Then, we tested several selection strategies based on selection indices, with or without dLFI records, to improve sow efficiency during lactation.Feed efficiency during lactation involves a set of phenotypic traits that form a complex system, with some traits exerting causal effects on the others. Information regarding such interrelationships can be used to predict the effect of external interventions on the system, and ultimately to optimize management practices and multi-trait selection strategies. Structural equation models can be used to infer the magnitude of the different causes of such interrelationships. The causal network necessary to fit structural equation models can be inferred using the inductive causation (IC) algorithm. By implementing these statistical tools, we inferred the causal association between the main energy sources and sinks involved in sow lactation feed efficiency for the first time, i.e., daily lactation feed intake (dLFI) in kg/day, daily sow weight balance (dSWB) in kg/day, daily litter weight gain (dLWG) in kg/day, daily back fat thickness balance (dBFTB) in mm/day, and sow metabolic body weight (SMBW) in kg95%) intervals resulted in a fully directed acyclic graph, in which dLFI and dLWG affected dSWB, the posterior mean of the corresponding structural coefficients (PMλ) being 0.12 and − 0.03, respectively. In turn, dSWB influenced dBFTB and SMBW, with PMλ equal to 0.70 and − 1.22, respectively. Multiple indirect effects contributed to the variances and covariances among the analyzed traits, with the most relevant indirect effects being those involved in the association between dSWB and dBFTB and between dSWB and SMBW. Selection strategies with or without phenotypic information on dLFI, or that hold this trait constant, led to the same pattern and similar responses in dLFI, dSWB, and dLWG.The IC algorithm using 95% highest posterior density (HPDSelection based on an index including only dBFTB and dLWG records can reduce dLFI, keep dSWB constant or increase it, and increase dLWG. However, a favorable response for all three traits is probably not achievable. Holding the amount of feed provided to the sows constant did not offer an advantage in terms of response over the other strategies.The online version contains supplementary material available at 10.1186/s12711-022-00744-4. Feed efficiency in livestock has been widely studied to establish strategies to reduce feed costs while reducing emissions to the environment and making sustainable use of resources. In the case of reproductive females, increasing feed efficiency during lactation (LFE) has additional benefits in terms of economic costs as well as of animal wellbeing, because milk production is one of the most energy-demanding processes in the productive life of a sow . When enIn pig production, most breeding programs include increasing feed efficiency during the growth/finish phase of production and litter size in the reproductive phase among the priority aims. Genetic improvement of these traits has had as correlated effects a reduction in appetite and feed intake capacity at fattening,which also extend to other stages of the animal’s life , as wellIn order to define an optimal selection strategy to improve LFE by genetic selection, knowledge about the variability and covariances among the target traits is required at both the genetic and environmental levels. Estimates of such parameters are usually obtained by implementing a multiple trait animal model (MTAM). However, a MTAM only describes associations among traits, without retrieving information about causal relationships. Associations can be due to common factors that directly affect two traits, or a causal relationship between the two traits, or a combination of these two. In the causal relationship case, effects that affect one trait can have an indirect effect on the other trait through a causal link that can exist from the first to the second trait. Association among traits due to direct and indirect effects cannot be distinguished with an MTAM because it does not consider causal relationships between traits. Knowledge about the causal structure allows the prediction of the effect of external interventions for a trait on another trait  .Structural equation models (SEM)  allow thComponents of LFE in sows have been described by Bergsma et al. . The eneThe objectives of our study were: (i) to investigate the potential causal effects that underlie the complex relationships between the main traits involved in LFE in sows, and (ii) to propose a selection strategy, with or without the inclusion of FI records, to improve sow productivity without impairing its body condition, as the latter is the main driver for future reproductive success.The data used for this analysis cover the first 10 generations of an experiment of divergent selection for RFI in growing pigs. The detailed selection process is in Gilbert et al. . InformaE) and at exit from maternity on weaning day (SWW), with an average duration of farrowing to weaning of 28.15 days. Backfat thickness was measured at the same time . Sow weight at farrowing (SWF) was estimated as in Bergsma et al. [Sow weight was recorded at entrance to maternity in the farrowing house  was used instead of litter weight at weaning. Litters with an abnormal average piglet weight at day 21 were removed. Daily litter weight gain  were also recorded. Only records from litters in which cross-fostering was carried out within 2 days after farrowing were included in the analysis. All piglets were weighed at farrowing and at weaning. This information was used to compute litter weight at farrowing, following cross-fostering  was calculated as the sum of daily feed intake records available from farrowing until weaning. Feed intake data were missing for some days and only 27% of the lactations had complete records. The average number of days with missing intake records during lactation was 0.65 ± 3.03. Most missing days were 1 or 2 days after farrowing. Daily lactation feed intake (dLFI) was computed by dividing FI by the number of daily records available.The traits dLFI, dSWB, dLWG, dBFTB, and SMBW were considered as the main components of LFE. After removing records with missing values for three or more of these traits, the dataset used for the analyses contained information on 1342 farrowings from 576 sows. The resulting numbers of records and descriptive statistics of the traits are in Table In order to assess the potential causal relationships between the main components of LFE, the following two-step procedure was implemented in a Bayesian approach.21) as covariates. The model for dLWG included the additional systematic effect of sire breed . With five traits involved , the number of possible causal structures was very large. Moreover, for some of these traits, no clear prior biological knowledge is available to establish the most likely causal structure of the system. Therefore, it was necessary to use algorithms that search for recursive causal structures  that are compatible with the joint distribution of the data. Because causal relationships can be masked by genetic covariances, such a search was performed on the joint distribution of the phenotypes conditional to unobservable genetic and permanent environmental effects, as proposed by Valente et al. . InformaThe joint distribution assumed for , and The model for The joint posterior distribution of all unknowns in the model is:We assumed standard prior distributions for all the unknowns, as reported in Sorensen and Gianola .The inductive causation (IC) algorithm was applied to samples of the residual covariance matrix using a program written in R  by ValenOnce the recursive causal structure was established, a SEM with that specific structure was fitted. The SEM for the Wu et al..As shown by Gianola and Sorensen , the modAll analyses were performed with the Gibbs sampling algorithm using the Gibbsf90 software . Single All proposed genetic selection strategies were based on selection indices including only sow’s phenotypes with or without constraints and for which the objective was always to increase dLWG, either by reducing or keeping dLFI constant, and either by increasing or keeping dSWB constant. Since there is no published information on economic weights of the analyzed traits, the selection index coefficients were computed for different combinations of three arbitrary values 0, 1, 2) for economic values, with the appropriate sign according to the selection objective. Different selection strategies were defined based on the traits that were recorded on the nucleus farm  were used, a DAG was returned with the same edges as obtained for the other HPD, but in this case, the edge between dLFI and dLWG disappeared   was usedMeans and standard deviations (SD) of posterior marginal distributions of variance components obtained from the MTAM and SEM are in Tables 95% intervals do not overlap) in the SEM compared to the MTAM. Likewise, the posterior mean of the additive genetic variance for dBFTB was statistically lower in the SEM than in the MTAM. All these results suggest a relevant contribution of indirect effects to the variances of these traits.For dSWB and dBFTB, the posterior means of the residual variances were statistically lower (HPD95%) of residual correlations from the MTAM are in Table 95% intervals did not include 0. All others correlations were not statistically different from 0, except for the correlation between dLFI and dBFTB.Posterior means (HPD95%) of the genetic correlations obtained from the MTAM and SEM models are in Table 95% were very large, these estimates were not statistically different from each other.Posterior means  between the traits. In an IC search, unobserved correlated genetic or environmental effects that are usually present for livestock production traits could be confounded with causal relationships. To avoid this problem, we implemented the IC algorithm on the joint distribution of phenotypes conditional to unobservable genetic and environmental effects, as proposed by Valente et al. , using aMBW Fig. .After implementing the SEM, the sign of the structural coefficients agreed with the sign of the residual correlations obtained with the MTAM. Estimates of the structural coefficients express the strength of each causal link between traits, which is essential to quantify the component of every element of the variance–covariance matrices that results from indirect sources of (co)variation. Estimates of variances and of ratios of variances, such as heritability, based on a SEM (direct effects) or a MTAM  are expected to be the same for the upstream traits . In our study, this principle was fulfilled for dLFI but not for dLWG because of the unexpected difference in estimates of the variance of permanent environmental effects, which was equal to 0.008 (0.005) based on the SEM and 0.02 (0.006) based on the MTAM. This difference could be due to the constraint imposed on the residual covariance which is set to zero in the SEM but not in the MTAM. For traits that are affected by other traits in the causal network, indirect effects may contribute to variances and ratios of variances, resulting in differences between estimates based on the MTAM and estimates based on the SEM. In our study, dBFTB was the most affected trait with the posterior mean (posterior SD) of the total additive genetic variance being 0.16 (0.03), while the additive genetic variance of direct effects was 0.07 (0.02), which resulted in relevant  differences between estimates of total and direct heritability for this trait (0.18 (0.04) and 0.12 (0.03), respectively). Therefore, the total genetic effects for this trait were largely due to indirect effects that originated from the upstream traits, mainly dSWB.Knowing which proportion of the relationship between two traits is due to direct and indirect effects is important to design new selection strategies based on external interventions for a trait without the need to perform an experiment to obtain covariance estimates with those interventions. Such external interventions are those that can change or block a causal relationship between traits  or that control the phenotypic value of one trait, e.g. by holding it constant , as was the case for one of our proposed selection strategies.In the specific case of the relationship between dLFI and dSWB, the causal structure indicates that dLFI positively affects dSWB, with an increase in dSWB of 0.12 kg/day for every 1 kg/day increase in dLFI. The mainly contribution of indirect effects correspond to the term ion Fig. .The causal effect of dLWG on dSWB was negative and the lowest in magnitude compared to all other causal effects among the analyzed traits. For every 1 kg/day increase in dLWG, dSWB is expected to decrease by 0.03 kg/day. Piles et al.  also fou95% were used instead of HPD intervals with smaller levels of probability content. Given the published information regarding the effect of dLFI on dLWG, and given our results using 70, 80, and 90% HPD intervals, we implemented a SEM that also included the corresponding structural coefficient between dLFI and dLWG. We found that this did not affect estimates of variance components of the model, which were very close to those obtained with the model that did not include this structural coefficient (results not shown), and that the estimate of the structural coefficient indicated a positive but small effect of dLFI on dLWG (0.03 kg/day for each 1 kg/day increase in dLFI).Previous studies have demonstrated the influence of lactation feed intake on litter weight gain. Eissen et al.  showed tBased on the posterior means of the structural coefficients, the most important causal effect was a negative effect of dSWB on SMBW. The estimate of the corresponding structural coefficient  intervals among traits based on the multiple trait animal model and on the structural equation model (SEM). Table S2. Posterior means of contemporary group correlations and 95% highest posterior density (HPD95%) intervals among traits based on the multiple trait animal model and on the structural equation model (SEM). Table S3. Posterior means (posterior SD) of correlated response to selection of each trait of the selection objective. Table S4. Posterior means (posterior SD) of correlated response to selection of each trait of the selection objective.


Multiservice cellular in Radio Access Network (RAN) Slicing has recently attained huge interest in enhancing isolation and flexibility. However, RAN slicing in heterogeneous networks (HetNet) architecture is not adequately explored. This study proposes a pairing-network slicing (NS) approach for Multiservice RAN that cares about quality of service (QoS), baseband resources, capacities of wireless fronthaul and backhaul links, and isolation. This intriguing approach helps address the increased need for mobile network traffic produced by a range of devices with various QoS requirements, including improved dependability, ultra-reliability low-latency communications (uRLLC), and enhanced broadband Mobile Services (eMBB). Our study displays a unique RAN slicing framework for user equipment (UE) for joint user-association. Multicell non-orthogonal multiple access (NOMA)-based resource allocation across 5G HetNet under successive interference cancelation (SIC) is seen to achieve the best performance. Joint user-slice pairing and association are optimization problems to maximize eMBB UE data rates while fulfilling uRLLC latency and reliability criteria. This is accomplished by guaranteeing the inter- and intra-isolation property of slicing to eliminate interferences between eMBB and uRLLC slices. We presented the UE-slice association (U-S. A) algorithm as a one-to-many matching game to create a stable connection between UE and one of the base stations (BSs). Next, we use the UE-slice pairing (U-S. P) algorithm to find stable uRLLC-eMBB pairs that coexist on the same spectrum. Numerical findings and performance analyses of the submitted association and pairing technique show they can all be RAN slicing criteria. We prove that the proposed algorithm optimizes system throughput while decreasing uRLLC latency by associating and pairing every uRLLC user in mini slots. The tremendous recent advances in mobile communication, intelligent user devices, and traffic demand have necessitated cell density optimization in extensive networks to provide high data throughput and low latency . Ultra-dOn the other hand, non-orthogonal multiple access (NOMA) has recently attracted attention by permitting sharing of the same radio resources among a set of UEs. NOMA can support more users than the number of available orthogonal resources , leadingThe 5G network services have been classified into three categories by the International Telecommunication Union (ITU): Enhanced Mobile Broadband (eMBB), Ultra-reliable and Low-latency Communications (uRLLC), and Massive Machine Type Communications (mMTC). The eMBB service focuses on high bandwidth requirement services, uRLLC focuses on latency-sensitive services, and mMTC focuses on services with high connection density requirements . HoweverThe uRLLC service is intended for event-driven, mission-critical, and industrial settings that may be helped in achieving QoS criteria such as ultra-low latency and ultra-high dependability. In addition, the standard uRLLC sets rigorous latency and reliability standards, with typical latency and reliability requirements of 1 ms/packet and up to 99% successful packet delivery . Since bConsequently, and motivated by the aforementioned benefits of NOMA and RAN slicing, this paper considers H-NOMA in RAN slicing and studies the problem of the coexistence of services with heterogeneous requirements. User association and pairing algorithms are considered the various types of UEs and their different connection demands in a HetNet.Wireless networks emphasize resource slicing to increase spectrum utilization from NS problems in HetNet, by including user association and resource allocation. Furthermore, most literature saw NS’s constraint-isolated resource allocation as an issue. In  EarliestMultiplexing the traffic from URLLC and eMBB users constitutes a significant challenge in 5G, hence it has been tackled several times in the literature very recently. Diverse QoS demands, in addition to the spectrum scarcity problem call for innovative approaches in addressing the resource management problem. In , a commuThere are many research efforts for better user association schemes suitable in NOMA for HetNets. In  power dooJoint user-association and pairing algorithms are considered for eMBB and uRLLC users in HetNets while considering the different association and pairing metrics required for each user type.oIn our system architecture, eMBB users are treated as downlink (DL) data-rate-hungry users and uRLLC users as latency and reliability-constrained users. The user-slice association and pairing processes are expressed as a multi-objective optimization problem to optimize the DL data rate for UEs and reduce the DL transmitted latency for uRLLC UEs whereas considering the users’ data rate-dependent QoS requirements and ensuring the intra-isolation for each slice by applying orthogonal frequency multiple access (OFDMA) technology between the similar service’s users; meanwhile, the inter-isolation between slices is assigned a DL threshold rate for each slice.oWe suggest a system model in which eMBB traffic is transmitted over long TTIs oWe separate the multi-objective optimization problem into UE-slice association and UE-slice pairing sub-problems. Moreover, we improve a framework based on a one-to-many matching game to find a solution for the UE-slice association sub-problem in which BSs and UEs rate each other based on clear preference measures that define UEs’ and BSs’ needs. Meanwhile, the UE-slice pairing sub-problem is optimized by a one-to-one matching game in which the associated uRLLC and eMBB UEs with the same BS rank one another through some mini slots. To our knowledge, no matching game has been researched in HetNet to solve the eMBB UEs and uRLLC UEs association and pairing problem.oWe represent utility functions for UEs and BSs that consider the UEs’ different demands in terms of attained data rate, DL latency reliability, the threshold rate of each slice, dynamic criteria for limiting the number of attached UEs in HetNet, and the number of paired uRLLC UE with eMBB UEs , to achieve a reference rate for UEs.oThe joint UE-slice association and UE-slice pairing algorithms are proposed to solve this game. Then, the proposed algorithms are proven to arrive at a stable matching. As well as the computation complexity study for the suggested algorithms is given. Simulation results illustrate that our submitted algorithms outperform the comparable approaches, especially regarding DL latency performance for uRLLC UEs and DL rate performance for eMBB and uRLLC UEs. To illustrate the effectiveness of the proposed algorithms, we also compare their performance with other search schemes.Utilizing the recent prosperity of using the matching theory to solve combinatorial optimization problem is proposed for eMBB UEs/uRLLC UEs association and pairing in HetNets in this paper. A scenario where eMBB and URLLC UEs with different requirements can be associated with different BSs and pair with each other is investigated. The main point of this paper can be summed up as follows in According to the following structure, the rest of this document is: b = 1 is a MBS. However, b = We consider a two-tier downlink H-NOMA cellular network which consists of wireless backhaul and radio access networks with a single infrastructure provider (InP), where 1st tier consists of an MBS while 2nd tier models SBSs. The set of BSs is denoted as um usage ,44. Alsoum usage , resulti slicing , all virLet us know a binary UE association matrix as To formulate the user association, we define the association matrix The adoption of PD-NOMA scheme by the userTwo types of interferences should be considered in the proposed multi-cell H-NOMA system. Firstly, the inter-BS interference is generated by the signals transmitted from the un-associated BSs. Secondly, the intra-BS interference is produced by the co-channel interference of H-NOMA schemes. In any coalition, the received signal at user  follows ,34 in FiWhen H-NOMA is applied, each PRB can mostly serve two different services UEs. Implementing H-NOMA brings more sophisticated co-channel interferences (CCI) to the existing networks; to optimize the main problem without CCI employing perfect SIC, both eMBB and uRLLC UEs receive the superimposed signal, and each UE executes SIC to decode its message . We assuAs well as, to guarantee inter-slice interference isolation between slices and ensure the QoS for each UE-slice according to H-NOMA technology, we assume  each BS ,48. The ieved by .Under the superposition scheme, the SINR The DL achievable data rate of a UE We denote the total received rate of a UE When a UE The uRLLC UEs are with delay-sensitive machine-type traffic and require high transmission reliability. Therefore, a UE The uRLLC’s bursts of small payload sizes of yload/s] . Due to yload/s]  i.e., is neglected since it is common for all BSs and is assumed to be ideal. Thus, the received signal-to-interference-plus-noise ratio (SINR) to the ot great ,52. Meanis pathloss exponent of WBH link.Thus, ion time ,50,53. I follows ,(14)TblTo compute the average DL packet transmission delay of this system for uRLLC UE l ,54, i.e.On the other side, the reliability of uRLLC can be improved by making sure that its outage probability is less than a certain threshold, according to ,(16)Pr If a uRLLC UE An association and pairing approach is now addressed by jointly considering eMBB and uRLLC UEs’ different demands. Since the uRLLC UEs should operate on a constrained received latency, DL latency should be considered during the connection process for uRLLC users. In contrast to uRLLC UEs’ needs, eMBB communications typically demand a high DL data rate. Thus, the DL data rate is a crucial association measure for eMBB users. Therefore, the UE-slice association and the UE-slice pairing indicators can be designed to maximize the overall DL data rate for eMBB UEs and minimize the DL transmitted latency for uRLLC UEs. Thus, the user-slice association (It can be observed that the O.P.T1 (18) is a nonconvex mixed-integer programming problem, where the ideal solution is challenging to obtain. The subsequent subsection will convert the problem into a pure combinatorial optimization issue. Therefore, we adopt a suboptimal method and decompose the O.P.T1 into two designed sub-problems, as described in the next sub-sections. The first sub-problem is to create the user-slice association decision matrix First, we concentrate on the association of users to BSs to boost overall DL data rates and minimize uRLLC latency while considering the RAN capacity for each BS and guaranteeing the intra-slice and inter-slice isolation. The U-S. A solution can be obtained by solving the following optimization sub-problem:Therefore, we observed that the ing game ,37,39 isThen, the optimum pairing for uRLLC UEs and eMBB UEs is achieved to completely maximize the network’s total throughput and maintain the QoS requirements for users using the superposition (H-NOMA) scheme between eMBB and uRLLC UEs, additionally considering the intra-slice and inter-slice isolation and the limited capacity for the service’s users, whereas we consider only the eMBB and uRLLC users are associated with the same BS and consider the same objective of (19) with fixed ing game ,55,55 isIn this section, we propose two matching algorithms to solve the U-S. A and U-S. P formulated sub-problems. Since There are diverse preferences utilities that can be supplied for players depending on their tendencies. For Since eMBB UEs are data-rate-hungry, we utilize the DL attainable data rate as the utility function Meanwhile, uRLLC UEs are deemed urgent-latency UEs; thus, the utility attained by an uRLLC UE when it is associated with the BS is introduced as a function of the DL transmitted latency and reliability as follows:The base station’s utility function must be efficient for the user-slice association. Where each BS wants to serve UEs with the highest rate to optimize the overall DL throughput based on the following utility function:Algorithm 1: Matching Game for User-Slice AssociationInput:1:  Output: Find stable Matching 2:  Initialization:3:  4:  Every UE construct Repeat5:  6:   fordo7:    fordo8:     whiledo9:      Ifthen10:        Ifthen11:        12:          13:          14:          else15:        16:          17:          whiledo18:          19:            21:            22:            23:            24:            Ifthen25:            26:             27:             28:             else29:            30:              31:              fordo32:              33:                until34:  The major details of the We can better understand the philosophy of the Firstly, each eMBB UE selects the lowest rate’s uRLLC UE for matching due to owning the entire PRB without a partner. Its preference utility can be represented as:On the other hand, each uRLLC UE ranks attached eMBB UEs at the same BS with the shortest transmission delay and the highest rate. Thus, each uRLLC UE’s preference utility is dependent on the following:Algorithm 2: Matching Game for User-Slice PairingInput:1:  Output: Find stable Matching 2:  Initialization:3:  Repeat4:  5:    fordo6:      7:        Sorts fordo8:        9:          10:          11:          Ifdo12:          13:           whiledo14:          Ifthen15:            16:             17:             18:             else19:            20:             21:             whiledo22:             23:              24:              25:              26:              27:              28:              until29:  Algorithm 2 describes the suggested matching-based le match ,42. We eWe consider a two-tier HetNet with four SBSs deployed within a macro cell coverage region radius of 250 m to assess the proposed matching game-based UE-slice association and UE-slice pairing algorithms. SBSs and UEs are uniformly distributed in the coverage area of the MBS. The simulations are dependent on 1000 runs, and the results are averaged. The essential simulation parameters are given in Most research projects on the coexistence between eMBB and uRLLC concur that the ratio of uRLLC to eMBB UEs is double per cell ,54,58. SThe number of eMBB UEs and uRLLC UEs are 25 and 50, respectively ,54. The We show the total DL throughput of uRLLC UEs with the different numbers of uRLLC when After documenting our idea to distribute power among various users’ PRB, it is time to display the other outputs and meet the goals of this study; as shown in Meanwhile, SBSs serve a relatively small number of users. Accordingly, many MBS-attached users may not be served because of the limited number of resources available in the MBS. In GA, BSs are unconcerned with the UEs’ QoS requirements and focus only on achieving a higher overall DL rate system. These are explanations for why MAX-SNR and GA have the worst performance rate compared to other schemes.based on ; In the In the future, further research can be pursued to investigate the following open issues. First, we can use one of the proposed ways to prove its effectiveness in minimizing co-channel interference, such as (a) a hybrid overlay-underlay spectrum access scheme in heterogeneous networks to improve energy efficiency . (b) cooIn this letter, joint user-slice association and user-slice pairing algorithms for eMBB and uRLLC UEs in HetNet are suggested based on game theory. The suggested algorithms are designed as an optimization problem to maximize the overall DL throughput while assuring the slice’s QoS, minimizing the latency of uRLLC traffic, and achieving intra and inter-isolation using flexible rate isolation. To improve its tractability, we have divided the problem between (1) dynamic association matching of BSs and UEs and (2) superimposing of uRLLC and eMBB UEs. Matching game algorithms for U-S. A and U-S. P are proposed to solve these sub-problems. Moreover, we propose a dynamic eMBB and uRLLC clustering technique called H-NOMA in HetNet systems to balance system performance. The computation complexity for the proposed algorithms is analyzed. Simulation results have confirmed that the submitted algorithm achieved throughput significantly above the compared algorithms and defeated uRLLC UE latency deterioration. The proposed algorithm had the highest throughput and the lowest latency compared with DAA-OMA, DAA-PUNC, EAA-NOMA, GA-NOMA, GA-OMA, MAX-SINR-NOMA, and MAX-SINR-OMA.


The digital cushion is linked to the development of claw horn lesions (CHL) in dairy cattle. The objectives of this study were to (1) estimate genetic parameters for digital cushion thickness (DCT), (2) estimate the genetic correlation between DCT and CHL, and (3) identify candidate genes associated with DCT. A cohort of 2,352 Holstein dairy cows were prospectively enrolled on 4 farms and assessed at 4 time points: before calving, immediately after calving, in early lactation, and in late lactation. At each time point, CHL was recorded by veterinary surgeons, and ultrasonographic images of the digital cushion were stored and retrospectively measured at 2 anatomical locations. Animals were genotyped and pedigree details extracted from the national database. Genetic parameters were estimated following a single-step approach implemented in AIREMLF90. Four traits were analyzed: the 2 DCT measurements, sole lesions (sole hemorrhage and sole ulcers), and white line lesions. All traits were analyzed with univariate linear mixed models; bivariate models were fit to estimate the genetic correlation between traits within and between time points. Single-marker and window-based genome-wide association analyses of DCT traits were conducted at each time point; candidate genes were mapped near (<0.2 Mb) or within the genomic markers or windows with the largest effects. Heritability estimates of DCT ranged from 0.14 to 0.44 depending on the location of DCT measurement and assessment time point. The genetic correlation between DCT and sole lesions was generally negative, notably between DCT immediately after calving and sole lesions in early or late lactation, and between DCT in early or late lactation and sole lesion severity in early or late lactation. Digital cushion thickness was not genetically correlated with white line lesions. A polygenic background to DCT was found; genes associated with inflammation, fat metabolism, and bone development were mapped near or within the top markers and windows. The moderate heritability of DCT provides an opportunity to use selective breeding to change DCT in a population. The negative genetic correlation between DCT and sole lesions at different stages of production lends support to current hypotheses of sole lesion pathogenesis. Highlighted candidate genes provide information regarding the complex genetic background of DCT in Holstein cows, but further studies are needed to explore and corroborate these findings. CHL) refers to foot lesions that arise from damaged corium, including sole hemorrhage (SH), sole ulcers (SU), and white line lesions (WL).The digital cushion of the bovine claw is composed of 3 parallel pads of soft fat and loose connective tissue that are thought to play an important role in protecting the corium from mechanical forces in the foot . New horDCT) has since been measured in a succession of studies, with a general agreement that a thin DCT represents an increased risk of subsequent CHL development  studies have used genomic markers to map QTL that may be associated with the genetic variance of DCT. Two recent GWA studies of around 600 Holstein and Jersey cows characterized DCT as a complex trait and identified candidate genes related to inflammation, fat tissue deposition, bone growth, and keratinocyte function  estimate genetic parameters for DCT at different stages during a production cycle; (2) estimate the genetic correlation between DCT and CHL, evaluating sole lesions (SH and SU) and WL separately; and (3) identify QTL associated with DCT.The study was conducted following ethical approval by the University of Liverpool Research Ethics Committee  and procedures regulated by the Animals (Scientific Procedures) Act were conducted under a United Kingdom (UK) Home Office License (P191F589B).A prospective cohort study was designed to measure the DCT in dairy cows and record CHL at 4 time points during a production cycle. Data were collected from 4 dairy herds (A–D) in the northwest of the United Kingdom. These herds were selected for convenience based on the practicalities of frequent visits and assessments. Herds A to C housed lactating cows year round, milked cows 3 times daily, and recorded 305-d milk yields of approximately 11,000 to 11,500 L. Herd D housed lactating cows year round except for lower yielding cows, which were grazed during the summer; cows were milked twice daily, and the 305-d milk yield was approximately 9,000 L. Parous cows in all herds were routinely foot-trimmed twice a year before drying-off and at 60 to 120 d after calving. In all herds, lactating cows were regularly footbathed after milking. Herd A footbathed cows 3 times a week with either copper sulfate or formalin, herd B footbathed cows twice daily with formalin, herd C footbathed cows daily with either copper sulfate or formalin, and herd D footbathed cows 3 times a week with formalin.T1-Precalving), immediately after parturition , in early lactation around the time of peak milk yield (T3-Early), and in late lactation (T4-Late). Sample size was determined by resource constraints; all eligible animals were enrolled until the final assessments (T4-Late) began, at which point further enrollments ended because simultaneous data collection at 4 time points was not feasible.All animals that were registered as Holsteins and expected to calve between April and December 2019 were prospectively enrolled with no additional inclusion or exclusion criteria applied. A total of 2,352 animals were enrolled. Data were collected during weekly or twice weekly visits to each herd from February 2019 to July 2020 (with a break from March to June 2020 due to COVID-19 restrictions). Animals were assessed for foot lesions at 4 time points: before parturition , as previously described . This siThe data collection procedure was the same at all time points with 2 exceptions. At T2-Calving on herd C, only hind feet were assessed to reduce the handling time of cows that had recently calved; this approach was only required in this herd owing to the large numbers of cows calving each week. The other exception was at the T4-Late assessments, which resumed in June 2020 following a break due to COVID-19 restrictions; data collection from this point onwards was more limited owing to social distancing protocols, and digital cushion images were not collected.DCT-MAX); this point corresponds to the interconnecting abaxial and axial pads of the digital cushion  in the midline of the claw (DCT-FT); at this point, the specific part of the digital cushion measured was assumed to be the middle pad in a typical cow . This approach was intended to capture the severity and distribution of sole lesions, while minimizing the diluting effect of healthy claws in animals with sole lesions. We followed the same process for WL  to create a variable called “white line lesion severity” (WL-Severity). Both SL-Severity and WL-Severity were analyzed as continuous traits.The 2 DCT measurements (DCT-MAX and DCT-FT) were analyzed as continuous traits. As per our research objectives, sole lesions (SH and SU) were analyzed separately from WL. It is thought that SH and SU represent different stages of the same disease process . TherefoBos taurus genome (ARS-UCD 1.2) . Genotypes were subsequently imputed to 80K SNP genotypes by Edinburgh Genetic Evaluation Services (EGENES) using an in-house procedure that has been developed for all national genomic evaluations of dairy cattle in the United Kingdom. Briefly, this imputation process uses the Illumina BovineSNP50 BeadChip and Illumina BovineHD BeadChip (Illumina Inc.), in addition to other commercial genotyping arrays, extra gene tests, and large-effect sequence variants. Following imputation, genotypes included 79,051 SNP spanning the entire genome. Chromosomal locations of the imputed 80K SNP panel were drawn from the latest assembly of the UCD 1.2) .Imputed genotypes were available for 2,250 animals. Genotype quality control was implemented using PREGSF90  within tlmerTest package ; b is a vector of the fixed effects including herd (4 levels), parity , season of calving , and days relative to parturition (continuous variable); a is a vector of random additive genetic effects for each animal; e is vector of random residual effects; and X and Z are incidence matrices for b and a, respectively. Random effects were assumed to be normally distributed with a mean of zero and covariance structure ofI is an identity matrix and H is the relationship matrix incorporating pedigree and genomic information in a single-step genomic analyses framework , M is the number of SNP, and ip is the minor allele frequency at locus i.Genetic parameters of each trait  were estimated at each time point separately  with single-trait linear mixed models, resulting in a total of 16 univariate models. Models were fit using the average information restricted maximum likelihood algorithm, implemented in AIREMLF90 . The genramework . The invework (H  is definionships . The genTo explore the genetic relationship between the 2 DCT traits (DCT-MAX and DCT-FT), bivariate models were fit for DCT-MAX and DCT-FT at each of the 4 time points. To estimate the genetic correlation between stages of production for each DCT trait, bivariate models were fit with each pairwise combination of time points , resulting in 6 bivariate models for DCT-MAX and 6 bivariate models for DCT-FT.One of our objectives was to evaluate the genetic relationship between DCT and CHL. Therefore, we fit bivariate models for combinations of DCT and CHL traits, both within the same time point and between time points. Specifically, we fit bivariate models for DCT-MAX and SL-Severity at each of the 4 time points and for every pairwise combination of time points, such as DCT-MAX at T2-Calving and SL-Severity at T3-Early, and so on. This process was repeated for DCT-FT and SL-Severity, DCT-MAX and WL-Severity, and finally for DCT-FT and WL-Severity, resulting in an additional 40 bivariate models.G0 is the genetic covariance matrix between traits due to animal additive genetic effects, R0 is the residual covariance matrix between traits, ⊗ is the Kronecker product, H is the relationship matrix, and I is an identity matrix.Bivariate models had the same parameters as the univariate models , and ranP-values, using POSTGSF90  at each of the 4 time points . The genOSTGSF90 , 2019.P ≤ 0.05, which was corrected for multiple testing to 7.67E-07 (P ≤ 0.05/number of tested markers). Suggestive SNP were defined using a genome-wide threshold equivalent to one false-positive result per genome scan (P ≤ 1/number of tested markers).In each GWA analysis, genomic inflation was assessed by calculating the inflation factor of the test statistic . We adjuome scan , the sugLD) in our study population (A window-based GWA approach was used to further explore the association between genomic regions and DCT traits (DCT-MAX and DCT-FT). The window size was determined by linkage disequilibrium (pulation . The magpulation . On averB. taurus genome (ARS-UCD 1.2) downloaded from the National Center for Biotechnology Information database (https://www.ncbi.nlm.nih.gov/assembly/GCF_002263795.1/). In each GWA analysis, the closest gene to each significant or suggestive SNP was identified, up to a maximum of 0.2 Mb upstream or downstream from the marker. Additionally, genes were explored if they were contained or partially contained within genomic windows that explained >0.5% of the total genetic variance. The UniProt database  were analyzed at 4 assessment time points with single-trait models, and estimates of variance components and heritability are provided in The genetic correlations between DCT traits  and CHL traits , both within each time point and between time points, are provided in B. taurus autosome (BTA)-4. Suggestive SNP were identified on BTA-3, BTA-5, BTA-6, BTA-13, BTA-14, BTA-23, and BTA-26  at each time point. The genomic inflation factor ranged from 0.94 to 1.00 in the 8 single-marker GWA analyses. Single-marker analyses revealed a polygenic background to both DCT-MAX and DCT-FT at each time point . From ald BTA-26 . PositioWindow-based GWA analyses showed a similarly complex genetic background to DCT-MAX and DCT-FT . The samGO) terms: positive regulation of I-kappaB kinase/NF-kappaB signaling (GO: 0043123), positive regulation of CREB transcription factor activity (GO: 0032793), cellular response to mechanical stimulus (GO: 0071260), cell adhesions (GO: 0007155), and positive regulation of phosphatidylinositol 3-kinase signaling (GO: 0014068).The set of positional candidate genes, identified from single-marker and window-based GWA analyses, were enriched in biological processes of 5 Gene Ontology  compared with the DCT measurement taken distal to the flexor tuberosity of distal phalanx . The DCT-FT measurement is arguably more clinically relevant than DCT-MAX for sole lesion development, as this corresponds to the predilection site for these lesions and DCT-FT has been shown to correlate with CHL risk phenotypically . We alsoA key objective of our study was to estimate the genetic correlation between DCT and CHL. The genetic correlation between DCT traits and WL-Severity was not statistically different from zero, except between DCT-MAX at T3-Early and WL-Severity at T4-Late when it was positive (0.29 ± 0.14). This single positive genetic correlation should be interpreted cautiously owing to the large standard errors of this estimate, and because this was the only nonzero genetic correlation between these traits. If a positive genetic correlation truly exists between DCT and WL, it may reflect previous observations of a potentially positive genetic correlation between body condition and DCT , a positOur results indicate that DCT traits were negatively correlated with SL-Severity at several time points, although the magnitude of the genetic correlation in these instances was relatively small. A negative genetic correlation between DCT and CHL incidence was reported by The strength of the genetic correlation between DCT traits and SL-Severity that we observed was generally weak, with large standard errors, and in many cases the 95% confidence interval included zero. Unbiased estimates of genetic correlation are effectively impossible to obtain , therefoWe observed a weak negative genetic correlation between the DCT immediately after calving and the severity of sole lesions later in lactation. The suspensory apparatus of the distal phalanx has been shown to be weaker around parturition, which may result in compression of the underlying soft tissues, including the digital cushion and corium . CompresPeriparturient compression of the digital cushion is an intuitive explanation for our observation that DCT was thinnest immediately after calving, a finding replicated elsewhere . Our resWe recorded the DCT to be thinner at T3-Early than at either T1-Precalving or T4-Late, in agreement with previous research . High-yiRELN gene. In cattle, RELN is primarily expressed in central nervous tissue and is involved in neuron development . This region explained 1.06% and 1.03% of the total genetic variation of DCT-MAX at T2-Calving and T3-Early, respectively, and contained 2 candidate genes, nnotated ; therefonnotated  and withnnotated . TherefoKHDRBS3. This gene has been associated with average daily gain in cattle , so KHDRBS3 may contribute to the genetic correlation between DCT and sole lesions.Other results of interest from GWA analyses include the genomic region on BTA-14 (5.88–6.53 Mb), which explained 0.78% and 0.95% of the total genetic variance for DCT-MAX at T1-Precalving and T3-Early, respectively. This window was also adjacent to a region (6.00–6.62 Mb) that explained 0.51% of the total genetic variance for DCT-MAX at T4-Late. The candidate gene in these windows was n cattle , and it n cattle . TherefoKCNQ3 and EFR3A. The KCNQ3 gene has previously been associated with milk fat percentage and milk yield in Holsteins , which explained 0.72% of the total genetic variation for DCT-FT at T1-Precalving, was also associated with SU development in GWA analysis of CHL using this data set . Candidate genes in this window were olsteins , while Eolsteins . The lipolsteins  and is colsteins . Althougolsteins , so KCNQOSR1 gene on BTA-11 (identified for DCT-MAX at T4-Late) has been linked to multiple conformation traits including feet and leg conformation, rear leg placement, and rump width  has previously been associated with foot angle , and one of the candidate genes for DCT identified by TRIM55. Although TRIM46 and TRIM55 are in different families (We did not identify any QTL or candidate genes that were highlighted by previous GWA studies of DCT ,b. Howevfamilies , TRIM prfamilies , and theOverall, in the context of the limited previous research in this area, our results replicate some of the reported findings as well as providing additional data. Given the number of markers tested in 8 GWA analyses, only a small number of markers were associated with significant or suggestive effects on DCT. Our results did not corroborate any of the specific QTL reported in 2 previous GWA studies of DCT by We have estimated the genetic parameters and characterized the genetic background of DCT using the largest data set currently available. In addition to the size of the study population, the prospective cohort study design and accuracy of phenotype recording are further strengths of this study; however, we acknowledge some important limitations.One of the limitations of this study population was the small number of farms included, which could reduce estimates of environmental variance and inflate the estimated heritability. This limitation also affects previous research, so we have insufficient context for speculating about how much it affects our results. It is also important to note that almost two-thirds of the study population were from a single herd; replication of results in a wider and more diverse population would strengthen interpretation of our findings.A relatively large proportion of animals had missing data for the DCT-FT measurement due to the absence or ambiguity of anatomical landmarks in the stored ultrasound images; we did not record DCT-FT from these images to maintain a high accuracy of this phenotype. We designed our study to collect and store images that were retrospectively blinded and measured. If we had measured images at the same time as data collection, we could have reduced the number of missing measurements; however, subconscious biases can influence this process unless measurements are made with blinding to factors such as stage of lactation, body condition, and presence of lesions . We applIt has recently been shown, albeit in a small cohort of animals, that ultrasound measurements of DCT in weight-bearing and non-weight-bearing feet are only weakly correlated ; therefoIn conclusion, it is reasonable to question whether DCT measured using ultrasonography is the most important property of the digital cushion in terms of force dissipation and CHL development. Previous studies have described the composition of the digital cushion and its relationship with body condition and foot lesions , but theCaution is required to generalize the genetic parameters and QTL reported in this study, particularly given the polygenic nature of DCT and the small number of herds. Our results are from a population of Holstein cows in 4 dairy herds that were all commercially run with operating practices common to many UK dairy farms, but they could not be considered representative of the full spectrum of dairy farms. Within these 4 herds, 3 were operating similar and relatively intensive systems of zero grazing and 3 times a day milking. The overall period prevalence of lame cows , based oKHDRBS3 gene may contribute to the susceptibility of cows to SU in addition to the thickness of the digital cushion. Further work is needed to investigate these candidate genes and establish the precise role of the digital cushion in the pathogenesis of sole lesions.The results from this prospective cohort study indicate that DCT is a heritable trait that has a weak negative genetic correlation with the severity of sole lesions, but not with WL. The strength of the genetic correlation between DCT and sole lesions depends on the stage of lactation at which both the digital cushion and sole lesions are assessed. Digital cushion thickness is a polygenic trait, and few QTL were associated with observable effects. Candidate genes identified for DCT are related to inflammation, fat metabolism, and bone development. Most notably, the


By correcting for skewness and kurtosis, we develop accurate p-value approximations, whose accuracy was verified by extensive simulations. We exemplify our methods by analyzing a set of 147 genotyped subjects with 16S rRNA microbiome profiles from non-malignant lung tissues. Correcting for skewness and kurtosis eliminated the dramatic deviation in the quantile–quantile plots. We provided preliminary evidence that six established lung cancer risk SNPs were collectively associated with microbiome composition for both unweighted (p = 0.0032) and weighted (p = 0.011) UniFrac distance matrices. In summary, our methods will facilitate analyzing large-scale genome-wide association studies of the human microbiome.The microbiome is the collection of all microbial genes and can be investigated by sequencing highly variable regions of 16S ribosomal RNA (rRNA) genes. Evidence suggests that environmental factors and host genetics may interact to impact human microbiome composition. Identifying host genetic variants associated with human microbiome composition not only provides clues for characterizing microbiome variation but also helps to elucidate biological mechanisms of genetic associations, prioritize genetic variants, and improve genetic risk prediction. Since a microbiota functions as a community, it is best characterized by β diversity; that is, a pairwise distance matrix. We develop a statistical framework and a computationally efficient software package, microbiomeGWAS, for identifying host genetic variants associated with microbiome β diversity with or without interacting with an environmental factor. We show that the score statistics have positive skewness and kurtosis due to the dependent nature of the pairwise data, which makes  The human body is colonized by bacteria, viruses, and other microbes that exceed the number of human cells by at least 10-fold and that exceed the number of human genes by at least 100-fold. The relationship between a person and his or her microbial population, termed the microbiota, is generally mutualistic. The microbiota may promote human health by inhibiting infection by pathogens, conditioning the immune system, synthesizing and digesting nutrients, and maintaining overall homeostasis. The microbiome, which is the collection of all microbial genes, can be investigated through massively parallel, next-generation DNA sequencing technologies. By amplifying and sequencing highly variable regions of 16S ribosomal RNA genes that are present in all eubacteria, cost-effective and informative microbiome profiles down to the genus level are obtained.The human microbiome has been associated with diseases, including obesity , inflammNOD2 was associated with the relative abundance of Enterobacteriaceae in the human gut microbiome. Tong et al. [FUT2 that increases the risk of developing Crohn’s Disease (CD) may modulate the energy metabolism of the gut microbiome. In both examples, the microbiome is a potential intermediate for explaining the association between risk SNPs and disease risks, although a formal mediation analysis is required based on samples with genotype, microbiome, and disease status data. Moreover, identifying microbiome-associated host genetic variants has the potential to prioritize SNPs for discovery and to improve the performance of polygenetic risk prediction.GWAS of complex human diseases have identified many risk SNPs; however, the biological mechanisms are largely unknown for the majority of the risk SNPs. QTL studies of intermediate traits, e.g., gene expression ,14, DNA g et al.  show thap < 5 × 10−8/200 = 2.5 × 10−10) or by controlling FDR at an appropriate level. Second, multiple α-diversity metrics [Three types of microbiome metrics can be derived as phenotypes for GWAS analysis. First, for each taxon at a specified taxonomic level , we calculate the relative abundance (RA) of the taxon as the ratio of the number of sequencing reads assigned to the taxon to the total number of sequencing reads. In 16S ribosomal RNA sequence profiles, approximately 100–200 taxa with average RAs ≥ 0.1% (from the phylum level to the genus level) across samples are abundant enough for QTL analysis. One can perform a Poisson regression to examine the association between the RA of each taxon and each SNP. Significant associations are identified using Bonferroni correction  of the microbial community. Microbiome distances can be defined in different ways, based on using phylogenetic tree information or each taxon’s abundance information. Bray–Curtis dissimilarity  quantifiIntuitively, the microbiome distances tend to be smaller for pairs of subjects with similar genotypic values at the associated SNP. In addition, it is also of great interest to identify host SNPs that interact with an environmental factor to affect microbiome composition. Importantly, β diversity is temporally more stable compared with RA of taxa and α-diversity metrics based on the data from the Human Microbiome Project , suggestp-values based on the asymptotic distribution too liberal, which easily yields false positive associations. Resampling methods, e.g., bootstrap or permutation, are computationally prohibitive for accurately approximating small p-values. We propose to improve the tail probability approximation by correcting for skewness and kurtosis of the score statistics. Numerical investigations demonstrate that our method provides a very accurate approximation, even for p = 5 × 10−8. MicrobiomeGWAS runs very efficiently, taking 36 min for analyzing main effects and 69 min for analyzing both main and interaction effects for a study with 2000 subjects and 500,000 SNPs, using a single core. MicrobiomeGWAS is available at https://github.com/lsncibb/microbiomeGWAS [In this paper, we develop a statistical framework and a computationally efficient package, microbiomeGWAS, for analyzing microbiome GWAS data. Our package allows the detection of host SNPs with the main effect or interaction with an environment factor; i.e., host SNPs interacting with an environment factor to affect the microbiome composition. We calculate the variance of the score statistics by appropriately considering the dependence of the pairwise distances. Importantly, we show that the score statistics have positive skewness and kurtosis due to the dependence in pairwise distances, which makes the approximation of small iomeGWAS , accessep-values were calculated based on asymptotic distributions, the quantile–quantile (QQ) plots strongly deviated from the uniform distribution. Nine loci also achieved genome-wide significance based on asymptotic approximations. Correcting for skewness and kurtosis eliminated the inflation and also the genome-wide significance of these loci. However, we provide evidence that the established lung cancer risk SNPs are associated with lung microbiome composition.We illustrate our methods by applying microbiomeGWAS to non-malignant lung tissue samples E) study ,32. BecaSuppose that we have a set of Intuitively, if the SNP is associated with the microbiome composition, the microbiome distances tend to be smaller for subject pairs with similar genotypic values, as is illustrated in We define The variance The details for calculating capscale in the vegan package [residuals function in the vegan package [In analyses of real data, we typically have to adjust for covariates, including demographic variables and principal component analysis (PCA) scores derived based on genotypes, to eliminate potential population stratification. Given a distance matrix  package . The res package , is now Let We estimate Let p-value is calculated asLet ur parts . The joi−7 based on p = 3.9 × 10−5 based on 108 permutations. The significance inflation becomes worse for smaller p-values and larger skewness Theoretic investigation suggests that the score statistics  liberal A,B. In aTo address this problem, we calculated the skewness under H0 . We propanalysis ,35. TechGiven the distance matrix d κI∝1/N . Thus, skurtosis C,D. Thuskurtosis C,D show p-values as Finally, we discuss how to approximate the tail probability of The main purpose of simulations was to investigate the type-I error of ct (AGP) . The OTUct (AGP)  (QIIME) 8 simulations under For each setting, the type-I error rates were evaluated based on 10https://github.com/lsncibb/microbiomeGWAS [−6 variants for the main effect and n = 3382 subjects in the SHIP-TREND cohort [We implemented our algorithms in a software package, microbiomeGWAS, which is freely available at iomeGWAS , accesseD cohort , it woulWe applied our methods to a set of lung cancer patients of Italian ancestry in the EAGLE  study. AOut of the 147 subjects, 78 are current smokers, 8 never smoked, and 61 are former smokers. Because of the small number of never smokers, we merged never and former smokers as non-current smokers. All of the genetic association analyses were adjusted for sex, age, smoking status, and the top three PCA scores derived based on genome-wide SNPs. Here, the top three PCA scores were selected for controlling population stratification because the other PCA scores were unassociated with the distance matrices. We included 383,263 common SNPs with MAF ≥ 10% because rarer SNPs were expected to have no statistical power given the current sample size. We first performed GWAS analysis using PLINK  to identp-values for the unweighted and weighted UniFrac distance matrices, respectively. For each distance matrix, we produced QQ plots for p-values based on the asymptotic approximation and for p-values adjusted for skewness and kurtosis. For both distance matrices, the QQ plots before adjustment strongly deviated from the expected uniform distribution. Our adjustment eliminated the deviation. In addition, consistent with the observation that the skewness and kurtosis were larger for the weighted UniFrac distance matrix, the QQ plot deviated more for the analysis based on the weighted UniFrac distance. Note that the skewness and kurtosis only affect the tail probabilities; thus, the inflation of the QQ plot is not reflected by the genomic control lambda value [p-values. In fact, lambda Next, we performed GWAS analysis using unweighted and weighted UniFrac distance matrices as a representation of eubacteria β diversity. The results for testing the main effects are reported in da value , calcula8 permutations. Importantly, skewness and kurtosis had a dramatic effect on tail probabilities. Here, we use SNP rs12785513 as an example, which was identified as the top SNP in both analyses. In the unweighted UniFrac analysis, p = 4.4 × 10−9 without adjustment and p = 1.6 × 10−6 after adjustment, a 364-fold inflation. The inflation was even larger for weighted UniFrac analysis because of larger skewness and kurtosis , rs2736100 and rs401681 at locus 5p15.33 [TERT/CLPTM1L), rs6489769 [RAD52), and rs1333040 at 9p21.3 [CDKN2A/CDKN2B). The SNPs at 15q25.1 and 5p15.33 have the largest effect sizes for lung cancer risk based on the meta-analysis from the Transdisciplinary Research in Cancer of the Lung (TRICL) consortium [BAT3/MSH5) was excluded because the MAF = 7.5%. No SNPs were significantly associated with taxa RAs or α-diversity metrics after correcting for multiple testing. However, association analysis based on the UniFrac distance matrices provided evidence that these SNPs may be associated with the lung microbiota  jointly testing additive and dominant effects; and (2) testing genetic associations using many microbiome distance matrices. We have assumed an additive effect model ; however. MiRKAT  has an oIn summary, GWAS of the microbiome of each body site has the potential to help one understand microbiome variation, to elucidate the biological mechanisms of genetic associations, to improve the power of identifying novel disease-associated genetic variants, and to improve the performance of genetic risk prediction. We expect our methods and software to be useful for large-scale GWAS of the human microbiome.


The yak is the largest mammal in the Qinghai–Tibetan Plateau and also supplies necessary sources of food and finance for the Tibetan people. Their body weight is a valuable trait for breeding. In the traditional breeding processes, pedigree data were used to evaluate individual genetic potency ability. However, based on the free range husbandry and random mating in domesticated yaks, the genetic improvement in yaks’ body weight is still very slow. In this study, we performed a genome-wide association study using whole genome sequencing data to detect the potential functional genes for body weight in yaks. In total three functional genes were identified as being associated with body weight. The results of this study are important for developing and improving body weight in yaks.p-values < 3.91 × 10−7) associated with the body weight trait,. Several candidate genes, including MFSD4, LRRC37B, and NCAM2, were identified. This research will help us achieve a better understanding of the genotype–phenotype relationship for body weight.The yak is the largest meat-producing mammal around the Tibetan Plateau, and it plays an important role in the economic development and maintenance of the ecological environment throughout much of the Asian highlands. Understanding the genetic components of body weight is key for future improvement in yak breeding; therefore, genome-wide association studies (GWAS) were performed, and the results were used to mine plant and animal genetic resources. We conducted whole genome sequencing on 406 Maiwa yaks at 10 × coverage. Using a multiple loci mixed linear model (MLMM), fixed and random model circulating probability unification (FarmCPU), and Bayesian-information and linkage-disequilibrium iteratively nested keyway (BLINK), we found that a total of 25,000 single-nucleotide polymorphisms (SNPs) were distributed across chromosomes, and seven markers were identified as significantly ( Bos grunniens) are the only large, native highland mammals on the Tibetan Plateau and were domesticated over 5000 years ago [The Tibetan Plateau is considered the world’s third pole. Yaks  are widely used to locate candidate genes or markers associated with phenotypes of interest using historical recombination information ,11,12. WIn this study, we evaluated BW in 406 Maiwa yak individuals and conducted genotyping by next-generation sequencing at an average coverage of 10×. A total of 25,000 SNP markers were detected and used for evaluation of the population stratification, heritability, identification of association markers, and candidate functional genes controlling BW.The Maiwa yaks used in this study were raised in the Hongyuan prairie  and were obtained from the Longri Breeding Farm of Sichuan Province. This population has undergone selective breeding since the 1980s and has a mortality rate of 5% per year. Currently, the herd is comprised of more than 2000 individuals, ranging in age from 1 to 10 years. In September 2019, the body weight of the majority of the population was measured using a stock weighbridge, and the values were linked to individual earmarks. The collection, breeding, and transportation was in accordance with the Chinese legislation and local stipulation. The protocol for Animal Care and Use was approved by the Animal Ethics and Welfare Association of the Southwest Minzu University (No. 16053), and the experiments were performed according to the regulations and guidelines established by this committee.We selected 406 male yaks from whole population that covered all age brackets of yaks. The blood samples of 406 yaks were collected, and DNA was extracted using the TIANamp Blood DNA Kit . After restriction enzyme cut, at least 5 µg whole genome DNA was divided into reads and linked with barcode adapters to construct a sequencing library following the manufacturer’s instructions . The Illumina Hiseq PE150  was used for sequencing at Novogene Bioinformatics Technology Co. Ltd. We utilized a total of 276 GB files downloaded from the sequencing database, and the average Q30 was 88%. The raw data were first quality filtered using fastp software (version 0.19.8)  with BWATo identify the population structure in all the accessions, principal component analysis (PCA) was used to indicate the clustered groups and their genetic distance. The Genome Association and Prediction Integrated Tools (GAPIT)  softwareIn this study, we used three multiple loci testing models, multiple loci mixed model (MLMM) , fixed aThe MLMM method can be written as belowp-values.Y is the observed phenotype vector. The age is the age bracket indicator matrix for 1 to 10 year old yaks. The PCA is fixed effect to explain the population stratification. The pseudoQTN is significant marker from previous loops that is null when the model begins. SNPi is testing marker in each loop. The K is the kinship between each individuals. The e is residual vector. When the MLMM begins, the model is similar to MLM. After first loop, all significant markers are put into the pseudoQTN, and the MLMM starts with next loop. When the heritability explained by K remains unchanged after loops, the MLMM will stop and calculate final marker effects and The FarmCPU method can be written as two modelsp-values. When the likelihood values of Fixed model (3) remain unchanged after loops, the FarmCPU will stop.All parameters are same for MLMM. The function (2) named Random model is used to select pseudoQTN, and the function (3) named Fixed model is used to calculate marker effects and p-values. Another difference is that the criterion of model convergence in BLINK is Bayesian information criterion.The BLINK method is similar to FarmCPU. A different is that the BLINK uses two fixed models, one is used to select pseudoQTN, and the other is used to calculate marker effects and The total weights in five continuous years were used as phenotype vector, and the age indicator, PCA, and testing markers were used as fixed parameters in each model. The Bonferroni correction  was used to avoid Type I error from multiple tests. The GWAS process was carried out following GAPIT default parameters. The Manhattan and quantile–quantile (QQ) plots of results were created with GAPIT software with default code.A total of 406 records of yaks’ body weight values were tested for normality. As shown in A total of 2.3 million markers including SNPs, indels, and other variants were detected using the BWA-SAMtools-GATK pipeline with default parameters. After filtering out the SNPs with a missing value >10%, minimum read depth >10, and minor allele frequency >5%, 25,537 SNPs remained. These SNPs were distributed across the 29 autosomes and 2 (X and Y) sex chromosomes A. All inIn this study, our yak population originated from a common farm that was composed of the previous three yak subpopulations from the 1980s. To analyze the population structure of the 406 Maiwa yaks, the whole genome 25,000 SNPs data generated by whole genome sequencing was used for PCA and population stratification. The PCA scatter plot showed a weak population structure for the 406 yaks D. The fip-values < 3.91 × 10−7) and were associated with BW , SAS-6 centriolar assembly protein (SASS6), tRNA methyltransferase 13 homolog (TRMT13), leucine-rich repeat-containing 39 (LRRC39), and dihydrolipoamide branched chain transacylase E2 (DBT). In this region, all these genes were reported by Liu et al. as being associated with milk production traits in water buffalo [MFSD genes family, MFSD4, was consistent for the main intake effect in skeletal muscle [MFSD14A gene, also called Hiat1, is a protein-coding gene with the product of a transmembrane protein with homology to a solute carrier protein family [MFSD14A was annotated with the transmembrane transporter activity Gene Ontology (GO) term. One of the LRRC gene’s family, LRRC37B, was consistent for body size in pigs [NCAM2 gene is protein binding.Based on the up and downstream 100 Kb LD interval information, the SNP rs137207  was annotated by Ensembl, with candidate genes containing major facilitator superfamily domain-containing 14A , which has been proved to be associated with body weight in Simmental cattle [NCAM2 gene is associated with body size in ducks [NCAM2 gene is protein binding and identical protein binding. This evidence will give us a better understanding of the function of the NCAM2 gene. The SNP rs118493  was only annotated with the tissue factor pathway inhibitor (TFPI). In 2017, a genome study using 76 Mongolian yaks’ sequencing data indicated TFPI and another 210 genes were located in the introgression segments [The SNP rs371363  was annotated with U1 spliceosomal RNA, indicating that the gene type is an snRNA. The SNP rs10942  was annotated with neural cell adhesion molecule 2 (l cattle . Anotherin ducks . In the MFSD4, LRRC37B, and NCAM2, were implicated in the BW phenotype. This research will help us achieve a better understanding of the relationship between the genotype and the BW phenotype. The results could serve as basic information for quantitative trait locus mapping or candidate gene cloning to understand the mechanism of BW in yaks.In conclusion, we conducted a GWAS analysis of BW in Maiwa yaks using whole genome sequencing with three multiple steps methods. Seven SNPs were shown to be associated with BW, and several candidate genes, including


Some studies have investigated the potential of genomic selection (GS) on stripe rust, leaf rust, Fusarium head blight (FHB), and leaf spot in wheat, but none of them have assessed the effect of the reaction norm model that incorporated GE interactions. In addition, the prediction accuracy on common bunt has not previously been studied. Here, we investigated within-population prediction accuracies using the baseline M1 model and two reaction norm models (M2 and M3) with three random cross-validation  schemes. Three Canadian spring wheat populations were evaluated in up to eight field environments and genotyped with 3158, 5732, and 23,795 polymorphic markers. The M3 model that incorporated GE interactions reduced residual variance by an average of 10.2% as compared with the main effect M2 model and increased prediction accuracies on average by 2–6%. In some traits, the M3 model increased prediction accuracies up to 54% as compared with the M2 model. The average prediction accuracies of the M3 model with CV1, CV2, and CV0 schemes varied from 0.02 to 0.48, from 0.25 to 0.84, and from 0.14 to 0.87, respectively. In both CV2 and CV0 schemes, stripe rust in all three populations, common bunt and leaf rust in two populations, as well as FHB severity, FHB index, and leaf spot in one population had high to very high (0.54–0.87) prediction accuracies. This is the first comprehensive genomic selection study on five major diseases in spring wheat. Puccinia triticina f. sp. tritici is common in mild temperature and moist conditions [P. striiformis f. sp. tritici) has been detected in western Canada every year since 2000, with serious epidemics reported in some parts in 2005, 2006, and 2011 [Puccinia graminis f. sp. tritici) epidemics were reported in the country in the early 1900s and from 1953 to 1955, which caused losses worth hundreds of millions of dollars [Tilletia tritici (syn. Tilletia caries) and T. laevis (syn. T. foetida) [Leaf rust, stripe (yellow) rust, stem rust, common bunt, Fusarium head blight (FHB), and leaf spot complex (the blotch diseases) are the most common and economically important wheat diseases in Canada and across the rest of the world ,2,3,4. Lnditions . Stripe  dollars . Althoug dollars . Common foetida) . The repFusarium graminearum (Schwabe) being the most destructive disease in parts of western Canada [Rht-D1b and/or Rht-B1b), which increase susceptibility to FHB by reducing anther extrusion [Pyrenophora tritici-repentis), septoria leaf blotch complex , and spot blotch (Cochliobolus sativus) [FHB, or scab, can be caused by multiple fungal species, with n Canada ,12. FHB n Canada . Second,n Canada . FHB mann Canada ,16,17. Nn Canada . Furtherxtrusion ,19,20. Lsativus) . These phttps://grainscanada.gc.ca/en/grain-quality/grain-grading/wheat-classes.html; accessed 20 March 2022), which must include at least intermediate levels of resistance to the three rusts, FHB, and common bunt. Genetically resistant cultivars can be developed using conventional breeding methods, marker-assisted selection (MAS), and genomic selection (GS). MAS involves introgressing a few genes or major effect quantitative trait loci (QTL) from trait donors into elite genetic backgrounds, which is often challenging due to (i) the need to pyramid different sources of resistance into the same genetic background, and (ii) concerns associated with the durability of introgressed genes that regulate qualitative or vertical resistance against multiple races. Vertical resistance tends to be expressed from seedling to adult plant stages, but they lose their effectiveness over time due to changes in pathogen populations. On the other hand, quantitative resistance is a partial level of resistance controlled by multiple minor to moderate effect genes and/or QTL, which are more durable but require the pyramiding of multiple favorable alleles, which makes the suitability of MAS more challenging. GS is a promising alternative to MAS for predicting the most likely performance of lines by incorporating all available molecular marker information into a model to compute genomic estimated breeding values for selection [In Canada, new varieties (cultivars) should possess a combination of 30–40 target traits depending on the market class  and tan spot in winter wheat [Although numerous proofs of concept and pilot GS studies have been conducted in wheat to investigate its potential for improving multiple agronomic traits, yield components, and end-use quality traits in wheat, only a few studies have been conducted on diseases. The latter include some studies conducted to evaluate the predictive ability of FHB , stripe er wheat ,40,41, aer wheat ,43,44. Eer wheat , which fThe multiplicative reaction norm model  is one oThe present study was conducted on 578 lines and cultivars  that repThe association mapping panel (hereafter referred to as BVC) consisted of 183 Canadian spring wheat cultivars and 20 unregistered spring wheat lines . It was P. tritici-repentis, which causes tan spot, is the most common leaf spotting disease in all wheat classes. Disease epidemics was initiated by spraying spreader rows of susceptible checks  with a spore suspension that consisted of an equal mixture of two isolates (AB7-2 and AB50-2) that belong to race 1 of P. tritici-repentis (Ptr). These two isolates contain the ToxA gene [The BVC panel was evaluated for its reaction to leaf spot for three years at the University of Alberta South Campus in 2016, 2017, and 2018. oxA gene  and belooxA gene . AlthougoxA gene . For botoxA gene  on a scaT. laevis and race T-19 of T. tritici spores. We then removed the excess inoculum by shaking the seed over a fine-mesh sieve and planted them in a randomized incomplete block design with two replications. At the dough stage, all spikes of each cultivar were examined for common bunt infection and recorded on a scale of 1 to 9, in the same manner as rusts and leaf spots. The reaction to FHB was evaluated at six environments at the Elora Research Station, Pilkington, Ontario in 2017, at the Morden RDC from 2017 to 2019 and 2021, and the Ian N. Morrison Research Farm, University of Manitoba, Carman, Manitoba in 2020. The inoculum suspension consisted of four F. graminearum isolates that belong to the 3-ADON chemotype (HSW-15-39 and HSW-15-87) and the 15-ADON chemotype (HSW-15-27 and HSW-15-57), as described in a previous study [The BVC panel was evaluated for its reaction to common bunt at the University of Alberta South Campus in 2016 and 2017, as described in a previous study . The scrus study . BrieflyThe ACG population was evaluated for reactions to leaf rust, leaf spot, and common bunt at three environments at the University of Alberta South Campus Research Station from 2012 to 2014, as described in our previous study . The ACG−1, and shipped to service laboratories for genotyping. DNA samples from both the BVC and ACG populations were genotyped with the wheat 90K iSelect array [https://www.diversityarrays.com/; accessed 20 March 2022). The DArTseq technology generated a total of 36,626 markers, of which 22,741 were SilicoDArT markers (present vs. absent variation) and the remaining 13,885 were SNPs. We also genotyped the ACG and PAC RIL populations with a few functional markers linked to the photoperiod response (Ppd-B1 and Ppd-D1) [Vrn-A1 and Vrn-B1) [Rht-B1 [p < 0.01. We finally retained a total of 23,795 SNPs in the BVC, 5732 markers (3840 SilicoDArT and 1892 SNPs) in the PAC, and 3158 SNPs in the ACG population for subsequent analyses (Genomic DNA was extracted following a modified cetyl trimethyl ammonium bromide (CTAB) method , and itsct array  at the U Vrn-B1) , and/or  [Rht-B1  genes at [Rht-B1 ,65,66. Ianalyses .https://hdl.handle.net/11529/10201; accessed 20 March 2022). Broad-sense heritability (H2) across all environments was computed as follows:2g, σ2e, σ2ge, and σ2ε are the genotypic, environmental, genotype-by-environment interaction, and residual (error) variance components, respectively, whereas Env and Rep are the number of environments and the average number of replicates within each environment, respectively. The disease ratings were analyzed separately for each environment and combined across all environments by considering genotypes (L) as a fixed effect and environment (E), replication, and GE interaction as random effects. Pearson correlations and coefficient of determination (2R) and different types of graphs were generated using both Minitab v.14  and JMP v16  statistical software’s. We computed the first three principal components from the genotype data of each population in TASSEL v5.2.72 [https://ics.hutton.ac.uk/curlywhirly/; accessed 20 March 2022).All data analyses were performed as described in our previous study . Briefly v5.2.72 , used thjth wheat line in the ith environment . The M1 model assumes the effects of the lines as independent with no borrowing of information among lines. The main effect M2 model is an extension of the M1 model, which adds the random effect of molecular markers or genomic  extends the M2 model (Equation (2) above) by including genomic and environment interaction effects  predicting the performance of 20% of wheat lines that have not been evaluated in any of the environments (CV1), (ii) predicting the performance of 20% of lines that were evaluated in some environments (CV2) but not in others, which used phenotypes of the same line at different environments as part of the training set, and (iii) predicting the performance of all lines in an unobserved environment using the remaining environments as a training set (CV0), which was conducted in a leave-one-out fashion. The CV0 scheme computed the correlation between predicted and observed values within each environment only once with no random process involved to assign lines into folds. All genome-wide prediction analyses were performed using imputed marker data in R and the Bayesian Generalized Linear Regression (BGLR) package, as described elsewhere [Notably, in Equation (3), the interaction term lsewhere .p < 0.05) differences for all diseases (diseases . Table 1diseases . The secp < 0.01), FHB incidence and FHB index , and FHB incidence and FHB severity  in the BVC population , both residual and environmental variances showed a significant negative correlation  with heritability. As compared with the main effect M2 model, the inclusion of GE interactions in the M3 model reduced the residual variances on average by 10.4% (range 3.9–28.8%). However, the residual variance per trait still accounted for an overall average of 28.7% (range 9.6–56.3%) in the M3 model, with the ACG population showing the highest average residual variance at 49.8% (range 36.9–56.3%).The proportion of variances due to environments, genotypes (lines), molecular markers (genomics), GE interactions, and residual (error or unexplained) components differing depending on the prediction models, traits, and genetic backgrounds . EnvironWe compared the predictive ability of the baseline M1 model that utilizes only phenotype data with the main effect M2 model that adds molecular markers to the M1 model, and the M3 model that incorporated GE interactions to the M2 model . In the p < 0.05) than both the M2 and M3 models  in two wheat RIL populations [Prediction accuracies obtained for common bunt when both CV0 and CV2 schemes were used along with the M3 model produced high accuracies in the BVC (0.62) and very high accuracies in the PAC 0.84–0.87) populations . For the–0.87 populations ,86. For The prediction accuracies for both FHB severity and FHB index obtained when we used the M3 model with CV1 (0.40–0.41), CV2 (0.62–0.63), and CV0 (0.60–0.61) were 24–36% greater than those for FHB incidence , which dThe average prediction accuracies for stripe rust using the M3 model with CV1, CV2, and CV0 schemes in our three spring wheat populations varied from 0.26 to 0.49, from 0.55 to 0.76, and from 0.54 to 0.77, respectively . The preFor leaf rust, the prediction accuracies obtained when we used the M3 model with both CV2 and CV0 schemes were smaller (0.25–0.33) in the ACG population than the BVC (0.59–0.64) and PAC (0.70–0.77) populations , which mWe compared prediction accuracies of the baseline model with two reaction norm models (M2 and M3) across five diseases recorded in three Canadian spring wheat populations. We found statistically significant differences in prediction accuracies among the three models in all three populations, but a significant difference between the M2 and M3 models was observed only in the association mapping panel. However, the M3 model that incorporated GE interactions showed some obvious advantages over the main effect M2 model, including increasing accuracies for traits up to 54% (2–6% on average per trait–population combination) as well as accounting for an overall average of 10.2% of residual variances that were not explained by the M2 model. The prediction accuracies from the CV1 scheme were smaller than both the CV2 and CV0 schemes, which suggests a less likely scenario in successfully implementing large-scale GS using newly developed lines that have not yet been phenotyped at any of the environments. The moderate to very high accuracies obtained with the CV2 and CV0 schemes, however, demonstrated highly likely scenarios for successfully implementing GS to develop disease-resistant spring wheat germplasm either by reducing the number of lines evaluated in each environment or predicting the performance of lines in future environments using data from some other environments. As far as we are aware, this is the first comprehensive genomic prediction study that has assessed the predictive ability of the reaction norm models across all five major wheat diseases in spring wheat and common bunt in wheat for the first time, which provides highly valuable information to breeders.