Arginine, Glycine to Serine, and Serine to Threonine, respectively. These changes grouped the aus cultivars into three haplotypes, the superior one haplotype A was the rare group with a high number of crown roots and significantly different from the others. AGR, one of the relative traits had a strong association with a QTL region on chromosome 4, this region had two important peptide transporters adjacent to each other; LOC_Os04g50940 (PTR5) and LOC_Os04g50950 (PTR6). These two genes are reported to be nitrogen transporters with high expression in the root during the vegetative stages. However, there was only one non-synonymous SNP in this region changing the amino acid from the wild-type isoleucine to mutant type valine in the PTR6 exon sequence.QTL regions and the candidate genomic regions were selected on the level of association, LD plots, and Manhattan peaks. The selection criteria for these genes were organ-specific, i.e., governing the growth and proliferation of the roots. Six different genomic regions are reported in detail in this study, of which three were related to root dry weight, one for crown root number, two for root length, and one for AGR. Two haplotypes concerning root dry weight were identified on chromosome 3, within the QTL region spanning from 3.00 to 3.09 Mb. The proposed candidate genes for these two haplotypes were of the family he roots . The nonOsRLCK234) and LOC_Os07g35390 (OsRLCK235) and according to the microarray transcriptomic data available in RiceXpro, both of them are highly expressed in the vegetative roots. We have found three non-synonymous SNPs in this entire stretch; 21,116,858, 21,121,651, and 21,141,586 bp leading to amino acid changes; Alanine to Serine, Glutamic acid to Valine, and Glycine to Aspartic acid, respectively. These substitutions divided the cultivars studied here into three haplotypes. The superior haplotype A had a mutation at 21,141,586 bp (Glycine to Aspartic acid) in the exon region of LOC_Os07g35330, which is identified as DUF26 kinases having homology with DUF26 containing loci. The other LD block around the same region associated with root length also had many loci without proper functional annotation that are yet to be validated. One of the major genes in this region was the LOC_Os07g35860 (UCL22). Only two non-synonymous SNPs were identified located at 21,359,776 and 21,378,144 bp leading to a change in amino acids from Alanine to Proline and Alanine to Serine, respectively. With the two non-synonymous substitutions, the aus cultivars in this study were grouped into four haplotypes. The superior haplotype was haplotype D, with non-synonymous change at 21,378,144 bp located in the exon regions of LOC_Os07g35690. As they displayed high peaks in the Manhattan plots and had significant LD values, we speculate this region to be coding for some major root length governing gene and can serve as a candidate region for developing vigorous root growing varieties for DSR condition.Two separate LD blocks were identified adjacent to each other regulating root length of 2 weeks old around the region from 21.12 to 21.46 Mb on chromosome 7. These two regions harbored gene loci that were constantly upregulated and had a strong association with root length, however, there were no earlier reports regarding these. The first block had the loci LOC_Os07g35280  but low in the case of AUS 68 (0.0008 g day–1) but with high root biomass. Such a trend further sheds light on the fact that biomass accumulation in the initial period must be very high, i.e., in the first 14 days. Such a trait is highly essential for a plant to establish itself successfully under the direct-seeded condition of rice. Two lines represented across inferior groups were also identified, the allelic mutations of these genotypes could serve as markers for a casual phenotype. These were Polman and NP97 with root dry weights of 0.0045 and 0.0054 g, respectively. The average number of crown roots was 7.2 and 5.4 for Polman and NP97, respectively.The identification of superior haplotypes also helped us to highlight well-performing genotypes from the BAAP panel that could serve as donors for various early root vigor traits which can be exploited in a haplotype-based breeding program to design ideal plants with ideal early root vigor. The root dry weight or the biomass accumulated over 28 days, root length, crown root number, and AGR root were the major traits that were analyzed for different genes in the haplotype studies, is an important criterion for categorizing ideal performing genotypes. The genotypes Lara (BAAP251), AUS 68 (BAAP29), and AUS 294 (BAAP60) were considered superior based on their representation in the superior haplotypes of the studied traits. The root lengths of these genotypes were 7.12, 6.94, and 6.29 cm at 14 days which was higher than the superior group average. The root dry weight at 28 days of Lara was 0.0168 g with AGR of the root being 0.0013 g dayOsPht1;1, OsPht1;2, OsPht1;3, OsPht1;8, OsPht1;9, OsPht1;10, OsPht1;6, PT26, and GLPT2. The Pht transporters (both high- and low-affinity transporters) have been known to play a wide range of roles in Pi uptake and its translocation to the shoots through OsPHO1:1 and OsPHO1:2. A slight variation in the protein sequence of the PHT1 proteins can lead to varying degrees of Pi acquisition   involved under upland aerobic conditions , nutrient acquisition by the roots, and its transport to plant parts above the ground. Thus, to model a plant with ideal early root vigor traits, one needs to understand the key players involved in regulating the above-mentioned features of the root. A list of 275 unique putative genes related to root architecture and nutrient acquisition were identified in this study from 97 QTLs. The identified genes associated significantly with various traits in this study have been studied to understand their role in the manifestation of various root characteristics  and are uisition . In this , multiconditions  and TOM1nditions . Nitrogeaus population was evaluated for early root vigor under direct-seeded conditions over two seasons (dry and wet seasons). The studied root traits exhibited significantly higher mean values in the dry season as compared to the plants grown during the wet season. The root dry weight at 28 days had a positive association with RGR, AGR, and CGR. Notably, shoot dry weight at 28 days had a high association with root dry weight at 28 days. The GWA study of 12 root traits and six growth rate parameters identified 275 unique putative genes expressed in roots related to root architecture and nutrient acquisition under direct-seeded conditions from 97 QTLs. Among them notably, ammonium transporters played a lead role in the nitrogen acquisition activity under high precipitation, while nitrate transporters were found expressed during the dry season. Compared to N-related genes, a maximum number of P-related genes, transporters, and transcription factors were found to play a major role in early root vigor under direct-seeded conditions. This suggests that P-related genes may have a significant role in root proliferation at an early stage of rice seedlings. The haplotype analysis serves to identify superior haplotypes for notable genes and novel QTLs involved in early root vigor. Besides, the donors with superior haplotypes that were identified would be useful for future studies to design ideal plants with ideal early root vigor for direct-seeded conditions to aid haplotype-assisted breeding.In this study, the The original contributions presented in this study are included in the article/AA designed and conducted the field experiments. AT developed the GWAS pipeline. SP, AA, SS, AP, and GN performed the data analysis and wrote the first draft of the manuscript. All authors read and approved the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Subsequent iteration over all blocks m-times produces chains of length m × n. We use this strategy to solve large-scale genomic prediction and fine-mapping problems using the Bayesian MCMC mixed-effects genetic model, BayesR3. We validate the method using simulated data, followed by analysis of empirical dairy cattle data using high dimension milk mid infra-red spectra data as an example of “omics” data and show its use to increase the precision of mapping variants affecting milk, fat, and protein yields relative to a univariate analysis of milk, fat, and protein.Bayesian methods, such as BayesR, for predicting the genetic value or risk of individuals from their genotypes, such as Single Nucleotide Polymorphisms (SNP), are often implemented using a Markov Chain Monte Carlo (MCMC) process. However, the generation of Markov chains is computationally slow. We introduce a form of blocked Gibbs sampling for estimating SNP effects from Markov chains that greatly reduces computational time by sampling each SNP effect iteratively  BayesR3 samples the polymorphisms affecting complex traits at reduced computational cost to predict the genetic value, breeding value, or individual risk of genotypes. Despite the availability of assays for many thousands of Single Nucleotide Polymorphisms (SNPs) for around 20 years, knowledge of the polymorphisms that explain the genetic variation in complex traits is still limited. There are two difficulties in mapping and identifying these causal variants—the effects are typically very small and linkage disequilibria (LD) between polymorphisms make it hard to identify the true causal variants. Consequently, the best strategy is likely to be to estimate the effect of variants simultaneously across the genome, where the effects on the trait, or phenotype, are treated as random variables sampled from a distribution. This analysis is known as genomic selection or genomic prediction (GP)7.Many important traits in medicine, agriculture, and evolution are complex and are quantitative traits controlled by many genes and environmental factors9. To represent such a distribution, it is common to use a slab and spike prior and the slab may represent a long-tailed distribution7. For instance, Erbe et al. introduced a model called BayesR in which the SNP effects follow a mixture of normal distributions including a component with zero variance and effects . Genomic prediction methods such as BayesR may provide information about the genetic architecture of complex trait, map the causal variants to regions of the genome, and predict the genetic value of individuals from their genotypes. For instance, this might be a prediction of a person’s risk of disease12 or, in agriculture, the genetic value of individual plants or animals so that the best are selected as parents of the next generation14.Methods of GP use a mixed-effects linear regression model in which the effect of the marker genotypes, such as SNPs, are treated as random effects, allowing these effects to be estimated even when their number is much greater than the number of phenotypic records. Bayesian methods to do this differ in the prior distribution assumed for the marker effects in this linear model. If they are assumed to be drawn from a normal distribution with mean zero and constant variance, the method is Best Linear Unbiased Prediction (BLUP). However, experimental evidence suggests that many SNPs have no effect, some a small effect and a few a large effect on the trait17 or variational Bayes, sacrifice prediction accuracy for speed. Therefore, attention has focused on making the MCMC process more efficient. A recent approach18 advocated estimating SNP effects in parallel, but it required many computer nodes, hundreds of cores, and twice the expected memory (RAM), thereby restricting its utility to all but the largest computer facilities. Residual updating within a Gibbs sampling scheme is a process analogous to a Gauss-Seidel solution of linear equations in which one SNP is processed at a time, conditional on knowing the other effects, and after the solution is updated, the residuals for all records are updated21.The updating of all the residuals for every SNP in every Gibbs cycle (iteration) is probably the main reason for the long compute time taken. Calus19 sped up the Bayesian MCMC procedure SSVS (stochastic search variable selection) by processing 5 or 6 SNPs at a time. Chen et al.22, exploiting sparsity between markers, produced an updating procedure by keeping V′V in memory, where V is the genotype matrix, and updating SNP effects only when SNP effects were estimated to change. This approach adds significantly to the amount of computer RAM required for analysis, especially as the number of phenotypes and SNPs increase. Still, these MCMC updating procedures remain slower than a BLUP solution23.SNP effects are commonly estimated using a Markov Chain Monte Carlo (MCMC) algorithm, but MCMC methods are slow. Faster non-MCMC solutions, such as EM algorithms13; multi-trait BayesMT24; and to perform BayesRC25 that uses prior information on the SNP effects. We demonstrate that our approach is faster than previous BayesR methods (12) and show its ability to describe the genetic architecture of complex traits, by fine-mapping SNP effects to genomic locations. We apply it to simulated phenotype data, coupled to real genotypes to demonstrate its properties, and then to empirical data on milk yield and composition in a large dairy cattle data set of 75,471 mixed breed Australian bulls and cows with genotypes from an imputed high density 717,463 SNP set. Further, we apply the method to high dimension milk mid-infrared spectral data to illustrate its potential application to “omics” data on traits that are intermediate between genotype and phenotype.Here, we propose an intermediate strategy in which a block of SNPs is processed together. We present an iterative Gibbs sampling of a block conditional posterior distributions of unknown variables. We use this approach  to estimate SNP effects for GP, as in standard BayesRy is an nR is the number of records; X is a u is a nF is the number of fixed effects; V is a coded genotype nM markers (see Methods); g is a vector containing the SNP effects, Z is an identity matrix a is a vector of random genetic effects not explained by the SNPs with polygenic variance represented as A is the relationship matrix. Note also, that W is a diagonal weight matrix as described in the methods.The model assumed for the phenotype or trait values is:13, but any number of distributions can be included in the mixture if needed. For example, it has been reported that adding the variance group 26. Therefore, the allocations values π are also estimated from the data and are assumed to be drawn from a Dirichlet distribution with parameter = , a uniform prior, such that any SNP a priori is equally likely to be assigned to any one of the 4 distributions.The mathematics used here for BayesR3 is given in detail in the methods, but briefly the SNP effects are modelled by a mixture of four normal distributions with zero mean and increasing variances as specified by:mentclass2pt{minimB non-overlapping blocks such that:The decrease in processing time reported below is mainly achieved by processing SNPs in blocks. Here the marker effects are divided sequentially into nB, is determined from the block size, n, and is defined as the least integer greater or equal to n times before the next block is processed. Then after m iterations across all blocks, Markov chains of length n inner cycles within a block and m outer cycles across blocks.The number of blocks, n2): 0.1 (H10) and 0.3 (H30). The genomic model fitted, also included two fixed effects, one for the mean and the other for breed (Holstein and Jersey). Also, a second set of phenotypes for 41,925 cows from 33,555 Holstein and 8370 Jersey genomes was simulated, which was a superset containing the original 20,000 individuals.We applied BayesR3 to data consisting of 400,000 SNPs on 20,000 individuals with simulated phenotypes. The SNP genotypes of the 20,000 individuals were real and were taken from 15,220 Holstein and 4780 Jersey cows. We then tested the predicted SNP effects by their ability to predict the simulated true breeding values (TBV) for 1725 Australian Red cows referred to here as RDC using their real genotypes but simulated SNP effects (see Methods). The traits simulated had two different levels of narrow-sense heritability  block size We compared BayesR with no blocking and n = 25; therefore, the Markov Chain lengths are the same as for BR; and (3) BR3+ where: n = 25. For BR3+ the results are graphed against the number of iterations divided by 25 so that the accuracy etc of BR3+ and BR can be compared when BR3+ has the same number of outer cycles as BR has total iterations. In summary: BR and BR3 produced chains of the same length, while BR3+ produced chains that were 25 times longer. It is seen in Fig. In Fig. u, given As well as high accuracy, we would like the estimated breeding values to be well-calibrated. That is, we would like the regression of true breeding value on estimated breeding value to = 1. . In Fig. r, then the correlation between the mean SNP effects from nC chains and the SNP effects from an infinitely long chain is The estimated SNP effects from an MCMC chain suffer from an error due to sampling. The limited number of samples taken. How many cycles are necessary for the estimated effects to approach the effects that would be obtained from an infinitely long chain? In practice, we run several chains and use the average SNP effect from the several chains. The chains are all independent so we will assume that the estimated effects from any one chain can be modelled as the value from an infinitely long chain plus a sampling error. If the correlation between the estimated SNP effects between two independent chains is Convergence can therefore be checked by comparing the correlation of the SNP effects across chains, and for 5 chains, the mean of 10 correlations is produced, as given in Fig. Figure see Fig. . HoweverThe model for the simulation and the analysis assumed the SNP effects were sampled from a mixture of normal distributions so we can assess the ability of BayesR3 to recover this distribution. The log2 of the number of SNPs falling into each of the 4 mixture components is shown in Fig. Figure nd correlation value is between the true 4000 causal SNP effects to their corresponding estimates, while the 3rd value is the correlation across all SNPs within each of the analysis to their true values, Fig. The values above Fig. The processing speeds for a training set of 20,000 records across 400,000 SNPs are given in Fig. R is the number of records and n is block size  and here this configuration is identified as BR3C. Then we analysed the simulated data where its 400,000 SNPs were assigned to two classes: class 1 contained the 4000 known causal variants, while class 2 contained the other 396,000 SNPs. The effect on predictions accuracy and bias for six test data sets are seen in Table BayesR, like most genomic prediction methods, assumes that the prior probability that a marker affects a trait is the same for all markers. To address this limitation BayesRC was introduced by MacLeod et al.15 and to GBLUP (MTG2 software27), using 25,000 animals with real phenotype data for milk, fat, and protein yields and 717,463 SNP effects shows that BayesR3 is as accurate as EM-BayesR, but 4.3%, on average, more accurate than a GBLUP  describing the mixture distributions. A SNP may be determined to be excluded from the model (meaning it affects none of the traits) or included in the model in which case it is then independently assigned to one of the four distributions for each trait. Therefore, it is possible but unlikely for a SNP to be included in the model but be assigned to the null distribution for all traits. As with the single-trait analysis, multi-trait BayesR3 processes SNPs in blocks to reduce processing time.Modern measurement techniques often generate data on many variables. This includes many “omic” technologies. Here BayesR3’s multi-trait facility was used to analyse mid-infra-red (MIR) spectrometry on milk samples of 9834 Australian dairy cows. The MIR data consisted of absorption peaks recorded for each cow at 537 wavenumbersh2 to decrease from PC1 to PC17  >0.9  of being included in the model > 0.9 was 20 as given in Supplementary Data 0.9 Fig. . The simTo further demonstrate the use of multi-trait BayesR3 for mapping QTL and to confirm the overlap with MIR QTL, a large data set was analysed of 65,637 dairy cattle recorded for milk, fat, and protein yield (traits converted to PC). The observed mixing proportions and heritabilities are in Supplementary Table GHR, and the inorganic pyrophosphate transport regulator, ANKH  >0.9  compared to the BayesR3 (N = 556 50-kb segments) analysis. The y-axis in Fig. BayesR3C was used to re-analyse the milk production data, but this time the SNPs were divided into 4 classes based on our prior knowledge of the posterior probability that they were associated with milk composition as estimated by the analysis of the MIR data. Classes 1 to 4 were in declining order of the MIR posterior probability. Supplementary Table 32. The more flexible prior usually results in higher prediction accuracy than methods that assume all SNP effects are drawn from a single normal distribution such as GBLUP. However, Bayesian methods that are implemented by MCMC require longer computer times than BLUP methods. This paper describes a faster method for implementing BayesR. The increase in speed is achieved by updating the SNP effects in blocks and cycling through the SNPs within a block several times before moving to the next block. That is, there are inner cycles within a block and outer cycles among the blocks.BayesR can be used for 3 purposes—it can describe the genetic architecture of a complex trait; it can map SNPs associated with the trait and it can predict the genetic value or breeding value or individual risk from an individual’s genotypes at markers such as SNPs. BayesR assumes a flexible distribution for SNP effects: it can accommodate many SNPs with no effect, some with a small effect and a very few with a large effect and this is the pattern we have found in this analysis and elsewhere22 is to store the V′V matrix and V′y vector in memory. This avoids processing all individuals for each SNP, but at the cost of a large matrix multiplication for every SNP. Consequently, this latter approach is not advantageous when the number of SNPs is large. The method proposed here is in between these two approaches—we form n times, which is also equal to the number of SNPs in the block, before returning to the outer loop by updating the residuals and moving to the next block.The most common method for implementing these Bayesian models is to update one SNP, then correct the residual phenotype for all individuals and proceed to the next SNP. Thus, in every cycle for every SNP a pass is made through the list of individuals causing the computer time to be proportional to 19 also used a method that divided the SNPs into blocks but with two important differences: They used blocks of approximately 4 to 6 SNPs depending on the number of records being processed, whereas we use blocks of size equal to approximately nR is the number of records and they did only one cycle while a block was in core. They achieved a reduction in time needed by coding a block of about 4 to 6 SNP genotypes into a single number. This reduced the time necessary to process the data on all individuals and appears to be competitive with the EM-Hybrid version of BayesR15. However, we found without hardware support, that storing 4–6 SNP genotypes as a single number offered little speed advantage compared to modern matrix routines with built-in vectorization.CalusThe simulation results show that BayesR3 can estimate the proportion of variance explained by the SNPs, the number of SNPs in each distribution, and the position of the causal variants. The multiple trait version was used to analyse empirical milk MIR spectra data represented by their first 17 PCs. Although the 17 PCs were uncorrelated, they are largely explained by the same SNPs, meaning that each MIR trait is mostly associated with the same set of SNPs.On average 3995 SNPs were included in the model and about 1000 of these influenced any given PC trait. The SNPs with a high posterior probability of being included in the model are presumably tracking causal variants with which they are in LD. 20 SNPs had a posterior probability >0.9 and many are close to known polymorphisms (QTL) affecting milk composition. The use of 17 PCs captures information on more specific traits, such as lactose concentration, in that QTL affecting lactose concentration, phosphorus, and other milk mineral concentrations were also detected by the analysis.The multi-trait BayesR3 on milk, fat, and protein yields, found that 35 SNPs were included in the model on >90% of MCMC cycles implying there may be a causal variant linked to these SNPs. However, often the signal from a causal variant is split among closely linked SNPs. Therefore, we calculated the sum of posterior probabilities for SNPs within a 50 kb segment and showed that 556 of such segments had sum(pp) > 0.9, indicating we mapped 556 QTL for milk, fat, and protein yields to within 50 kb segments of the genome.As expected, we found considerable overlap between the SNPs that affected milk, fat, and protein and those that affected the milk MIR spectra. We used the MIR data to help map the variants causing variation in milk, fat, and protein using BayesR3C, which allows different mixing proportions among classes of SNPs. In this case, we analysed milk, fat, and protein traits but defined classes based on whether the SNP affected the MIR PCs. The 992 SNPs with the largest posterior probability to affect MIR traits were enriched for effects on milk, fat, and protein yield and for large effects on these 3 traits. For instance, of the 992 SNPs with biggest effect on MIR, 48 SNPs per iteration were included in the model for milk, fat, and protein. However, among the other 634,879 SNPs, 10,810 were included in the model for milk, fat, and protein. That is, the 992 SNPs with the biggest effects on MIR spectra comprise only 0.4% of the total SNPs affecting milk, fat, and protein. This may illustrate a common problem with using “omic” traits to identify variants affecting target complex traits: the individual “omics” datatypes detect only a minority of the variants affecting the target traits.In the simulated data, BayesR3C achieved much higher accuracy in predicting genetic value of individuals than BayesR3. In this data the classes defined were extremely different in the proportion of causal variants contained, that is class 1 contained all the causal variants. However, in the milk, fat, and protein yield data BayesR3C did not achieve a higher accuracy than BayesR3  decreases substantially the computer time needed for regressing phenotypes against genotypes such that it is now comparable with a GBLUP analysis. By applying BR3 to milk yield and composition data, we estimate that approximately 10,000 high-density SNPs are independently associated with these traits and for 627 of them we map the causal variant to within 50 kb. BR3 can also analyse high dimensionality ‘omic’ data and can incorporate prior biological knowledge about the genome variants used. Using these facilities, we show that milk MIR spectra identify many variants that affect milk, fat, and protein yield, but there are 1000’s of variants affecting milk, fat, and protein yield that were not detected by the MIR spectral data.33 and one of a pair were pruned for high linkage disequilibrium (LD r2 > 0.9 in 0.5 Mb windows). Variants with MAF < 0.002 were removed, intergenic variants were reduced to the set overlapping the High-Density Illumina BovineHD 800 K panel , and half of the remaining variants within and close to genes (up to 5000 bp from gene start and end positions) were randomly removed leaving the final set of 983,116 variants. The QTN effects and trait phenotypes were simulated following the approach described in ref. 25. Briefly, QTN effects were simulated by sampling 15, 500, and 3485 effects from each of 3 normal distributions with variance 0.01jth QTL effect and vij represents the jth genotype  for record i.Phenotypes were simulated using 64,345 real cattle genotypes by randomly selecting a set of 4000 genome-wide SNP as causal variants (QTN). The 4000 QTNs were chosen from a set of 983,116 imputed autosomal sequence variants. The sequence variants were imputed using Run5 of the 1000 Bull Genomes Project2) of either 0.1 (“H10”) or 0.3 (“H30”). The same 4000 QTN positions were used for both trait heritabilities and a new set of QTN effects were simulated for each trait. The cattle were mainly purebred Holstein, with some purebred Jersey and Australian Reds (RDC). All 1725 RDC were used as a validation set, while Holstein and Jersey animals were allocated to the training populations. From this simulated data, we randomly selected two training sets for analyses in this study: one with 41,925 Holstein and Jerseys and a second set of 20,000. From the 983,116 SNP genotypes available for each animal, we randomly selected three subsets of genotypes from the SNP map file, but also included the 4000 QTN: 400,000, 40,000, and 4000 SNP. Thus, the latter set represents the QTN only.An environmental effect for each animal was sampled from a normal distribution and was added to the genetic value to produce a phenotypic trait record with a heritability  where the raw data was pre-corrected for known fixed effects . The bull data was derived from daughter records. The cattle included Holstein (80%), Jersey (15%), and crossbreds (5%). All animals were genotyped for either low (~9000 SNP), medium (~50 K SNP), or high density (HD 800 K SNP) panels. The low-density panels mainly overlapped the 50 K panel but also included a custom set of ~ 1000 variants that have been found to be more predictive than random markers for milk and other traits. Animals with low-density genotypes were imputed to 50 K  and all 50 K genotypes were imputed to the HD panel . All markers not overlapping either the HD or 50 K panel were also imputed for all individuals to generate a final genotype set of 717,463 SNP. All SNP markers were mapped to the ARS-UCD1.2 reference genome15 and a GBLUP (Genomic Best Linear Unbiased Prediction) approach using MTG227. The reference set composition was 13,413 Holstein cows, 6623 Jersey cows, 4,289 Holstein bulls, 675 Jersey bulls. Accuracy was tested using 3 validation sets: 398 Jersey bulls, 702 Holstein bulls, and 3082 RDC cows. Any sires/dams or sons/daughters of the validation animals were removed from the training set.A subset of 25,000 animals of the above set of 65,637 (purebred Holstein and Jersey only) were used as a training set to run a comparison of computational efficiency and accuracy of the BayesR3 to the previously published EM-BayesR−1 regions. Several mathematical treatments were applied to the raw spectra, including removal of noisy and uninformative area, eliminating outliers, using a standardized Mahalanobis distance calculated with the ‘mahalanobis’ function of the ‘stats’ R package , and taking the first derivative of the MIR signal using the ‘gapDer’ R function36, as commonly recommended for MIR studies28. This resulted in 537 wavenumbers per sample. Each cow supplied on average 3.7 milk samples; therefore, multiple spectra were averaged resulting in a single spectrum being assigned to each cow for the analysis. These wavenumbers were then corrected for Herd ID, and age of calving, leaving only breed (3 levels) and the mean as the fixed effects used in the BayesR animal genetic model for analysis. The genotype set assigned to each cow was the same 717,463 SNP set as explained for the milk production data above. Note the 9834 cows used in the MIR analysis are separate from the 65,637 dairy cows used in milk production data analysis described above.Milk samples of 9834 Australian Holstein (83%), Jersey (9%), and cross-bred cows (8%) calved in Spring 2017 from 21 commercial herds were taken (2 to 8 times/cow) and analysed for milk composition by an infrared spectrometer  and the corresponding spectra were stored for this study. Each single spectrum included 899 data points, with each point representing the absorption of infrared light through the milk sample at wavelengths from 649 to 3999 cmV were scaled and centred: i at SNP j. The genotypes are represented by 0 for one homozygote, 1 for heterozygote and 2 for the other homozygote, j in the nR records. Note, SNP j is considered monomorphic if its Minor Allelic Frequency (MAF) is less than 0.002 and it is excluded from the analysis.The elements of y is an nR is the number of records; X is a u is a nF is the number of fixed effects. V is a coded genotype nM markers; g is a vector containing the SNP effects, Z is an identity matrix a is a vector of random genetic effects not explained by the SNPs with additive variance represented as BayesR and Gibbs sampling was used to implement the mixed effects model: A is the additive relationship matrix, 37. The trait variance kth mixture distribution that the jth SNP is in.In BayesR the SNP effects are modelled by a mixture of four normal distributions all with zero mean and with zero, very small, small to moderate variances, respectively. The prior distributions for the BayesR parameters are given as:25. It does this by dividing the variants into classes based on this prior information. Then the mixing proportions that describe the distribution of variant effects is estimated separately for each class. When there is only 1 class the model is that for standard BayesR.BayesR3 can also include prior biological knowledge about the variants being analysed as done in BayesRCtth trait is given by Wt is a diagonal matrix of weights for trait t and et are its residuals. If a record i is missing on trait, t then W = I the identity matrix. The weighted mean of each trait was determined from wi,t is the ith diagonal element of Wt and representing the ith record. Therefore, an initial estimate of the phenotypic variance, nW is the number of non-zero weights, and t and is a user-specified value, which can be a best guess.In terms of a multi-trait model the residual variance for the Vg component of the genetic modelled, Eq. , the effects for each block are determined sequentially. On block entry, the right-hand sides for the block rb are set up by:W is a diagonal weight matrix and e is the current state of the residuals in the model, Eq.  the variances were sampled using inverse scaled Chi-square distributions via: m) is determined from nL is the total number of samples to be drawn and therefore, nL represents the Markov chain length. The rate of the extra sampling events is determined by sr = max nM is the number of SNPs and sr is the sampling rate, and to that end the block size ideally should be in the range sr blocks are processed, the sampling of fixed and pedigree effects and the sampling of the variance To ensure all model effects are sampled within the block scheme the same number of times as the SNP effects, a sampling scheduling was set up for scheduling the sampling of these extra effects and variances, by interlacing their sampling within the outer cycles. The number of outer cycles  is sampled at the end of each outer iteration using: The probabilities that a SNP is in the model  to be pre-calculated prior to running GBLUP so we first calculated the GRM using GCTA software40 invoking the multi-threading option.The computational efficiency of BayesR3 was compared to a GBLUP approach as well as the previously published fast version of BayesR, referred to as EM-BayesR15 using in house software written in C++. The EM part of the analysis completed either when convergence of 1e-7 was reached or a maximum of 1500 iterations, whichever came first. The BayesR part of the analysis was set to run for 4000 iterations. For both the EM-BayesR and the BayesR3, five MCMC chains were run in parallel to check that the results had stabilised across chains. BayesR3 was run for 40,000 iterations, with 20,000 as burn-in. The accuracy of prediction was calculated as the correlation between the predicted and known phenotypes for each of the three validation sets. The accuracy and bias were calculated for each chain and then averaged.The EM-BayesR approach was implemented as described in ref. The analyses for all three methods were run on a Linux High Performance Computer cluster (described below) using Intel® Xeon® Platinum 8168 Processors (2.70 GHz), each with 24 cores, 48 CPU, and 740 Gb memory.The software is written in C++ using the Eigen (version 3.4.0) C++ template library for linear algebra. It has been compiled for the Linux platform using Intel’s compiler ICPC with the Eigen’s Intel MKL and openMP library options turned on, and it has also been built for the Windows 10 platform using Visual Studio Community (2022) edition of C++ version 17.1.6The Agriculture Victoria Biosciences Advanced Scientific Computing platform (BASC) was used here. It is a Beowulf style cluster that consists of 129 Nodes, with a total of 5832 cores, 103TiB of RAM and 1.5PiB of local scratch disk. 2 × DDN GS14Ks, running Spectrum Scale, that provided 8PiB capable of delivering an aggregate of 50 GB/s. A Full fat-tree network running at 100 Gb/s backbone and 25 Gb/s to each compute node. System software included: OS: Centos Linux 7.6.1810, Resource Manager: SLURM 19.05.2, Software Build System: EasyBuild 4.1.1, and Filesystem: IBM Spectrum Scale 5.0.3–3. Program were run on a dual socket system with 2 × Xeon Platinum 8168 CPUs, with a total of 48 cores and Hyperthreading disabled. 24 × DDR4-2666 ECC REG DIMM, 24 TB of local scratch space.Further information on research design is available in the Peer Review FileSupplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Software 1Reporting summary