Calf counts averaged 12.2 ± 10.7 and SC averaged 35.4 ± 2.30 cm. Bulls had an average of 1.30 records and there were 23.9 ± 11.1 bulls per contemporary group. The model for CC included fixed effects of age during the breeding season (in years) and contemporary group (concatenation of breeding pasture and year). Random effects included additive genetic and permanent environmental effects, and a residual. The model for SC included fixed effects of age (in days) and contemporary group (concatenation of month and year of measurement). Random effects included an additive genetic effect and a residual. Univariate model heritability estimates for CC and SC were 0.178 ± 0.142 and 0.455 ± 0.072, respectively. Similarly, the bivariate model resulted in heritability estimates for CC and SC of 0.184 ± 0.142 and 0.457 ± 0.072, respectively. Repeatability estimates for CC from univariate and bivariate models were 0.315 ± 0.080 and 0.317 ± 0.080, respectively. The estimate of genetic correlation between CC and SC was 0.268 ± 0.274. Heritability estimates suggest that both CC and SC would respond favorably to selection. Moreover, CC is lowly repeatable and although favorably correlated, SC appears to be weakly associated with CC.The commercial beef cattle industry relies heavily on the use of natural service sires. When artificial insemination is deemed difficult to implement, multisire breeding pastures are used to increase reproductive rates in large breeding herds or to safe-guard against bull injury during the breeding season. Although each bull might be given an equal opportunity to produce offspring, evidence suggest that there is substantial variation in the number of calves sired by each bull in a breeding pasture. With the use of DNA-based paternity testing, correctly assigning calves to their respective sires in multisire pastures is possible and presents an opportunity to investigate the degree to which this trait complex is under genetic control. Field data from a large commercial ranch was used to estimate genetic parameters for calf count  and yearling scrotal circumference (SC;  Natural service multiple-sire breeding pastures are common in the beef industry when artificial insemination is deemed difficult to implement. Multisire breeding pastures enable improved reproduction rates and serve as a means of protecting against bull injury during the breeding season. Although an a priori assumption made by beef cattle producers is that each bull has an equal likelihood of producing calves, there often exists considerable variation in the number of calves sired by bulls despite each having passed a breeding soundness exam . Unfortue (number of lambs), reported heritability and repeatability estimates of 0.26 ± 0.12 and 0.40 ± 0.09, respectively  to be used throughout the ranch. Outside germplasm was restricted to semen from AI sires used in the seedstock herds. In addition to AI matings in the seedstock herds, natural service sires were used in multisire pastures. Breeding season lengths were either approximately 25–30 d (heifers) or 56–70 d (cows). All females were either 2 or 3 yr of age at calving. All bulls passed a breeding soundness exam prior to the breeding season. To enable pedigree formation and to facilitate genetic evaluation, DNA-based parentage testing was employed using a commercially available panel of 96 single nucleotide polymorphisms (SNP). The data for this study included bulls used in multisire breeding pastures in the years 2006–2011, their contemporaries, and their offspring.All AI sires were removed from the data leaving only bulls that had an opportunity to serve as a natural service sire. Additionally, sires were removed if they were not genotyped or were contained in breeding group that produced less than 100 calves. Finally, sires who had counts of calves that were clearly erroneous  were also removed. After edits there were 443 unique sires with 574 observations from 24 contemporary groups for further analysis of calf count (CC). Bulls had, on average, 1.30 records for CC and the age at exposure to females was 1.64 ± 0.983 yr. Distribution of CC data by contemporary group is described in All analyses were conducted using the ASREML 4.1 software package . The uniThe bivariate animal model included all fixed and random effects from both univariate models to estimate (co)variance components using starting values obtained from the univariate analyses. In matrix notation, the bivariate model can be represented as:y is a vector of observations for the traits CC and SC, X, Z and W are incidence matrices relating observations in y to levels of fixed effects in b, breeding values in u, and permanent environmental effects in p, respectively, and e is a vector of residuals. In the bivariate model, the vector of genetic effects, p, were assumed to be distributed as where Estimates of variance components and their ratios from univariate and bivariate models are reported in The evidence of prolificacy being heritable opens up the possibility of reducing the number of bulls required in breeding pastures to adequately service cows and possibly departing from widely held maxims such as bull to female ratios (BFR) of 1:25 for bulls who have undergone breeding soundness examination (BSE). Bulls that have passed BSE can service more females, meaning that BFR is not the limiting factor and that bulls held to this ratio are inefficient . ThroughThe heritability estimate for SC reported from the current study was higher than the 0.38 estimate reported by Bos indicus animals. The lower estimate of repeatability reported herein could be due to the limited number of repeated records in the population used, as well as, the small number of records for CC (n = 574) used in the study. Although literature estimates suggest that a bull’s performance, in terms of number of offspring produced, in one breeding season is predictive of his performance in subsequent breeding seasons the estimate from the current study suggests such a prediction would be lowly accurate. Repeatability is the proportion of phenotypic variation that can be attributed to variation in genetics and permanent environmental effects. Only additive genetic effects were explicitly modeled in the current study. However, the sires were admixed and thus breed and some degree of heterotic effects might be present that were unaccounted for. These unmodeled effects (breed proportion of heterosis) could have influenced the magnitude of the estimate of (narrow sense) heritability and repeatability in the current study. Regardless, the repeatability estimate clearly shows that bull prolificacy comes about through a combination of inherent differences between bulls, unknown permanent environmental effects, and temporary environmental effects .Estimates of repeatability for CC from univariate and bivariate models were 0.315 ± 0.080 and 0.317 ± 0.080, respectively. The low repeatability estimate reported in the current study are below the range of 0.43–0.69 reported by The estimate of genetic correlation between CC and SC was low and positive (0.268 ± 0.274) with a large standard error. The point estimate suggests that approximately 7.18% (genetic correlation squared) of the additive genetic variation in CC is shared with SC. Given this estimate, SC could be a valuable indicator of CC at a relatively early age before CC data becomes available. Furthermore, this estimate suggests that indirect improvement in CC could be achieved by selection for increased SC at yearling, albeit inefficient compared to having direct measurements of CC.Sire prolificacy is a complex trait, and is comprised of several more refined characteristics including male fertility, libido, and the interactions among bulls in the same breeding pasture. When comparing libido measured though testing between rams, high libido sires produced twice the number of progeny than lower libido sires . There dSocial ranking and dominance are more related to seniority than age or weight , howeverThe current study suggests that bull prolificacy, as defined by the count of calves sired in multisire breeding pastures, is heritable and would respond to selection. Moreover, estimates suggest this trait complex is lowly repeatable, and thus, performance across successive breeding seasons/years is lowly correlated and thus multiple measurements would enhance accuracy of genetic predictions. Although positively genetically correlated, yearling scrotal circumference does not appear to be a strong indicator of the genetic potential of prolificacy. Given the large standard errors associated with the genetic parameter estimates reported herein, additional studies from larger populations would be beneficial to further quantify the genetic control of bull prolificacy and its relationship with scrotal circumference. As DNA-based paternity assignment becomes more common in commercial settings, this trait complex can be further investigated to bring more resolution to the limited genetic parameter estimates that exist for bull prolificacy.


Mutant alleles (MAs) that have been classically recognised have large effects on phenotype and tend to be deleterious to traits and fitness. Is this the case for mutations with small effects? We infer MAs for 8 million sequence variants in 113k cattle and quantify the effects of MA on 37 complex traits. Heterozygosity for variants at genomic sites conserved across 100 vertebrate species increase fertility, stature, and milk production, positively associating these traits with fitness. MAs decrease stature and fat and protein concentration in milk, but increase gestation length and somatic cell count in milk (the latter indicative of mastitis). However, the frequency of MAs decreasing stature and fat and protein concentration, increasing gestation length and somatic cell count were lower than the frequency of MAs with the opposite effect. These results suggest bias in the mutations direction of effect (e.g. towards reduced protein in milk), but selection operating to reduce the frequency of these MAs. Taken together, our results imply two classes of genomic sites subject to long-term selection: sites conserved across vertebrates show hybrid vigour while sites subject to less long-term selection show a bias in mutation towards undesirable alleles. Xiang and colleagues infer mutant alleles in 113,000 cattle to quantify the effect of these mutations on complex traits including body size, fertility and milk production, and compare these mutation sites across 100 species of vertebrates. Some sites show long term selective pressure, are heavily conserved and demonstrate hybrid vigour, whereas sites selected over shorter time periods are biased towards undesirable mutation. However, the majority of the genetic variance in complex traits is due to mutations with small effects. Do these small-effect mutations show the same characteristics as those classical large-effect mutations? A study in Escherichia coli showed that mutations with small effects on fitness tend to be deleterious to protein function4. However, how mutations affect complex traits such as body size, health and fertility is unknown.Mutant alleles (MAs) that have been classically recognised tend to largely decrease fitness, decrease fitness-related traits and be partially recessive5. Genomic selection, which is widely used in animal breeding6, has been demonstrated to be enhanced by fitting variants with biological priors8. Therefore, it may be an advantage to also know a priori whether mutations are more likely to increase or decrease traits of interest.A better understanding of the consequence of mutations not only updates scientific knowledge but also has practical implications. Domestic cattle support humans by providing food, labour, clothing material and transportation. Today, there are over 4 billion cattle across the world and over ~900 million tonnes of dairy products have been produced annually for human consumption9. Therefore, the first objective of this study is to determine whether mutations, defined as the non-ancestral allele  at segregating sites, tend to increase or decrease individual complex traits and whether this depends on the trait’s association with fitness.In particular, if a trait is related to fitness, one might expect mutations to be deleterious10. Conversely, fitness generally increases with heterozygosity11. Therefore, directional dominance can be used to link traits to fitness. Here we introduce a test for directional dominance on traits of cattle by estimating the heterozygosity at genomic sites and use this method to identify traits that are associated with fitness. Then, we classify traits showing directional dominance as ‘fitness-related traits’.Traits that are related to fitness typically show inbreeding depression and heterosis caused by directional dominance. That is, fitness decreases with increased inbreeding due to increased homozygosity at loci with recessive deleterious allelesA likely cause of directional dominance is that mutations tend to be deleterious and partially recessive. However, not all sites in the genome affecting a trait may show this pattern. Our second objective was to test the hypothesis that sites, where the same allele has been conserved across vertebrate evolution, are the most likely to show directional dominance. Therefore, we consider conserved sites and other polymorphic sites in this analysis.12. Modern cattle are derived from at least two different subspecies of wild aurochs, i.e. Bos primigenius primigenius (Eurasian aurochs) and Bos primigenius namadicus (Indian aurochs), which diverged up to 0.5 million years ago20. Domestication of Bos p. primigenius led to the humpless Bos taurus subspecies, which has evolved some highly productive breeds for agriculture, such as the Holstein breed with superior milk productivity. Besides natural selection, dairy cattle breeds experienced very recent and intensive selection for milk production traits22 and stature23. Domestication of Bos p. namadicus gave rise to the humped Bos indicus subspecies which evolved breeds with strong resistance to hot climates, such as Brahman and Gir cattle.Cattle present a unique opportunity for studying the effects of mutation. The cattle family diverged from other artiodactyls up to 30 million years agoIn the present study, we use yak, sheep and camel as outgroup species to assign cattle ancestral alleles for 8 M sequence variants (at 8 M genomic sites). For each of these variants, the alternative to the ancestral allele is the MA. We estimate the effects of the genotypes based on the MA at these 8 M variable sites on 37 traits of 113k cattle from 4 breeds. We also estimate the collective effect of heterozygosity on these traits using either conserved sites or all genomic sites.25, which provided validation of our results. Additional analyses of MAs with strong effects on milk production traits27 suggested that the direction of phenotypic effects of these MAs correlates with their direction of effects on the expression of genes in milk cells25.If MAs decrease fitness we expect selection to reduce their allele frequency compared with MAs that either have no effect or increase fitness. Therefore, we compared the allele frequency of MAs that increased and decreased each trait. We expanded the analysis of MA frequency to additional breeds of ancient and modern cattle from the 1000 Bull Genomes databaseR2 > 0.4 and the minor allele frequency (MAF) > 0.005 available for variant–trait association analysis. Approximately half of these could be assigned with ancestral alleles and this subset was used for analyses related to MAs (described later). For the analysis of the effect of heterozygosity, we fitted covariates of: (1) the average heterozygosity of sequence variants at 317,279 genomic sites conserved across 100 vertebrate species . Out of 42,573,455 equivalent sites between the 4 species, 39,998,084 sites had the ancestral allele assigned with high confidence (probability >0.8). We compared our results with a previous study using different methods29. Of the 1,925,328 sites that were assigned ancestral alleles with high confidence in both studies, 1,904,598 (98.7%) sites agreed. However, we assigned ancestral alleles with high confidence to ~10 times more sites than the previous study due to the use of a large sample size and whole-genome sequence data. The full results are publicly available at https://melbourne.figshare.com/articles/dataset/The_assignment_of_cattle_ancestral_alleles/13546472.To assign the MAs in cattle, we first determined the alternative, ancestral alleles using artiodactyls, including cattle as the focal species  and cows (N ~ 104k) separately (see ‘Methods’). For 7,910,190 variants where the ancestral allele was assigned, we compared the direction (increase or decrease) of the effect of the MAs on the trait  of 37 traits using over 16 million imputed sequence variants in bulls  < 5e−8 where the effect direction agreed in both sexes; (2) medium-effect variants, i.e. 5e−8 < = pgwas < 5e−5 where the effect direction agreed in both sexes; and (3) small-effect variants, i.e. 5e−5 < = pgwas < 0.05 where the effect direction agreed in both sexes. Here the effect size refers to the amount of variance explained by variants which is inversely related to the p value. We used different effect sizes because mutations of small and large effects may be different in their direction of effect. Selecting variants that have the same effect direction between different GWAS populations30, such as bulls and cows, helped to eliminate variants with spurious trait associations from the comparison. Based on a previous method30, the True Discovery Rate by Effect Direction (TDRed) of GWAS was calculated between the two sexes across 37 analysed traits for the small-, medium- and large-effect variants resulting in scores of 0.8, 0.98 and 0.99, respectively. On average, each variant from the large, medium and small-effect category explained 0.31% (±0.043%), 0.07% (±0.009%) and 0.015% (±0.0004%) of the variance in cow traits, respectively  large-effect variants, i.e. GWAS xes; and  small-ef31, which jointly fitted on average 4.3 million variants per trait  of the difference in the effect distribution between ancestral and MAs (see ‘Methods’). We also tested the significance of bias using linkage disequilibrium (LD)-clumped (r2 < 0.3)32 variants to calculate the standard error  to the number of variants where the MA decreased the trait (negative effect). Across 37 traits and the three effect-size groups, MAs showed diverse trait effect patterns  genes, see ‘Methods’) in milk cells27. For four out of five sets of variants where the MA decreased the trait, we found the MA tended to decrease the expression of cis eQTL genes. For another four out of five sets of variants where MAs increased the trait, the MA tended to increase the expression of cis eQTL genes  MAs within the large- and small-effect categories for milk production traits as these two sets of MAs showed distinct effect direction patterns Fig. , and (2)3 predicts that the majority of MAs, or mutations, are deleterious or slightly deleterious. In our study, MAs consistently showed biases towards decreasing protein and fat concentration 32 variants. As an external validation, we also considered this analysis in a selection of 7 subspecies/breeds of 1720 ancient and modern cattle from the 1000 Bull Genomes Project25  or increasing the trait (MA+) and compared their allele frequency in over 110k Holstein, Jersey, crossbreds and Australian Red bulls and cows Fig. . To accot25 Fig. .Fig. 3ThFor fat%, protein%, docility and stature MAs that increased the trait had higher allele frequency than MAs that decreased the trait. For somatic cell count and gestation length, the reverse was true. That is, MAs increasing somatic cell count and gestation length had lower allele frequency than MAs that decreased the trait Fig. . Thus, ar = −0.83 and −0.78, respectively).For other traits, the results were less clear-cut. For milk yield, the majority of MAs of large effect tended to decrease the trait Fig. . Interesr2 < 0.3)32 variants.The above results for MA frequency at trait-associated variants imply selection. The selection could have been consistent across breeds which would limit the divergence of allele frequency between breeds or it could have been different between breeds leading to divergence in allele frequency. We compared the average of Wright’s fixation index , we expect that an increase in the trait leads to an increase in fitness. It is these traits that typically show heterosis and inbreeding depression due to directional dominance. The simplest explanation for these observations is that mutations at sites affecting the trait tend to reduce the trait and be partially recessive. However, our results show that it was not all sites affecting these traits that showed directional dominance but only those where the same allele was highly conserved across vertebrates. This result explains why the mutations tend to lead to a decrease in the trait—long-term selection has nearly fixed the favourable allele and so any mutation will cause a decrease in the trait and in fitness. We partially confirm this explanation by finding that mutations for these traits  do tend to decrease the trait although, for milk and protein yield, it was only mutations of large effect for which the effects tended to be negative. This long term selection cannot be directly on traits involving lactation since the same allele was conserved in vertebrates other than mammals.B. indicus breeds.For other traits, we expected that an intermediate value leads to the highest fitness. For instance, too high or too low a fat% in milk might be detrimental to the fitness of the mother or the infant or both. These traits do not typically show inbreeding depression or heterosis. The fittest allele might vary between species and environments. Therefore, one might expect that mutations are equally likely to increase or decrease the trait. However, that is not what we found: for fat% and protein% mutations tended to decrease the trait whereas for SCC and gestation length they tended to increase the trait. We hypothesise that at some of the genomic sites affecting these traits selection has been consistent enough in mammals, or at least in cattle so that mutations cause a decrease in fat% and protein% and an increase in mastitis or SCC and gestation length . This hypothesis was supported by our finding that selection decreased the allele frequency of these mutations. This low allele frequency was not only seen in dairy cattle but in beef breeds and DGAT1 and GHR loci that increase milk yield but decrease fat% and protein% . The equation predicting genetic value uses the effect of each SNP on the trait estimated in a training population. The best methods treat the SNP effects as random variables drawn from a prior distribution. To date it has been assumed that the effects of a mutation are equally likely to be positive or negative on the trait but, if it was known that one direction of effect was more likely, this could be built into the prior distribution resulting in an increase in the accuracy with which genetic value is predicted.Genomic selectionIn conclusion, our results support a hypothesis which provides a new picture of the effects of mutation and selection on mammalian complex traits. Directional dominance, which causes heterosis and inbreeding depression, is characteristic of loci where mutations decrease the trait and fitness and this pattern has been consistent over the evolution of vertebrates. More recent selection, although not causing directional dominance, leads to a bias in the direction of mutation because the mutation results in an allele which is less fit than the ancestral allele and tends to affect a complex trait in a consistent direction. This hypothesis, if supported by future research, adds to our understanding of the evolution of complex traits and has practical value in the artificial selection of livestock and other species.Bos grunniens), sheep (Ovis aries) and camel (Camelus dromedarius). According to the evolutionary relationships reported previously12, among ruminants, yak is an outgroup species closely related to cattle, while sheep is less closely related to cattle than yak. Goat is equivalent to sheep in its relationship to cattle, but we chose sheep in the current study. Camel without a rumen is distantly related to ruminant cattle, as they are artiodactyls. For the cattle species, we used whole-genome sequence data of 98 breeds, one individual per breed, from Run 7 of the 1000 Bull Genomes Project25. Only those whole-genome sequence samples with coverage >10× were selected and if multiple individuals were found for a breed, the whole-genome sequence sample with the highest coverage was chosen. Both B. taurus and B. indicus subspecies were included (Supplementary Table 36. Only BAM files from 1000 Bull Genomes partners are collected and processed by the consortium. The latest published data from the 1000 Bull Genomes Project (1832 samples) can be found at https://www.ebi.ac.uk/eva/?eva-study=PRJEB42783. The details of variant calling can be found in ref. 37. Briefly, Genome Analysis Toolkit (GATK v.3.8)38 was used for variant calling. Variants from the GATK VQSR  99.90 to 100.00 Tranche for SNP and INDEL were excluded, and Beagle v.4.039 was used to impute variants with sporadic missing genotypes. Whole-genome sequence data in VCF format for these 98 cattle, as a subset from the 1000 Bull Genomes Project database, was generated for further analysis.The assignment of bovine ancestral alleles was based on a model comparison of alleles from cattle with alleles from outgroups of yak , we used whole-genome sequence data of 46 mammals stored in the Multiple Alignment File generated by Ensembl EPO pipeline28 with the model choice of the Kimura two-parameter (K2), which accounts for allele frequency of the focal species to determine the probability of an allele being ancestral at each available site. The method was implemented in estsfs28 and the K2 model was chosen due to its equivalent accuracy to other models but better computation efficiency. As described above, the sequence data of three outgroup species were used. The order of phylogenetic tree topology was cattle → yak → sheep → camel. As required by the software, allele counts of A, C, G and T were determined for the focal species (cattle) and for out species at each available site. For cattle, the total allele count for each site was 196 (98 × 2). For each outgroup species, the total allele count for genome sequences at each site was up to 1. Missing sequence data in the outgroup species were treated as 0 counts. For each site, estsfs produced a probability (Pancs) of the major allele in the focal species being ancestral. We then determined alleles which were major at a site with Pancs > 0.8 or those alleles that were minor at a site with Pancs < 0.2 to be ancestral. For those sites where the major or minor alleles could not be determined but the Pancs > 0.8 or <0.2, the cattle allele with the highest frequency in the 3 out species was assigned ancestral. The rest of the sites were determined as ambiguous as no clear ancestral alleles could be determined. The detailed results of ancestral alleles for those 42,573,455 sites across 4 species and the probability of the alleles being ancestral or ambiguous is publicly available at: https://melbourne.figshare.com/articles/dataset/The_assignment_of_cattle_ancestral_alleles/13546472.We used the method proposed by Keightley et al.34. Briefly, conservation was determined by the criteria of PhastCon score42 >0.9 based on the sequence data of those 100 species. The choice of 0.9 as the cutoff was arbitrary. However, since PhastCons score ranges from 0 to 1, this cutoff kept relatively highly conserved sites. Also, in a previous study34, cattle variants from sites with PhastCon score >0.9 were highly enriched for the heritability of cattle traits (occupying 2% of the genome to explain up to 42% heritability of traits). The conserved sites were primarily determined using the human genome coordinates (hg38) and were lifted over to the bovine genome ARS-UCD1.2 using the LiftOver software43 with a lift-over rate >92%. In total, 317,279 variants in the current study were assigned as the conserved variants.The variant selection followed previous procedureshttp://www.datagene.com.au/) for the official May 2020 release of National breeding values. No live animal experimentation was required. DataGene provided the bull and cow phenotypes as de-regressed breeding values or trait deviations for cows and daughter trait deviations for bulls (i.e. progeny test data for bulls). DataGene corrected the phenotypes for herd, year, season and lactation following the procedures used for routine genetic evaluations in Australian dairy cattle. Phenotype data included a total of 8,949 bulls and 103,350 cows from DataGene, including Holstein , Jersey , cross-breed (36♂/5037♀) and Australian Red dairy (265♂/3379♀) breeds. In total, 37 traits were studied that related to milk production, mastitis, fertility, temperament and body conformation  or a high-density SNP array  and most cows were genotyped with a low-density panel of approximately 6.9k SNPs overlapping with the standard-50K panel. The low-density genotypes were first imputed to the Standard-50K panel and then all 50 K genotypes were imputed to the HD panel using Fimpute v346. Prior to sequence imputation, the HD genotypes were converted to forward sequence format. Then all HD genotypes were imputed to sequence using Minimac3 with Eagle (v2) to pre-phase genotypes47. The reference set for imputation included sequences of 3090 B. taurus animals from Run7 of the 1000 Bull Genomes Project24 aligned to the ARS-UCD1.2 reference bovine genome48. The accuracy of the sequence data for individual animals in the 1000 Bull Genomes Project is routinely checked against their own high-density SNP array genotypes and the concordance has been >95%37. The empirical accuracy of imputation to sequence using the 1000 Bull Genomes project has been routinely tested for dairy breeds: for example, in Holsteins, the average correlation between imputed and real sequence variants was 0.92 to 0.95 using Run5 of the 1000 Bull Genomes project (N = 1577)49. Therefore, we believe our imputed data are more accurate: first, because the number of reference animals has almost doubled and second because in our study we impose a Minimac3 R2 filter to remove poorly imputed variants. A Minimac3 R2 threshold of 0.4 was used because our in-house tests demonstrate that this is approximately equivalent to an empirical imputation accuracy (correlation) of 0.85.The genotypes used in the current study included a total of 16,035,443 imputed bi-allelic sequence variants with Minimac350:y = vector of phenotypes for bulls or cows, breed = three breeds for bulls, Holstein, Jersey and Australian Red and four breeds for cows ; bx = regression coefficient b on variant genotypes x; a = random polygenic effects ~N where G = genomic relatedness matrix based on all variants and σg2 = random polygenic variance; error = the vector of random residual effects ∼N, where I = the identity matrix and σe2 the residual variance. The purpose of fitting breeds as fixed effects together with the GRM in the model was to have strong control of the population structure which may cause spurious associations between variants and phenotype. The construction of GRM followed the default setting (--make-grm) in GCTA50. In the results of GWAS (the same for results from BayesR described below), we matched the allele with which the beta was estimated to the MA. Then this effect is defined as the effects of the MA. Note that, for a variant, the effect of a MA is identical to −1× the effect of the ancestral allele.The above-mentioned traits were analysed one trait at a time in each sex with linear mixed models using GCTA31. For each trait, variants that showed the same sign between bulls and cows  and could be assigned with an ancestral allele were analysed with BayesR. Across 37 traits, the number of variants analysed ranged from 3,961,180 to 4,737,492. To reduce the computational burden of BayesR, we estimated the joint effects of these variants for each trait in bulls. BayesR models the variant effects as mixture distribution of four normal distributions including a null distribution, 51 with a single genomic relationship matrix made of all 16 M sequence variants. The statistical model used in the single-trait BayesR was:y was a vector of phenotypic records; W was the design matrix of marker genotypes; centred and standardised to have a unit variance; v was the vector of variant effects, distributed as a mixture of the four distributions as described above; X was the design matrix allocating phenotypes to fixed effects; b was the vector of fixed effects of breeds; e = vector of residual errors. As a result, the effect v for each variant jointly estimated with other variants were obtained for further analysis.In the above-described GWAS, sequence variants, many of which are in high LD, were analysed one at a time. In order to assess variant effects and account for LD, we fitted selected variants jointly in BayesRr2 < 0.3 within 1 Mb windows) variants with small, medium and large effects using default settings in plink1.932.For an analysed variant, one allele is ancestral and then the other is mutant. If there is a bias in effect direction in ancestral alleles or MAs in a given set of variants, the effect distribution of the ancestral and MAs would be different. For example, for a given set of variants, if their MAs had a bias in effect direction towards increasing the trait, their ancestral alleles would have a bias in effect direction towards decreasing the trait. This then would create a difference in effect distribution between mutant and ancestral alleles. We tested if the distribution of the effect of ancestral alleles estimated from BayesR was significantly different from that of MAs using the two-sample Kolmogorov–Smirnov test implemented by ks.test in R v3.6.1. The coding was ks.test where a was the vector of variant effects based on the ancestral alleles and m was a vector of variant effects based on the MAs. To be more conservative, we also tested the significance of biases using LD-clumped . Our previous work showed that conserved sites across 100 vertebrate species significantly contribute to trait variation54, the genetic value (G′) of an individual can be partitioned into the mean (µ), additive genetic value (A) arising from additive effect (a) and dominance genetic value (D) arising from dominance deviation (d). At a single locus, let the allele frequency of the three genotype classes of AA, AB and BB be p2, 2pq and q2, respectively. In a simple genetic model, the genetic value can be decomposed as:i, which were usually coded as 0, 1 and 2, respectively, to represent the additive component, and i, respectively, which differentiates the homozygous and heterozygous to represent the dominance component. Therefore, in the simplest form, the genome-wide heterozygosity of the individual j can be calculated as:Hj is the simple genome-wide heterozygosity of individual j and N is the total number of variants. Note that such calculation of Hj can also be used to derive inbreeding coefficient, where Ij was the inbreeding coefficient for the jth individual.According to quantitative genetics theoryxA and zD under Hardy–Weinberg equilibrium (HWE), the estimation of a and d is not independent, i.e. Hj not being independent of the additive components. Therefore, we proposed to re-parameterise this model to estimate a and d independently.In Eq. 53 at this locus, the additive effects can be derived using the regression of genetic value on the number of A alleles, where α is the allele substitution effect: q, p − q and −2p for genotype of AA, AB and BB of variant i, respectively, to represent the additive component and pq, i, respectively, to represent the dominance component. Such re-parametrisation has the following features: (1) The covariance between the additive and dominance effects is zero; (2) the variance of the additive effects gives the additive variance; and (3) The variance of the dominance deviations gives the dominance variance. Equation j, i and N was the total number of variants. We then applied Eq. 51.According to Falconermentclass2pt{minimFST was the curated whole-genome sequence data of 1720 cattle from the 1000 Bull Genomes database (Run 7)25, which we refer to as modern and ancient cattle. Samples that met the quality criteria of the 1000 Bull Genomes project were selected and they included 210 Brahman, 25 Tibetan, 10 Eurasian Aurochs, 242 Simmental, 95 Jersey, 843 Holstein and 295 Angus. Genome sequences from 6 Gir and 12 Nellore cattle from the 1000 Bull Genomes database were also analysed to support the results of MA frequency of B. indicus. Additional information on these 1720 animals including related accession numbers (if available) can be found in Supplementary Data 18 who processed and published the original data (PRJEB31621 at European Nucleotide Archive). These data were collected by Run 7 of the 1000 Bull Genomes Project and processed by its standard pipeline36.Two sets of data were used for this analysis. The first data set was the Australian dairy cattle  used for GWAS as described above. The second data set used for the analysis of MA frequency and FST (described below) were all estimated using LD-clumped variants in the same procedure in plink32 as described above. For variants associated with milk production traits, i.e. the yield of milk protein, fat and milk and percentage of protein and fat, we selected variants with large  and small  effects to focus on. For other trait-associated variants, the group with the largest effects available were selected for this comparison. For example, for stature, there were no variants with p value < 5e−8 in both sexes, we then selected the medium-effect variants . For fertility, there was no variants with p value < 5e−5 in both sexes, we then selected the small-effect variants  for the comparison. Average MA frequency and the standard error were also calculated for all 7.9 M variants analysed as the baseline. The analysis procedure for allele frequency on the Australian dairy cattle was applied to these 1000 Bull Genomes individuals.Sequence data at 7,910,190 variants assigned with MAs were retrieved for these animals to make a plink (v1.9) binary genotype file. The A1 allele of the plink genotypes was set to the MA and its frequency was calculated using the ‘--freq’ function for different selections of populations and variant sets. Average MA frequency and the standard error were calculated for different selections of variants, e.g. variants with MAs increasing or decreasing traits. Standard errors for frequency and t value (bi/se), i from GWAS; N was the sample size of the GWAS; bi was the GWAS beta of varianti and se is the standard error of bi. Equation pi was the MAF of varianti. However, Eq. To quantify the trait variance explained by variants with large-, medium- and small-effect from GWAS results, the following formula was used:50 was used to calculate the FST value with the method described in Weir55 with the option of ‘--fst’ and ‘--sub-pop’. The average FST value with standard errors was then calculated for different selections of variants in the same fashion for selecting variant groups to compare the MA frequency as described above.With the same plink binary genotype file described above and the population structure for dairy cattle (four dairy breeds) and for ancient and modern cattle (seven breeds/subspecies), GCTA27. The raw reads of these data were aligned to the ARS-UCD1.2 reference bovine genome using STAR56. Qualimap 257 and RseQC58 were used to check data quality. FeatureCount59 was used to extract gene counts and the voom60 normalised counts were used in the following analyses. The normalised gene expression was analysed as phenotypes in the same GWAS model as Eq. pgwas < 5e−8) on protein yield, fat yield, milk yield, protein% and fat%. For these variants, the normalised expression of genes within ±1 Mb distance to them were analysed as phenotype. In other words, the analysis focussed on cis eQTL genes for these large-effect variants were analysed. When GWAS results of gene expression were obtained (cis eQTL), the effect allele was mapped to the ancestral allele to determine the effects of MAs. For quantifying the number of eQTL for each effect direction of MAs, only the SNPs with the smallest p value were considered.This analysis was based on 105 Holstein cattle that had RNA-seq data in milk cells described and published previously (NCBI SRA SRP111067)Further information on research design is available in the Peer Review FileSupplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Reporting Summary


Trait and functional trait approaches have revolutionized ecology improving our understanding of community assembly, species coexistence, and biodiversity loss. Focusing on traits promotes comparability across spatial and organizational scales, but terms must be used consistently. While several papers have offered definitions, it remains unclear how ecologists operationalize “trait” and “functional trait” terms. Here, we evaluate how researchers and the published literatures use these terms and explore differences among subdisciplines and study systems (taxa and biome). By conducting both a survey and a literature review, we test the hypothesis that ecologists’ working definition of “trait” is adapted or altered when confronting the realities of collecting, analyzing and presenting data. From 486 survey responses and 712 reviewed papers, we identified inconsistencies in the understanding and use of terminology among researchers, but also limited inclusion of definitions within the published literature. Discrepancies were not explained by subdiscipline, system of study, or respondent characteristics, suggesting there could be an inconsistent understanding even among those working in related topics. Consistencies among survey responses included the use of morphological, phonological, and physiological traits. Previous studies have called for unification of terminology; yet, our study shows that proposed definitions are not consistently used or accepted. Sources of disagreement include trait heritability, defining and interpreting function, and dealing with organisms in which individuals are not clearly recognizable. We discuss and offer guidelines for overcoming these disagreements. The diversity of life on Earth means traits can represent different features that can be measured and reported in different ways, and thus, narrow definitions that work for one system will fail in others. We recommend ecologists embrace the breadth of biodiversity using a simplified definition of “trait” more consistent with its common use. Trait‐based approaches will be most powerful if we accept that traits are at least as diverse as trait ecologists. Trait and functional trait approaches are now widely used in ecology, but how ecologists operationalize trait terminology often is unclear. We use survey data and a literature review to evaluate how researchers across subdisciplines and study systems use functional trait terminology. We found inconsistencies in the use of “trait” and “functional trait” terms, but these inconsistencies were not explained by sub‐discipline or study system. The survey was publicly available from January to April 2019. We recruited participants through our network of contacts and diverse communicating platforms; for example, email lists, Twitter feeds. Participation was voluntary, and all participants were informed of the purpose of the survey and about their rights to refuse to answer any questions and to withdraw from participation at any time. While the survey was available for anyone to complete, we did ask participants to select categories of study area and research experience. Informed consent was obtained, anonymity and confidentiality were explicitly granted, and we did not include any information that could be used to identify individual respondents. All data were thus anonymized prior to analyses and are available . We examined this question by creating a matrix of participant dissimilarity based on answers to survey questions using the R function “trova”  or North America (20%), with 10% based in South America, 6% in Africa and <5% in Asia and Oceania. Respondents worked primarily on forest (35%), grassland (29%), or freshwater (11%) ecosystems, and defined their research in very diverse ways, with community ecology (17%), ecosystems ecology (11%), conservation science (11%), and population ecology (8%) being the most frequent answers. Most respondents had substantial experience with trait‐based approaches ; 18% of respondents had not worked with trait‐based approaches .When asked about what should be considered a “trait,” respondents agreed in some cases but also showed divided opinions. Ecologists largely agreed that “morphological” (99% agree), “phenological” (94%), “physiological” (92%) and “behavioral” (83%) are acceptable trait categories, whereas “geographic” is not , we found less agreement within individual scales: “organ system” (77%) and “clonal line” (69%). Division among researchers was also clear for larger scales . When asIn the remaining questions, the respondents were asked to show their degree of agreement with several statements, and as above, we found variation in responses. When asked about their agreement with “A biological “trait” must not be defined by its relation to the environment,” 10.2% of respondents were “unsure,” 38% agreed and 44% disagreed, and 18% had a “neutral” opinion. Opinions were more certain about “A biological ‘trait’ must be heritable” with only 3% respondents being “unsure,” but opinions remained divided with half the respondents disagreeing and 36% agreeing. Finally, 81% of respondents considered that the terms “traits” and “characteristic” could be interchangeable , whereas 19% did not consider this equivalent meaning as generally correct (8% “never” and 11% “few times”).The estimated average Rao value for different subdisciplines did not explain terminology preferences of the research community. Within community, diversity  was much higher than between community diversity . If variation in responses was associated with communities  then gamma diversity should be much greater than alpha diversity. Instead, we found that for all features, >99% of the total diversity occurred within communities . For example, respondents working with vascular plants, fungi, or invertebrates were not more likely to have similar responses to each other, showing that contrary to our prediction, personal and professional backgrounds (at least those aspects we studied) do not explain the lack of consistency in the understanding of traits among ecologists Figure .Overall, our questionnaire revealed a high degree of disagreement over what constitutes a trait that cannot be easily explained by differences in lines of research, studied taxa, subfield, geographical origin, or experience.4American Naturalist, AREES, Ecography, Ecology, Ecology Letters, Ecological Monographs, Global Ecology and Biogeography, Functional Ecology, Journal of Animal Ecology, Journal of Applied Ecology, Journal of Ecology, Nature Ecology and Evolution, Oecologia, Oikos, PNAS, and TREE. Submissions to these journals were considered to represent expert authors and lead contributions to functional trait ecology research. We searched all articles published in 2018 in which “trait*” appeared in the title, abstract and/or keywords. This resulted in 758 papers, which were randomly assigned to eight co‐authors. Data papers, medical papers, and papers in which “trait” was only used generically, or only in the abstract, were removed, which left 712 papers.To examine how functional traits are described and presented in peer‐reviewed publications, we undertook a literature review. This review focused on 16 journals where functional trait‐based studies are often published: For each of the 712 papers, we recorded the following data: (a) number of times “trait” and “functional trait” were used; (b) whether a definition for these terms was provided; (c) whether trait types from our survey  or multiple biomes . A total of 105 papers (14.7%) focused on more than one continent, or were global in scope (11 were entirely marine focused). In 254 of these papers (35.7%), the term “functional trait” appeared at least once in the body of the text. In the remaining 458 (64.3%), only “trait” was used. Definitions and citations for “functional trait” and “trait” were provided in 31 (4.4%) and 22 (3.1%) papers, respectively. Two additional papers defined “trait” but did not provide a citation. Throughout our analyses, results did not qualitatively differ when only papers that included the term “functional trait” were used in the summary statistics see . Most paLargely, the taxa on which a paper focused had little effect on the types of traits mentioned in the paper. The exception to this observation was for behavioral traits, which were mentioned in 40% of papers focused on vertebrates and invertebrates compared with 7.3% papers on other organisms Figure . AlthougOverall, we found little evidence in the literature for major differences in the acknowledgement of different trait types across taxa and regions, although trait papers focusing on plants used the term “functional trait” more often, and trait papers focused on animals were more likely to mention behavioral traits. The latter is unsurprising given behavioral traits tend to be animal‐specific, similar to photosynthetic traits only being measured in plants.66.1The survey results suggest that researchers generally conceive traits the same way they are used in the literature. The significant disagreements in trait definition in the survey were unexpectedly not attributable to any particular taxa, biome or continent, and were evenly spread among subdisciplines. The large disagreements in the survey about trait definitions and the conditions necessary for a trait to be considered “functional” would be hard to detect in the literature; few of the studies we reviewed provided definitions or citations of the terms “trait” or “functional trait.” If researchers disagree on the meaning of a term and yet fail to provide definitions when they use it, it could be because they are either unaware that others are using the term trait and functional trait differently or are aware and do not wish to “open that can of worms” in their publications by providing a definition that may be viewed as wrong by reviewers, editors, and readers. Either way, this presents a problem. Publishing papers with unrecognized ambiguous terminology hampers one of the central tenets of functional ecology: that focusing on functional traits enables and enhances comparability between studies and analyses across spatial and organizational scales  hardly appeared in the reviewed papers. Two possible explanations for this are that plants continue to dominate the trait literature and that morphological traits are the easiest to measure, and thereby the most widely used. Nonmorphological traits may also be under‐explored because they are perceived as being less informative or less widely recognized, therefore studies based on these less used traits  may be more difficult to publish. Whatever the explanation, the outcome is a bias in the literature toward morphological traits despite the fact that many researchers recognized other trait types. By focusing heavily on morphological traits, we may be missing important processes and insights. We cannot fully operationalize trait research across organisms without first directly addressing what constitutes a trait and how they can be used.6.2It appears that although classic definitions, such as Violle et al.  and McGiH2) or additive  genetic values  of an individual organism that is measured at either the individual or other relevant level of organization.True comparability will require a truly universal definition applicable to the diversity of life and conditions on the planet, a difficult order to fill. To start, we recommend studies, at a minimum, state or reference definitions they are practicing for trait terminology. Definitions can provide clarification on a study level with minimal effort on the part of the researcher, and make it easier to compare and draw generalities from research in the future. We also propose a return to the basics, embracing a simplified definition that could satisfy more trait ecologists:While traits are more commonly defined and measured at the individual level, our definition allows for needed exceptions: life‐forms in which individuals are difficult to define for measurement purposes  or in which many individuals act as a single unit , are otherwise functionally relevant to questions in trait ecology. Hence, the heritability qualification is typically irrelevant . For example, plant photosynthetic rates might be highly relevant for investigating community dynamics, even if not all species within a community of interest have variation in the genetic values underlying this trait. We also remove the mention of required independence of environmental conditions because while traits should be defined without reference to the environment, trait values  generally require references to environmental conditions. The distinction between a trait and a trait value is subtle and this may be the source of confusion reported in the survey. For example, growth rate is the speed at which an organism increases its mass/size and reporting of measurements should include the temperature/humidity/resources provided/etc. To avoid future confusion, we recommend following Violle et al.  and usindoes not have a function at some level, under some set of circumstances, either individually or by interacting with other traits ; Project administration (lead); Supervision ; Writing‐original draft (lead); Writing‐review & editing (lead). Carlos Pérez Carmona: Conceptualization (lead); Data curation ; Formal analysis (lead); Methodology ; Project administration (supporting); Writing‐original draft ; Writing‐review & editing . Manuela González‐Suárez: Conceptualization (lead); Methodology (supporting); Writing‐original draft ; Writing‐review & editing . Mari Jönsson: Conceptualization (lead); Data curation (lead); Funding acquisition ; Methodology ; Project administration ; Writing‐original draft ; Writing‐review & editing . Filipe Chichorro: Data curation ; Investigation (supporting); Writing‐original draft (supporting); Writing‐review & editing (supporting). Max Mallen‐Cooper: Data curation ; Investigation (supporting); Writing‐original draft (supporting); Writing‐review & editing (supporting). Yolanda Melero: Data curation ; Investigation (supporting); Writing‐original draft (supporting); Writing‐review & editing (supporting). Helen Moor: Data curation ; Investigation (supporting); Methodology (supporting); Writing‐original draft (supporting); Writing‐review & editing (supporting). John P. Simaika: Data curation ; Investigation (supporting); Methodology (supporting); Writing‐original draft (supporting); Writing‐review & editing (supporting). Alexander Bradley Duthie: Conceptualization (lead); Investigation ; Methodology ; Project administration (lead); Visualization ; Writing‐original draft ; Writing‐review & editing .Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.Supplementary MaterialClick here for additional data file.


RORA, TIMELESS and PPARGC1A), which were selected for this study because they were plausibly linked with the response to Li. The three original and two revised Alda ratings showed low levels of discordance (misclassification rates: 8–12%). However, the significance of associations with circadian genes differed when examining previously recommended categorical and continuous phenotypes versus machine-learning derived phenotypes. Findings using machine learning approaches identified more putative signals of the Li response. Established approaches to Li response phenotyping are easy to use but may lead to a significant loss of data  due to recent attempts to improve the reliability of the original rating system. While machine learning approaches require additional modeling to generate Li response phenotypes, they may offer a more nuanced approach, which, in turn, would enhance the probability of identifying significant signals in genetic studies.Optimal classification of the response to lithium (Li) is crucial in genetic and biomarker research. This proof of concept study aims at exploring whether different approaches to phenotyping the response to Li may influence the likelihood of detecting associations between the response and genetic markers. We operationalized Li response phenotypes using the Retrospective Assessment of Response to Lithium Scale  in a sample of 164 cases with bipolar disorder (BD). Three phenotypes were defined using the established approaches, whilst two phenotypes were generated by machine learning algorithms. We examined whether these five different Li response phenotypes showed different levels of statistically significant associations with polymorphisms of three candidate circadian genes ( Clinical practice guidelines identify lithium (Li) as a first-line treatment for mood stabilization in bipolar disorders (BD) ,2. UnforThe ideal research assessment of the Li response would involve the systematic prospective follow-up of Li-naive cases that are prescribed this medication for the first time . HoweverMore recently, we examined alternative approaches to improving the performance of the Alda scale . We systTIMELESS and RORA genotypes and circadian phenotypes (phase preference and amplitude of rhythms) in BD cases and found that the Li response may be associated with some PPARGC1A and/or RORA genotypes [TIMELESS) may be associated with the level of Li response [RORA, TIMELESS and PPARGC1A) and that these genes may be plausible candidates for this proof of principle study.To select plausible genes for this proof of principle study, we decided to focus on genes involved in the circadian system. We argue that this is justified as it is repeatedly suggested that the therapeutic action of Li can be partly explained by modifications and stabilization of circadian rhythms ,20. For enotypes ,27. Otheresponse ,29. GiveIn sum, although the Alda scale is the most widely employed rating of Li response, there is a lack of consensus on how best to ascertain clinical phenotypes, which potentially hinders progress in this research field. This paper describes a database study of Li response that explores the strengths and weaknesses of different approaches to rating the Alda scale in a well-characterized clinical sample of adults with a diagnosis of BD. We report overall agreement between different approaches to evaluating Li response phenotypes and rates of discordance. Then, we examine associations between each clinical phenotype for Li response and genetic variants in three candidate circadian genes. Finally, we consider the advantages and disadvantages of the different approaches.As shown in n = 35) of cases were classified as GR according to the original categorical approach (Alda Cats) and, using a continuous measure of Li response, the mean TS  was 3.7 . Using the approach proposed by Manchia et al. 2013 for estimating Li response, we found that there were 106 cases with a B score < 4; in this subgroup, the mean A scale score was 6.9 . Machine learning classified 26% cases (n = 43) as GR ; the nearest equivalent of the continuous measurement of Li response, namely the probability of GR (GRp), was estimated as GRp > 0.62.According to the original approaches, 21% , we found that the PPVs were all >80%, the NPVs were all >95% and overall agreements were all >90%. The proportion of cases with discordant classifications was lowest for categorical phenotypes (8%) and highest for A/Low B versus GRp (12%). The latter was likely influenced by the reduced sample size (as only 106 cases met the A/Low B criteria).TIMELESS); TS showed a significant association with TIMELESS, whilst Alda Cats showed significant associations with TIMELESS and PPARGCIA. The Algo classification showed significant associations with all three SNPs, whilst GRp showed associations with TIMELESS and PPARGC1A (with a trend for RORA).As shown in TIMELESS genotype met the criteria for inclusion in the tree based on Alda Cats . Overall, 89% of TIMELESS GG homozygotes were NR (Node 1), whilst 43% of those with TIMELESS AA/AG genotypes were GR (Node 2). The most obvious difference in the classification tree  and TIMELESS  genotypes were included in the model . For RORA, 91% of CC homozygotes were NR (Node 1), while 47% of TT homozygotes were GR (Node 3). Among individuals with a RORA TC genotype (Node 2), 80% of TIMELESS GG homozygotes were NR (Node 4), whilst 43% of individuals with a TIMELESS AA/AG genotype were GR (Node 5).The classification trees for Li response categories are shown in ion tree b based op value), which then branches and grows iteratively into internal and terminal nodes (the latter represent variables that carry the maximum information). The order of importance of explanatory variables is represented by the tree structure and the percentages shown within the nodes are an indicator of the relevance of each characteristic as a primary predictor of Li response status (similar to PPV and NPV). In the current study, the classification rates are reported for different combinations of genotypes. As the roots and nodes may link in different ways (following an “if–then” type sequence), there may be more than one classification rate associated with variables included in the tree. Tree building ends when the p values of all the observed independent variables are above the specified threshold for statistical significance, so the absence of any genotype or demographic variables from the trees that we report indicates that those items  did not make a meaningful additional contribution to case classification. We have not reported summary statistics for each root and node .For readers less familiar with CHAID (Chi-Square Automatic Interaction Detector) analysis, we briefly summarize here how to interpret the outputs. A CHAID analysis generates a bifurcating decision tree composed of a root node , but to examine if machine learning approaches to clinical phenotyping are viable and have any advantages over established strategies. This is important as it is increasingly acknowledged that advances in precision psychiatry need an integrated science approach to ensure reliable and valid ascertainment of clinical phenotypes and of any differential associations with genetic and/or other type of biomarkers of disease or treatment outcome . In thisTIMELESS and RORA) and the revised categorical (Algo) phenotype that was not discovered by the original (Alda Cats) approach to the classification of responders.We demonstrated that, although discordance rates for case classification between the different approaches to phenotyping were low, the subtle shifts in the balance between GR and NR may enable the revised approaches to identify more potential genetic signals of Li response than the traditional approaches. Further, an exploratory data mining analysis  identified a subtle inter-relationship between genotypes  that allows a maximum Type I error rate of alpha = 0.05. Despite these limitations, the potential strength of this study is that it highlights that the three established and most widely used approaches to operationalizing the Li response do not produce consistent signals. This is important as nearly all genetic studies of the Li response have reported their findings based on the Alda Cats approach alongside one of the two continuous measures [Of course, our findings must be treated with caution as the study population was recruited from a limited number of academic psychiatry clinics in the same country and represents a convenience sample extracted from a pre-existing dataset. Importantly, the selection and number of candidate genes and SNPs may be questioned, as we focused on one candidate biological pathway and used only one SNP per gene, which is obviously restrictive and likely biased. This selection of candidate genes is, by definition, debatable and other approaches may have focused rather on genes that reached (or nearly reached) significant thresholds in previous GWAS studies ,31. Moremeasures . The disOf the three original approaches, the A/Low B strategy is the newest estimate of Li response, and it was introduced because of concerns over the accuracy of the TS and, by default, of the Alda Cats . It can The most obvious advantage of the best estimate approach to phenotyping is that it offers a more nuanced approach to defining the Li response as the machine learning algorithms address the differential impact on response (or confidence in assessing response) of some confounders and/or the complexity of inter-relationships between confounders within a given study population. The Algo classification is easier to replicate and interpret, as it balances GR versus NR. Further, the Algo and GRp approaches appear to show more similarities than differences . However, we believe that the model for generating GRp requires more work . Overall, the main advantage of the best estimate approach is that, unlike the ‘A/Low B’ strategy, the GR/NR split is empirically derived, and the algorithm attempts to classify all cases without exception .At a practical level, the machine learning approaches to evaluating the Li response can be applied in two ways. For investigators with limited resources, existing machine learning algorithms can be applied to generate Li response phenotypes . AltIn conclusion, we note that the original TS/Alda Cats approaches to rating the Alda scale are somewhat simplistic. For instance, it fails to address the issue of Li non-response due to minimal direct benefit from Li (A score rating) versus non-response associated with high levels of confounding . The A/Low B approach has some advantages, not least that it can be efficiently applied. However, this more stringent approach leads to a reduction in sample size. This might be accommodated in large studies, but it is a significant issue in smaller-scale studies. Furthermore, this approach actively deselects cases with high B scores . This may be appropriate for signal detection in genetic research, but it undermines clinical research aimed at understanding the Li response in difficult-to-treat cases . The latter represent a real-world clinical population where response prediction would be highly valued. The next step for the current project is to replicate the findings in a larger study designed with the specific aim of testing the revised approaches to phenotyping in a representative clinical cohort, at the level of the entire circadian system genes and/or at a genome-wide level.The study received ethical approval from the French Ethics and Data Protection and Freedom of Information Commissions . Here, we briefly outline the methodology; full details regarding machine learning, genotyping procedures and analyses are available elsewhere and/or are summarized in the published protocol ,17 Original approaches to rating the Alda scale-Total Score (TS): a continuous measure represented by the TS ; if B > A, then the TS is reported as zero.-Original classification (Alda Cats): Li response categorized as GR (TS >= 7) or NR (TS < 7).-A score in cases with a low B scale score (A/Low B): Li response is represented by the A scale score (continuous variable), but assessment is restricted to individuals with B < 4; those with high B scores are excluded from the analysis.The three most widely used approaches are:(b)Machine learning approach to rating the Alda scaleIn the best estimate classification approach, a machine learning algorithm determines a set of “if–then” rules for determining the probability of GR and NR. The analysis enters the B scale item scores in a sequence; this usually starts with treatment complexity (adherence and polypharmacy), then duration of Li treatment and/or illness activity (the exact sequence and combination of item scores is generated by the machine learning model). The algorithm stops running once the optimal classification is reached, irrespective of whether all B items have been included . Here, Lithium response was estimated from ratings of the two subscales (A and B) of the Alda scale . The A sRORA, PPARGC1A and TIMELESS and within 10 kilobase pairs (Kbp) upstream and downstream from the coding sequence ) were used to explore exonic and intronic regions, as well as cis-regulatory regions. SNPs were included in the following association analysis if they fulfilled the following quality criteria : (1) minor allele frequencies (MAF) greater than or equal to 5%; (2) genotyping call rate for at least 97% of SNPs; (3) call rate averaged 90% and (4) SNP heterozygosis between (m−3 s.d.) and (m+3 s.d.). In order to select the SNPs, we used PLINK to determine the associations between SNPs and the Alda total score. Briefly, for each gene, the program: (1) determines which SNPs are in linkage disequilibrium (LD) ; (2) performs a single SNP association analysis using a non-parametric approach; and (3) determines the associated SNP having the highest statistical significance (selection of the “best SNP” option). This method allowed us to identify, among all available SNPs within a given gene, which SNP was the most strongly associated with the phenotype (whatever the level of significance). Among all available SNPs in the three selected genes , this approach retained rs17204910 in RORA, rs2932965 in PPARGC1A and rs774045 in TIMELESS. For these three SNPs, all genotypes were in Hardy–Weinberg equilibrium.Genomic DNA samples were extracted from peripheral blood leukocytes or B-lymphoblastoid cell lines by standard procedures. Genotyping was performed at the Centre National de Genotypage  using HumanHap550 or 610-Quad Beadchips . Analyses were performed using PLINK v1.07 30 . All avahttps://www.cebm.ox.ac.uk, accessed on 18 October 2021). To interpret the findings, we used the indicators established for diagnostic test comparisons used in clinical settings, which suggested that we could expect the new Alda ratings to show PPV, NPV and accuracy estimates of >80–85% (compared with established ratings).First, we compared estimates of Li response using the original and new approaches to rating the Alda scale, reporting the positive and negative predictive values , the overall accuracy and discordance rates. For the purposes of the analyses, we assumed that the original ratings represent the “gold standard” . The classification obtained for Alda Categories was compared with Algo, whilst the A score/Low B measure was compared with GR according to the Algo , RORA (CC versus TC versus TT) and PPARGC1A (GG versus GA/AA) and Li response phenotypes are reported as −log10(p), and levels of statistical significance are reported as p < 0.017 (corrected for 3 genes) and p < 0.003 (corrected for 3 genes and 5 phenotypes).Associations between genotypes of p values of all the observed independent variables were above the specified threshold for statistical significance .Next, for categorical classifications (Alda Cats and Algo), we employed Chi-Square Automatic Interaction Detector (CHAID) analysis to explore whether any combinations of genes improved the ascertainment of GR or NR cases. This analysis generated a classification tree, which represents a sequential model consisting of a set of if–then rules for the partition of heterogenous input data into groups that are homogenous regarding the dependent/outcome variable categories. To avoid overfitting of CHAID, we adjusted the model for age and sex  and analyses were cross-validated. In the figures shown, the order of importance of explanatory variables is explicitly represented by the tree structure, and tree building ended when the Established approaches to Li response phenotyping are easy to use but may lead to a significant loss of data  due to recent attempts to improve the reliability of the original rating system. While machine learning approaches require additional modeling to generate Li response phenotypes, they may offer a more nuanced approach, which, in turn, would enhance the probability of identifying significant signals in genetic studies.