Diplotaxis acris occurring in hyperarid deserts. Given the advance of warming and aridity in vast regions occupied by drylands, D. acris can indicate the successful evolutionary trajectory that many other annual plant species may follow in expanding drylands. To this end, we conducted a greenhouse experiment with 176 D. acris individuals from five Saudi populations to quantify the genetic component of variation in architectural and life history traits. We found low among‐population divergence but high among‐individual variation in all traits. In addition, all traits showed a high degree of genetic determination in our study experimental conditions. We did not find significant effects of recruitment and fecundity on fitness. Finally, all architectural traits exhibited a strong correlation pattern among them, whereas for life history traits, only higher seed germination implied earlier flowering. Seed weight appeared to be an important trait in D. acris as individuals with heavier seeds tended to advance flowering and have a more vigorous branching pattern, which led to higher fecundity. Population divergence in D. acris might be constrained by the severity of the hyperarid environment, but populations maintain high among‐individual genetic variation in all traits. Furthermore, D. acris showed phenotypic integration for architectural traits and, to a lesser extent, for life history traits. Overall, we hypothesize that D. acris may be fine‐tuned to its demanding extreme environments. Evolutionary speaking, annual plants facing increasing warming, aridity, and environmental seasonality might modify their phenotypic spaces toward new phenotypic configurations strongly dominated by correlated architectural traits enhancing fecundity and seed‐related traits advancing flowering time.The phenotypic space encompasses the assemblage of trait combinations yielding well‐suited integrated phenotypes. At the population level, understanding the phenotypic space structure requires the quantification of among‐ and within‐population variations in traits and the correlation pattern among them. Here, we studied the phenotypic space of the annual plant  Diplotaxis acris individuals from five Saudi populations to quantify the genetic component of variation in architectural and lifehistory traits. Overall, we conclude that D. acris may exhibit fine‐tuned phenotypes in its demanding extreme environments.The phenotypic space encompasses the assemblage of trait combinations yielding well‐suited integrated phenotypes. We conducted a greenhouse experiment with 176  Over generations, a population molds its genetic composition and builds its phenotypic space  influenced mean trait values and also the pattern of trait covariation within populations  Boiss. (Brassicaceae). The species occurs in hyperarid deserts where natural selection exerts strong pressures on standing genetic variation and resulting phenotypic distribution. We undertook a greenhouse experiment to quantify among‐ and within‐population genetic variations in architectural and life history traits in 176 D. acris individuals from five populations from the Arabian Desert. We computed broad‐sense heritability values for all traits, which provides an estimation of all genetic contributions to within‐population phenotypic variation. We also evaluated the effects of selection on recruitment and flowering time, the two major fitness‐related developmental transitions in annuals, and computed correlations among traits to estimate the degree of phenotypic integration in D. acris. Given the generalized trend for increasing temperatures and aridity is several world regions, particularly since the turn of the 21st century across the approximately 41% of the terrestrial land surface characterized as drylands  Boiss. (Brassicaceae) is an annual desert herb  are purple and arranged in dense racemes. Plants can produce a single flowering stalk, but they can also lose apical dominance.b Figure . The speb Figure , but theD. acris populations . All populations, separated by 5–30 km from each other, were located around Sakaka city, Saudi Arabia , and exhibited similar D. acris densities .We sampled 30–40 individuals  from five haphazardly chosen a Figure . In partD. acris populations harbored a similar plant community. Major co‐occurring perennial species were Haloxylon salicornicum (Moq.) Bunge ex Boiss. (Chenopodiaceae), Nauplius graveolens (Forssk.) Wiklund (Asteraceae), and Artemisia judaica L. (Asteraceae). The annual plant community included Savignya parviflora (Delile) Webb (Brassicaceae), Erodium laciniatum var. pulverulentum (Cav.) Boiss. (Geraniaceae), Schismus barbatus (L.) Thell. (Poaceae), Plantago ciliata Desf. (Plantaginaceae), Plantago ovata Forssk. (Plantaginaceae), Trigonella stellata Forssk. (Fabaceae), and Spergularia bocconei (Scheele) Graebn. (Caryophyllaceae).Vegetation in hyperarid deserts is composed of widely spaced perennial shrubs, whereas annuals occupy barren shrub interspaces. Except slight differences, all five 2.22) within each population. We kept seeds in 1.5‐ml plastic tubes at room temperature (20–24°C) in darkness until the sowing day. We used mean seed weight as a covariate to control for environmental maternal effects in the statistical analyses (see below) because environmental maternal effects can be an issue when testing genetic differentiation in offspring traits  and 264,000 seeds . We watered plants as needed throughout the experiment to avoid hydric stress and to evaluate the full potential of D. acris plants growing in optimal conditions.To estimate quantitative genetic variation in architectural and life history traits in We estimated the proportion of germinated seeds 2 weeks after the sowing date  when we observed the maximum number of seedlings per replicate. Two weeks later, 1 month after sowing, we thinned out replicates to one juvenile plant per replicate Figure  to avoidr = .99).In addition, we estimated fecundity by counting the number of seeds in 10 fruits per replicate  and multiplying the average number of seeds per fruit by the total number of fruits per plant. We did not detect any significant ovule abortion or seed loss during the counting. We saw some bees inside the greenhouse when flowering was quite advanced . Nevertheless, we believe that the vast majority of seeds came from self‐fertilization. To avoid redundancies, we excluded from the analyses some traits due to strong correlation with other traits or practically no among‐individual variability. These traits included the number of stalks emerging from the base , the mean length of all stalks , and the number of fruits  and belowground biomass , and significantly negatively correlated with the root‐to‐shoot ratio .We terminated the experiment when all plants were completely fruited . We dug up, rinsed, and dried out all plants (70°C for 48 h) in an FED 115 oven . Then, we estimated the aboveground biomass, the belowground biomass, and the root‐to‐shoot ratio. We used the root‐to‐shoot ratio as a measure of individual fitness as biomass‐related traits may represent a good estimate of fitness in plants  for all traits, except for seed germination. For the latter, we fitted generalized linear mixed models (GLMM), using the gamma distribution as the inverse link function. We carried out these analyses with the R package lme4  and individual (random factor) nested within the population on variation in architectural and life history traits of h2) values as h2 = GV/(GV + EV), where GV is the estimated among‐individual variance component and EV is the residual variance  for all traits, we estimated broad sense heritability  and selection differentials (s and C) for the major fitness‐related developmental transitions in annuals , using a generalized additive model‐based (GAM) characterization of the fitness function with the R package gsg  but only significant in one population . Overall, linear models indicated that variation among individuals mostly accounted for variation in both architectural and life history traits (Table R2 = .00–.19) than that explained by individuals  values for all traits. All h2 values were high . The lowest h2 values were for the root‐to‐shoot ratio and flowering time  and selection differentials (s and C) for recruitment (given by the seed germination fraction) and flowering time with a GAM‐based approach to evaluate how natural selection acted upon D. acris individuals. Despite some marginal significances, the results showed that neither recruitment nor flowering time significantly contributed to fitness, estimated by the root‐to‐shoot ratio ; Formal analysis (supporting); Investigation ; Methodology ; Resources (lead); Validation ; Writing‐original draft (supporting). F. Xavier Picó: Conceptualization ; Formal analysis (lead); Investigation ; Methodology ; Resources (supporting); Validation ; Writing‐original draft (lead).No permits were required.Figure S1‐S2Click here for additional data file.


Growing evidence suggests a mutual interaction between gut microbiome alterations and ALS pathogenesis. However, previous studies were susceptible to potential confounding factors and reverse causation bias, likely leading to inconsistent and biased results.To decipher the potentially mutual relationship between gut microbiota and ALS, we used a bidirectional two-sample MR approach to examine the associations between the gut microbiome and ALS.OTU10032 unclassified Enterobacteriaceae species-level OTU and unclassified Acidaminococcaceae were associated with a higher risk of ALS . Importantly, Gamma-Glu-Phe was showed potential deleterious effects on the risk of ALS . Sensitivity analysis of the two candidate genera and metabolites using the MR-Egger and weighted-median methods produced similar estimates, and no horizontal pleiotropy or outliers were observed. Intriguingly, genetically predicted ALS was associated with an increase in the relative abundance of OTU4607_Sutterella  and Lactobacillales_ORDER .Using the inverse variance-weighted method, Our findings provide novel evidence supporting the bidirectional relationship between the gut microbiota and ALS. These results may contribute to designing microbiome- and microbiome-dependent metabolite interventions in future ALS clinical trials.The online version contains supplementary material available at 10.1186/s12883-021-02522-z. Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative motor neuron disease accompanied by both systemic and central nervous system–specific inflammation as well as energy dysmetabolism –3. StrucSod1-Tg mice found that Akkermansia muciniphila (AM) and AM-associated nicotinamide ameliorate symptoms of ALS. In humans, distinct microbiome and metabolite configurations have been observed in a small preliminary study that compared 37 patients with ALS with household controls [Observational studies have shown that the interface between the host and the gut microbiome may be altered in mouse models of ALS , 10, inccontrols .Sod1-Tg mice could demonstrate causal relationships but are scarce, and the number of commensal bacteria that have been investigated is limited [Growing but conflicting evidence is attractive, raising the hypothesis of a mutual interaction between gut microbiome alterations and ALS pathogenesis. However, it has been difficult to determine whether these changes in the intestinal microbiota are causative of ALS disease, an exacerbating factor for disease, or a consequence of disease. The composition and diversity of the gut microbiome can be easily altered as a result of bacterial infections, antibiotic treatment, lifestyle changes, surgery, and long-term changes in diet . Availab limited .The Mendelian randomization (MR) approach is a widely used genetic epidemiological method for assessing causal associations between risk factors and disease by exploiting genetic variants as instrumental variables (IVs) for exposure –20. This). Notably, the gut microbiome is remote from the disease site of ALS, it is suggested that a potential systemic influx of microbiome-regulated metabolites may affect the susceptibility of motor neurons in ALS. We also estimated the effects of potential metabolites on ALS in MR design.Therefore, to decipher the potentially mutual relationship between the gut microbiota and ALS, we used a bidirectional two-sample MR approach to examine the associations between the gut microbiome and ALS Fig. . NotablyThe detailed approach of selection of IVs for exposures, genome-wide association study (GWAS) summary statistics for ALS, and MR analysis were previously described . The MR P < 5 × 10− 8) were obtained from available GWAS data of stool samples in humans [Genetic instruments of the abundance of 98 genera of gut microbiota at the level of genome-wide significance (n humans . As a re2 > 0.9) (https://ldlink.nci.nih.gov/) was used instead, if available. We checked the phenotypes of selected SNPs using comprehensive genotype-to-phenotype cross-references  and repvariance .A transsynaptic, glutaminergic, excitotoxic mechanism  has been proposed as a pathophysiological biomarker in ALS . We therP < 1 × 10− 5 as candidate IVs of the specific metabolite. Then, a clumping procedure was conducted with European 1000G as a reference panel to identify the independent variants, with a linkage disequilibrium threshold of r2 < 0.01 in a 500-kb window.For each of the metabolites, we selected SNPs that showed an association at P < 5 × 10− 8 [We drew on summary statistics from the largest and most recent GWAS of ALS  patients × 10− 8 .For each direction of the potential relationship, we combined MR estimates using an inverse variance-weighted method (IVW) meta-analysis, which essentially translates to a weighted regression of SNP outcome effects on SNP exposure effects where the intercept is constrained to zero. The IV assumptions can be biased if instrument SNPs show horizontal pleiotropy, influencing the outcome through causal pathways other than exposure . TherefoTo assess the robustness of significant results, we conducted further tests for horizontal pleiotropy using meta-analytic methods to detect heterogeneous outcomes, including leave-1-SNP-out analyses and the MR Egger intercept test of deviation from the null .The analyses were performed with R version 3.1.1 (R foundation) and Stata version 11.2 . All human research was approved by the relevant institutional review boards and conducted according to the Declaration of Helsinki. Ethical approval was obtained from relevant Research Ethics Committees and from the review boards of Peking University Third Hospital.The resulting lists of instrument SNPs for each genus of gut microbiota are given in Table OTU10032 unclassified Enterobacteriaceae was associated with a higher risk of ALS   .On the basis of 2 independent SNPs, P = 0.012) . Sensitivity analysis for the metabolites using the MR-Egger and weighted-median methods produced similar estimates, and no horizontal pleiotropy or outliers were observed (eTable 4).Importantly, gamma-glutamyl amino acids showed potential deleterious effects on the risk of ALS. Gamma-glutamylphenylalanine (Gamma-Glu-Phe), a peptide in the gamma-glutamyl pathway, showed a significantly increased risk of ALS  increase in the level of Gamma-Glu-Phe: OR, 1.96; 95% CI, 1.50–2.55; 12) Fig. . In addiOTU4607_Sutterella . The risk of ALS on each OTU4607_Sutterella-related SNP effect was estimated and is shown in eFigure Lactobacillales_order . Single Lactobacillales_ORDER-related SNP effect was estimated and is shown in eFigure On the basis of 2 independent SNPs, genetically predicted ALS was associated with an increase in the relative abundance of This study assessed the causal effects of potential microbiome modulators of human ALS and added intriguing evidence implicating some genera of the gut microbiome in modifying susceptibility to ALS. These genera attenuate ALS risk through gamma-glutamyl-related metabolite levels, supporting that a trans-synaptic, glutaminergic, excitotoxic mechanism could provide a pathogenic basis for ALS. These results may contribute to designing microbiome- and microbiome-dependent metabolite interventions in future ALS clinical trials. We further provide genetic evidence that the pathophysiology of ALS is associated with an altered relative abundance of the microbiota, strengthening the bidirectional relationship between the gut microbiota and ALS.Enterobacteriaceae includes over 30 genera and 120 species of Enterobacteriaceae, but more than 95% of clinically significant strains fall into 10 genera and fewer than 25 species. All members of the Enterobacteriaceae family ferment glucose with acid production and nitrogen metabolism. Glutamine synthetases (GSs) are key enzymes of nitrogen metabolism, and their activity is modulated by nitrogen repression [Acidaminococcaceae, an important glutamate-fermenting family of microbes, produces ammonia as the major end product through glutamate fermentation [The gut microbiome is a source of these potentially disease-modifying bioactive metabolites and has recently been suggested to contribute to the pathogenesis of neurological disorders , 34. Thepression . Acidamientation . It is pentation .OTU4607_Sutterella and Lactobacillales_ORDER. In previous studies, gut dysbiosis, particularly reduced levels of butyrate-producing bacteria and higher E. coli and Enterobacteria abundance, was also found in ALS mice and ALS patients [Our study showed that higher ALS susceptibility was associated with a higher relative abundance of patients , 38. Furpatients , 40. HowF-statistic > 10). Second, another potential source of bias in MR analyses is population stratification. We reduced this bias because the dataset for gut microbiota, metabolites and ALS was restricted to individuals of European ancestry. Replication with functionally relevant genetic prediction of gut microbiota is warranted given the substantial difference in gut microbiota composition among different populations. Finally, 16S rRNA gene sequencing only permits resolution from the genus to the phylum level rather than at a more specific level, resulting in biased results if some specific species contributed to ALS.There are several strengths in the present study, including the assessment of genera of gut microbiota and promising metabolites in relation to ALS, the use of data from the largest GWASs to date and bidirectional MR design. This design technique minimizes confounding by known and unknown factors and avoids reverse causation. In addition, consistent results from several sensitivity analyses, including the use of weighted mode, weighted median, and MR-Egger methods, indicate the robustness of our findings. Several limitations merit consideration. First, we used a limited number of gut microbiota and ALS SNPs as IVs; we cannot exclude that our findings might have been affected by weak instrument bias, although all genetic instruments were associated with exposure OTU10032 unclassifed Enterobacteriaceae Species-level OUT and (b)Unclassifed Acidaminococcaceae From SNiPA Pairwise LD.Additional file 2: eTable 2. Associations between gut microbiota and amyotrophic lateral sclerosis in sensitivity analyses.Additional file 3: eTable 3. Associations between gut microbiota and amyotrophic lateral sclerosis in in a leave-one-out approach.Additional file 4: eTable 4. Associations between gut microbiota and amyotrophic lateral sclerosis in sensitivity analyses.Additional file 5: eTable 5. Effect estimates for association of genetically predicted amyotrophic lateral sclerosis with gut microbiota using inverse variance weighting method.Additional file 6: eFigure 1. Association of genetically predicted OTU10032 unclassified Enterobacteriaceae species-level OTU with amyotrophic lateral sclerosis. Squares represent the odd ratios of amyotrophic lateral sclerosisper 1-allele increase in single nucleotide polymorphisms related to greater abundance of OTU10032 unclassified Enterobacteriaceae Species-level OTU; horizontal lines represent 95% confidence intervals (CIs); diamond represent the overall odds ratio with its 95% CI.Additional file 7: eFigure 2. Association of genetically predicted unclassified Acidaminococcaceae with amyotrophic lateral sclerosis. Squares represent the odd ratios of amyotrophic lateral sclerosisper 1-allele increase in single nucleotide polymorphisms related to greater abundance of unclassified Acidaminococcaceae; horizontal lines represent 95% confidence intervals (CIs); diamond represent the overall odds ratio with its 95% CI.Additional file 8: eFigure 3. Association of genetically predicted amyotrophic lateral sclerosis with OTU4607 Sutterella. Squares represent the effect estimates of the relative abundance ofOTU4607 Sutterellaper 1-unit higher log odds of amyotrophic lateral sclerosis; horizontal lines represent 95% confidence intervals (CIs); diamond represent the effect size with its 95% CI.Additional file 9: eFigure 4. Association of genetically predicted amyotrophic lateral sclerosis with Lactobacillalesorder. Squares represent the effect estimates of the relative abundance ofLactobacillalesorderper 1-unit higher log odds of amyotrophic lateral sclerosis; horizontal lines represent 95% confidence intervals (CIs); diamond represent the effect size with its 95% CI.


Offspring resemble their parents for both genetic and environmental reasons. Understanding the relative magnitude of these alternatives has long been a core interest in behavioral genetics research, but traditional designs, which compare phenotypic covariances to make inferences about unmeasured genetic and environmental factors, have struggled to disentangle them. Recently, Kong et al. (2018) showed that by correlating offspring phenotypic values with the measured polygenic score of parents’ nontransmitted alleles, one can estimate the effect of “genetic nurture”—a type of passive gene–environment covariation that arises when heritable parental traits directly influence offspring traits. Here, we instantiate this basic idea in a set of causal models that provide novel insights into the estimation of parental influences on offspring. Most importantly, we show how jointly modeling the parental polygenic scores and the offspring phenotypes can provide an unbiased estimate of the variation attributable to the environmental influence of parents on offspring, even when the polygenic score accounts for a small fraction of trait heritability. This model can be further extended to (a) account for the influence of different types of assortative mating, (b) estimate the total variation due to additive genetic effects and their covariance with the familial environment , and (c) model situations where a parental trait influences a different offspring trait. By utilizing structural equation modeling techniques developed for extended twin family designs, our approach provides a general framework for modeling polygenic scores in family studies and allows for various model extensions that can be used to answer old questions about familial influences in new ways.The online version of this article (10.1007/s10519-020-10032-w) contains supplementary material, which is available to authorized users. However, parents also help create and shape their offspring’s environment, which may have an enduring influence for certain traits. If the parental traits that impact their children’s environment are themselves heritable, a covariance will develop between the genetic effects underlying those traits and the environmental effects provided by the parents. Educated parents, for example, provide to their offspring not only genes that predispose to higher education, but also a familial environment that is likely conducive to higher education. Thus, offspring who inherit genes that predispose to higher education are also more likely to be influenced by a familial environment that encourages education. This phenomenon is a type of The occurrence of genetic nurture has important implications for understanding complex trait genetics. Genetic nurture increases the phenotypic variation in the population over what it would otherwise be, and can bias estimates of genetic or environmental influences. In genome-wide association studies (GWAS’s), genetic nurture inflates estimates of SNP associations. This bias can be quantified in part by comparing within-family estimates, which are immune to this inflation, to standard between-family estimates. For example, Lee et al.  found thWhile genetic nurture cannot be estimated in classical twin designs, it can in principle be detected using extended twin family designs  and they provided no estimate of the magnitude of VT. Secondly, as explained below, primary phenotypic assortative mating  is a competing explanation for the relationship between the nontransmitted PGS and the offspring phenotype. Kong et al. attempted to account for the influence of AM, but because they found evidence that AM for educational attainment in Iceland occurred only in the parental generation (and not before), their approach assumes this specific type of disequilibrium assortment. Third, much of the math presented by Kong et al. was derived from first principles, limiting the generalizability of their approach and not easily allowing it to be extended to other situations.structural equation modeling (SEM) framework of their basic idea that uses transmitted and nontransmitted PGS’s to understand genetic and environmental parental influences. These models can be used to obtain unbiased estimates of total variation due to additive genetic effects  relationships between variables by finding estimates jointly instead of individually. For scenarios such as those involving VT and AM, this can greatly simplify otherwise intractable math. In addition, SEM is advantageous because it encourages a focus on effect sizes rather than m et al. .causal model—a set of assumed causal connections between measured and unmeasured variables. SEM can then be used to find estimates that maximize the likelihood of the observed variances and covariances given the assumed causal model. Although sometimes misunderstood, SEM does not test causation but rather assesses the degree to which a set of observed variances and covariances is consistent with a particular causal model  for the model to be identified . Even for identified models, certain assumptions about causal relationships between variables can lead to high correlations among estimates, increasing their standard errors and potentially necessitating that one or more parameters be fixed.A causal model is considered latent variables—theorized causes of variation and covariation among observed variables. Single-headed arrows from one variable to another signify causal relationships from the former to the latter, with their associated path coefficients being akin to partial regression coefficients. Double-headed arrows, meanwhile, signify covariances when connecting two variables to each other and variances when connecting variables to themselves. Finally, a straight line with no arrows is called a copath and is used to model AM. The copath is a more recent innovation in SEM . However, once a double-headed arrow has been traversed, the direction reverses such that the chain now travels forwards, in the direction of the arrows.A chain must include exactly one double-headed arrow (a variance or a covariance term), which is equivalent to stating that a chain must change directions exactly once. This is necessary because double-headed arrows provide the proper scaling for the coefficients in each chain.All chains must be counted exactly once and each must be unique. However, the order of the links in the chains matters. For example, despite being algebraically equivalent, the chain mentclass2pt{minimCopaths may only be traversed once in a given chain, and a chain must be legitimate before traversing the copath. However, once the copath is crossed, the first two rules above reset. A chain must therefore contain exactly one double-headed arrow before traversing the copath, and one double-headed arrow after traversing the copath. Thus, copaths connect two legitimate chains to create a single, longer chain.To demonstrate the first three rules (the fourth is demonstrated below), we derive the expected To derive expectations using a path diagram, one must identify all legitimate paths that connect two variables (for expected covariances) or that connect a variable back to itself (for expected variances). These paths can be thought of as chains, with each individual arrow or copath representing a link in a particular chain. The expected value of a chain is equal to the product of all the coefficients associated with each of its links, and the final expected variance or covariance is equal to the sum of all legitimate chains. A chain is considered legitimate if it abides by the following path tracing rules: mentclass2pt{minimp, m, and o for paternal, maternal, and offspring, respectively. To reduce redundancy, we use [N]T to denote either NT (the nontransmitted) or T (the transmitted) haplotypic PGS, and we use the p or m but not both within a single term. For example, w, f, Although the path tracing procedures described above are simple and algorithmic, the number of unique chains grows rapidly as models become more complicated, making the process error-prone. To simplify chains and reduce the probability of errors, we substitute variables  ; w the genetic nurture effect; and f and w, and F), and unique environmental score  that can estimate their values iteratively.This model assumes that parameters have reached equilibrium, which implies that variances and covariances are the same across parental and offspring generations. The equilibrium assumption allows the parameters that change over time , and the increase in genetic covariation between mates and close relatives variance of the PGS under AM, w, can be derived by counting two chains w remains an estimate of genetic nurture with its value being inflated by a factor w after removing the influence of AM, and thus In the same manner, the estimate of genetic nurture, w, the presence of AM causes the expectation of Finally, as was the case for a). Here, we take the first approach by assuming that parental phenotypes are measured , denoted g and a), which increases to the degree that f. In addition to a, there are four additional parameters  in this model. None of these are estimated. Rather, their values are determined from non-linear constraints, which we turn to in order.Model 2 includes two additional observed variables , j is the variance of a latent construct and could thereby take any arbitrary value. The simplest choice is to define j so as to be consistent with k. Specifically, if the PGS is standardized in the base population (where The variance of the haplotypic LGS (h) can be estimated under the reasonable assumption that the increase in the variance of the LGS from the base to the current population is proportionate to that of the PGS from the base to the current population. This assumption could be violated if the genes that drive the PGS association are more or less correlated with the trait actually being assorted on than the genes underlying the LGS, which seems unlikely. This assumption is equivalent to h and g are the same only when the PGS and LGS explain the same amount  of the total heritability. Furthermore, similar to h can also be found by path tracingh to be equal leads to the nonlinear constraintF and the LGS’s (denoted by v), we make a similar assumption that the ratio of genetic nurture to direct genetic effects is the same for observed as for latent genetic effects. This assumption could be violated if the genes driving the PGS association are more or less correlated with the trait that VT works through than the genes underlying the LGS, which again seems unlikely. This assumption is equivalent to v via path tracing, and the resulting non-linear constraint, areg) and among LGS’s (h), it also induces a covariance between PGS’s and LGS’s, which we call i. From path tracing, the expected value of i isi) inflates both the genetic nurture part of i, the observed The increase in the variance of the haplotypic LGS due to AM . When using this strategy, it is therefore important to have decent estimates of heritability in the base population that account for the influences of genetic nurture and AM. Estimates from twin studies are biased under these conditions, but estimates from extended twin family models should be much less so  effects are equivalent in parents and offspring. This assumption would be violated if there are gene-by-age or gene-by-cohort effects. Kong et al. provide some evidence of this in their data: the correlation between the PGS and educational attainment was significantly higher among offspring (.22) than among parents (.12). When parental phenotypes are measured in Model 2, or when parental phenotypes are unmeasured but there are independent estimates of the PGS effects in the parental generation, accounting for such effects is possible by estimating two different It may also be of interest to understand how one parental trait influences a different offspring trait. For example, Kong et al. showed a covariance between the nontransmitted PGS of educational attainment and offspring health, consistent with cross-trait  VT and genetic nurture. Such cross-trait genetic nurture would contribute to apparent genetic correlations that have nothing to do with pleiotropy. To investigate cross-trait VT using the above example under the current framework, one could use the PGS and parental values of educational attainment along with the offspring values of health, and plug them into the above models without modification. This is similar to the approach taken by Kong et al. However, such an approach does not account for AM within  or across  traits, nor does it account for within-trait genetic nurture effects. For these reasons, we believe that cross-trait VT and genetic nurture effects are optimally modeled bivariately, using the PGS’s and phenotypic values of the two traits in both parents and offspring; including more than two traits would also be possible, but results from such a model would likely be incomprehensibly complex. The parameters from the above models would be 2-by-2 full (in the case of path coefficients) or symmetric (in the case of variance–covariance) matrices. Conveniently, nothing about the derivations in this paper would change except for keeping track of when matrices should be transposed, which obeys an additional path tracing rule (Vogler and Cockerham g (see Model 1). The g estimates is significantly greater than 0 tests whether mate similarity  has led to genetic covariance, as predicted by primary AM. Additionally, of these 10 estimates of g, 6 provide information on cis (within-person) genetic covariances and 4 provide information on trans (across-mate) genetic covariances. The g vs. cis g would suggest that AM is at disequilibrium. Similarly, if trans g estimates are significantly greater than 0 while cis g estimates are not, this would support the hypothesis that only a single generation of AM has occurred . Furthermore, the ten estimates of g can be used to derive expected values of g. On the other hand, primary AM on a trait that is more genetically than phenotypically correlated with the measured trait (a form of genetic homogamy) would predict that observed gWhile our models have thus far assumed primary phenotypic AM under equilibrium, other mechanisms of assortment are possible. Indeed, there is considerable power for testing different mechanisms of AM, which could itself be used as a focus of these models. This power stems from the amount of information in this model relevant to AM. There are a total of 10 observed haplotypic PGS variances or covariances which collectively provide 10 estimates of g, h, and i to zero. Furthermore, social and genetic homogamy can be modeled by assuming that AM occurs on a latent trait, Y through either environmental or genetic pathways, respectively  can be modeled by setting expectations of cis Genetic nurture, the covariance between genes and parentally provided environmental influences, can amplify genetic effects in a way that neither GWAS nor heritability studies have been able to sufficiently account for. While estimating direct genetic effects after removing their covariance with the environment is important, we argue that the converse—estimating the direct environmental effect after removing its covariance with genetic effects—is at least as important. The models presented above allow for estimates of this direct environmental influences of parents on offspring, and also suggest several important extensions. For example, there exists much more GWAS data with siblings than with parents, and so extending the models above to include siblings, twins, and potentially other collateral relatives remains a next step. Furthermore, as shown by Kong et al. with enough data it is straightforward to estimate differential genetic nurture effects depending on the parent of origin; thus, it is equally straightforward to estimate differential VT effects from fathers vs. mothers. Finally, as noted above, future multivariate extensions to this model would provide insight into how one parental trait influences a different childhood trait.the specific trait assessed by the PGS. For example, the vertical transmission variance in a model that uses an educational attainment PGS only estimates how traits genetically related to parental educational attainment influence offspring educational attainment. If other parental traits, such as intelligence, warmth, work ethic, conscientiousness, etc. also influence offspring educational attainment, then the portion of variance due to these and other parental influences that are genetically uncorrelated to educational attainment will be missed.There are several important caveats and limitations to the present approach. We discuss here the central ones. One very important caveat is that estimated The above caveat is related to the limitation that, in order to accurately characterize the influence of a parental trait on an offspring trait, sufficiently predictive PGS’s  as opposed to horizontal (such as sibling) transmission. For certain traits, such as experimentation with drugs and alcohol, horizontal transmission seems at least as likely as VT. In a model that includes both parents and siblings, there would be sufficient power to differentiate horizontal transmission from VT. In the meantime, it must be kept in mind that estimates of To our knowledge, this is the first treatment of how transmitted and nontransmitted PGS’s can be used to estimate the direct effect of parents on their offspring, and the first to account for the influence of different types of AM on these estimates. It builds upon the seminal work by Zhang et al.  and KongElectronic supplementary material 1 (PDF 687 kb)Below is the link to the electronic supplementary material.


In the current study, a cohort of populations and parents were created to evaluate and understand heterosis across generations  in lentil, a self-pollinated annual diploid (2n = 2× = 14) crop species. Lentil plants were evaluated for heterotic traits in terms of plant height, biomass fresh weight, seed number, yield per plant and 100 grain weight. A total of 47 selected lentil genotypes were cross hybridized to generate 72 F1 hybrids. The F1 hybrids from the top five crosses exhibited between 31%–62% heterosis for seed number with reference to the better parent. The five best performing heterotic crosses were selected with a negative control for evaluation at the subsequent F2 generation and only the tails of the distribution taken forward to be assessed in the F3 generation as a sub selection. Overall, heterosis decreases across the subsequent generations for all traits studied. However, some individual genotypes were identified at the F2 and sub-selected F3 generations with higher levels of heterosis than the best F1 mean value (hybrid mimics). The phenotypic data for the selected F2 and sub selected F3 hybrids were analysed, and the study suggested that 100 grain weight was the biggest driver of yield followed by seed number. A genetic diversity analysis of all the F1 parents failed to correlate genetic distance and divergence among parents with heterotic F1’s. Therefore, genetic distance was not a key factor to determine heterosis in lentil. The study highlights the challenges associated with different breeding systems for heterosis  but demonstrates the potential significant gains that could be achieved in lentil productivity.Heterosis is defined as increased performance of the F Lens culinaris Medik.), a self-pollinated annual diploid (2n = 2× = 14) cool season grain legume is mostly used for human consumption due to its high level of protein, vitamins, and minerals [Lentil  for evaluation. A total of five F3 plants per family  were screened in a randomised block trial  in 140 mm plastic pots at 22 ± 2°C with a photoperiod of 16/8-h (light/dark). Both F1, F2, F3 generational assessment) to quantify heterosis, where each individual was assessed for seed number, seed weight, biomass fresh weight and plant height at time of harvest. Each plant was harvested by taking all the above ground biomass, packing the biomass in a pre-measured paper bag, and weighed for biomass fresh weight on a balance . Subsequently, these plants were oven-dried at 37°C for 48–72 h and threshed for seeds. Seeds were collected from each individual plant and the number of seeds generated was counted using an automatic seed counter  as well as generating a total yield value in terms of total seed weight per plant. In addition, a hundred seed weight per plant value was calculated by dividing the total seed weight by the number of seeds and then multiplying by a hundred. The data was evaluated for mean, and standard error using ASREML (v 4.1.0) [A number of yield related traits were measured in each experiment (Fv 4.1.0) .1 phenotypic data, a spatial analysis was performed, and predicted mean values were calculated for seed number, yield, biomass fresh weight, and plant height using ASREML [For the Fg ASREML . In addi2 and F3 generation evaluation, the data was analysed on a single plant basis since it was not possible to have genetic replicates of the population. However, mean values of the replicated parents along with their standard errors have been considered to understand environmental variance in the glasshouse trial.For the FCorrelation coefficients between plant height, biomass fresh weight, seed number, and yield per plant were determined using R software (v4.0.0).1, F2 and F3 as better parent heterosis (BPH), which was computed BPH = (F1-BP)/BP × 100, where BP referred to the better-parent value.The percentage of heterosis was analysed in F2 and F3 generations using library Tidyverse in R software (v4.0.0). A single multivariate regression model was created to predict yield based on four predictor variables, such as, biomass fresh weight, plant height, seed number and hundred grain weight.Multiple Linear Regression analysis was performed in F® Plant Mini Kit  following manufacturer’s instructions. RNA-Seq libraries with an approximate insert size of 350 bp were prepared using Sure Select Strand Specific RNA library prep kit and evaluated using the Tape Station 2200 platform with HSD1000 Screen Tape System  according to the manufacturer’s protocols. Equal mass of each sequencing library with a unique barcode was combined to create a single pooled sample for sequencing. All reads were pair-end sequenced using the HiSeq 3000 and MiSeq platforms . Raw data has been deposited to NCBI under accession number GSE184819 ); Data Type: transcriptome or gene expression).Leaf tissues from multiple nodes were collected from 4 weeks-old plants and were frozen immediately in liquid nitrogen and stored at −80 °C until required. Total RNA (tRNA) was extracted using RNeasyFollowing Fastq data generation, the raw sequence reads were filtered using a custom perl script  to removGenetic diversity analysis was performed using the abovementioned filtered SNP data from all accessions. Genetic distances for each lentil accession were calculated using Nei’s method within the StAMPP package . A phylo1’s, 43 crosses exhibited positive heterosis based on seed number. Overall, the range of heterosis observed varied between -59% to 62%, with 18 out of 72 crosses exhibiting greater than 20% heterosis  has also been recorded in commercial F1 hybrid cultivars of Chinese cabbage [Heterosis for seed number, yield, and biomass fresh weight at the Fof 31±1%  quantify hybrids . Similarneration , 43. Dinneration  reported cabbage .2 generation , with phenotypes at the extreme of the distribution that performed better than the F1 generation mean value  leads to unreliable selection before homozygosity is attained. As a result, future studies would be suggested to be conducted from the entire F2 derived F3 families rather than making selections and taking the tails of the distribution. Alternatively, it might be suggested to ignore the F2 generation evaluation entirely and simply perform a seed multiplication to advance generations and useF2:3 families to retrospectively calculate F2 genotype values. This would allow a form of within family replication. Alternatively modelling of rates of selection, recombination and inbreeding could indicate the most efficient strategy to advance either the entire populations or sub selected fractions to achieve advanced populations that would still have small proportions of the extreme heterotic individuals.To understand the trend of heterosis at further generations, Fneration . The meaneration , represean value . This vaRebetzke  also dis1 generation supports the concept that the hybrid mimic breeding strategy could be deployed for lentil varietal development. This approach utilizes recurrent selection for the critical hybrid vigor trait to advance generations while stabilising and multiplying the population to retain heterosis in pure breeding lines [5 lines derived from hybrid plants performed equivalent to F1 hybrid in wheat. Similar findings have been reported in pea and tomato where researchers have been able to develop stable F5-F6 lines with the same characteristics as the parental F1 hybrids [5 lines in pea as compared to F1 hybrids (out yielded the best parent by up to 11%). Similar findings have been reported in pea, tomato, and tobacco where researchers have been able to develop stable F5-F6 lines with the same characteristics as the parental F1 hybrids [1 and as discussed, the method of generation advance needs careful work, consideration, and experimentation. Sarawat et al. [5 performed better than the F1 mean. The limited scale of valuable lines and attrition in the multiplication process does present additional logistical challenges on a commercial scale for hybrid mimics and necessitates the screening of a large number of lines and reliable germplasm to work with. It is likely that due to the aforementioned complexities, hybrid mimics have not been more widely commercially exploited so far.The identification of individuals at sequential generations that outperform the Fng lines , 19. Resng lines  reported hybrids , 33. Sar hybrids  reported hybrids , 33, 54.t et al.  reportedB. napus, and sunflower, cytoplasmic or nuclear encoded male sterility has been explored [It is understood that there are some challenges associated with the development of hybrid mimics. An alternative way to utilise heterosis is through wide hybridisation heterosis using pollination control mechanisms. Different pollination control systems have been used to breed for heterosis. In some crops such as rice, maize, wheat, explored . Future explored  and furt1 hybrids exhibited a subtly different pattern of heterosis for plant height. As compared to other traits, the level of heterosis was significantly lower for plant height except for cross-1  but not for plant height [In comparison to other traits in the study, the F cross-1 . Heterosected F3 . The popectively . There ht height , 57. van1, F2 and sub selected F3 populations (r = 0.23–0.99) except for cross-2 where yield was not significantly correlated to 100 grain weight at F1. Also, cross-1 showed no significant correlation between yield and plant height at F2. The degree of correlation was evaluated across the generations in all the crosses under investigation and it was observed that yield correlated to plant height (r = 0.23–0.99), biomass fresh weight (r = 0.37–0.98), seed number (r = 0.32–0.98), and 100 grain weight (r = 0.26–0.66). Multiple regression analysis also confirmed that yield per plant at F1, F2 and sub selected F3 generation could be predicted by hundred grain weight (coefficient = 0.061–2.10) and seed number (coefficient = 0.01–0.06) within each generation in all the populations under study  for both trait performance and mid parent heterosis [2 = 0.87) but moderate heritability has been observed for yield  they did not exhibit heterosis Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S5 Table(XLSX)Click here for additional data file.


The combined analysis of variance showed highly significant effects of salinity and genotypes (generations) on all the traits. The scaling tests did not support the three-parameter model (additive-dominance model); hence, the six-parameter model was used to assess the genetic effects governing the traits in this study. The epistatic gene effects were crucial, as were additive and dominance gene effects for plant height, K/Na, and yield in salinity stress conditions. The highest heritability was observed for total chlorophyll, carotenoid, SPAD chlorophyll, and K/Na ratio in saline conditions. The additive genetic variance was more important than the dominance variance for grain weight, K, K/Na in salinity conditions. The findings of the current study may have important implications in the quantitative genetics of salinity tolerance and the development of cultivars tolerant to salinity in wheat.Understanding the genetics of salt tolerance is of utmost need to combat the rising prevalence of soil salinity through employing tolerant cultivars. The current study was carried out to investigate the quantitative genetic basis of agronomical and physiological-related traits of salinity-stressed plants using seven generations (parental cultivars, F Triticum aestivum L.) is a crucial staple food with global production of over 700 million tones, contributes significantly to the diet of the world population by supplying 20% of protein and daily calories to 4.5 billion people worldwide [Triticum spp.) [Common wheat  , is one + and Cl−) accumulate to high concentrations beyond the plant-specific thresholds in the leaves. Plants that tolerate osmotic stress can be maintained their growth rate in the initial stage of salinity exposure [The adverse effects of salinity on plant growth and development can be implemented in two phases according to the classical view , 3. In texposure . TherefoSalinity tolerance is a complex polygenic trait highly influenced by environmental factors and genetic-environment interaction, but we do not yet fully understand the genetic architecture . Generat2 populations of durum wheat to assess the broad-sense heritability of leaf Na content and the K/Na ratio of hydroponically-grown plants exposed to 100 mM NaCl at the seedling stage under greenhouse conditions. They reported a high broad-sense heritability for shoot Na+ concentration. In another study by Munns and coworkers [2s of durum wheat. Notably, the results of a pot experiment in common wheat suggested the importance of epistatic effects in governing salinity tolerance [Although there are some studies on the inheritance of salinity tolerance in crop plants, most of them were done with young plants cultivated in pots under greenhouse conditions (see ). Koch eoworkers  a moderaolerance . In addiolerance  and barlolerance , 14.1, F2, F3, BC1, and BC2) grown in normal and saline field conditions.Despite the large body of data on the genetic studies carried out in non-saline field conditions –18, litt1, F2, F3, BC1, and BC2, at Research Farm of Isfahan Agricultural and Natural Resources Research and Education Center. ‘Barat’ cultivar has a pedigree of SLVS*2/PASTOR, was selected from 24th SAWSN of International Maize and Wheat Improvement Center (CIMMYT), and released in the warm and dry areas of South Iran [A salt tolerant (‘Barat’) and a salt-sensitive  wheat cultivar were crossed to produce the following filial and backcross progenies: Futh Iran . This cuuth Iran . In contuth Iran  and is auth Iran . This cuuth Iran .1 and P2) and F1, four rows for F2, BC1, BC2, and one row for each of the 176 F3 families. The rows were 1.5 m long and 30 cm apart with 5 cm between plants (30 plants/row). The seeds of the parents and progenies were handplanted in the rows within a replication. The plants in the normal experiment were irrigated with freshwater , while in the salinity-stress experiment were irrigated with brackish groundwater with the EC of 13 dS m−1 . The saline irrigation was applied eight times, starting from the four-leaf stage (Zadoks growth stage 14) to ripening stage. No precipitation was recorded during the salinity treatment period. Soil samples were taken from the 0 to 30 cm depth to determine the EC of saturated soil–paste extracts (ECe) at the beginning and just after harvest. The ECe was determined following the Rhoades [e within the root zone (30 cm) for the normal and saline field conditions was determined as 1.8 and 9.6 dS m−1, respectively. Based on soil sample analysis, 30 kg P ha−1 and 120 kg N ha−1 fertilizers were applied before sowing. Nitrogen fertilizer was splitted into three parts and applied at sowing, tillering, and anthesis stages.Two parental cultivars and their five derived populations (seven generations) were planted in normal and salt-stress experiments using a randomized complete block design with three replicates. Each replicate or block consisted of 194 rows including two rows for parents , number of days to pollination date (DP), number of days to maturity date (DM), plant height (PH), peduncle length (PL), single grain weight (GW), number of spikes per plant (NS), number of grains per spike (GN), grain yield per plant (yield). To measure the agronomical traits, samples were obtained from 15 plants of each Pcate see .1, P2, and F1, 20 plants of each BC and F2, and five plants from each F3 families per replicate  were incinerated at 550°C for 4 h. Inorganic ions were then extracted using 10 mL HCl (2 N), and the volume of each sample was standardized to 100 ml. The sodium and potassium contents of the solutions were determined by flame photometry . A standard curve was used to determine the Na and K concentrations . The K/NA sample of fresh leaves was weighed (FW) immediately after cutting into pieces, placed in 20 mL of distilled water, and left in the dark for 24 h at room temperature. Then the weight of turgid leaves was used as turgid weight (TW). The oven-dried (70°C for 48 h) samples were weighted to determine the dry weights (DW). The total RWC was then determined using the below formula :%RWC=[Chlorophyll a, Chlorophyll b and total carotenoid concentrations were measured using the spectrophotometer method (Hitachi F-2500 fluorescence spectrophotometer) with reading absorbance at 646, 663, and 470 nm, respectively. To determine photosynthetic pigments, 0.1 g fresh leaf tissue sampled at early heading stage (Zadoks growth stage 58) were homogenized and extracted in 15 mL acetone 80% using a centrifuge at 5000 rpm for 15 min. Chlorophylls (a and b) and carotenoids (Car) concentrations (mg/g FW) were calculated using below equations :ChloroTotal chloroyll (Tchl) was calculated as the sum of chlorophyll a and b. Only Tchl and Car were subjected to genetic analysis.Flag leaf blade chlorophyll  was estimated using three randomly selected flag leaves from each plot by a SPAD chlorophyll meter . The measurements were conducted at the early heading stage (Zadoks growth stage 58). Flag leaf area (FLA) was measured by a leaf area meter. The measurements were carried out at the full heading stage (Zadoks growth stage 60).The data were initially checked for normality of distribution and homogeneity of variance using Kolmogorov–Smirnov and Bartlett’s tests, respectively. A combined analysis of variance (ANOVA) was used to test the effects of the environment , generation, and generation × environment interaction by mixed-model ANOVA using the Mixed Procedure of SAS. Replicate and environment were considered fixed factors, and generation was random. The statistical analyses were carried out using the SAS software package  and SPSS (version 26). Tukey’s Honest Significant Difference (HSD) test was used to compare trait means obtained from each set of the seven generation groups (two parents and five progenies).2, 2αβ and β2 are the coefficients of these genetic parameters, respectively. A weighted least-squares analysis was used following the model originally developed by Cavalli [th generation and Vi = the variance of the ith generation mean.Generation mean analysis was conducted following Mather and Jinks  model as Cavalli  and exte Cavalli  to obtai2). The best fit model is the one with a non-significant chi-square and significant estimates of the scales. If the results point out the role of epistasis, then a six-parameter genetic model  should be fitted to the generation means [Mather’s scaling test A, B, C and D was initially conducted and then followed by the Joint scaling test of Cavalli  to examion means . Broad-son means :h2b=10Components of genetic variance were calculated based on the data of six generations using the relationships suggested by Mather and Jinks  as folloE = environmental variance; D = additive variance; H = dominance variance; VF2, VF1, VBC1, VBC2, VP1 and VP2 are variance of F2, F1, BC1, BC2, P1 and P2, respectively; and F = joint contribution on all loci.Where, VThe results of combined-ANOVA for the traits studied in both normal and salinity stress conditions are presented in 1 were higher than those of the two parents in normal and salinity stress conditions. The F1 values for PL, DH, DM, SPAD were almost intermediate between those of the parents in both treatments. The mean of trait values in the F2 generation was lower than the corresponding values for the F1 generation  or non-significant effect of epistasis . The results of both individual and joint scaling tests summarized in The estimates of additive, dominance, and epistatic genetic effects controlling the traits evaluated in normal and salinity-stress field conditions are given in Tables Additive and additive × additive were the main types of gene actions related to the inheritance of leaf K and Na concentrations in both environmental conditions. At the same time, additive, dominance, additive × additive, and dominance × dominance effects were the likely mode of gene actions in the inheritance of K/Na ratio under both conditions Tables  and 6. A2b), narrow-sense heritability (h2n), and for the traits in normal and salinity stress conditions are presented in Table 2b estimates were higher than the h2n estimates for all the traits in both environments. Moreover, both the h2b and h2n estimates were higher for normal , and NS (33%) intermediate for K/Na (29%), and lower for SPAD (13%), DP (12%), PH (10%), and yield (1%) under stress conditions. The low h2n estimates in normal conditions were 16% for K, 15% for DP, and 14% for yield. The highest h2b values were recorded for Tchl (94%) followed by Car (83%), DP (66%), Na (60%), and K/Na (50%) in normal conditions, whereas the highest values were observed for Car (75%), Tchl (63%), Na (60%), and K/Na (48%) in saline conditions.The components of genetic variance , average degree of dominance, broad-sense heritability ½ for some of the traits was lower than one, indicating the likely importance of the overdominance type of gene action in the inheritance of these traits. The direction of dominance (F) was positive for NS, RWC, Na, Tchl, Car, and yield in both environments, DP and GN in normal, and PH and SPAD in stress environment. These show the existence of more dominant alleles than recessives alleles in parents for the traits mentioned above, that showed positive F values. The negative ’F’ value of K and K/Na showed the predominance of recessive alleles governing these traits in the parents grown under saline conditions. In contrast, it was reversed in the case of Na.The significance of dominance effects relating to the additive deviations of genes is determined by the average degree of dominance [(H/D)p < 0.01) among parental, F1, F2, BC1, and BC2 generations allows us to conduct the genetic analysis; (ii) the rejection of null-hypothesis of the additive-dominance model (three-parameter) guides us to consider an alternative model (six-parameter); and (iii) the significant mean effect “m” revealed by the six-parameter model for all the traits, supports the quantitative inheritance of the traits studied. One of the central findings from our study was that different gene actions governing the traits in the two environmental conditions . Does this imply that breeding strategy for each trait should be developed per a basic gene action in the trait of interest in each of the environments? In general, the answer is “yes”, though we should expand an identical strategy to those are similar in gene action.Knowledge of genetic components of tolerance would be vital for developing salinity tolerant cultivars in wheat through its implications for the design and deployment of appropriate tools and strategies . For theAll the four ’A’, ’B’, ’C’, and ’D’ scales were significant for DM and yield in stress conditions. These shows that not only additive and dominance but also other types of gene action such as epistasis may likely contribute to the genetics of DM and yield in wheat when grown under saline conditions. These results are in close agreement with the recent report of Attri et al.  on DM anAdditive gene action was found to be one of the positive and significant genetic components in the inheritance of Na, K, and K/Na in salinity stress conditions. Therefore, recurrent selection-based breeding schemes are effective in improving salinity tolerance since we deal with a fixable component of genetic variance . SimilarSignificant additive × additive effect for DP in normal conditions suggests that epistasis between alleles of different loci contributes to decreasing the DP expression . The yieThe significant effects of the additive and additive × additive that were higher than the dominance effect for NS in salinity stress conditions may reflect an appreciation of enhanced response to selection. Negative additive × additive interaction for some of the studied traits, such as DP in normal treatment, shows the potential for reducing these traits along with fixation of additive effects in the subsequent generations . The sli+/Na+ ratio in the leaves with the established knowledge of mechanism underlying the substantial contribution of the Kna1 locus in salinity tolerance via shoot Na+ exclusion in bread wheat ., 35.+/Nad wheat Click here for additional data file.S2 Table(XLSX)Click here for additional data file.


Littorina saxatilis provides an ideal study system. Divergent ecotypes adapted to wave action and crab predation occur in close proximity on intertidal shores with gene flow between them. Here, we used F2 individuals obtained from crosses between the ecotypes to test for associations between genomic regions and traits distinguishing the Crab‐/Wave‐adapted ecotypes including size, shape, shell thickness, and behavior. We show that most of these traits are influenced by two previously detected inversion regions that are divergent between ecotypes. We thus gain a better understanding of one important underlying mechanism responsible for the rapid and repeated formation of ecotypes: divergent selection acting on inversions. We also found that some inversions contributed to more than one trait suggesting that they may contain several loci involved in adaptation, consistent with the hypothesis that suppression of recombination within inversions facilitates differentiation in the presence of gene flow.Chromosomal inversions have long been recognized for their role in local adaptation. By suppressing recombination in heterozygous individuals, they can maintain coadapted gene complexes and protect them from homogenizing effects of gene flow. However, to fully understand their importance for local adaptation we need to know their influence on phenotypes under divergent selection. For this, the marine snail  L. saxatilis, that has evolved ecotypes adapted to wave exposure or crab predation. These two types occur in close proximity on different parts of the shore. Gene flow between them exists in contact zones. However, they exhibit strong phenotypic divergence in several traits under habitat‐specific selection including size, shape, and behavior. We used crosses between these ecotypes to identify genomic regions that explain variation in these traits. We could show that previously detected inversion regions contribute to adaptive divergence. Some inversions influenced multiple traits suggesting that they contain sets of locally adaptive alleles. Our study also identified regions without known inversions that are important for phenotypic divergence. Thus, we provide a more complete overview of the importance of inversions in relation to the remaining genome.Chromosomal inversion polymorphisms, segments of chromosomes that are flipped in orientation and occur in reversed order in some individuals, have long been recognized to play an important role in local adaptation. They can reduce recombination in heterozygous individuals and, thus, help to maintain sets of locally adapted alleles. In a wide range of organisms, populations adapted to different habitats differ in frequency of inversion arrangements. However, getting a full understanding of the importance of inversions for adaptation requires confirmation of their influence on traits under divergent selection. Here, we studied a marine snail, Understanding the mechanisms that promote phenotypic diversification is of central interest in evolutionary biology. Some of the differences we observe in nature may not be caused by genetic divergence but by environmental effects. However, in many cases there is evidence for heritability of traits contributing to local adaptation Hereford , confirmTheoretical studies have found that certain genetic architectures favor local adaptation and protect locally advantageous alleles ; Faria et al. Here, we explored the role of inversions in phenotypic divergence in a well‐studied system, the marine snail To investigate the influence of inversions on local adaptation, we applied a powerful approach using more than 380 lab‐reared individuals resulting from crosses between the two divergent ecotypes. This strategy allowed us to remove confounding environmental effects and homogenize the genomic background of individuals. We used QTL mapping to test for associations between genomic regions and phenotypic traits distinguishing ecotypes. Furthermore, we applied variance partitioning across linkage groups to test whether chromosomes harboring inversions that differ in frequency between ecotypes contributed disproportionately to phenotypic variation. By using complementary approaches, we were able to capture different aspects of the genetic architecture of local adaptation beyond inversions and identify additional regions important for phenotypic divergence.Crossing was performed between Crab and Wave ecotype individuals collected on the Swedish West Coast at Ängklåvebukten , where both ecotypes occur in close proximity  as described in Faria et al.  by visual matching to color cards by one of us (KJ). To obtain a continuous variable, we converted RAL categories to rgb‐color values . For boldness behavior, snails were disturbed to induce retraction and time recorded until an individual crawled out , relative thickness (size‐independent), shell shape, shell color, and boldness behavior that were previously found to differ between ecotypes  with 22,095 markers and combined all families for construction of one linkage map. The “ParentCall2” module was used  to calculate the most accurate parental genotype posteriors and to obtain missing parental information from offspring. We used the LepMap3 filtering module to remove markers with significant segregation distortion (dataTolerance = 0.01). Markers were grouped into Linkage Groups (LG) with the “SeparateChromosomes2” module, using a LOD score limit of 16 and sizeLimit = 100. We set lodLimit = 16 since this resulted in 17 LGs as was expected based on chromosome number : Phenotype ∼ batch + sex + additive genetic effects . Next, we fitted three models for each LG:Relationships between individuals were based on genomic relationships inferred from genetic marker data using the same marker set as in the linkage map. Pairwise genomic relationship matrices were calculated using the method proposed by Yang et al.  as impleModel B: including a relatedness matrix based on all markers except those on the focal LG: Phenotype ∼ batch + sex + additive genetic effects Model C: including a relatedness matrix based on all markers except those on the focal LG and a second relatedness matrix using only markers from the focal LG. Phenotype ∼ batch + sex + additive genetic effects  + additive genetic effects Model D: including relatedness using all markers plus a second relatedness matrix using only markers from the focal LG. Phenotype ∼ batch + sex + additive genetic effects  + additive genetic effects .model C  with the log likelihood of the model B . Under a polygenic architecture with many contributing loci that are evenly distributed across the genome, we expect that variance explained increases with length of the LG. To identify certain LGs that deviate from this expectation and explain more variance than expected based on their length, we compared whether model D  was significantly better than model A (genome‐wide model)  on LG 6. Shell thickness and length showed an almost identical pattern  that did not pass the significance threshold (P = 0.05). We found significant QTLs for the shape parameters: Height Growth  and Aperture Position  on LG 17, as well as for aperture shape on LG 6  and Aperture Size on LG 17  and LG 12 . Color  showed significant peaks on LG 6 and LG 17  or for Bold Score  in the QTL analysis Fig. . We deteern Fig.  but with 17 Fig. . In contAll significant and most suggestive QTLs mapped to regions on LG 6 and LG 17. Closer inspection revealed that QTLs and their confidence intervals often overlapped with regions that were previously described as putative inversions  estimates obtained from a model that included markers from all LGs combined  were mainly consistent with variance partitioning across LGs. Significant regions were predominantly found on chromosomes that contributed significantly to trait variation and were almost always adjacent, with all regions of one LG often showing similar estimates, namely on inversion regions on LG 6, LG 12, LG 14, LG 17 Fig. . Such a We found that most of the studied traits showed significant genetic correlations Fig. . Traits L. saxatilis ecotypes allowed us to avoid confounding environmental effects and enabled us to identify genomic regions important for phenotypic divergence between ecotypes. We show that traits that have diverged between ecotypes are significantly influenced by genomic regions previously described as putative inversions , we detected significant associations with several traits. Since selection acts on phenotypes, gaining a deeper understanding of the process leading to phenotypic divergence and local adaptation requires establishing the link between observed phenotypic and genetic differentiation. Our results, thus, complement these previous studies and confirm the role of inversions in ecotype divergence and local adaptation. They also add evidence that observed frequency clines of inversions across the habitat transition zone are not solely the product of neutral processes, for example, isolation by distance, genome‐wide barrier effects, or hitchhiking with a beneficial allele outside the inversion . Size almost universally shows a positive correlation with reproductive output and thus often appears under positive selection  had been shown to vary clinally across the contact zone at the Swedish site. SNPs associated with these colors were found on LG 5 and LG 9  (Pritchard and Di Rienzo Almost all traits show clear deviations from the pattern expected under a purely polygenic architecture, where variance explained should increase with chromosomal length Fig. . This inLittorina saxatilis does not seem to have heteromorphic sex chromosomes (García‐Souto et al. Particularly interesting is LG 12 that most likely includes a sex‐determination locus. RHM, where each linkage group is divided into equally sized smaller regions was used to get more information at a finer scale. In the case of Height and Width Growth, we could show in this way that high variance explained by LG 2 is not solely caused by its length and a simple cumulative effect of many loci evenly distributed along the LG. RHM showed an accumulation of regions contributing disproportionally to phenotypic variance in the center of this LG consistent with an enrichment of Crab/Wave outliers that was found before (Morales et al. L. saxatilis in rapidly evolving locally adapted populations multiple times (Johannesson et al. Using bivariate animal models for estimation of genetic correlation provided insights into the extent to which different traits share a genetic basis and may, thus, be prevented from evolving independently. Genetic correlations among traits may either increase or decrease the rate of adaptation, depending on the direction of maximum genetic variance relative to selection acting on the different traits (Lande and Arnold Genetic correlations alone do not provide any information on whether they are caused by pleiotropic effects, strong linkage between loci or which regions in the genome contribute to them. Here, the QTL analysis gave additional insights by showing that some inversions influence several traits Fig. . If adapAlthough this hypothesis of beneficial recombination suppression has been very popular and is in line with the frequent observation of inversions involved in ecotype formation and speciation (Kirkpatrick and Barton L. saxatilis could be the result of indirect selection acting on other traits. We found evidence that color was influenced by an inversion on LG 6 that contribute to many other traits under divergent selection. Thus, coloration might be cosegregating with other traits directly targeted by selection, potentially explaining the large amount of color polymorphism in this species (Johannesson and Butlin Genetic covariances can also help us to disentangle the causative drivers of phenotypic clines observed in nature. Two potential problems when analyzing clines are high confounding of environmental factors and also identifying the target of selection when many traits change simultaneously. It is possible that some of the phenotypic clines observed in Littorina saxatilis shows a large range of differently adapted ecotypes with different shapes and sizes (Reid The exact mechanisms by which inversions influence phenotypes are still unknown. Measuring gene expression, testing whether transcript abundance for reads mapped to inversion regions differs between karyotypes, may help to test whether allelic content or directionality are more important for phenotypic variation. While tight linkage between alleles within an inversion might have facilitated adaptation to Crab/Wave habitats, it also means a reduced evolutionary flexibility since some traits cannot evolve independently. For instance, a high genetic correlation between shape and aperture size found here indicates that evolution of forms with narrow apertures but the globular wave shape might be unlikely or limited. In contrast, correlation between size measures and shape is lower meaning they can evolve independently. zes Reid . It remaRKB and KJ conceived the study; KJ, AMW, RKB, JL, ARL, and EML collected data; ELK, HM, JL, and RF analyzed data; ELK drafted the initial version of the manuscript, and all authors contributed to later versions of the manuscript.The authors declare no conflict of interest.https://doi.org/10.5061/dryad.zgmsbccb4.Data and scripts are available from the Dryad Digital Repository. The dyrad doi is Figure S1: Linkage MapFigure S2: QTL scans for relative thickness and boldnessFigure S3: Regional heritability for color, shell length, thickness, Aperture Shape, Width Growth, Aperture Position, Aperture Size, relative thicknessFigure S4: Phenotypic correlations between traitsFigure S5: Inversion effects on phenotypesTable S1: Map position of putatively inverted regionsTable S2: Inversion genotypes of F1 and F2 individualsTable S3: Correspondence between linkage groups of the new map with previous mapTable S4: Results of QTL analysisTable S5: Results of variance partitioning across linkage groupsTable S6: Genetic covariancesTable S7: Inversion effects on phenotypes: statistical test resultsTable S8: List of all capture sequencing probesAppendix S1: Crossing experiment, genotyping, and validation of full‐sib familiesClick here for additional data file.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.


Vaccinium corymbosum and hybrids) is a specialty crop with expanding production and consumption worldwide. The blueberry breeding program at the University of Florida (UF) has greatly contributed to expanding production areas by developing low-chilling cultivars better adapted to subtropical and Mediterranean climates of the globe. The breeding program has historically focused on recurrent phenotypic selection. As an autopolyploid, outcrossing, perennial, long juvenile phase crop, blueberry breeding cycles are costly and time consuming, which results in low genetic gains per unit of time. Motivated by applying molecular markers for a more accurate selection in the early stages of breeding, we performed pioneering genomic selection studies and optimization for its implementation in the blueberry breeding program. We have also addressed some complexities of sequence-based genotyping and model parametrization for an autopolyploid crop, providing empirical contributions that can be extended to other polyploid species. We herein revisited some of our previous genomic selection studies and showed for the first time its application in an independent validation set. In this paper, our contribution is three-fold: (i) summarize previous results on the relevance of model parametrizations, such as diploid or polyploid methods, and inclusion of dominance effects; (ii) assess the importance of sequence depth of coverage and genotype dosage calling steps; (iii) demonstrate the real impact of genomic selection on leveraging breeding decisions by using an independent validation set. Altogether, we propose a strategy for using genomic selection in blueberry, with the potential to be applied to other polyploid species of a similar background.Blueberry ( Vaccinium corymbosum and hybrids) is recognized worldwide for its health benefits due to the high content and diversity of polyphenolic compounds  and endemic US southern species , selecting for low-chill requirements to break the dormancy of flower buds  imposes additional challenges for analyzing and interpreting genetic data. Autopolyploids possess genomes with multiple sets of homologous chromosomes, resulting in non-preferential pairing and potential polysomic inheritance during meiosis. Given the presence of higher allele dosage , a higher number of genotypic classes are possible  summarize previous results on the relevance of model parametrizations, such as diploid or polyploid methods, and inclusion of additive and non-additive gene actions for prediction; (ii) assess the importance of accurate dosage estimation for genomic prediction under low and high sequencing depth scenarios; (iii) demonstrate the realized impact of GS over breeding cycles by using an independent validation set. Altogether, we anticipate challenges and directions for future studies in blueberry that could be applied to other polyploid and fruit species of a similar breeding background.calibration set and testing set, were used for different purposes.The southern highbush blueberry populations used in this study were generated as part of the breeding program at the University of Florida. Two phenotypic datasets, referred to as calibration set comprises a large breeding population already described in previous studies , size (mm), and weight (g) were evaluated over two seasons (2014 and 2015), while soluble solid (°Brix) was evaluated only in 2015. Given the large representative population, all genomic prediction models reported in this study were calibrated using this dataset. The empirical best linear unbiased estimates (eBLUEs) were estimated for each genotype based on a linear model. Genotype and year were considered fixed effects, as described by Amadeu et al. , some of them (16 common genotypes) in different locations throughout Florida. As these phenotypes were collected from plants in different physiological phases and multiple environments, we adjusted the phenotypes using a linear model, including separate fixed effects for the year, location, and plant age. The eBLUEs of each genotype per trait were used as the phenotypic value in subsequent genomic prediction analyses. All phenotypic analyses were carried out using the ASReml-R software . Sequencing was carried out in the Illumina HiSeq2000 platform using 150 cycle paired-end runs. To ensure that the same group of single nucleotide polymorphisms (SNPs) will be called in both calibration and testing sets, we included the next-generation sequence data from both sets under the same SNP calling pipeline. First, raw reads were cleaned and trimmed. Then, the remaining reads were aligned using Mosaik v.2.2.3  were compared under scenarios of high sequencing depth (random sampling for the mean number of 60 reads – 60×) and low sequencing depth (random sampling for the mean number of 6 reads – 6×). Specifically, we assumed the sequencing reads of each allele  for a given marker come from a multinomial distribution, with probability equal to the number of the reads divided by the total number of reads across all the alleles, markers, and individuals (N). Then, we sampled N/10 reads from this multinomial distribution. We performed this sampling 10 times, and each sampling result was used in a different cross-validation fold. To avoid an eventual confounding between the number of markers and the predictive ability over the four scenarios, we kept the same number of SNPs  across all scenarios. Therefore, in total, four scenarios were tested: ratio_60x, ratio_6x, dosage_60x, and dosage_6x.We first investigated the importance of accurate genotype calling for genomic prediction by testing r et al.  and applr et al. . For thecalibration and test sets according to the “norm model” in the updog 2.1.0 R package ; and h is a scale factor, where zi centered marker i  and restricted maximum likelihood approach (REML) to estimate variance components, as following: VanRaden  as descrVanRaden . All genVanRaden . For comVanRaden , using tVanRaden .ratio and dosage methods under high (60×) and low (6×) sequencing depth scenarios using only the calibration set in a 10-fold cross-validation scheme. To this end, the calibration set was randomly divided into 10 groups, where one group was used as a validation test, while the remaining nine groups were used as training. Models were trained in the validation test using the genomic best linear unbiased prediction (GBLUP) approach. For each fold, predictive abilities were estimated using Pearson's correlation between genomic estimated breeding values (GEBVs) and the corresponding eBLUEs. We also evaluated the correspondence between the top 20 groups of individuals ranked using dosage_60x and the other scenarios. A post-hoc Tukey test  was used for intergroup comparisons between the top 20 ranked genotypes.Predictive performances were assessed for the across-stages scenario refers to 114 individuals from the calibration set that were clonally propagated in 2014 and planted in a commercial condition in a single location, becoming the testing set – prediction accuracy in this scenario can demonstrate the potential losses when models are trained at earlier stages (high density) and used at late stages of selection ; (ii) general scenario stands for models trained in the calibration set and predictions carried out in the testing data, in which the target phenotypic values were pre-corrected for year, location, and age fixed effects; (iii) stratified scenario comprises models trained in the calibration set that were tested for predictions across four regions in Florida  – in contrast to the general predictions, in this scenario the target phenotypic values were pre-corrected only for the year effect per region. In all scenarios, predictive performances were assessed via Pearson's correlation.For the independent GS validation over the breeding cycles, we assessed the robustness of our predictive model over different scenarios: (i) lm function.A summary of all validation scenarios is illustrated in In the last two decades, GS has become a reality for many animal and plant breeding programs. Despite the optimism and proven efficacy, its wide implementation is still hindered by investment costs and the analytical skills required  for traits with simple genetic architecture is a more feasible approach, and it is a current research line of the breeding program. In this regard, the example of MAS implementation in early selection stages is reported in strawberry . All plants stay in the same field plot, in high density. Further visual phenotypic evaluations are performed for the next 3 years. At this stage, we are implementing genomic prediction to increase genetic gains by improving phenotyping accuracy and selecting parents at early stages. Therefore, at Stage II, all plants will be genotyped. The GEBVs will be predicted for five fruit quality traits , yield, and consumers panel liking scores. Using a selection index according to trait importance , around 15–20 plants selected from Stage IIIs with consistent and outstanding performances are propagated and planted at commercial trial sites across Florida. The different locations comprise two production systems according to the accumulation of chilling hours: evergreen and deciduous  and low-to-mid sequencing depth (6x–12x), we achieved similar predictive accuracies as the ones obtained using higher depths for blueberry traits with different genetic architectures . When compared to within-sample cross-validation schemes, as originally reported by de Bem Oliveira et al.  over pedigree-based methods . More accurate phenotypic data to annually recalibrate the model also has the potential to improve predictability.Genomic information can also provide new opportunities to integrate biotechnology and quantitative genetics into modern breeding programs, creating platforms for both deliveries of new products and biological discovery  and bacterial wilt . A similar strategy has been implemented in strawberries  showed the best balance between efficiency and accuracy. Considering the particularities of autopolyploid genetic data, we showed that for GS, low depth of sequencing (6×-12×) simplifies the allele dosage information  resulted in similar prediction accuracies as those obtained using more refined scenarios. Finally, the genomic prediction was incorporated in a recurrent selection breeding scheme at the practical level, whereby variety development and populational improvement run in parallel. So far, GEBVs have been primarily used for parental selection to increase genetic gains while keeping the genetic diversity. A more objective reduction in the number of years to develop a cultivar would be selecting the top-ranked genotypes from Stage II directly to IV, skipping at least 3 years of evaluations at Stage III.Finally, we highlight some challenges and opportunities for further studies in blueberries. First, recalibrating the model with more accurate phenotypic data can yield better predictive ability. In this sense, phenomics is also a cutting-edge area of research that could leverage the number of traits and samples collected during a season and improve the quality of phenotypic data. For example, yield is a complex and time-consuming trait to be phenotyped over the season. We envision that image-based phenotyping may aid in evaluating yield and other traits, such as plant architecture and diseases. For the future, it would also be important to incorporate additional statistical checks (common genotypes) across years and locations to understand better the effects of GxE interaction on genomic predictions and recalibrate our models according to the environmental targets. On integrating multi-omics data, we expect that we will predict flavor preferences through volatile quantification and perform an early selection for more flavorful cultivars. Statistically, testing new algorithms for mate allocation and using haplotypes for prediction and imputation methods are some potential areas that could further improve genomic predictions.The original contributions presented in the study are included in the article/PM and LF conceived and supervised the study. JB coordinated the collection and genotyping of the samples. IB coordinated the data collection for real validation. LF and RA analyzed and interpreted the phenotypic and genomic selection results. LF wrote the paper and included the revision from all authors. All authors read and approved the final version of the manuscript for publication.IB was employed by company Hortifrut North America, Inc.; however, she participated in this research while at University of Florida. 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.


Osteosarcoma (OSA) is a devastating disease that is common in the Irish Wolfhound breed. The aim of this study was to use a pedigree-based approach to determine the heritability of OSA in the Irish Wolfhound using data from a large publically available database.The pedigree used for this study included 5110 pure-bred Irish Wolfhounds, including 332 dogs diagnosed with OSA and 360 control dogs; dogs were considered controls if they lived over 10 years of age and were not reported to have developed OSA. The estimated heritability of OSA in the Irish Wolfhound was 0.65.The results of this study indicate that OSA in the Irish Wolfhound is highly heritable, and support the need for future research investigating associated genetic mutations. Osteosarcoma is a devastating condition that is prevalent in the Irish Wolfhound breed. In this study, our aim was to estimate heritability of osteosarcoma in the Irish Wolfhound breed. We undertook a pedigree-based analysis to estimate heritability of osteosarcoma in the Irish Wolfhound. The pedigree used included 5110 pure-bred Irish Wolfhounds, including 332 dogs diagnosed with osteosarcoma and 360 control dogs. We considered dogs to be controls if they were over 10 years of age and were not reported to have developed osteosarcoma. This study found the heritability estimate of osteosarcoma in the Irish Wolfhound to be 0.65. This score means that osteosarcoma in this breed is: 1) highly heritable and 2) a complex trait, which means that both environmental and genetic factors influence disease risk. Overall, our results provide support for further investigation into the genetic variants involved in the development of osteosarcoma in Irish Wolfhounds. Osteosarcoma (OSA) is an aggressive bone cancer characterized by early metastasis and high mortality rates. Primary tumor removal and chemotherapy results in median survival times of 8–11 months . In dogsOSA in dogs has proven a robust treatment model for OSA in children . As a caHeritability of disease is important to define when comprehensively investigating the genetic architecture of a complex disease. Simply, heritability defines how much genetics influence a trait in a given population versus how much of disease risk is associated with environmental and epigenetic effects . Thus, hOSA in the Irish Wolfhound breed is devastating both on an individual level and as a breed. We utilized a large publicly available online Irish Wolfhound pedigree database, through which age and cause of death of thousands of pure-bred Irish Wolfhounds are available . Given tTo evaluate pedigree structure for the Irish Wolfhound dog sample we used in this study, we extracted the summary statistics, as reported in Table To evaluate the pedigree based inbreeding coefficient, we created numerator relationship linkage matrix. Figure Within this population, 52.66% were not inbred and 47.34% of dogs showed some degree of inbreeding. In total, 90.33% of the study population showed an inbreeding coefficients less than 0.1. The average inbreeding coefficient for the entire study population was 0.0282 and the average inbreeding coefficient in the inbred dogs was 0.0597. The maximum and minimum inbreeding coefficients were 0.3696 and 1.48e-05, respectively.h2OSA = 0.648 ± 0.089). The credible interval measured by highest posterior density interval (HPD) at 95% level resulted in lowest and highest interval limits of 0.473 and 0.809, respectively. The quantiles of marginal posterior density of h2OSA were 0.461 (2.5%), 0.589 (25%), 0.653 (50%), 0.714 (75%), and 0.801 (97.5%). Also, the posterior mean for the additive genetic variance component (A) is solely due to additive genetic variation.To estimate OSA heritability, we used a Probit model. The posterior marginal density and histogram plot of the estimated heritability for OSA is graphically presented Fig. A. The meOf the 5110 dogs included in the pedigree analysis, 332 were OSA cases and 360 were assigned as controls. Noteably, there were no OSA affected dogs over 10 years of age found during the construction of this study population. Of the 332 cases, 136 had at least one known parental phenotype. Of these dogs, 68 (50%) had at least one affected parent. Seventeen dogs had known phenotypes of both parents; 5 had 1 affected parent, 4 had 2 affected parents, and 8 had both parents assigned as controls  in the Irish Wolfhound to be 0.654, indicating that OSA in the Irish Wolfhound breed is a highly heritable complex disease. This heritability estimate indicates that environmental and epigenetic factors also influence disease risk. These results align with an earlier genome wide association study investigating OSA in the Irish Wolfhound, where only four genomic regions were found to associate with disease [We estimated the heritability of OSA , which reflects the additive genetic relationships (variance-covariance) between all animals. This matrix was originally introduced by Henderson [A matrix in the R environment and obtained inbreeding coefficients for each individual dog. Computationally, the A matrix is a square symmetric, and has dimensions equal to the total number of individuals in the pedigree (N × N). Its off-diagonal elements (Aik), are twice the probability that an allele drawn from individual i is identical by descent to an allele in individual k and its diagonal element is (Aii = 1 + Fi), where Fi indicates the inbreeding coefficient for animal i. The MCMCglmm R package [To fit a linear mixed model and estimate variance components and subsequently obtain heritability of disease, we created a numerator relationships linkage matrix , can be modeled as:We implemented a probit Bayesian linear mixed model to estimate genetic variance components and obtain the posterior distribution of heritability for OSA in Irish Wolfhound dogs. Our disease outcomes followed a binary disease response , so the assumption was made that OSA in the Irish Wolfhound is a trait dictated by an underlying normally distributed latent variable. An individual’s value of the liability determines which of two categories a given individual falls into. Therefore, we consider that the probability of OSA for the j-th outcome on the i-th dog ; βij is the unknown vector of effects associated with sex effect; ai is the additive genetic contribution to OSA status for the i-th dog and assumed to be sampled from a multivariate normal density with A being the numerator relationship matrix as described above. In this model the residuals were assumed to follow a multivariate normal distribution with mean zero and identity variance (I) i.e., Where μ is the total population mean which is constant common to all dogs; tifiable . A solut package , availab package , was useν) and V. For our analysis, we set nu = 0.002 and V = 1, to permit a long flat right-skewness distribution, which effectively creates a diffuse prior for the unknown additive genetic variance The prior distribution for the fixed effects was the default setting that is an independent normal density with null means and variances of e10, which is a relevant and consensual choice. The prior distribution for the random genetic effect and variance components were assumed to follow an inverse-Wishart density, which is a standard assumption. In the MCMCglmm package, this distribution is parametrized by two parameters, nu (