Jatropha curcas breeding for bioenergy. To this end, the grain yield trait of 730 individuals of 73 half-sib families was evaluated over six harvests. The Markov Chain Monte Carlo algorithm was used to estimate genetic parameters and genetic values. Genetic correlation between pairs of measures were estimated and four selective intensities  were used to compute the selection gains. The full model was selected based on deviance information criterion. Genetic correlations of low (ρg ≤ 0.33), moderate (0.34 ≤ ρg ≤ 0.66), and high magnitude (ρg ≥ 0.67) were observed between pairs of harvests. Bayesian analyses provide robust inference of genetic parameters and genetic values, with high selective accuracies. In summary, the multiple-trait Bayesian model allowed the reliable selection of superior Jatropha curcas progenies. Therefore, we recommend this model to genetic evaluation of Jatropha curcas genotypes, and its generalization, in other perennials.Multiple-trait model tends to be the best alternative for the analysis of repeated measures, since they consider the genetic and residual correlations between measures and improve the selective accuracy. Thus, the objective of this study was to propose a multiple-trait Bayesian model for repeated measures analysis in  Thus, the posterior mean estimates were obtained for the variance components, which suggested density with qui square and normal shape appearances . M1 to MThe Bayesian MTM led to the estimation of variance components for each environment individually. For the grain yield trait, genetic variances ranged from 0.004 to 0.290 . This di the MTM .ρg) presented high values (ρg > 0.66) for the 2011–2014, 2010–2013, 2013–2014, 2013–2015 and 2014–2015 pairs of harvests (ρg < 0.33). The remaining values were moderate (0.34 < ρg < 0.66). The phenotypic correlation between pairs of harvests (ρp) was lower (ρp < 0.33) in all pairs of harvests, except for the pair 2014–2015, which was moderate (0.34 < ρp < 0.66) (The mean selective accuracies in the six measures presented high magnitudes (^g>0.70) . Geneticharvests . On the  < 0.66) .The additive index indicated a selection gain of 17.29%, when selecting five families, namely, 41, 15, 10, 36 and 37. As expected, the selection gains decreased with the increase of selected families: 10 progenies (SG = 14.74%), 15 progenies (SG = 13.04%), and 20 progenies (SG = 11.60%). The ranking with the 20 progenies selected was presented in The chains convergence ensures that the most likely estimate for each co(variance) component was achieved. The significance of genetic effects indicates genetic variability among the 73 half-sib families, which allows the genetic selection. Deviance information criterion is widely applied as a criterion to evaluate the goodness of fit of models in Bayesian inference . The HPDOne advantage of the Bayesian inference in relation with the frequentist inference is the possibility of obtaining the HPD intervals. The HPD intervals are more accurate, when compared with the confidence intervals from frequentist inference, which increases the reliability of the variance components and genetic parameters estimated through Bayesian inference. High values of selective accuracies  . In addiJatropha curcas breeding. It is worth mentioning that high selective accuracy directly affects the success of breeding program, since the selective accuracy is the most relevant parameter for evaluation of the effectiveness of the inference about the estimated genetic value of a genotype.The HPD intervals and selective accuracies magnitudes demonstrate the reliability and usefulness of the Bayesian inference in Jatropha curcas progenies evaluated in this study are non-domesticated, with great potential of improvement [Jatropha curcas breeding programs is the addition of new accessions.The rovement , 5, 27. rovement –31. In trovement , 32. AnoJatropha curcas genotypes for the grain yield trait.The selective accuracies increased in the last two harvests, as well as the genetic and phenotypic correlations, which were higher between the last harvests. As indicated by , at leasJatropha curcas genotypes.The heritability estimates present a fluctuating pattern, going up and down from one measure to another. Such trend could be related with the genotype × year interactions, especially in the early stages of growth, where the plants are more sensitive to environmental variations, and to the fact that the metabolism of young perennials often benefit the vegetative over reproductive growth, implying in an uneven genetic response in the early stages , 34. TheTwo aspects in which the Bayesian MTM can outperform the frequentist MTM should be highlighted: (i) it provides the HPD intervals , and .(DOCX)Click here for additional data file.S2 TableThe asterisk represents those estimates that are significant by HPD intervals.(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.


Yucca, the two species of Joshua tree (Yucca brevifolia and Yucca jaegeriana) are involved in a tightly coevolved mutualism with yucca moths. There is strong evidence of a history of coevolution between Joshua trees and their moth pollinators. We use a geographic clines approach in the Joshua tree hybrid zone to ask if selection by the moths may currently contribute to maintaining separation between these species. We compare genomic, phenotypic, and pollinator frequency clines to test whether pollinators maintain the hybrid zone or follow it as passive participants. The results reveal dramatic overlapping genomic and pollinator clines, consistent with a narrow hybrid zone maintained by strong selection. Wider phenotypic clines and a chloroplast genomic cline displaced opposite the expected direction suggest that pollinators are not the main source of selection maintaining the hybrid zone. Rather, it seems that high levels of reproductive isolation, likely acting through multiple barriers and involving many parts of the genome, keep the hybrid zone narrow.Coevolution frequently plays an important role in diversification, but the role of obligate pollination mutualisms in the maintenance of hybrid zones has rarely been investigated. Like most members of the genus  Understanding the forces that drive speciation has been a question of interest since the field of evolutionary biology began, and continues to generate complex questions, including the role of intrinsic and ecological factors . The impEcological forces contributing to speciation can be divided into biotic and abiotic forces, with both playing important and varying roles depending on the system . InteracYucca in general is a useful system for studying speciation and mutualism due to the tight relationship between many Yucca species and their moth pollinators (Tegeticula spp.). The vast majority of Yucca are pollinated exclusively by the obligate mutualist moths, often in a reciprocally obligate relationship . Tegeticula are nursery pollinators, laying their eggs in the developing fruits of the flowers they pollinate. The resulting larvae exact a cost on the plants, eating many of the developing seeds. In many of these plant-moth pairs, there is phylogenetic evidence of co-speciation, with the patterns of divergence in moths and plants frequently matching (The genus matching . This ramatching . One groYucca brevifolia and Yucca jaegeriana) offer the opportunity to fill this gap, taking advantage of natural variation in both mutualists across an existing hybrid zone (Y. brevifolia and Y. jaegeriana) and their moth pollinators (Tegeticula synthetica and Tegeticula antithethica) have coevolved   . This paer body) .Y. brevifolia and Y. jaegeriana, located in Tikaboo Valley in southern Nevada . Additionally, analyses of single nucleotide polymorphisms associated with trait variation show strong divergent selection in allopatry and disruptive selection in the hybrid zone on style length, as expected if style length is a key trait in divergence , with heaviest sampling in the hybrid zone . Trees wTegeticula moths stuck to the traps were identified to species using diagnostic variations in the cytochrome oxidase gene sequenced in one direction from the 5′ end using Sanger sequencing by Eurofins   across the zone of sympatry during the springs of 2011–2013 and 2015. In each year, the sticky traps were left in place for the length of the flowering season.  States) , 2009.Yucca using sequence from five chloroplast genes found no variation in the hybrid zone (1), including segments from the consensus chloroplast genome of each species in the alignment. We combined the genotypes at both variant sites to identify chloroplast haplotypes.Leaf tissue for genotyping trees was collected in the field and dried with silica gel, or flash frozen in liquid nitrogen and later transferred to −80°C. DNA was extracted using the Qiagen  DNEasy Plant mini kit. Ten microsatellite loci were amplified from 1469 trees following the protocol of rid zone . To idenSTRUCTURE 2.3.4 (STRUCTURE runs at levels of K from 1 to 7 (one more than the number of populations sampled). We performed 10 runs per level of K using random seeds with 30,000 burnin followed by 150,000 iterations of MCMC, using the ancestry model with alpha inferred and default parameters . Summary statistics for the runs were obtained using STRUCTURE HARVESTER (CLUMPAK (STRUCTURE as originating in the eastern species Y. jaegeriana as the hybrid index score (Q). Qscores calculated using microsatellite genotypes at 10 loci previously shown to be informative in these species  using the Bayesian clustering software RE 2.3.4 . We firsARVESTER , and indARVESTER  to confi(CLUMPAK . We used species  were useT. synthetica/T. antithethica) ∼ Qscore + distance from center of geographic cline transect.To test the roles of location in the hybrid zone and genetic identity of the tree in shaping pollinator host choice, we performed a Pearson product-moment correlation test to quantify the correlation between Qscore and location in the hybrid zone, and attempted to disentangle the effects of the two variables on pollinator host choice using a general linear model designating the binomial family, with a model: (Frequency of ARCGIS ARCMAP 10.3 (ESRI). We used the hybrid index scores to estimate a 0.5 hybrid contour (the center of the hybrid zone) using Empirical Bayesian Kriging (an interpolation method) with prediction and eight sectors. We then estimated the shortest distance between each tree and the 0.5 hybrid contour line using the Near Table tool. The geographic cline of the hybrid zone results from plotting the location of each tree along a single line representing the distance of each from the center of the hybrid zone (the 0.5 hybrid contour line), and then grouping trees that are a similar distance from the center  when there was a difference, and eliminated one haphazardly when they were statistically indistinguishable. We fitted clines to the SNPs with the highest FST , using the FST analysis performed by ST, and one SNP was significantly associated with variation in both style length and trunk height. The 100 random SNPs did not include any from the GWAS or high FST sets. For each cline, allele frequencies for each bin were output directly from the genomic analysis software STACKS , and transformed when possible to attain normality . Only moth frequency  was unable to be successfully transformed; we fitted the clines on the untransformed distribution. Distance along the cline for each bin was calculated as the mean distance of all the trees included in the bin.For phenotypic traits, SNP-based Qscore, and moth abundance data, we standardized the data to a scale from 0 to 1, then ran a linear regression of bin mean trait value on distance along the transect of the hybrid zone. Traits with no significant linear regression were considered to not have clines . For those that did change significantly across the hybrid zone, we fitted clines to the data using rid zone . Trait d0/2 and theta0); and (III) six-parameter models with two separate parameters for each asymmetric introgression tail  (y-axis minimum and maximum (pmin and pmax), corresponding to a mean trait value or allele/haplotype frequency in parental populations. For each model type, the parameters and log likelihood of the best-fitting model were used for analysis. For SNP clines, all three models were compared to a null model run in HZAR, which would be a line with constant slope between pmin and pmax . We determined the best-fitting model for each trait using AIC values output by HZAR; we selected the model with the lowest AIC, or the simplest model if dAIC < 2.For all clines, we fitted three models: (I) a simple two-parameter model, setting only a center and width for the cline; (II) a four-parameter model, describing the shape of symmetric introgression tails (β theta1) . All modST, random, trunk height, and style length). We then assessed whether there was overlap with the 95% CI of other clines (lack of overlap indicates a significant difference). To evaluate possible sources of selection, we compared cline centers.We compared clines by assessing overlap in centers and widths, using the 2 log likelihood (km) estimate . SNP clines that best fit the null model were excluded from calculations of the mean SNP cline parameters for each category  will be heterozygous at all loci (H = 1.0). Similar analytical predictions can be made for other early generation classes, including backcrossed individuals and hybrid intercrosses . However, if loci are not completely diagnostic, allele sharing at loci muddies these predictions, making it more difficult to interpret empirical patterns.Understanding what classes of hybrids are present in a hybrid zone  can be helpful in interpreting clines and understanding how advanced speciation is. While hybrid index scores give information about the proportion of the genome originating in each parent, they cannot distinguish between F1s and advanced generation hybrids that maintain equal proportions of the two genetic backgrounds. To do this, it is necessary to incorporate the degree of heterozygosity at each locus into the analysis. When populations are fixed for different alleles at a set of unlinked, biallelic loci, patterns of hybridization can be inferred from hybrid index scores combined with heterozygosities. For example, crossing pure individuals will produce an FY. jaegeriana and Y. brevifolia based on their STRUCTURE (Q) scores and geographic distributions. We then used the program hybrid lab  on its hybrid index score (HI) defined here as the proportion of alleles coming from pure population i. Note that the simulations assume that markers recombine freely (r = 0.5), so if some of these loci are tightly linked, we would be underestimating the number of generations of hybridization required to generate hybrid classes beyond the F1.Given that the 101 most highly differentiated loci are only semi-diagnostic in these taxa, we used individual-based simulations to generate distributions of multilocus genotypes that are expected to result from hybridization. To do this, we created two groups of “pure” individuals of brid lab  to produt = 7.23, p = 1.22∗10–8, df = 38). The general linear model showed significant effects of both tree Qscore and location in predicting moth visitation, with Qscore being much more strongly significant .We found both pollinator species co-occurring in the center of the hybrid zone, over a 4.2 km wide band ranging from ∼1.1 km west of the center to ∼3.1 km east of the center, with 90% of trees with both species observed on them located between 0.4 km west and 2.4 km east. There are instances of moths choosing the “wrong” host, including trees with Q-scores beyond the threshold for identification as “pure” parentals. However, the strong geographic structure in the location of different tree identities leads to a strong correlation between tree location in the hybrid zone and tree Qscore . However, the majority of even random SNPs (80%) exhibit clines  (ST clines (62%) and several trunk height and style length clines fit the more complex model II, with non-negligible proportion of high-FST clines fit best by model III (19%)  . The majII (19%) . All of II (19%) .ST cline shows the least consistency in the style SNPs, with half having centers significantly offset from the high-FST mean . Trunk SNPs showed a more bimodal pattern, with one group fitting the high-FST pattern fairly well and the other diverging in similar ways to the style SNPs. Just over a third of the trunk height SNP clines had centers significantly offset from the high-FST mean . In addition to being more frequent, the aberrations in style SNPs are more extreme than those in trunk SNPs .We found two chloroplast haplotypes in the hybrid zone, one clearly associated with each Joshua tree species, allowing us to perform a successful geographic cline analysis on this genotype. The cline center for chloroplast haplotype frequency is significantly offset from the nuclear genomic clines, and opposite the direction we predicted—to the west rather than the east . The chlthe east  . A single morphological trait cline, petal width, is significantly offset to the east .Pollinator species abundances shift sharply in the center of the hybrid zone. The cline for moth species is, as predicted, most closely coincident with the style length cline. It also clusters with the nuclear genomic, phenotypic trunk height, and phenotypic leaf length clines .Y. brevifolia than in Y. jaegeriana  in egeriana .Y. jaegeriana chloroplasts dominating in the hybrid zone. Because the sample size of trees genotyped at both SNPs and the chloroplast was small, we used Qscores calculated with microsatellite genotypes for the nuclear genome estimate (the same used to set the 0.5 hybrid index line for the clines) instead. This produced a set of 183 trees with data on cytonuclear genotypes . Of the 43 trees in this set that are genomically hybrids  to chloroplast genotype, we see some dissociation of nuclear and cytoplasmic genomes, with H) on hybrid index score (HI), which revealed clear evidence for extensive genetic mixing between Y. brevifolia and Y. jaegeriana , so there may be little opportunity for pure individuals to mate with one another.We estimated how many of the trees in our study were likely F1 hybrids, parental, backcrosses, or advanced generation hybrids (F2+) by plotting heterozygosity  or negligible (T. synthetica), reproducing little if at all. Moths would therefore rarely be found more than one generation’s dispersal distance from their host species. The other possibility is that they are excellent at detecting the correct host species, and their distribution mirrors that of the host because of behavior rather than selection-dispersal balance. Our statistical test suggests both mechanisms may be important, but the genetic identity of the tree is likely most important (this in spite of the strong correlation between genotype and location in the hybrid zone). Consistent with this, Tegeticula movement in the hybrid zone show individual moths move an average of at least ∼30 meters . Thus it seems likely that the matching clines of pollinator and host are due to a combination of choice, natural selection, and low dispersal.The concordance of the clines for moths and tree hybrid index is striking, with both being quite narrow, showing sudden and dramatic transitions in the center of the hybrid zone. The cline centers are offset, but overlap substantially over the geographic area of transition (width) in spite of steep transitions . There aGiven the steep, narrow cline for pollinator species occurrence, we would expect strong selection from moths on style length to produce coincident and equally dramatic clines for the trait and correlated SNPs. Evidence for this is mixed. The phenotypic style length cline is coincident and concordant with the moth cline—in fact, the moth cline fits the style length cline better than it fits the hybrid index cline, and style length is the only phenotypic cline for which both the center and width are statistically indistinguishable from that of moths . HoweverST SNPs)  . This isST SNPs)  Table 2ST SNPs (ST SNPs) . These tentiated . The inaY. brevifolia, based on higher rates of allele fixation in Y. jaegeriana across all nuclear markers   show introgression into Y. brevifolia (We found higher genetic diversity in vifolia) , 5. Thisevifolia , and we evifolia , in the evifolia .The exception to the overall coincidence of clines, and perhaps our most surprising result, is the chloroplast cline center that is offset from nuclear clines opposite the direction we predicted . CytonucY. jaegeriana chloroplasts into Y. brevifolia, introgression could be due to the Y. jaegeriana haplotype being inherently superior, the Y. jaegeriana haplotype being better adapted locally  carry the Y. jaegeriana chloroplast haplotype. In addition, while all trees with genomic compositions consistent with backcrossing to Y. jaegeriana (Qscore > 0.5) have Y. jaegeriana chloroplast haplotypes, those with Qscores consistent with backcrossing to Y. brevifolia are narrowly dominated by the Y. jaegeriana chloroplast haplotype as well (58%). While far from decisive, these data suggest a role for selection and reinforce that gene flow cannot explain the chloroplast cline.The cytonuclear genotypes present in the hybrid zone suggest cytonuclear incompatibilities may well play a role. With the large number of advanced hybrids and backcrosses present , the hybAtriplex canescens, a highly salt tolerant species of salt bush that is widespread throughout western North America  . This is roughly similar to estimates of Yucca filamentosa pollen dispersal by its moth pollinator, Tegeticula yuccasella: mean 4.66 ± 10.23 m . Evidence for direct phenotypic selection from pollinators is weak by comparison. These results suggest several new clear avenues for further work. First, a focus on how pollinators interact with advanced-generation hybrids (pollinator choice and performance). Previous work focused on reproductive isolation, comparing performance of pollinators on the opposite host. In fact, it seems that the formation of F1 hybrids is quite rare, so the movement of pollen between advanced generation hybrids (particularly backcrossed ones) and parentals is much more relevant to understanding gene flow in the current hybrid zone. In addition, the clear and unexpected pattern of chloroplast haplotype displacement to the west sets up several testable alternate hypotheses. The work described above on pollinator behavior may reveal pollen movement patterns that differ from those described in crosses between pure parental plants, consistent with chloroplast introgression. Additional work quantifying investment in male and female reproduction by hybrids with different chloroplast haplotypes (ovule and pollen counts) should reveal whether cytonuclear incompatibility is lowering overall fitness in hybrids with the  species .The original contributions presented in the study are included in the article/AR contributed to design, performed the analyses, and wrote the manuscript. JW-H collected and genotyped moths. CS provided phenotypic and genomic data, funding, and input into writing and interpretation.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.


Improving swine climatic resilience through genomic selection has the potential to minimize welfare issues and increase the industry profitability. The main objective of this study was to investigate the genetic and genomic determinism of tolerance to heat stress in four independent purebred populations of swine. Three female reproductive traits were investigated: total number of piglets born (TNB), number of piglets born alive (NBA) and average birth weight (ABW). More than 80,000 phenotypic and 12,000 genotyped individuals were included in this study. Genomic random-regression models were fitted regressing the phenotypes of interest on a set of 95 environmental covariates extracted from public weather station records. The models yielded estimates of (genomic) reactions norms for individual pigs, as indicator of heat tolerance. Heat tolerance is a heritable trait, although the heritabilities are larger under comfortable than heat-stress conditions . TNB showed the lowest genetic correlation (-38%) between divergent climatic conditions, being the trait with the strongest impact of genotype by environment interaction, while NBA and ABW showed values slightly negative or equal to zero reporting a milder impact of the genotype by environment interaction. After estimating genetic parameters, a genome-wide association study was performed based on the single-step GBLUP method. Heat tolerance was observed to be a highly polygenic trait. Multiple and non-overlapping genomic regions were identified for each trait based on the genomic breeding values for reproductive performance under comfortable or heat stress conditions. Relevant regions were found on chromosomes (SSC) 1, 3, 5, 6, 9, 11, and 12, although there were important regions across all autosomal chromosomes. The genomic region located on SSC9 appears to be of particular interest since it was identified for two traits (TNB and NBA) and in two independent populations. Heat tolerance based on reproductive performance indicators is a heritable trait and genetic progress for heat tolerance can be achieved through genetic or genomic selection. Various genomic regions and candidate genes with important biological functions were identified, which will be of great value for future functional genomic studies. Heat stress (HS) is a major welfare issue in the swine industry, especially as global temperatures trend upwards. Over the past decades, genetic selection has played a major role in improving productive and reproductive performance in pigs Merks, . HoweverExcessive heat and humidity are the main factor contributing to seasonal infertility, which has important economic implications as producers cannot maintain a constant flow of individuals throughout the farm during the whole year. Pigs have low capacity of dissipating body temperature under high ambient temperatures  in livestock species, including pigs , Texas (n = 1), Illinois (n = 6), Alabama (n = 1), Nebraska (n = 1) and Indiana (n = 1). The traits analyzed were: total number of piglets born (TNB), number of piglets born alive (NBA), and the average birth weight of the piglets . The phenotypic datasets were edited independently for each population by removing records deviating 3.5 SD from the mean.Datasets from four maternal-line pig populations were used for the current study. Nucleus-herd farrowing records were obtained from January 2008 to June 2016 for 11,163 Landrace  and 12,184 Large White  sows from the Smithfield Premium Genetics company (SPG) and from August 2011 to June 2016 for 11,537 Landrace  and 5,318 Yorkshire (TML_YS) sows  from The Maschhoffs company (TML). Farms were located in North Carolina (www.ncdc.noaa.gov/cdo-web/datatools/lcd?prior\=\N). Zip codes were obtained for each nucleus farm, converted to geological coordinates and matched to the closest weather station using the packages “zipcode” . The total number of individuals with genotypes involved in further analyses is reported in A total of 12,200 animals  across the four populations were genotyped with either the PorcineSNP60K Bead Chip  or the GGP Porcine HD v1 80K . The missing genotypes were imputed using the FImpute v2.2 software , Parj is the fixed effect of the parity of the sow , β is the fixed regression coefficient on the ENV, φk1 is the ENV vector (standardized between −1 and 1) at the value k, aol and al1 are the random regression coefficients for the intercept and slope of the additive genetic effect of individual l, pm is the random permanent environmental effect for sow m and eijklmn is the random residual error for record n. The following assumptions with regards to the additive genetic effects were made: N . G is a 2 × 2 (co)variance matrix for the intercept and slope effects: 10 (and σ01) is the covariance between the two aforementioned effects. The contemporary group effect was defined only based on sow birth year to account for genetic trend while avoiding collinearity with the ENV effect.Where H matrix was constructed using the preGSf90 software  and a SNP-derived genomic relationship matrix variance matrix between the intercept and slope terms (described above), Φ is a matrix of number of rows equal to the number of unique values of the ENV and two columns (a vector of “1” and the ENV). Heritability of each single value k of ENV , were calculated as rk = α1+βφk1 and rk is the predicted value k at the population level, and rkl is the predicted value k for the individual l, and all other parameters are as described before.Where ΓA GWAS was carried out for each of the three reproductive traits, performed on the population that showed the largest estimate of www.ensembl.org/index.html). Subsequently, biological processes, metabolic pathways, and enrichment analyses were performed using the DAVID 6.8 .The genomic windows that were selected and passed the bootstrapping test were used for the subsequent functional genomic analyses. Firstly, the biomaRt package  did not include the value 0 in the confidence intervals only for the TML populations. In these populations the estimates ranged from −3.25 to −2.01, with larger values for TML_LR and TML_YS. Further results will be reported only for the scenarios with the largest estimate of RH in similar gestation periods  was selected. Also, RH in the third week of gestation was selected for ABW in TML_LR. In addition, Max.T was selected for TNB  and ABW in SPG_LR (from 21 to 14 days before conception). For NBA, average THI recorded from 86 to 93 days into pregnancy was selected in TML_LR while Min.T recorded from 72 to 79 days into pregnancy was selected in TML_YS. The variance components estimates were partially consistent within trait and across populations. The proportion of variance explained by the intercept term  KEGG pathway identified was: “ssc00061:Fatty acid biosynthesis.” The main biological processes identified  were: cardiac conduction system development, ventricular cardiac muscle tissue development, genitalia development, epithelium development, embryonic forelimb morphogenesis, tube development, and somatic diversification of immune receptors via germline recombination within a single locus. The significant  cellular components associated with the candidate genes identified are: intermediate filament cytoskeleton, supramolecular fiber, cytoskeleton, non-membrane-bounded organelle, and intracellular part. The significant  metabolic functions identified are structural molecular activity and core promoter binding. Furthermore, The positional candidate genes identified are presented in g status , S3b. Thp-value < 0.05) KEGG pathways identified were: “Oocyte meiosis,” “Insulin resistance,” “Neutrophin signaling pathway,” “Insulin signaling pathway,” “Basal transcription factors,” and “Acute myeloid leukemia.” The biological processes identified  were: regulation of cellular response to stress, response to starvation, regulation of cell proliferation, cellular response to nutrient levels, hemoglobin metabolic process, mitotic cell cycle response, macromolecule modification, regulation of catabolic process, regulation of protein metabolic process, regulation of kinase activity, apoptotic signaling pathway, regulation of phosphate metabolic process, DNA methylation or demethylation, cellular response to extracellular stimulus, regulation of immune system process, and animal organ development. The genes and genomic regions identified to be associated with the intercept term have been previously linked to a variety of trait groups, including: spinal curvature, growth traits, meat fatty acid composition, meat quality, gestation length, NBA, testicular width and length, semen pH, number of mummified piglets, glucose level, age at puberty, gait score, corpus luteum number, litter size, number of non-viable fetuses, skin thickness, time spent lying, maternal infanticide, body length, chest circumference, birth weight variability, cortisol level, piglet mortality, teat number, and scrotal hernia , S4a. ThIn the present study we performed a series of comprehensive analyses to reveal the genomic background of heat tolerance based on routinely-measured phenotypic records and publicly recorded weather variables, and provide the basic knowledge needed for implementation of genomic selection for heat tolerance in maternal-line swine breeds. We focused on four independent lines of sows to test the discoveries over genetically-different populations that were raised under different management systems, therefore also testing the portability of the methods employed in the study. We finally explored the genetic basis of heat tolerance for the three traits in selected populations. The use of four independent pig populations greatly validates the results identified and conclusions drawn in this study.The reproductive performance observed in the four populations  are withIn the present study, climate records from the National Climatic Data Center weather stations were used to describe the environmental conditions experienced by the sows at different stages of ovulation and pregnancy. While these climate records are usually publicly available and have been successfully employed in other worldwide studies focusing on sow HT  the possibility to discover a critical time in which the sows appear to show different tolerance to HS for at least one trait and (2) the ability to leverage on a larger variation in ENV, since averaging the environmental conditions found in a 114-d span could reduce the observed variability. As for point (1), in our data we found that the autocorrelation for ENV in consecutive weeks is relatively large  so that such step would be unnecessary in future analyses.In general, HS occurring before conception or early pregnancy had a remarkable impact on prolificacy. For the SPG populations on both TNB and ABW, and for SPG_LR on NBA, the ENV covariates reported during ovulation and conception were selected to be the best environmental stressors to assess heat tolerance. The negative effect of pre-conception HS has been reported in other populations as well. For instance, Iida and Koketsu  found a Seven of the 12 ENV selected were built upon RH as climate variable, one was built upon THI and only four used temperature (with Min.T in one case and Max.T in three other scenarios). The preponderance of RH, rather than temperature, in challenging sows was also found by Tummaruk et al. . This miWe used genomic random-regression models for the estimation of genetic parameters, including additive genetic variance for the trait performance in a standard environment  environmental conditions. The identification of such genetic resources  can be easily performed graphically as shown in vice versa. A comparison of the number of genotyped individuals  of the total additive genetic variance, indicating that HT is a largely polygenic trait. However, the functional analyses performed confirm that the indicator traits analyzed are involved in important biological mechanisms of HS response. For instance, the genomic regions identified were previously reported to be associated with traits such as body temperature, hemoglobin content, coping behavior, cortisol levels and heart size. Various pathways associated with fatty acid biosynthesis were also identified.As expected, the genomic regions associated with the intercept  were previously linked with reproductive traits such as litter size, number of mummified piglets, corpus luteum number, number of non-viable fetuses, maternal infanticide, testicular width and length, and semen pH. The fact that the present study identified genomic regions previously reported to be associated with related variables validates the indicator traits used in this study.ALDH1A3 and LRRK1 genes have been highly associated with multiple reproductive traits  in LW pigs  genes family plays an important role in embryo formation and development, cell proliferation and differentiation  were also identified. ESR2 has been previously reported to be associated with reproductive traits  in various pig breeds  previously linked to carcass fatness, fatty acid biosynthesis, average daily gain, and body weight in various pig breeds, including LW and LR  were previously reported in the literature as well. For instance, In the present study, we used four independent populations to explore the genetic and genomic background of heat tolerance in maternal-line pigs, based on three reproductive traits and multiple environmental covariates. Our results indicate that heat tolerance based on reproductive traits is heritable and therefore genetic progress for HT can be achieve through genetic or genomic selection. Higher heritability estimates were observed in comfortable environments, indicating that selection for improved heat tolerance based on reproductive traits is feasible, although genetic progress will be slow. Therefore, considering that there is substantial additive genetic variance for heat tolerance, there is a need to identify novel indicators that better capture the biological mechanisms of HS response. Various genomic regions distributed across all autosomal chromosomes and explaining a small proportion of the total additive genetic variance were identified, indicating that heat tolerance is a highly polygenic trait. Results validated across the populations seem to point out to a genomic region located on SSC9 showing a sizable impact on heat tolerance measured both on TNB and NBA. This region will require future validation and refinement in future studies. In summary, we have shown that selection for improved heat tolerance in swine based on reproductive performance and public weather station data is possible. Selection for heat tolerance is expected to alter important biological mechanisms underlying several traits. Future research should focus on elucidating these mechanisms on a wide array of economically important traits before heat tolerance can be included among the breeding goals.justin.fix@pigsrus.net; Kent Gray, kgray@smithfield.com.Phenotypic and genomic data used in this study are property of the industry partners that contributed to the study. The data were given as in kind for conducting the study being published. The industry partners retain exclusive access to the data since it includes information about animals' performance and genetic background. The industry partners require that all data is deleted once the study is conducted. Requests to access these datasets may be granted under a negotiated research agreement and should be directed to Justin Fix, Ethical review and approval was not required for the animal study because The data used in this study came from pre-collected commercial datasets. Written informed consent for participation was not obtained from the owners because Representatives of owner companies contributed to the study and are listed as co-authors.FT and CM conceived and designed this study. FT carried out the analyses. FT, CM, and LB interpreted and discussed the results and wrote the manuscript. JH, YH, KG, JF, and CS supervised the data collection and provided inputs for the analyses of the data. All the authors reviewed and approved the final manuscript.The study used at that were provided as in kind by companies Smithfield Premium Genetics and The Maschhoffs LLC. JH, YH, and KG were employed by the company Smithfield Premium Genetics. CS and JF were employed by The Maschhoffs LLC. At the time of submission. The results are commercially of interest to the above mentioned companies but this interest did not influence the results presented in this manuscript in any matter. The remaining 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.


Direct selection for litter size or weight at weaning in pigs is often hindered by external interventions such as cross‐fostering. The objective of this study was to infer the causal structure among phenotypes of reproductive traits in pigs to enable subsequent direct selection for these traits. Examined traits included: number born alive (NBA), litter size on day 21 (LS21), and litter weight on day 21 (LW21). The study included 6,240 litters from 1,673 Landrace dams and 5,393 litters from 1,484 Large White dams. The inductive causation (IC) algorithm was used to infer the causal structure, which was then fitted to a structural equation model (SEM) to estimate causal coefficients and genetic parameters. Based on the IC algorithm and temporal and biological information, the causal structure among traits was identified as: NBA → LS21 → LW21 and NBA → LW21. Owing to the causal effect of NBA on LS21 and LW21, the genetic, permanent environmental, and residual variances of LS21 and LW21were much lower in the SEM than in the multiple‐trait model for both breeds. Given the strong effect of NBA on LS21 and LW21, the SEM and causal information might assist with selective breeding for LS21 and LW21 when cross‐fostering occurs. Direct selection for these traits is often restricted in practice due to external interventions such as cross‐fostering, whereby piglets are transferred between sows to equalize litter size. As a result, the number of nursing piglets at a sow can be different from the number of farrowing piglets. The purpose of cross‐fostering is to reduce piglet mortality at preweaning , and litter weight on day 21 (LW21) after farrowing. Descriptive statistics for each trait are presented in Table 2.3y is a vector of observations; β is a vector of systematic effects, including farrowing year (17 levels), farrowing month (12 levels), parity (8 levels), farm (2 levels), and mating sire breed (3 levels); u is a vector of random additive genetic effects; c is a vector of permanent environmental effects on the dams; e is a vector of random residuals; and X, Z, and W are known incidence matrices.A multiple‐trait animal model (MTM) was used for initial analysis. The following MTM was considered:u, c, and e was given by:G0 is the additive genetic (co)variance matrix, A is the additive (numerator) genetic relationship matrix, C0 is the permanent environmental (co)variance matrix, I is an identity matrix with suitable dimensions, and R0 is the residual (co)variance matrix. Such (co)variance matrices can be expressed as:σui2 is the additive genetic variance of trait i, σuiuj is the additive genetic covariance between traits i and j, σci2 is the permanent environmental variance of trait i, σcicj is the permanent environmental covariance between traits i and j, σei2 is the residual variance of trait i, σeiej is the residual covariance between traits i and j, and i and j for 1, 2, and 3 represent NBA, LS21, and LW21, respectively.The joint distribution of the random vectors The program GIBBS2F90  between traits and consists of the following three steps  algorithm was applied to the residual (co)variances obtained from MTM analysis to infer a potential causal structure among the three traits, as already proposed by Valente, Rosa, de los Campos, Gianola, and Silva . The ress Pearl, :ρ, a statistical decision is made as to whether two traits are connected by an undirected edge. If ρ conditioning of the combination of all other traits between traits Y1 and Y2 differs from 0, Y1 and Y2 are connected by an undirected edge (Y1–Y2).Step 1: Based on ρ, a statistical decision is made about the existence of an unshielded collider. When three traits Y1, Y2, and Y3 are connected with undirected edges to form a trio such as Y1–Y2–Y3, whereby two nonadjacent traits (Y1 and Y3) have a common adjacent trait (Y2), and Y1 and Y3 are conditionally dependent on any possible set that includes the adjacent trait Y2, the edges should be oriented toward the common adjacent trait; for example, Y1 → Y2 ← Y3, then Y2 is considered an unshielded collider. If Y1 depends on Y3 or Y3 depends on Y1  in this case, Y2 is considered a shielded collider, which the IC algorithm cannot detect because Y1 and Y3 are always conditionally dependent on any possible set.Step 2: Based on Step 3: When possible, the remaining undirected edges are oriented so that no new unshielded colliders or cycles are introduced.ρ as null or not were based on from 75% to 95% highest posterior density (HPD) intervals, in 5% increments. If the intervals contained the value 0, the correlation was declared null. The analysis was performed using an R  or 0 on the off‐diagonals, G0∗ is the SEM additive genetic (co)variance matrix (it describes variance and covariances of direct genetic effects), Γ0∗ is a diagonal matrix with the SEM permanent environmental variances, and Ψ0∗ is a diagonal matrix with the SEM residual variances. These permanent environmental and residual covariances were assumed to be 0 in the SEM. Such direct SEM (co)variance matrices can be expressed as:σui∗2 is the additive genetic variance of trait i, σui∗uj∗ is the additive genetic covariance between traits i and j, σci∗2 is the permanent environmental variance of trait i, σei∗2 is the residual variance of trait i, and i and j for 1, 2, and 3 represent NBA, LS21, and LW21, respectively.The SEM was fitted to the causal network inferred by the IC algorithm. The model can be described as:This model was fitted to estimate genetic parameters and causal coefficients representing causal effects with the assumed causal structure mentioned above. The covariances of permanent environmental and residual effect were conducted as diagonal to achieve parameter identifiability. Importantly, in the SEM, the causal parents of a given trait  are included as covariates in the SEM assigned to that trait. The program GIBBS2F90 was used to fit this model and to obtain posterior samples for SEM parameters; a Gibbs sampling strategy similar to that used for the MTM was employed here as well.3G0, C0, and R0 obtained with the MTM for each breed are listed in Table The posterior means and 95% HPD intervals describing R0, ρ between traits was estimated and applied in Step 1 for causal structure search using different HPD interval contents. None of the HPD intervals contained 0, indicating that the three traits were connected by an undirected edge  was positive. The indirect effect of NBA on LW21 via LS21  was also positive, but the direct effect of NBA on LW21  was negative. Finally, the total effect of NBA on LW21  was positive. Although all coefficients were significantly different between both breeds, their signs were always in the same direction.The dispersion parameters and their structural coefficients were fitted into the SEM with the assumed structure Figure  and are 4The objective of this study was to investigate the causal structure and estimate the causal coefficients among preweaning and weaning traits in pigs, which could then be used for direct selection based on litter size and litter weight at weaning when cross‐fostering is employed. Although it was impossible to artificially change the empirical NBA values, we assumed that this artificial change could be done by cross‐fostering just after farrowing and NBA assessment. This assumption allowed us to determine the causal structure among NBA, LS21, and LW21, as well as estimate the causal coefficients.The IC algorithm was based on 95% HPD intervals and returned a completely undirected structure. This result indicated that the structure was very reliable because the level for statistical decision was high and all causal coefficients were still statistically different from 0. Although many studies have reported a genetic relationship among reproductive traits , and uLW21∗ may represent total volume and quality of milk produced  effects on each trait. In contrast, the effects represent only direct effects in the SEM  (Valente et al., In general, residual covariance matrix is constructed as diagonal to achieve parameter identifiability. The permanent environmental and residual covariance matrices were set as diagonal in the SEM of this study. Although this restriction was strong it was necessary to identify the parameters, previous studies used the same method to identify them (Bouwman et al., In conclusion, we describe here the causal structure among NBA, LS21, and LW21 based on the IC algorithm and temporal and biological information. The causal structure allowed for the estimation of causal coefficients. A comparison of dispersion parameters for LS21 and LW21 between the MTM and SEM indicated that the phenotype arising from LS21 and LW21 traits could be strongly affected by the NBA trait. This finding suggests that cross‐fostering could have a big impact on LS21 and LW21, and thus the causal information might be useful for direct selection based on LS21 and LW21 when cross‐fostering is employed.


FTO, NDUFAF6 and CEBPA previously associated with growth and FE traits in monogastric species. Candidate genes associated with behavioral patterns were also identified. Overall, our results can be considered as the foundation for future functional research to unravel the actual causal mutations regulating growth and FE in rabbits.Feed efficiency (FE) is one of the most economically and environmentally relevant traits in the animal production sector. The objective of this study was to gain knowledge about the genetic control of FE in rabbits. To this end, GWASs were conducted for individual growth under two feeding regimes (full feeding and restricted) and FE traits collected from cage groups, using 114 604 autosome SNPs segregating in 438 rabbits. Two different models were implemented: (1) an animal model with a linear regression on each SNP allele for growth trait; and (2) a two‐trait animal model, jointly fitting the performance trait and each SNP allele content, for FE traits. This last modeling strategy is a new tool applied to GWAS and allows information to be considered from non‐genotyped individuals whose contribution is relevant in the group average traits. A total of 189 SNPs in 17 chromosomal regions were declared to be significantly associated with any of the five analyzed traits at a chromosome‐wide level. In 12 of these regions, 20 candidate genes were proposed to explain the variation of the analyzed traits, including genes such as  Before the availability of feeding devices for individual recording of feed intake (FI) of animals raised in groups, breeding programs to improve the feed efficiency (FE) of monogastric species achieved important genetic responses by using traits that could be measured individually in animals housed in groups and were genetically correlated with feed efficiency as selection criteria. In this context, FE should be understood as a general concept that reflects the degree of efficacy in the use of feed resources for performance. In the case of rabbits . Piles & Sánchez  studied et al. et al.  or restricted to 75% of the ad libitum intake (R). In order to obtain homogeneous groups regarding animal size, the kits under each FR were assigned to one of two groups based on their BW at weaning: large size  and small size . Animals from the same litter were distributed to both FRs. To obtain feed restriction to 75% of the ad libitum FI, the amount of feed supplied during week 1 was computed as 0.75 times the average feed intake of kits on F in a specific group j (j = LS or SS) during the previous week (i.e. i–1), plus 10% corresponding to the estimated increase in FI as the animals grew, i.e. FIR,ji=0.75×(1+0.1)×FIF,ji‐1 for i = 1–5 and j = LS or SS.After weaning, kits were randomly assigned to one of two feeding regimen (FR) treatments: ad libitum intake in LS and SS kits respectively. A maximum of two kits per litter were allocated to the same cage in order to minimize collinearity between maternal and pre‐weaning environmental effects and cage effects.This amount of feed was multiplied by the number of animals present in the cage to determine group feed requirements. The amount of feed for week 1 was computed from data that were recorded in previous experiments on the same production line with animals raised in the same season. The actual amounts of feed provided to the restricted animals were, on average, 75 and 74% the In both experimental groups (F and R), the recorded raw data consisted of weekly individual BW, and for the case of the F weekly cage, FI. In both groups, kits were fed the same standard pellet diet, supplied once per day in a feeder with three places, and containing prescribed antibiotics to control gut disorders. In both experimental facilities, feed was changed to a standard feed without drugs during the last week of fattening. Thus, records from the last week were discarded for the analysis because of the effect that the lack of antibiotics in the feed might have on growth rate, FI and the derived FE measures. Therefore, in both farms, the growing period controlled was from 30 to 56 days of age; thus, a total of four weekly individual BW records were retained per animal and three weekly group FI measurements were considered per cage.ad libitum (ADGF) or restricted (ADGR) FR. For the 99 cages on F, individual average daily feed intake (ADFI¯F) was computed as the total feed intake of the cage during the whole fattening period divided by the number of days and number of rabbits present in the cage during the whole fattening period. Also, individual average daily feed conversion ratio (ADFCR¯F) and individual average daily residual feed intake (ADRFI¯F) were computed. The first was the ratio between ADFI¯F and ADGF cage average, and the second was the residual of a batch‐nested multiple regression of ADFI¯F on the ADGF cage average and the cage average of the mid fattening period day metabolic weight.From these raw records, individual average daily gain (ADG) was computed as the regression coefficient of the within‐animal BW records on their ages. This was done for each FR, obtaining individual ADG on F and ADGR) of genotyped animals (438) and another including growth from genotyped animals as well as from all their non‐genotyped cage mates (438 + 1032). This second dataset also included cage average traits . Table Two datasets were employed in the analyses, one containing individual growth (ADGes 438 + 032. Thisr2) decay pattern from our population was assessed using plink 1.9  commercial kit from liver samples of 438 rabbits collected immediately after slaughter (66 days of age). DNA extracts were sent to an Affymetrix platform to conduct genotyping using the Axiom Rabbit Genotyping Array ‘Axiom_OrCunSNP’ (Thermo Fisher Scientific), which includes 199 692 variants. Only 161 830 were segregating in our population and, after retaining the SNPs mapped in autosomes in the OryCun2.0 assembly and applying standard quality control criteria, 114 604 SNPs were kept for further analysis. The applied quality control criteria comprised retaining animals having at least 90% of SNPs correctly genotyped, SNPs with less than 5% missing genotype data and SNPs with a MAF higher than 5%. The LD (Two different modeling approaches were adopted to conduct the GWASs:F and ADGR) and was implemented using QXPAK  – ADGF or ADGR – (one at the time) is explained by the effect of the allele content  in the pth genomic position of the ith animal, reflected by the regression coefficient at that particular position (αp) which represents the allele substitution effect, the effect of the jth batch level , the effect of the kth level of the order of parity in which the animal was born , the effect of the lth level of size of the litter in which the animal was born , the effect of the mth level of the type of cage , the effect of the nth cage (nC), the oth litter (ol) and the ith breeding value (ia), the last three being random effects. Thus, each random factor had associated with it a variance component to be estimated. For cage and litter effects, a diagonal structure was assumed between the different levels, whereas for the additive genetic effect the numerator relationship matrix was used to define the covariance between the individuals. Finally, a diagonal normal distribution was assumed for the residual term, eijklmno.where a particular record of a given trait under study  the regression on the SNP allele content (1). Then, likelihood values at their maximum were compared using likelihood ratio tests. This ratio follows, under the null hypothesis, a chi‐squared distribution with 1 degree of freedom; F and ADGR), the model was the same as that fitting the null hypothesis in the case of regression analysis. For explaining cage records , a model similar to that considered by Piles & Sánchez . In this second case, we considered individual records from both genotyped animals and their non‐genotyped cage mates.In the case of the analysis of group records, the equations involved in the bivariate model were the following:yjmn¯, i.e. traits of interests , are explained by the effect of the jth batch level , the effect of the mth level of the type of cage  and the averages of litters (nkl) and additive genetic effects  associated with the nN individuals in the nth cage. Litter, additive genetic and residual effects are random factors, assumed to follow normal distributions, indexed by their respective (co)variances to be estimated using an EM‐REML procedure.Group means, Breeding values for the two traits analyzed at a time were assumed to follow a joint multivariate normal distribution of the following form:Similarly, for the residual term, the assumed distribution was the following:σa1,a2) under the alternative model was assumed to be non‐null, representing in this case the association, at a genetic level, between breeding values for the trait of interest and the SNP genotypes. Under the null model, σa1,a2 was set to zero. The REML likelihood values at their maximum were used to construct likelihood ratio tests allowing exploration of the significance of σa1,a2 estimates. This was done by computing P‐values from the theoretical distribution of the ratio under the null hypothesis, a chi‐squared distribution with one degree of freedom. From this model, the estimated effect for each SNP position was calculated as a function of the estimated additive genetic covariance  and the SNP frequency (fp) .Oryctolagus cuniculus chromosome (OCC) regions  were declared as significantly associated with any of the five studied traits, i.e. ADGR, ADGF, ADFI¯F, FCR¯F and ADRFI¯F.At genome‐wide level, after multiple testing correction, neither of the methods returned significant associations. However, when multiple test correction was applied within each chromosome, 189 SNPs Table  located It is important to describe the LD pattern decay Fig.  to propeTable F , was identified in the region 100.99–101.11 Mb, whereas two candidate genes, NADH:ubiquinone oxidoreductase complex assembly factor 6 (NDUFAF6) and tumor protein p53 inducible nuclear protein 1 (TP53INP1), were proposed for ADGF in the region 109.07–110.88 Mb of OCC 3  was identified at 9.07 Mb in OCC 5  gene  identified among the 71 ensembl_gene_ids annotated in this region , out of 37 annotated ensembl_gene_ids, were found in this region   and 16 (82.86–83.26 Mb). The estimated effects of the SNPs with the strongest statistical association within these regions were large – 0.47 and 0.52 feed conversion units ((grams of feed/day)/(grams of growth/day)) respectively. The most significant SNP on OCC 6 had a low MAF (0.06), whereas that of the most significant SNPs on the region of OCC 16 was much higher (0.42). For FCR¯F, 63 ensembl_gene_ids were annotated (Table SIK1B) on OCC 6 and phospholipase A2 group IVA (PLA2G4A) on OCC 16  Table . For FCRed Table  and two 26.28–26.4 Mb and ADRFI¯F, significant associations were detected in three regions of OCC 21: 3.89–4.33 and 7.16–7.70 Mb, and one single SNP at 9.21 Mb. The second region was particularly relevant as it also contained SNPs significantly associated with ADGF. The MAF of the most significant SNP within this region was 0.37, and its estimated effect was 2.16 g/day. A total of 146 ensembl_gene_ids were annotated on OCC 21  within the region and its frequency. The additive variances of the QTL regions in Table F, ADGR, and both ADFI¯F and ADRFI¯F respectively. The percentage of phenotypic variance explained by the additive genetic effect for one of the QTL regions declared for FCR¯F is particularly high – 65% for the region on OCC 16. It could be difficult to propose a validation method for these results free from the assumptions in the model for the analysis, because FCR¯F is recorded as the group average. Nevertheless, a simple regression of group FCR¯F on group average genotype for the SNP AX‐147107945 at bp 82858725 in OCC 16, the SNP with the strongest association within the region (Table P = 3.38 × 10−5). This means that the expected FCR in a cage with all of the animals heterozygous for this SNP will be 0.20 units larger than that in a cage with all of the animals homozygous of one type and 0.20 units lower than that in a cage with all of the animals homozygous of the other type.As stated, given the available information on the cage performance records, the expected statistical power was low. Thus, in order to allow for a certain degree of signal detection, the threshold for significance declaration was deliberately reduced to a chromosome‐wide level. In this situation, we have successfully identified 17 chromosomal regions associated with the analyzed traits. To allow comparison between traits, the estimated SNP effects within the regions can be expressed relative to their estimated phenotypic variance Table . To thison Table , also shFTO gene, annotated on OCC 5 for ADGF, which has been previously associated with growth traits in rabbits , TRAF‐type zinc finger domain containing 1 (TRAFD1) and protein tyrosine phosphatase non‐receptor type 11 (PTPN11) genes as they map in a region of OCC 21 with a pleiotropic effect for both ADGF and ADRFI¯F and have 11 significant SNPs located in their introns. Identifying pleiotropic regions for both ADGF and ADRFI¯F could be considered an unexpected result as ADRFI¯F is a trait obtained after the phenotypic correction of FI by growth and metabolic weight. However, this phenotypic correction does not grant a null genetic correlation, and in fact, in the population under study it has been reported that the genetic correlation between ADGF and ADRFI¯F was 0.58  is a trait genetically different from growth recorded in animals fed ad libitum. Our results could be said to support this as for ADGR we have declared chromosomal regions different from those declared for ADGF. Nonetheless, this could be also a simple consequence of our reduced statistical power. In these regions, candidate genes associated with behavioral patterns  or involved in immunity and/or lipid metabolism  were identified. Finally, it is worth highlighting the CCAAT enhancer‐binding protein alpha (CEBPA) gene, annotated on OCC 5 for ADFI¯F, which has recently been identified as an upstream regulator of several differentially expressed genes down‐regulated in adipose tissue of high‐feed‐efficiency pigs (Horodyska et al. Piles & Sanchez  showed tIn spite of our loose significance threshold setting, we feel relatively confident of having adequately controlled the rate of false‐positive signals that we have declared. In support of our results, we have identified some candidate genes that have already been associated with similar traits in other rabbit and pigs populations.ad libitum as we have identified different QTL regions for both traits. It is remarkable that genes related to behavioral patterns have been proposed as candidates for ADGR. Regarding FE, some of the QTL regions that we declared to harbor candidate genes which are involved in lipid and energy metabolism have a pleiotropic effect for both ADGF and ADRFI¯F. In spite of these promising results, further functional research is warranted to validate these genes. Overall, our results lay an important foundation for future studies to unravel the underlying genetic bases driving growth and FE regulation in rabbits.We have proposed a number of QTL regions linked to the observed variation of the studied traits using a complex statistical model for fitting cage FE and feed intake, jointly with individual genotypes. To our knowledge, this is the first time this type of statistical model has been used within the framework of GWAS studies. The information content on cage average performances is quite limited, thus we have reduced the threshold for significance declaration to a chromosome‐wide level. In spite of this loose significance threshold definition, the declared QTL seem to harbor genes that can clearly be regarded as functional candidates for the traits of interest. Our results seem to support the idea that the growth of animals fed on restriction is under a different genetic control that that of animals fed https://doi.org/10.5281/zenodo.3611097Genotypes can be found here: Table S1. Description of the 189 chromosome‐wise significant SNPs and features annotated to them.Click here for additional data file.Table S2. List of genes annotated in the QTL regions.Click here for additional data file.


Innovations in the breeding and management of pigs are needed to improve the performance and welfare of animals raised in social groups, and in particular to minimise biting and damage to group mates. Depending on the context, social interactions between pigs can be frequent or infrequent, aggressive, or non-aggressive. Injuries or emotional distress may follow. The behaviours leading to damage to conspecifics include progeny savaging, tail, ear or vulva biting, and excessive aggression. In combination with changes in husbandry practices designed to improve living conditions, refined methods of genetic selection may be a solution reducing these behaviours. Knowledge gaps relating to lack of data and limits in statistical analyses have been identified. The originality of this paper lies in its proposal of several statistical methods for common use in analysing and predicting unwanted behaviours, and for genetic use in the breeding context. We focus on models of interaction reflecting the identity and behaviour of group mates which can be applied directly to damaging traits, social network analysis to define new and more integrative traits, and capture-recapture analysis to replace missing data by estimating the probability of behaviours. We provide the rationale for each method and suggest they should be combined for a more accurate estimation of the variation underlying damaging behaviours. Pigs are intelligent and explorative animals. However, in modern husbandry they are kept in environments where there is very little more than other pigs to explore. Around 30-70% of European pig farms have problems with tail biting  is known to occur when two or more genotypes respond differently to the same environmental change. GxE may influence behavioural traits, and it was found in sows in relation to savaging by Baxter et al.  and in fMeasuring behavioural traits remains challenging despite technological advances in the field of automated recording. Injured animals can be identified by repeated visual monitoring, a method that is highly time-consuming and only provides estimates of infrequent, sporadic or unpredictable behaviours. Lesions on the tail, ears, vulva or skin identify the victim but not the biter, and it is the latter that is of particular interest in breeding against the behaviour. Identifying biters is very complicated, as there is wide variation in their characteristics and a lack of reliable predictors of engagement in biting activity  to models with two genetic effects, i.e., the direct effect of the animal and a social effect describing the genetic influence of an individual on the phenotype of its group members. The initial social model proposed by Griffing  and MoorIn pigs, studies using the social model have primarily targeted performance traits such as growth rate  and indirect interactions , as described by Büttner et al. ,b. It quDamaging behaviours in a group evolve over time. As mentioned above, tail biting shows similarities with the spread of infectious disease  than it did for being a victim (h2 = 0.05)   must be considered. Studies of GxE address the variation in relative performance of two or more genotypes between different environments. Thus, two genotypes showing the same amount of damaging behaviour in one environment may show markedly different amounts in a second environment . This maGxE has been observed across a wide range of behavioural traits, including behavioural indicators of coping with stress and cognitive ability  is the sum of the genotype and the environment. By setting up an equation for each animal and incorporating pedigree information  we can estimate the genetic and environmental variances and breeding values. This model is far from perfect, since the number of killed piglets does not follow a normal distribution. In most cases there is no savaging, and often when there is savaging all of the piglets are killed. Furthermore, savaging (like many other damaging behaviours) is usually recorded as a categorical trait with two records: savaging or no savaging. If the records consist of only 0 and 1, the ordinary linear model will underestimate genetic variance and thus heritability.Threshold-linear models are often used for categorical traits with a quantitative genetic background. Savaging behaviour seems to be related to low plasma oxytocin levels Gilbert, . Let us Savaging is more common in first parities than it is in later parities, but older sows sometimes display the behaviour too  was 200 g lower than the average for all piglets . To account for the influence of both sow and piglet genes on savaging, two genetic effects—the direct genetic effect of the piglet and the maternal genetic effect of the sow—can be included in the model. Such a direct-maternal model , the genotype of the piglet could influence the risk of being savaged. It seems likely that vigorous, heavy piglets have a better chance of escaping an attacking sow. Grandinson et al.  found thFarine and Whitehead  providedKleinhappel et al.  have recTo perform social network analyses, information listing all dyadic interactions that occur in the group over the study period  is needed. Nodes and edges depict the relative positions of individuals in the network; animals are regarded as the nodes, and edges represent interactions between two individuals. Edges frequently reflect the quality of the relationships, including affiliation between nodes and frequency of interactions  at each time point, victim and non-victim, and these cannot be observed . The state process is modelled by a Markov chain, generally of first order, with transition probabilities v and nv the “victim” and “non-victim” states, ot = 1 if no tail lesions are observed at time t, ot = 2 if tail lesions are observed at time t, and ot = 0 if the animal is not observed at time t). The observed history of the animal can then be reduced to the series (102). The model assumes that, given the victim state at time t, the distribution of the observations is independent of all previous states and observations: ℙ(ot = 1 | St = k) = bk, t1. In the present illustration, we use the matrix bnv, t1 is the probability of observing no tail lesions given that the animal is not a victim. The probability of observing tail lesions given that the animal is not a victim is null. The initial state probability is π = (ℙ(S1 = v), ℙ(S1 = nv)). Given these parameters, it is possible to express the probability of the history of the animal depicted in Tailored to the studies of damaging behaviour, the multi-event multi-state model can be illustrated as follows . Considel et al. .To reduce the number of parameters to estimate Parameter estimations can be performed by the (restricted) maximum likelihood method  are also of great interest in the analysis of damaging traits. The victim and aggressive states can be viewed as independent phenomena, and thus they can be processed with two separate hidden Markov chains. However, in real social interactions, assumed independence of the two traits may be unrealistic and it would be preferable to consider states that combine the different behaviours potentially expressed by the animal. If we note b = biter and nb = non-biter, there are four hidden states: v.b/nv.b/v.nb/nv.nb. This also enables account to be taken of the fact that pigs can change status from aggressor/biter to victim over time and throughout their life stages . In the case of being a biter, if we note the observations animal biting = 1, not biting = 2, not observed = 0, then bna, t1 = 0 , but ba, t1 is also low because attacks are of very short duration. To overcome this difficulty, we suggest referring to an additional phenotype that is predictive of the biting activity. Chewing on the tail of a conspecific is often a precursor of damaging behaviour. Chewing group mates' tails, or other parts of their bodies, is more frequent than attacks  linked to the biter status under the form of a probability whereby, by definition, the probability of being a tail biter will be higher if the pig was a chewer earlier. This will facilitate use of the multi-event multi-state model and improve the completeness of the database.A difficulty when determining the unobserved state (and one that exacerbates the difficulties of convergence of the model) emerges if the observation is not specific to a given state  genetic effect is its effect on the phenotype of its social partners  with the total heritable variance relative to phenotypic variance (T2) that accounts for social variation allows the contribution of social genetic effects to heritable variation to be quantified. For instance, the heritable variance detected for pig growth can be substantially greater than it is within a classical model . If the genetic correlation is positive (rADS > 0), cooperation occurs and selection of the animal with the highest DBV will not harm group members. In this case, accounting for social genetic effects would also yield an advantage in the selection response, as compared with that obtained in a model with only the direct effect  through to a positive covariance   determines the sign of the correlation between the direct and the social genetic effects, i.e., the direct-social genetic correlations (rADS) . However, because biting is modelled as a stochastic process, there is also a probability that an individual will not receive any bites in a week. This probability follows from the Poisson distribution and equals P(k = 0) = eΔt−λ. With λ = 0.5 bites/day, the probability equals 0.03 (3%) in the current example. Following Anche et al.  receives from its pen mate j (biter), λ0 is the population average pair-wise biting rate, Di is the direct effect of the focal individual i (victim effect), Sj is the social effect of its group mate j (biter effect), and the average values of D and S are ~1  rate, say λ, also known as a probability per unit of time. This rate is analogous to the hazard in survival time analysis. For example, with a rate of λ = 0.5 bites/day, a pig receives on average 1 bite per 2 days. The average time until the next bite equals 1/λ, which is 2 days in this example. The number of bites an individual receives in a time-slot of Δt days follows a Poisson distribution with mean λΔt. For example, with λ = 0.5 bites/day, a pig receives on average 3.5 bites per week . The breeding values can be interpreted, approximately, as percentages. Thus, an individual with a DBV of AD,i = +0.1 has Di ≈ 1.10 and therefore receives ~10% more bites than the average individual. A log-normal distribution is skewed to the right, indicating that some individuals may perform or receive excessive biting, in line with empirical observations  × 0.1 = 0.3 bites per day. If the focal individual has AD,i = +0.1, and its three group mates have AS = +0.2, −0.15, and +0.3 then the focal individual receives on average Suppose we have groups of 4 pigs and a mean pair-wise biting rate of λBecause this model is non-linear and the number of bites an individual receives does not follow a normal distribution, an ordinary linear mixed model for analysing bite number is not statistically suitable. Box 2Assuming that bite number follows a Poisson distribution, we can fit a generalised linear mixed model with a log-link function. Application of the log-link function yields the following linear model  is an intercept fitted as a fixed effect, AD,i is the direct breeding value of the focal pig, n−1), n is the group size, and the term ln(n−1) + ln(Δt) is a so-called offset, a known value that is subtracted from the dependent variable. As usual, the direct and social breeding values are random effects following a bivariate normal distribution with zero mean. The offset is needed only when group size varies and/or when the time interval Δt varies among records. The term ln(n−1) in the offset assumes that the number of bites a pig receives is proportional to its number of group mates (n−1). If this assumption is too strong, one may drop ln(n−1) from the offset, and fit a fixed group-size effect instead.where E), and E[y] is now the mean of the 0/1 trait. The interpretation of the estimates is the same as above. It is, however, important to remember that records of the number of bites are much more informative than 0/1 records.If we only have data on whether (1) or not (0) a pig has received bites over a certain time interval—e.g., based on changes in tail status in an interval—we can fit the same model but then use a complementary log-log link function  and enrichment  applied at herd level. Tracking such detailed information at the different stages of a pig's life helps in the analysis and interpretation of results.When the environment can be described as a gradient—e.g., from low to high, poor to rich, or unfavourable to favourable—the expression of a behaviour along the gradient can be presented as a reaction norm describing potential expressions of its genotype across varying environments . To account for GxE in the analyses, phenotypic data from a genetic line or breed needs to be collected in at least two different environments or under different environmental conditions or treatments. GxE has been considered in a one-generation selection experiment in which the biting behaviours of groups of pigs selected for low or high SBV for growth were compared in contrasting environments  variation related to damaging behaviours in pigs. In this discussion section we explore how the different models could potentially be combined in order to improve our ability to detect and accurately quantify both phenotypic and genetic variation in these hard to measure traits.Behavioural characteristics and their genetic expression can be investigated from several angles. We have presented five different models: social network analysis and the capture-recapture model to analyse the behaviour measured on farm; the direct genetic effect model and the social genetic effect model Each of the models would benefit from more frequently collected and more accurate phenotypic data, and some of the modelling strategies  are entirely dependent upon the availability of data on social interactions. Recording behaviour or relevant proxy measures  is time-consuming, and observation by humans has its limitations partly as a result of the low frequency and sporadic nature of these behaviours. The development of automated technology for recording behaviour is progressing rapidly  is removed from the group, this needs to be recorded along with the date. In practice this takes little time, but removal is often not registered. The use of electronic tags to follow animals as they are moved across different pens or buildings on the farm has been tested in experimental herds. Its expansion to commercial herds will facilitate the recording of animal movements. Since each pen has its own specific micro-environment which may contribute to damaging behaviour , recording of the identity of the pen will help to disentangle the effects caused by the group mates and those caused by the physical environment. Intrinsic phenotypes such as states related to growth, and extrinsic factors such as feeding system, must be recorded if behaviours are to be contextualised and analysed properly. How previous life stages may influence damaging behaviours is becoming a key question. Longitudinal records over the lifespan are needed to account for previous rearing conditions and past social experiences, with a particular interest in early-life effects . Second, since the likelihood that an individual expresses or receives biting may depend also on its experience at earlier stages of its life, longitudinal studies may provide more insight than cross sectional studies. It is important to keep track of all animal movements between groups when integrating life information in longitudinal genetic studies. If the combination of models is preferable, offering significant added value, computational difficulties will be exacerbated by longitudinal analyses. However, difficulties associated with the low-frequency of these behaviours might be alleviated as records across a pig's life are accumulated.A possible limitation to the implementation of all of these models at large scale arises from the need to account for GxE effects when they have a substantial impact on behavioural traits. It will be necessary to characterise the way in which different genotypes perform under different environmental conditions in more detail. Methods to investigate GxE are available, from simple comparison of re-ranking to estimation of genetic correlations among environments (Rauw et al., Group size can have an impact on the prevalence of damaging behaviours, and the detection of its effect on the genetic expression of traits is a form of GxE. Until now, we have assumed that social genetic effects are independent of group size. This independence exists when, irrespective of group size, each animal is affected by the same level of social genetic effect. An example mentioned by Bijma,  is alarmDamaging behaviours can cause severe injuries and lead to significant impairment of animal welfare. Their prevalence can be reduced with improved environmental conditions, but it is increasingly being recognised that housing conditions as such do not eliminate all welfare problems, and that changes to housing are often limited by affordability. Genetic selection could be used as a lever to improve animal welfare by reducing the prevalence of damaging behaviours, but geneticists need better tools and methods both to harvest more data and to analyse it. With developments in automated animal identification, tracking and behavioural recording, we hope that new and improved records will be available in the near future. We have illustrated ways in which future studies can be designed, and we explained how different statistical and genetic models could be used to improve the analysis of social behaviour in group-housed pigs, with relevance to social behaviours in other livestock species. As is expected with multifactorial and complex traits, GxE effects may occur, and these should be accounted for in genetic evaluations designed to reduce damaging behaviours.LC, PB, ID, IC, AM, WR, LZ, LF-G, ST, CL, and LR wrote the manuscript. All authors contributed to the article and approved the submitted version.LF-G was employed by the company AXIOM. LZ was employed by the company Topigs Norsvin. The remaining 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.