Maternal genetic effects can be defined as the effect of a mother’s genotype on the phenotype of her offspring, independent of the offspring’s genotype. Maternal genetic effects can act via the intrauterine environment during pregnancy and/or via the postnatal environment. In this manuscript, we present a simple extension to the basic adoption design that uses structural equation modelling (SEM) to partition maternal genetic effects into prenatal and postnatal effects. We examine the power, utility and type I error rate of our model using simulations and asymptotic power calculations. We apply our model to polygenic scores of educational attainment and birth weight associated variants, in up to 5,178 adopted singletons, 943 trios, 2687 mother-offspring pairs, 712 father-offspring pairs and 347,980 singletons from the UK Biobank. Our results show the expected pattern of maternal genetic effects on offspring birth weight, but unexpectedly large prenatal maternal genetic effects on offspring educational attainment. Sensitivity and simulation analyses suggest this result may be at least partially due to adopted individuals in the UK Biobank being raised by their biological relatives. We show that accurate modelling of these sorts of cryptic relationships is sufficient to bring type I error rate under control and produce asymptotically unbiased estimates of prenatal and postnatal maternal genetic effects. We conclude that there would be considerable value in following up adopted individuals in the UK Biobank to determine whether they were raised by their biological relatives, and if so, to precisely ascertain the nature of these relationships. These adopted individuals could then be incorporated into informative statistical genetics models like the one described in our manuscript to further elucidate the genetic architecture of complex traits and diseases. Maternal genetic effects can be defined as the causal influence of maternal genotypes on offspring phenotypes over and above that which results from the transmission of genes from mothers to their offspring . Over thIn this manuscript, we develop a simple method for partitioning maternal genetic effects into prenatal and postnatal components that leverages information provided by adopted individuals. We assume that an adopted individual’s phenotype is influenced by prenatal intrauterine factors as proxied by their biological mother’s genome, and postnatal influences as proxied by their adoptive mother’s and father’s genomes. In contrast, we assume that the phenotype of individuals who have not been adopted are influenced by prenatal intrauterine factors resulting from their biological mother’s genome, and postnatal factors as proxied by their biological mother’s and father’s genomes. This model leads to different expectations for the covariance between an individual’s phenotype and their own and their relatives’ genotypes depending on whether they have been adopted or not.One of the challenges in applying this kind of framework to real life situations is the paucity of cohorts containing large numbers of adoptive families . RestricIn this manuscript, we introduce a new structural equation model (SEM) to estimate prenatal and postnatal maternal genetic effects on offspring phenotypes. The SEM framework allows us to model the contributions from missing individuals as latent variables, facilitating the inclusion of information from adopted singleton individuals whose adoptive and/or biological parents are not available for analysis. We estimate the asymptotic power of our model to partition maternal genetic effects into prenatal and postnatal components and confirm these results by simulation. We code our routines into a freely available R shiny app web utility that researchers can use to perform their own power calculations. Finally, we apply our methods to birth weight and educational attainment data in the UK Biobank- two phenotypes known to be affected by maternal genetic effects. We investigate the effect of inadvertently including adopted singleton individuals whose adoptive parents are genetically related to them in our model, adjust our model to correct for this misspecification and quantify the effect of this adjustment on type 1 error rates and power. We discuss the implications of model misspecification for using the UK Biobank resource in this context in future studies more broadly.We consider seven different family structures  which wem, Zp and Zo represent maternal, paternal and offspring genotypes. Likewise, let Zm_b and Zp_b denote the genotypes of the biological mother and father of an adopted individual respectively, and let Zm_a and Zp_a represent the genotypes of the adoptive mother and father of the adopted individual. These variables may be observed , paternal genetic effects (pϐ) and offspring genetic effects (oϐ) on the offspring phenotype (Y). We are specifically interested in partitioning maternal genetic effects into prenatal (γm) and postnatal genetic effects (mϐ) and we assume that the effect of the prenatal maternal genetic effect and postnatal maternal genetic effect on the offspring phenotype is additive (i.e. m + ϐmγ). We assume in the case of biological families (i.e. G1 to G4 in Let the variables ZΦ) of each individual and assume that it is the same in mothers, fathers, their children, and across both biological and adopted individuals under random mating . We account for possible covariance between maternal and paternal genotypes (e.g. through assortative mating) by estimating the covariance path ρ. This is equivalent to modelling one round of assortative mating in the parental generation and has the effect of inflating the total genotypic variance in the offspring generation from Φ under random mating to Φ + ½ρ. Finally, to accommodate the possibility that adopted individuals may have different phenotypic variances to individuals raised by their biological relatives, we permit the variance of residual sources of variation to differ across adopted and biological family structures , contribute important information for the partitioning of maternal genetic effects, since the covariance between their own genetic score and phenotype is a function of offspring genetic effects and prenatal maternal effects, but not postnatal maternal effects . This coWe used OpenMx  to calcu2χ distribution with where arameter .α=0.05) using sample sizes roughly similar to the number of European individuals in the resource who reported their educational attainment . We investigated the effect of different combinations of prenatal maternal genetic effects, postnatal maternal genetic effects, postnatal paternal genetic effects and offspring genetic effects . We also examined the effect of modifying the covariance between parental genotypes . Finally, we were curious as to the effect of increasing the number of the different family structures on statistical power, and in particular, on whether including increasing numbers of more attainable/accessible biological relatives  could increase power to partition maternal genetic effects for a fixed number of adopted individuals. We also investigated the effect of varying the sample size of adopted individuals (G5), adoptive mother-adopted offspring duos (G6), and biological mother-adopted offspring duos (G7) on power. We used our calculator to determine 80% power (α=0.05).As we were interested in whether there might be enough adopted individuals in the UK Biobank for the informative partitioning of maternal genetic effects into prenatal and postnatal sources of variation, we first calculated power  divided by 1000.https://evansgroup.di.uq.edu.au/ADOPTED). Our power calculator is built using the R shiny app (https://shiny.rstudio.com/) running the R studio software , followed by trios (G1), mother-offspring duos (G2), and then father-offspring duos (G3).We applied our model to self-reported birth weight and educational attainment data from the UK Biobank resource. The UK Biobank study was approved by the UK National Health Service National Research Ethics Service. Written consent was obtained from both the participants and their parents (for subjects younger than 18 years old). This study was approved by the Human Research Ethics Committee at the University of Queensland . We only included individuals of European ancestry, determined by: (i) projecting their genetic principal components onto the 1,000 Genome sample and then K-means clustering or (ii) those who self-reported ethnic background of either ‘British’, ‘Irish’, ‘Irish’, ‘White’, or ‘Any other white background’. Family relationships were determined by the pairwise kinship estimated across the whole UK Biobank sample using the software KING . Adoptio–8 from a recent GWAS of birth weight , Higher National Diploma (HNC), or equivalent = 19 years; other professional qualification = 15 years; A level/AS level or equivalent = 13 years; O level/General Certificate of Secondary Education (GCSE) or equivalent = 10 years; Certificate of Secondary Education (CSE) or equivalent = 10 years; none of the above = 7 years of education. We regressed years of education on year of birth, sex and the first five genetic principal components and used the residuals in the analysis. The final dataset included 943 biological parent-offspring trios, 2687 biological mother-offspring pairs, 712 biological father-offspring pairs, 347,980 singletons from biological families, 5178 adopted singletons and 39 biological mother-adopted offspring pairs. We calculated weighted PRS  and unweighted PRS  using 1267 SNPs from the current largest GWAS of educational attainment . We were concerned about the possibility that some individuals in UK Biobank might have been adopted by their biological relatives in which case our model in We were concerned about the effect that misclassifying adopted “singleton” individuals as unrelated to their adoptive parents  might have on type I error rates and estimates of prenatal and postnatal maternal genetic effects generated by our model. We therefore simulated data under four scenarios: (i) adopted singletons where 0%, 20%, 40%, 60%, or 80% had adoptive mothers who were siblings or cousins of their biological mothers, (ii) adopted singletons where 0%, 20%, 40%, 60%, or 80% had adoptive mother who were siblings or cousins of biological fathers, (iii) adopted singletons where 0%, 20%, 40%, 60%, or 80% had adoptive fathers who were siblings or cousins of biological fathers, and (vi) adopted singletons where 0%, 20%, 40%, 60%, or 80% had adoptive fathers who were siblings or cousins of biological mothers. We assumed that sample sizes and the number of individuals in the other groups were the same as in our asymptotic power calculations.r) between the genotypes of adoptive and biological parents. The covariance between the genotypes of adoptive and biological parents was fixed to r=0.5 х Φ when the adoptive parent was a sibling of the biological parent and r=0.125 х Φ when they were cousins.We further investigated type 1 error rates and estimates of prenatal and postnatal maternal genetic effects after correctly modelling the relationship between biological and adoptive parents. We created four additional family structures  to detect prenatal maternal and postnatal maternal genetic effects that account for 1.5% and 0.9% of the variance in the offspring phenotype, respectively . The power to detect prenatal and postnatal maternal genetic effects also increased slightly with increasing covariance between maternal and paternal genotypes , whereas biological mother-adopted child pairs provide a direct estimate of the prenatal maternal genetic effect (m). Likewise, adopted singleton individuals do not provide direct estimates of either prenatal or postnatal maternal genetic effects, and therefore contribute proportionally less in terms of statistical power than adoptive mother-adopted child or biological mother-adopted child pairs.The power to detect prenatal and postnatal maternal genetic effects increased with the number of adopted singleton individuals, and more dramatically when the number of adoptive mother-adopted offspring pairs and/or biological mother-adopted offspring pairs increased . Power tInterestingly, the power to detect prenatal and postnatal maternal genetic effects also increased with the number of biological families in the analysis (G1 to G4) ; howeverPRS for birth weight exhibited significant evidence of prenatal maternal genetic effects, offspring genetic effects (in the opposite direction), and no significant evidence for postnatal maternal or paternal genetic effects . This paIn the case of offspring educational attainment, our analyses showed evidence for a prenatal maternal genetic effect, a paternal genetic effect, and an offspring genetic effect . The absWe therefore performed sensitivity analyses where we excluded adopted individuals who reported breastfeeding information . The results of these analyses showed that estimates of the prenatal maternal genetic effect reduced in size and became non-significant. Whilst the postnatal maternal effect remained non-significant, the direction of effect changed from negative to positive. Sensitivity analyses using PRS constructed using the 72 genome-wide significant SNPs from the Our simulations showed that the presence of adoptive parents who were genetically related to their adopted offspring could in some cases increase the type 1 error rate to detect prenatal maternal genetic effects and bias estimates of prenatal and postnatal maternal genetic effects when these relationships were not accurately modelled in the SEM . In gener approaches zero .In the case of adoptive mothers being genetically related to biological parents , the prers G8 in , and adors G8 in - implyinLikewise, our simulations showed that the presence of paternal genetic effects . This makes sense since offspring and paternal genetic effects are estimated directly from the covariance between observed genotypes and phenotypes , whereas the estimation of prenatal and postnatal maternal genetic effects have to be inferred indirectly using latent (not directly observed) genotypes and the difference in the covariance between offspring genotype and phenotype in biological and adoptive families.When we correctly modelled the relationship between biological and adoptive parents’ genotypes, there was no inflation in type 1 error rates and effect estimates were unbiased . Howeverr). The consequence is that the reduced model doesn’t fit the data as well and increased power to detect association. Similar thought experiments can be used to provide intuition for the other results in In contrast, power to detect prenatal and postnatal maternal genetic effects increased when adopted singletons whose adoptive fathers were related to their biological parents were included (and modelled correctly) in the analysis. In order to understand this result intuitively, it is useful to consider the case where the offspring trait is affected by concordant prenatal and postnatal maternal genetic effects  effects. Whilst our method does not provide explicit mechanistic insight into the reason for the existence of maternal genetic effects , follow up studies could help elucidate these mechanisms by for example examining the association between maternal PRS and different prenatal and postnatal maternal phenotypes, and performing mediation and Mendelian randomization analyses .We are not the first to note that information from adopted individuals could be used to provide valuable information on the effect of the prenatal environment on offspring traits . We are We are also not the first to have used adopted individuals in the UK Biobank to estimate the contribution of indirect genetic effects to phenotypic variability.  contrastIn a previous study of cognitive and non-cognitive effects on educational attainment , used thOur power calculations show that in principle the number of adopted individuals in the UK Biobank is unlikely to be sufficient to resolve effects at individual genetic loci but may be large enough to detect evidence for prenatal/postnatal maternal genetic effects in the case of PRS. It is worth noting that, whilst primarily a function of the number of adoptive families in the analysis, the power to partition maternal genetic effects was also influenced by the number of biological families analysed. Intuitively, this is because the other family structures contribute to more precise estimation of for example paternal genetic effects, which in turn provides information on the total size of the maternal genetic component. This observation is important, because the number of adopted individuals in an analysis is likely to be severely constrained, whereas power can sometimes be improved  by increasing the sample size of other relative types that may be easier to ascertain. Regardless, the most efficient way to increase the power to detect prenatal and/or postnatal maternal genetic effects is to genotype adoptive mother-adopted child pairs and/or biological mother-adopted child pairs.Our empirical analyses in the UK Biobank showed the expected pattern of maternal genetic effects on offspring birth weight  but not on offspring educational attainment. Parental educational attainment is known to causally affect offspring educational attainment . Whilst Our model relies on several strong assumptions, some of which are shown explicitly in Whilst we expect some of these assumptions to hold , we expect that others will show varying degrees of violation with differing consequences for the parameter estimates obtained under the misspecified model. For example, it is well appreciated that adopted individuals and adoptive families may differ in several respects to the general population. For example, some studies have reported that adoptive families are better educated and have higher socio-economic status than the population average . We arguWe argue that of greater consequence for the validity of our model is that any genetic relationship between adoptive and biological parents is accurately modelled and included in the SEM. Through simulation, we have shown that the consequences of model misspecification depend upon which biological and adoptive parents are related, the nature of this relationship, and the proportion of adopted individuals in the sample who have had their relationship misspecified. Our simulations also showed that correctly modelling this relationship returns asymptotically unbiased effect estimates and correct type I error rates. Clearly, knowing these cryptic relationships in the UK Biobank would allow us to properly model them and better estimate prenatal and postnatal maternal genetic effects using this resource. We emphasize that accurately modelling these relationships does not require that actual genotypes for adoptive and/or biological parents be obtained  as our SEM allows us to model these relationships in terms of latent variables. Indeed, as large-scale resources like the UK Biobank become more common, we expect that the number of adopted individuals who have GWAS will also increase, and consequently models like the one espoused in this manuscript will become increasingly useful. High quality phenotypic information on these adopted individuals and their adoptive parents including whether they share any biological relationship will be critical to making the most of these resources.r=0.285; birth weight: r=0.076) and PRS  in complete parent-offspring trios in the UK Biobank suggest that assortative mating is likely present for educational attainment, and potentially to a lesser degree for (phenotypes correlated with) birth weight. Recent work by We have also not modelled the complex effects of assortative mating in our SEM other than including covariance terms between maternal and paternal genotypes and assuming equal genetic variances in parents and their offspring under random mating . Positive assortment induces a number of complications when attempting to decompose the offspring phenotypic variance into its constituent sources of variation, including increasing homozygosity and the genetic variance at loci for the trait undergoing assortment relative to that expected under Hardy-Weinberg equilibrium, and inducing correlations between assorting loci across the rest of the genome both within and between individuals in the same family. Spousal correlations for phenotypes  suggests that the effect of assortative mating on parameter estimates from our SEM is likely to be minor.Finally, it has not been lost on us, that our framework may provide a basis for correcting Mendelian randomization (MR) studies of intrauterine/early life environmental exposures for some of the contaminating effects of horizontal genetic pleiotropy . The preIn conclusion, we present a simple extension to the basic adoption design that includes measured genotypes and enables partitioning of maternal genetic effects into prenatal and postnatal sources of variation. We show in principle that adopted singleton individuals in the UK Biobank combined with biologically related parent-offspring trios and pairs is sufficient to partition maternal genetic effects into prenatal and postnatal sources of variation. However, power calculations suggest that such a partitioning would currently only be realistic for PRS explaining substantial proportions of the variance in offspring phenotype, and that much larger numbers of individuals would be required to achieve such a partitioning at individual loci. In addition, failure to correctly model cryptic relationships between adoptive and biological parents may produce biased estimates of maternal genetic effects and increased type I error rates. Accurate modelling of cryptic relationships is sufficient to bring type I error rate under control and produce unbiased effect estimates. We suggest that there is a possibility that many individuals in the UK Biobank who report being adopted could have been raised by their biological relatives. We conclude that there would be considerable value in following up adopted individuals in the UK Biobank to determine whether they were raised by biological relatives, and if so, to precisely ascertain the nature of the relationship. These adopted individuals could then be used in informative statistical genetics models like the one described in the present manuscript to further elucidate the genetic architecture of complex traits and diseases.R code for performing the analyses described in this manuscript is available in the Source Code File. The authors propose an innovative and sound method to leverage the adoption of a design for disentangling prenatal and postnatal genetic effects. This work will be of interest to scientists interested in the intergenerational transmission of phenotypes through genetic pathways. public reviews designed to be posted alongside the preprint for the benefit of readers; ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: i) Decision letter after peer review:eLife. Your article has been reviewed by 2 peer reviewers, and the evaluation has been overseen by George Perry as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Stephane Paquin (Reviewer #2).Thank you for submitting your article "Using adopted individuals to partition indirect maternal genetic effects into prenatal and postnatal effects on offspring phenotypes" for consideration by The Reviewing Editor has drafted this to help you prepare a revised submission.The reviewers of your paper were positive about your work, but also identified several limitations that are not properly accounted in the current version of the paper. Alongside the critiques the reviews are so constructive that reasonable paths forward on each of the points raised below – primarily with thorough textual changes only – should be readily apparent.Reviewer #1 (Recommendations for the authors):GWAS data used for polygenic scoresThe decision to include only genome-wide significant SNPs was not justified. Please could the authors fill the readers in on this? Especially for EA, a highly polygenic trait, why not include all SNPs? It is also not clear why they performed the sensitivity analysis with the less powered Okbay GWAS – perhaps this could be put in the Supplementary Information. Can the authors comment on how their results are affected by pre- and post-natal IGEs being captured by the original GWAS used to construct polygenic scores ?Positioning among prior workThe authors could spell out more for readers their answer to the 'big picture' question of why it is useful to distinguish pre- and post-natal maternal effects, instead of just saying it's a natural question (see Introduction). Also in the introduction, it does not seem accurate to say that partitioning variation could yield mechanistic insights. Although the current contribution is very valuable, don't we need different kinds of designs and measures to understand mechanisms? In this regard, the authors should discuss the merits of their study compared to that of Armstrong-Carter et al. That study does not offer a principled way to separate pre- and post-natal effects, but it does try to work out which kinds of maternal phenotypes are involved in so-called pre-natal genetic nurture effects captured by EA PGS.The authors should also engage more with other studies to clarify the novel aspects of their contribution. They describe in the Discussion the Domingue and Fletcher (2020) paper, but more relevant is Cheesman et al's., (2020) study design using the nonadopted-adopted polygenic score comparison in UKBB to estimate post-natal parental indirect genetic effects. Demange et al., (2021) estimated pre-natal parental indirect genetic effects by comparing estimates from adoption and sibling designs . Although this was for a non-cognitive skills polygenic score and not EA or BW, it is worth discussing their approach and comparing against their estimates. The Demange et al., approach means that estimates of pre-natal maternal genetic effects may also include assortative mating and population stratification. There is a general paragraph on AM in the Discussion, but how do the authors think that AM and popstrat will load in their model? Recent evidence from UKBB suggests that it is important to consider the role of population stratification particularly when studying EA .Misc.It is neat to have a negative control phenotype for post-natal genetic effects (birthweight). Can the authors try out a negative control for pre-natal genetic effects too? If the maternal pre-natal effect were significant for something paternal substance use, this would bolster the idea that relatedness among adoptees and their adoptive parents causes inflation of this estimate.The use of breastfeeding data to identify those who were not adopted by relatives is smart. It would be worth checking how selected this sample is for some key traits . Also, could more information be leveraged to increase accuracy? Many participants just don't know the answer to that question, could have remembered incorrectly, and wetnurses  also used to be common. Adoptions in later cohorts might have become more 'organized' (happening earlier in life and involving non-relatives). Perhaps it's worth cutting out some of the older adoptees? The authors could also try limiting the sample further to those who also report their birthweight.Was a relatedness cut-off used to ensure that each family was independent?The authors could cite Wang et al., (2021) when saying that it is unfeasible for paternal genetic effects to be so much bigger than maternal effects – this meta-analysis found equal effects of paternal and maternal EA PGS on offspring educational outcomes.ReferencesArmstrong-Carter E, Trejo S, Hill LJ, Crossley KL, Mason D, Domingue BW. The earliest origins of genetic nurture: The prenatal environment mediates the association between maternal genetics and child development. Psychological science. 2020 Jul;31(7):781-91.Cheesman R, Hunjan A, Coleman JR, Ahmadzadeh Y, Plomin R, McAdams TA, Eley TC, Breen G. Comparison of adopted and nonadopted individuals reveals gene-environment interplay for education in the UK Biobank. Psychological science. 2020 May;31(5):582-91.Demange PA, Hottenga JJ, Abdellaoui A, Eilertsen EM, Malanchini M, Domingue BW, de Zeeuw EL, Rimfeld K, Eley TC, Boomsma DI, van Bergen E. Estimating effects of parents' cognitive and non-cognitive skills on offspring education using polygenic scores. bioRxiv. 2021 Jan 1:2020-09.Fletcher J, Wu Y, Li T, Lu Q. Interpreting polygenic score effects in sibling analysis. bioRxiv. 2021 Jan 1.Wang B, Baldwin JR, Schoeler T, Cheesman R, Barkhuizen W, Dudbridge F, Bann D, Morris TT, Pingault JB. Robust genetic nurture effects on education: A systematic review and meta-analysis based on 38,654 families across 8 cohorts. The American Journal of Human Genetics. 2021 Aug 19.Young AI, Nehzati SM, Lee C, Benonisdottir S, Cesarini D, Benjamin DJ, Turley P, Kong A. Mendelian imputation of parental genotypes for genome-wide estimation of direct and indirect genetic effects. BioRxiv. 2020 Jan 1.Reviewer #2 (Recommendations for the authors):I have no other specific recommendations. I think the approach and code provided are sound. I would mostly appreciate that the authors consider adding more details on the limitations (and possible extensions) of their approach regarding gene-environment interplay (both gene-environment moderation and gene-environment correlation). Reviewer #1 (Recommendations for the authors):GWAS data used for polygenic scoresThe decision to include only genome-wide significant SNPs was not justified. Please could the authors fill the readers in on this? Especially for EA, a highly polygenic trait, why not include all SNPs? It is also not clear why they performed the sensitivity analysis with the less powered Okbay GWAS – perhaps this could be put in the Supplementary Information. Can the authors comment on how their results are affected by pre- and post-natal IGEs being captured by the original GWAS used to construct polygenic scores ?We included only genome-wide significant SNPs in the construction of the EA score because the most recent GWAS meta-analysis by Lee et al., (2018) included UKBiobank individuals (and likewise for birthweight). We were concerned that sample overlap may inflate estimates of the association between the PRS and educational attainment (and any bias would be most severe for the hundreds of thousands of SNPs that did not reach genome-wide significance) which may in turn bias parameter estimates from our model. This was also our reason for including the less powered Okbay et al., GWAS as a sensitivity analysis. We have modified the text in the methods to make this clear for the reader:“We included only genome-wide significant SNPs in the construction of these scores because the most recent GWAS meta-analysis of educational attainment by Lee et al., (2018) included UKBiobank individuals. We were concerned that sample overlap would inflate estimates of the association between the PRS and educational attainment (and any inflation would be most severe for the hundreds of thousands of SNPs that did not reach genome-wide significance) and in turn bias parameter estimates from our model. For this reason, we also performed a sensitivity analysis using a second set of PRS of educational attainment using 72 SNPs from a GWAS of non-UK Biobank individuals .”As suggested by the reviewer, we have moved the results of the Okbay et al., PRS to the Supplementary Information (Supplementary File 5).weighted polygenic risk scores in a sibling between/within design. In contrast, our design doesn’t use siblings, and we have also conducted analyses using both weighted and unweighted polygenic risk scores. Unweighted scores should not be influenced by the sort of biases that Fletcher et al., describe.The Fletcher et al., (2021) study (which it is important to note at this stage is only a pre-print and has not been peer-reviewed) involves using Positioning among prior workThe authors could spell out more for readers their answer to the 'big picture' question of why it is useful to distinguish pre- and post-natal maternal effects, instead of just saying it's a natural question (see Introduction). Also in the introduction, it does not seem accurate to say that partitioning variation could yield mechanistic insights. Although the current contribution is very valuable, don't we need different kinds of designs and measures to understand mechanisms? In this regard, the authors should discuss the merits of their study compared to that of Armstrong-Carter et al. That study does not offer a principled way to separate pre- and post-natal effects, but it does try to work out which kinds of maternal phenotypes are involved in so-called pre-natal genetic nurture effects captured by EA PGS.We have changed the last two sentences of the first paragraph of the introduction to read:“Given the increasing number of variants identified in GWAS that exhibit robust maternal genetic effects, a natural question to ask is whether these loci exert their effects on offspring phenotypes through intrauterine mechanisms, the postnatal environment, or both. Indeed, resolving maternal effects into prenatal and postnatal sources of variation could be a valuable first step in eventually elucidating the underlying mechanisms behind these associations , directing investigators to where they should focus their attention, and in the case of disease-related phenotypes, yielding potentially important information regarding the optimal timing of interventions. For example, the demonstration of maternal prenatal effects on offspring IQ/educational attainment, suggests that if the mediating factors that were responsible could be identified, then improvements in the prenatal care of mothers and their unborn babies which target these factors, could yield useful increases in offspring IQ/educational attainment.”We have also added the following sentences to the discussion:“Whilst our method does not provide explicit mechanistic insight into the reason for the existence of maternal genetic effects , follow up studies could help elucidate these mechanisms by e.g. examining the association between maternal PRS and different pre- and postnatal maternal phenotypes, and performing mediation and Mendelian randomization analyses .”The authors should also engage more with other studies to clarify the novel aspects of their contribution. They describe in the Discussion the Domingue and Fletcher (2020) paper, but more relevant is Cheesman et al.,’s (2020) study design using the nonadopted-adopted polygenic score comparison in UKBB to estimate post-natal parental indirect genetic effects. Demange et al., (2021) estimated pre-natal parental indirect genetic effects by comparing estimates from adoption and sibling designs . Although this was for a non-cognitive skills polygenic score and not EA or BW, it is worth discussing their approach and comparing against their estimates. The Demange et al., approach means that estimates of pre-natal maternal genetic effects may also include assortative mating and population stratification. There is a general paragraph on AM in the Discussion, but how do the authors think that AM and popstrat will load in their model? Recent evidence from UKBB suggests that it is important to consider the role of population stratification particularly when studying EA .In order to discuss the Cheesman et al., (2020) and Demange et al., (2021) results in relation to our findings, we have added the following text to the Discussion section:“We are also not the first to have used adopted individuals in the UK Biobank to estimate the contribution of indirect genetic effects to phenotypic variability. Cheesman et al., (2020) contrasted adopted and non-adopted individuals in the UK Biobank to investigate evidence for indirect genetic effects on educational attainment and the existence of gene-environment correlation. The authors found that a genome-wide PRS for educational attainment was more strongly associated with educational attainment in non-adopted compared to adopted individuals consistent with the existence of indirect genetic effects on educational attainment. Likewise, G-REML estimates of SNP heritability were also lower in adopted individuals compared to non-adopted individuals .In a previous study of cognitive and non-cognitive effects on educational attainment, Demange et al., (2021) used three different sorts of study design to estimate the contribution of indirect genetic effects on educational attainment. They estimated indirect genetic effects by comparing between family and within family genetic effects in sibling pairs , by estimating the effect of non-transmitted parental alleles on offspring phenotype in parent-offspring trios, and by computing the difference in PRS associations between adopted and non-adopted individuals. In general, the authors found that estimates of indirect effects using the adoption study design were lower than those produced by the other two models. They interpreted this as being a consequence of the adoption study methodology not capturing the impact of prenatal maternal genetic effects  in contrast to the two other study designs. The present study explicitly capitalizes on differences between adopted and non-adopted individuals in their pattern of genotype-trait covariances to estimate the relative size of pre- and postnatal maternal genetic effects and to provide formal statistical tests for their presence. Indeed, both Demange et al.,’s (2021) and our findings are consistent with the existence of prenatal effects on educational attainment .”In order to discuss the potential impact of population stratification and assortment on our model, we ran some basic simulations to gain intuition for their likely effect on our model (not shown), and have included the following text in the discussion:2,6. It is possible that our basic model could be extended in a similar fashion to incorporate the effect of assortment and estimate some of these effects also.“We have also not modelled the complex effects of assortative mating in our SEM other than including covariance terms between maternal and paternal genotypes and assuming equal genetic variances in parents and their offspring under random mating . Positive assortment induces a number of complications when attempting to decompose the offspring phenotypic variance into its constituent sources of variation, including increasing homozygosity and the genetic variance at loci for the trait undergoing assortment relative to that expected under Hardy-Weinberg equilibrium, and inducing correlations between assorting loci across the rest of the genome both within and between individuals in the same family. Spousal correlations for phenotypes  and PRS  in complete parent-offspring trios in the UK Biobank suggest that assortative mating is likely present for educational attainment, and potentially to a lesser degree for (phenotypes correlated with) birthweight. Recent work by Balboa et al., (2021) and Kim et al., (2021) have shown how PRS of transmitted and non-transmitted alleles in parent-offspring trios can be used to estimate direct and indirect genetic effects on offspring phenotype and the variation attributable to the environmental influence of parents on offspring under phenotypic assortment Also relevant to this discussion is a series of data simulations performed by Demange et al., (2021) who found that estimates of indirect genetic effects obtained in adoption designs  were less biased by assortative mating and population stratification than estimates of indirect genetic effects obtained in biologically related parent-offspring trio designs . In the case of population stratification, the intuition behind this observation is that the contaminating effects of substructure are present in both adopted and non-adopted individuals. This contamination cancels out when the PRS-trait association in adopted individuals is subtracted from the PRS-trait association in non-adopted individuals. However, this is not the case in parent-offspring trios, where estimates of indirect genetic effects remain contaminated.In the context of our SEM, we expect that unmodelled population stratification will bias estimates of maternal prenatal and postnatal effects away from the null since population stratification will increase the covariance between maternal genotype and offspring phenotype, as well as the covariance between offspring genotype and phenotype in adopted and non-adopted individuals. Because we have limited our empirical analyses to individuals of white European ancestry and residualized the phenotypes for the first five genetic principal components prior to analysis in the SEM, any influence due to population stratification is likely to have been minor in our empirical analyses in the UK Biobank. The influence of assortative mating on our model is more difficult to predict, but our limited exploration of this issue by simulation (data not shown) suggests that the effect of assortative mating on parameter estimates from our SEM is likely to be minor.”Misc.It is neat to have a negative control phenotype for post-natal genetic effects (birthweight). Can the authors try out a negative control for pre-natal genetic effects too? If the maternal pre-natal effect were significant for something paternal substance use, this would bolster the idea that relatedness among adoptees and their adoptive parents causes inflation of this estimate.We like the reviewer’s idea of investigating a control phenotype, but it is exceedingly difficult to think of a trait for which (a) there is confirmed evidence for maternal genetic effects, (b) the maternal genetic effects are so strong that we have adequate power to demonstrate and partition them in our sample, and (c) we can be confident that the maternal genetic effects are postnatal but not prenatal effects.That being said, we have hit upon the idea of using individual’s report of maternal hypertension as a control phenotype. In theory, an individual’s report of maternal hypertension should show  association with a maternal PRS for hypertension in biological families  and with offspring PRS . In contrast, in adoptive families (G5-G7), and assuming adoptive parents are not biologically related to their adopted children, we would expect no association between reports of maternal hypertension (in adoptive mothers) and their adopted offspring’s PRS. Under these conditions, our SEM should “correctly” partition the maternal genetic effect entirely into a postnatal maternal genetic component. In contrast, if adopted individuals are biologically related to their adoptive mothers, then this will tend to lead to spurious associations between adopted individuals’ PRS and (adopted mothers’) maternal hypertension. Within the context of our SEM, this will increase evidence for a prenatal maternal genetic effect and decrease evidence for a postnatal maternal genetic effect. In other words, the degree to which our SEM produces evidence for a prenatal maternal genetic effect for individual’s report of maternal hypertension provides evidence consistent with the possibility that at least some adoptive individuals in the UK Biobank are biologically related to their adoptive parents.The results of our analyses are as follows, see In summary, estimates for the fetal and paternal genetic effects are what we would expect (i.e. close to zero). In contrast, the coefficients for the maternal genetic effects are larger and in the case of the pre-natal maternal genetic effect, potentially consistent with at least a proportion of adopted individuals in the UK Biobank being biologically related to their adoptive parents. However, a complication of this analysis is that self-reported maternal hypertension is a dichotomous, rather than quantitative phenotype. The corollary is that whilst we expect the point estimates of the parameters to be consistent estimates of the true population values in a large sample such as the UK Biobank , the standard errors and tests of significance will not be appropriate for this phenotype. We have spoken extensively with the developers of OpenMx  about the possibility of fitting the SEM as an ordinal model, but the developers have told us that this is not computationally feasible at the present time. For this reason, our preference is not to include these analyses in the published manuscript, but we have included them here for the reviewers’ information and in support of our contention that there is likely to be some degree of relatedness between adopted individuals and their adoptive parents in the UK Biobank.The use of breastfeeding data to identify those who were not adopted by relatives is smart. It would be worth checking how selected this sample is for some key traits . Also, could more information be leveraged to increase accuracy? Many participants just don’t know the answer to that question, could have remembered incorrectly, and wetnurses  also used to be common. Adoptions in later cohorts might have become more ‘organized’ (happening earlier in life and involving non-relatives). Perhaps it’s worth cutting out some of the older adoptees? The authors could also try limiting the sample further to those who also report their birthweight.Adopted individuals who knew their birthweight were more educated on average than those who did not, but did not differ on average in their birthweight.Following the reviewer’s suggestion, we stratified adopted individuals into those above and below age 60 and re-ran the analysis for EA. The results suggests that the deflation in post-natal maternal effects comes from adoptions in later cohorts, see It is possible that more recent adoptions are more likely to involve biological relatives of the adopted individual. We also removed individuals who reported their birthweight in addition to breastfeeding data. However, this only removed a further 223 adopted individuals, and did not appreciably affect our results. Given that the analyses have not materially affected our interpretation of the results, we have elected not to include them in the main manuscript.Was a relatedness cut-off used to ensure that each family was independent?rd degree of relatives defined by the pair-wise kinship >0.044 . In our original analysis, families in each of the 7 groups were not related based on this cut-off. However, we did not remove families that were related across groups. We have now removed all related families from our analysis. We maximized the number of families from adopted singletons (G5), followed by trios (G1), mother-offspring duos (G2), and then father-offspring duos (G3). Results from the new analysis are similar to our original analysis and do not affect our conclusions.We would like to thank the reviewer for bringing this to our attention. The relatedness cut-off was set at 3The authors could cite Wang et al., (2021) when saying that it is unfeasible for paternal genetic effects to be so much bigger than maternal effects – this meta-analysis found equal effects of paternal and maternal EA PGS on offspring educational outcomes.similar effect sizes for maternal and paternal genetic effects . Nevertheless, we appreciate that equal paternal and maternal effects on offspring educational attainment implies the absence of maternal prenatal effects. We have therefore at the reviewer’s suggestion included the Wang et al., reference and modified some of the text in the discussion:We thank the reviewer for this suggestion- however, our analyses actually showed “The absence of a significant postnatal maternal genetic effect on offspring educational attainment was surprising given that maternal genetic effects should be mediated through maternal educational attainment, and therefore should mostly involve postnatal pathways , and previous studies have shown that the effect of paternal and maternal PRS on educational attainment are roughly similar  i.e. suggesting the absence of prenatal maternal genetic effects.”Reviewer #2 (Recommendations for the authors):I have no other specific recommendations. I think the approach and code provided are sound. I would mostly appreciate that the authors consider adding more details on the limitations (and possible extensions) of their approach regarding gene-environment interplay (both gene-environment moderation and gene-environment correlation).We have added this information to Supplementary File 6 which discusses gene-environment interaction, gene-environment correlation and other limitations.


Three ecotypes of rapeseed, winter, spring, and semi-winter, have been formed to enable the plant to adapt to different geographic areas. Although several major loci had been found to contribute to the flowering divergence, the genomic footprints and associated dynamic plant architecture in the vegetative growth stage underlying the ecotype divergence remain largely unknown in rapeseed. Here, a set of 41 dynamic i-traits and 30 growth-related traits were obtained by high-throughput phenotyping of 171 diverse rapeseed accessions. Large phenotypic variation and high broad-sense heritability were observed for these i-traits across all developmental stages. Of these, 19 i-traits were identified to contribute to the divergence of three ecotypes using random forest model of machine learning approach, and could serve as biomarkers to predict the ecotype. Furthermore, we analyzed genomic variations of the population, QTL information of all dynamic i-traits, and genomic basis of the ecotype differentiation. It was found that 213, 237, and 184 QTLs responsible for the differentiated i-traits overlapped with the signals of ecotype divergence between winter and spring, winter and semi-winter, and spring and semi-winter, respectively. Of which, there were four common divergent regions between winter and spring/semi-winter and the strongest divergent regions between spring and semi-winter were found to overlap with the dynamic QTLs responsible for the differentiated i-traits at multiple growth stages. Our study provides important insights into the divergence of plant architecture in the vegetative growth stage among the three ecotypes, which was contributed to by the genetic differentiation, and might contribute to environmental adaption and yield improvement. Crop species undergo multi−staged domestication from a particular center and then expand to a wider geographical distribution . Long-teB. napus) is a relatively new species and originates from interspecific hybridization between the ancestor of European turnip  and the common ancestor of kohlrabi, cauliflower, broccoli, and Chinese kale  less than 7500 years ago , single gene haplotype analysis, and transgenic validation  is a set of computational approaches to find predictive patterns in data and has been widely used to identify biomarkers for subspecies discrimination and yield heterosis prediction . Previouhttp://plantphenomics.hzau.edu.cn/usercrop/Rape/image/2014-2015-GWAS, selecting of “2014-2015-GWAS”). A set of 41 dynamic i-traits (18 i-traits in top view and 23 i-traits in side view) and 30 growth-related traits reflecting the growth speed were obtained using the image analysis pipeline, described previously , random forest (RF), support vector machine (SVM), multilayer perceptron (MLP), and convolutional neural network (CNN), were performed to distinguish different ecotypes, based on the 18 i-traits in top view from T1 to T11 and 23 i-traits in side view from T7 to T11, respectively. DCA was performed by IBM SPSS 20.0. RF, SVM, MLP, and CNN were built by Python3.6. The detailed parameters were as follows: (1) Bayesian basis DCA expression was established to distinguish different ecotypes and i-traits with high contribution which were acquired with stepwise establishment of discriminant expressions. (2) CART algorithm was used to split nodes in building RF. (3) SVM with radial basis kernel was built for a best decision edge with the highest confidence between ecotypes, which was searched for by adjusting the slack variable and penalty factor C. (4) Multilayer perceptron (MLP) and convolutional neural network (CNN) were activated by softmax on the last layer. For each model, the i-traits were divided into training sets and testing sets and the capability of the model was evaluated by the performance using the test set. Finally, the i-traits excavated by RF model with high contribution to divergence of ecotype were used for subsequent analysis.https://github.com//hanzhanggit//StackGAN) was used to construct the rapeseed images. StackGANv1 was built by python 2.7 with tensorflow 0.12 and accelerated with GEFORCE RTX2080 SUPER. Stage I (i-traits to images) and stage II (images to images) were trained 800 times and 200 times, respectively. After the simulated images were obtained by the StackGANv1, three parameters, MSE, SSIM, and PSNR, were calculated to evaluate the image similarity between real and simulated images.Based on the i-traits excavated by RF model with high contribution to divergence, a text-to-images model StackGANv1 (http://cbi.hzau.edu.cn/bnapus/index.php).Sequence data (PE100 reads) of the 171 rapeseed lines were obtained from our previous study . The var2r value between two SNPs in each window and plotted using custom R script.To build a phylogenetic tree and perform principal component analysis, a subset of 131,319 SNPs was selected randomly with a step of 5-kb window across the genome. These SNPs were distributed evenly among the genome and better reflect population structure and demography. The phylogenetic tree was constructed using MEGA X software , with thπ), measuring the degree of variability within a population, was calculated for 100-kb sliding windows with a step size of 10 kb using the VCFtools (STF) was estimated for 100-kb sliding windows with a step size of 10 kb using the PopGenome (https://popgenome.weebly.com/). The average STF from all sliding windows was used to reflect the degree of population divergence among different ecotypes. Sliding windows with the top 1% STF value were selected as putative significant differentiated windows. Of these, the top 1% had STF≥0.72, 0.66, and 0.5 for W vs S, W vs SW, and S vs SW, respectively. Neighboring windows, the distance <20 kb, were then merged into one region. These regions were regarded as highly diverged across ecotype.Nucleotide diversity  was set as the significance threshold. The GWAS signals of all traits was identified according to the following two steps. Firstly, all P value of SNPs responsible for each i-trait were used as a query of function “clump” of PLINK software. The function was used to obtain the independent peak SNPs of each i-trait with a sliding window based on the decay of LD. The parameter of PLINK was –clump-p1 8.67×10-7 –clump-p2 1×10-5 –clump-r2 0.3 –clump-kb 500 –clump-allow-overlap. The QTL intervals for each i-trait were defined as the minimum and the maximum position of the SNPs meeting these criteria. Secondly, all QTLs with overlapping intervals were categorized as nonredundant QTLs.Genome-wide association study (GWAS) was performed using a mixed linear model (MLM) in genome-wide efficient mixed model association (GEMMA) software, such as that described previously . The eff2H) of the 41 dynamic i-traits. The magnitude of diversity varied drastically among different i-traits in the rapeseed accessions at each time point , random forest (RF), support vector machine (SVM), multilayer perceptron (MLP), and convolutional neural network (CNN), were established using i-traits in top view from T1 to T11 and side view from T7 to T11, respectively. The classification accuracy of different models through all dynamic time points were shown in It would be beneficial if the ecotype could be distinguished in early growth stage. Notably, RF with the contributed i-traits was established and displayed an impressive accuracy at the first inspection stage of top-view (T1) and side-view (T7); 78.0% samples were correctly classified in T1 and 81.7% samples were correctly classified in T7 D. A subThe plant architecture reflected by the contributed i-traits might be associated with the environmental adaption and yield improvement among the ecotypes, which are the two important breeding processes in rapeseed . Of thesThe 171 rapeseed accessions consisted of 14 W ecotypes, 24 S ecotypes, and 133 SW ecotypes. These lines had a wide geographic distribution, including Europe , Canada, Australia, China, and Japan  and vari-3) was higher than that of S (π=1.56×10-3) and W (π=1.17×10-3) (B. rapa contribute more to A genome of B. napus than B. oleracea to C genome of B. napus diversity (2r) occurred at 20.6 kb in our population, with 52 kb in W ecotype, 23.5 kb in S ecotype, and 18.4 kb in SW ecotype  of 171 accessions using randomly selected SNP markers. The neighbor-joining tree revealed the accession within W, S, and SW ecotype clustered each other, (17×10-3) , which siversity . The decersity r2 occurredersity r2 occurredersity r2 occurredersity r2 occurred ecotype .χ2-test, p = 0.95).We performed GWAS using a set of 5,324,005 SNPs, which allowed us to identify the genetic basis of 41 dynamic i-traits and 30 growth-related traits. We detected a total of 4,088 loci associated with 66 traits across different time points, including 1,421, 1,753, and 914 loci associated with i-traits in top view, i-traits in side view, and growth-related traits, respectively , which sSTF) across different ecotypes. There were 78, 73, and 79 such regions with an STF value greater than 0.72, 0.67, and 0.50 between W and S ecotypes, W and SW ecotypes, and S and SW ecotypes, respectively  can be found in the article/The datasets presented in this study can be found in HF, CG, HL, and WY performed the experiments, analyzed the data, and wrote the manuscript. ZL, GC, YG, QZ, ZG, and JW assisted in the experiment performance, data analysis, and database information construction. KL, HL, and WY supervised the project and designed the research. All authors contributed to the article and approved the submitted version.This work was supported by grants from the National Key Research and Development Program (2020YFD1000904-1-3), National Natural Science Foundation of China , Key projects of Natural Science Foundation of Hubei Province (2021CFA059), Fundamental Research Funds for the Central Universities , and the HZAU-AGIS Cooperation Fund (SZYJY2022014).The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The koala, one of the most iconic Australian wildlife species, is facing several concomitant threats that are driving population declines. Some threats are well known and have clear methods of prevention , whereas others are less easily addressed. One of the major current threats to koalas is chlamydial disease, which can have major impacts on individual survival and reproduction rates and can translate into population declines. Effective management strategies for the disease in the wild are currently lacking, and, to date, we know little about the determinants of individual susceptibility to disease. Here, we investigated the genetic basis of variation in susceptibility to chlamydia using one of the most intensively studied wild koala populations. We combined data from veterinary examinations, chlamydia testing, genetic sampling and movement monitoring. Out of our sample of 342 wild koalas, 60 were found to have chlamydia. Using genotype information on 5007 SNPs to investigate the role of genetic variation in determining disease status, we found no evidence of inbreeding depression, but a heritability of 0.11 (95% CI: 0.06–0.23) for the probability that koalas had chlamydia. Heritability of susceptibility to chlamydia could be relevant for future disease management, as it suggests adaptive potential for the population. Whilst the bushfires decimated large areas of koala habitat, the bacterial pathogen Chlamydia has been identified as a major threat to their survival . The data set included some joeys (N = 4) because dependent joeys have been found to be infected by chlamydia as young as 9 months old , and described in detail in  and scientific purposes permits .2.2Chlamydia pecorum and C. pneumoniae), C. pecorum is consistently more prevalent  and more pathogenic  assessed for clinical signs of chlamydial disease. Tests for C. pecorum were conducted using either quantitative real‐time PCR (qPCR) targeting a fragment of the C. pecorum 16 s rRNA gene . We therefore opted to use whether koalas tested positive (“chlamydia status”) as our response variable in all analyses.Of the two species of chlamydia that infect koalas , we selected to only use chlamydia status at their first capture. This was because during the project individual koalas were treated for any illness or injury they presented at veterinary examinations , and some individuals were also included in a chlamydia vaccination trial  resulting in repeated measures of disease status gathered at scheduled veterinary examinations , linkage disequilibrium (r2 < .4) in Cervus 3.0.7 as per Schultz et al.  as for pairwise relatedness, we calculated “internal relatedness” (IR) for each individual . The average number of sightings per individual was 186 (interquartile range = 48–346). Utilization distributions were estimated using the adehabitatHR package , and all models were fit with the following fixed effects: age in years at time of capture, season in which the individual was caught (breeding vs. nonbreeding), sex, IR, and the interaction between age and IR. The effect of IR tested for evidence for inbreeding depression, predicting that if there was evidence for inbreeding depression, more inbred individuals would have poorer health outcomes and would therefore be more likely to test positive for C. pecorum. We also included an interaction between IR and age to test whether the effect of inbreeding changes with age  using the R package inbreedR to estimate identity disequilibrium (N = 342), and decomposed variance not accounted for by the fixed effects into two components: additive genetic effects and shared‐environment effects. Additive genetic effects were estimated by fitting the relatedness matrix as a covariance matrix. This was therefore an ‘animal model’, which extends linear mixed effects models to incorporate relatedness information, and partitions phenotypic variance into additive genetic effects and other sources of variance . The observed spatial overlap matrix was positive definite and therefore did not require transformation.The first model we fitted used the full data set including all individuals for which we had disease, genetic, and spatial data . This is necessary because heritability estimates may be inflated when maternal effects are not accounted for . Although analytically possible, we considered this reduced sample size too small and lacking in statistical power to fully partition variance in disease status into additive genetic effects, maternal effects, and shared environment effects. Instead, we aimed to (1) estimate the extent of maternal effect variance, and (2) ensure that our heritability estimates were not inflated by potential mother‐offspring transmission of disease. To do this, we again fitted the model with the relatedness matrix (as explained above), but here included maternal ID as an additional random effect (instead of the shared environment effect). The maternal ID term estimates the phenotypic variance that is attributed to individuals sharing the same mother, over and above that due to shared additive genetic effects  as the amount of additive genetic variance divided by the total phenotypic variance . Because the model was fitted with binary data, all variance estimates of the model were calculated on a latent scale. It is possible to measure heritability on either the latent trait scale or the observed data‐scale, the selection of which depends on inferences being made  which may influence the probability of contracting chlamydia. To convert parameter estimates, we used the qgglmm package in R  and 187 females (of which three were joeys <1 year old caught with their mothers). We were able to detect maternities for 195 individuals, who were the offspring of 106 unique mothers.FIS, was estimated as 0.196. The identity disequilibrium proxy (g2) in our 5007 SNP data set differed significantly from zero , where permutations = 1000 and bootstraps = 1000. This indicated that our data set met the requirements of variance between individuals in levels of inbreeding, which is required for detecting if there is inbreeding depression in a population. Accordingly, IR varied substantially between individuals, ranging from a minimum estimate of −0.39  to 0.38   was estimated as 0.278, and the population average inbreeding coefficient, C. pecorum  on both latent and observed data scales, whereby the posterior distribution was clearly different from zero on both scales  for the probability of being diseased was estimated at 0.57 on the latent scale , and 0.11 on the observed scale . The posterior distribution for VS (measured using the home range overlap matrix) was very low and bordered zero on both the latent and observed data scales . Finally, VA estimates did not vary qualitatively between models with and without the home range overlap matrix, suggesting that its inclusion did not affect our reported estimates of h2 (see Table We found no evidence that the probability of testing positive for N = 195), we found only a small maternal effect variance (VME) in the probability of testing positive for C. pecorum. More specifically, the posterior mode of VME was estimated as 0.005 on the latent scale, and <0.001 on the observed data‐scale, and the lower tail of the posterior distribution bordered zero on both scales (see Table ME), with no indication that ICCME was statistically different from zero , we found that VME did not differ  to that estimated when fitting both simultaneously . Together, this suggests that maternal effects explained little to none of the phenotypic variance in the probability of individuals testing positive for C. pecorum. Finally, estimates for VA and for h2 did not differ qualitatively between the model containing the maternal effect versus without, suggesting that our reported heritability estimates . We discuss these results in more detail below.Our results showed that aging and breeding season increased the probability of testing positive for 4.1Inbreeding depression can be defined as heterozygosity‐fitness correlations , as calculated in this study, can be used to predict the response to selection across generations (Walsh & Lynch, Narrow sense heritability (There are several possible reasons for the maintenance of genetic variance in disease susceptibility in this population. First, genetic variance may be maintained through antagonistic pleiotropy with traits associated with other fitness components (Cotter et al., 4.3Management of the threat of chlamydia to koalas has been difficult thus far: vaccine development is promising, but still a work in progress (Khan et al., Disease management is one of the greatest challenges of wildlife management. It is hard to gain knowledge of diseases in the wild, although noninvasive methods are promising. For example, surveillance can be enhanced by the use of detection dogs and pathogen detection from scats (for examples with koalas and chlamydia see (Cristescu et al., Romane H. Cristescu, Kasha Strickland and Céline H. Frère conceived and designed the research; Deidre de Villiers collected data; Anthony J. Schultz and Kasha Strickland analysed SNP data to generate relatedness and internal relatedness information; Kasha Strickland analysed the data, with input from Loeske E. B. Kruuk and Céline H. Frère; Kasha Strickland and Romane H. Cristescu wrote the manuscript, and all authors contributed to reviewing and editing.All authors declare no conflict of interests.Appendix S1Click here for additional data file.


The Markhoz goat is the only breed that can produce high-quality fiber called mohair in Iran; however, the size of its population has faced a dramatic decline during the last decades, mainly due to the reluctance of farmers to rear Markhoz goats caused by a reduction in goat production income. Litter size at birth (LSB) and weaning (LSW) are two economically important reproductive traits for local goat breeders and have the potential of increasing the population growth rate. The present study was aimed to identify possible genomic regions that are associated with LSB and LSW in Markhoz goats using a genome-wide association study (GWAS).To this end, 136 Markhoz goats with record(s) of kidding were selected for GWAS using the Illumina Caprine 50K bead chip. The individual breeding values (BV) of available LSB and LSW records estimated under an animal mixed model were used as the dependent variable in the GWAS, thereby incorporating repeated categorical variables of litter size.p < 0.05) with LSB after multiple testing correction under a Bayesian-information and Linkage-disequilibrium Iteratively Nested Keyway (BLINK) model. Least-square analysis was performed to investigate the effects of detected genotypes on LSB. Ultimately, the GWAS results introduced six candidate genes, including GABRA5, AKAP13, SV2B, PPP1R1C, SSFA2 and TRNAS-GCU in a 100 kb adjacent region of the identified SNPs. Previous studies proposed functional roles of GABRA5 and AKAP13 genes in reproductive processes; however, the role of other candidate genes in reproduction is not clear.Four SNPs on chromosomes 2, 20 and 21 were identified to be significantly associated (FDR These findings warrant further investigation for use in marker-assisted selection programs in Markhoz goats. Throughout history, goats have been a primary production species for mankind due to their ability to withstand variable and harsh environmental conditions and their desirable production of meat, milk, fiber, and skin. Improving economic traits in goats, such as prolificacy and viability, can be very profitable for rural people in countries with low-quality grazing lands, where goat farming is one of the primary sources of income.Markhoz goats are the only mohair producing breed in Iran with different coat colors such as white, black, and various shades of brown . The popGDF9, BMP15, GnRH1, KISS1, KITLG, NGF, POU1F1, PRLR and promoter of miR-9 gene in various breeds of goats (Litter size at birth (LSB) and litter size at weaning (LSW) are two reproductive traits that are known to be controlled by several underlying genes in goats . Specifiof goats –11. Howeof goats ] for varof goats , body moof goats , conformof goats . Similarof goats –19. Howeof goats  and no GDetection of significantly associated SNPs with LSB and LSW in goat would lead to enhanced efficacy of animal selection in breeding strategies by reducing the cost and time required to raise and phenotypically characterize animals as they mature. As complex traits, LSB and LSW are known to be controlled by many genes with variants having a small effect. Hence, the possibility of incorporating genetic variants into selection strategies will likely accelerate the rate of improvement of such reproductive traits as compared to traditional phenotypic selection. The purpose of this study was to conduct GWAS to detect possible genomic regions and variants associated with LSB and LSW in Markhoz goats, with the potential of applying results in genomic selection.n = 184) existing at the Markhoz Goat Performance Testing Station in Sanandaj, Kurdistan, Iran, were selected for inclusion in the study. The herd is reared under a semi-intensive management system, in which animals graze on natural pastures from spring to early autumn and fed a diet consisting of alfalfa and wheat straw for the rest of the year. At the age of 16–18 months, does are mated for the first time. The kidding season starts in late winter and ends in early spring. Litter size at birth (LSB) and litter size at weaning (LSW) were the two reproductive traits evaluated. LSB described the number of live kids born to the doe. LSW described the number of live kids at weaning for each doe, typically evaluating kids at 22–27 weeks old. LSB and LSW were categorical variables potentially repeated per doe as they aged and had subsequent litters.All female goats  for LSB and LSW were generated for use in the GWAS to capture the repeated categorical values of LSB and LSW. A total of 3,410 litter size records for the Markhoz goats were collected from 1994 to 2019 for use in predicting breeding values. Accuracy of EBVs is based on the amount of performance information available on the animal and its close relatives. Selection using EBVs is more accurate, especially for low heritable traits like litter size, which allows for faster genetic gain compared to mass selection using phenotypes. Breeding values have the advantage that they are free of systematic environmental effects on measured phenotypes, as these effects are considered in the statistical model used for the estimation of EBVs. Additionally, they reflect the genetic makeup more accurately because they do not solely rely on own records but include information from all measured relatives. The pedigree file included 5,396 animals with 1,533 dams and 252 sires. The number of founders, individuals with progeny, and individuals without progeny were 343, 1,785 and 3,611, respectively. Breeding values for each individual was estimated, applying a repeatability threshold animal model using ASReml 2.0  as follo2EDTA as an anticoagulant were used to collect whole blood (5 ml) samples from the jugular vein of goats. Samples were immediately stored at −20°C until DNA extraction. A standard Phenol-Chloroform DNA extraction method was utilized for extracting genomic DNA . Vacutainer tubes containing Komic DNA . The IllFigure 2). The BLINK (r2 > 0.7) with the most significant marker are excluded from the analysis and the maximum likelihood of a random effect model is approximated by using the Bayesian Information Content (BIC) of a fixed-effects model. By applying that, the most significant markers will be selected among all markers that remained after LD exclusion and then used as cofactors in the model to test all markers across the genome. Because of the abovementioned reasons, the BLINK method had improved statistical power and better control on false positives in comparison with kinship-based methods , Mixed Linear Model (MLM), Multi Locus Mixed Model (MLMM), Compressed Mixed Linear Model (CMLM), Enriched Compressed Mixed Linear Model (ECMLM), Factored spectrally transformed Linear Mixed Model (Fast-LMM), Settlement of MLM Under Progressively Exclusive Relationship (SUPER), Fixed and random model Circulating Probability Unification (FarmCPU), Efficient Mixed-Model Association (EMMA), Efficient Mixed Model Association eXpedited (EMMAX) and BLINK were performed to find the best model for fitting PBV LSB and LSW data  adjusted an plots . The genan plots .Least-square analyses were conducted to investigate the negative/positive effects of detected genotypes on studied traits using PROC MIXED of SAS v8.2 software . PhenotyCapra hircus ARS1 assembly . Finally, gene databases, such as Genecards, National Center for Biotechnology Information (NCBI), Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) were scrutinized to find the functions and pathway of identified genes.A region with a distance of 100 kbp up-stream and 100 kbp down-stream of significant SNPs was explored to detect the nearest gene using assembly  in the NThe descriptive statistics and predicted breeding values for LSB and LSW traits are presented in p-value = 1.35e−07), chromosome 20  and chromosome 21  were identified for PBV LSB . Furthermore, analysis of the genotypic correlation between these traits showed a strong genetic relationship of 0.725 (P < 0.01).The phenotypic correlation between LSB and LSW was 0.697 . The detected genes harboring SNPs, their distance from SNPs and the roles of each gene are presented in Six candidate genes were found within the 100 kb windows up- and down-stream of the identified SNPs located on the genome of In Iran, the Markhoz goat is the only breed that can produce mohair in black, gray, white and varying shades of brown color. The fiber obtained from the Markhoz goat is both culturally and socially important for Kurdish people costumes . Thus, tGC = 1.01). In contrast, the results of the GWAS failed to reveal significant association with the PBV of LSW  were included in the model to correct for population structure. A total of four SNPs, found on chromosomes 2, 20, and 21, were significantly associated with the PBV of LSB . The Q–QV of LSW .GABRA5 gene. GABRA5 encodes a 462 amino acid protein of the GABA receptors family known as GABA-A. It has been suggested that GABA acts at GABA-A receptors in the central and peripheral nervous systems as the major inhibitory neurotransmitter  in the regulation of reproductive processes. For instance, GABA increases Kiss1 expression by affecting GABA-A receptors in early embryo development. In addition, at the time of ovulation in adults, a main double excitatory input to (GnRH) neurons is provided by the AVPV/PeN neuron population, leading to the expression of GABA and kisspeptin.The most significantly associated variant (rs268288690) with the PBV of LSB is located within the nsmitter . Watanabnsmitter  investigo et al.  demonstrAKAP13 gene. AKAP13 is a member of the AKAP family which is a structurally diverse protein and is involved in the binding process to the regulatory subunit of protein kinase A (PKA) and confining the holoenzyme to discrete locations within the cell. Luconi et al.  is located 99,644 bp upstream of the i et al.  reported oocytes .PPP1R1C, SV2B, TRNAS-GCU and SSFA2 genes, there is no evidence to suspect a causative association with the LSB trait in our study. Whereas, both GABRA5 and AKAP13, are the more likely genes potentially influencing LSB based on their influence of reproductive processes.Based on the functional role of p < 0.01) so that goats having two copies of the mutated allele (GG genotype) had more kids within the litter than those carrying one or no copy of the mutated allele (AG and AA genotypes). The GG genotype of rs268258357 SNP indicated the highest litter size (1.822 ± 0.161) among all identified genotypes. Similarly, rs268267345 SNP also had a positive impact on litter size. These findings revealed that only rs268256209 SNP negatively affected litter size, while the other three SNPs identified from GWAS positively influenced the number of kids in Markhoz goats.The results of least-square analyses showed that rs268288690 SNP leads to a significant increase in litter size in Markhoz goats  and pedigree  records, while only 136 genotyped individuals were used in the LDAK method to predict genomic heritability. Besides, much of the heritability of traits may not be accounted for by rare, low-frequency genetic variants, known as the missing heritability problem .The SNP genotype data and EBVs for LSB and LSW are available in the Zenodo repository . Written informed consent was obtained from the owners for the participation of their animals in this study.PM performed data curation, formal analysis, visualization, methodology, and writing—original draft. AR and JR managed the project and contributed to writing— review and editing manuscript. AN-G conducted data curation, interpreted the results and contributed to review and editing manuscript. MR was responsible for data visualization. HH contributed to review and editing manuscript and provided SNP data and financial support. All authors contributed to the article and approved the submitted version.Funding for the Markhoz goats' genotyping and part of the analysis has been supported by the laboratory of HH at Cornell University.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Long-term selection should lead to reduction in heritability, due to fixation of positive alleles. Selection on multiple traits should lead to negative genetic correlations because alleles with positive effects on both traits will respond first to selection, leaving alleles with opposing effects. Efficient selection for milk production traits began in Israel in the 1980s, and selection for female fertility in 2000. Introduction of genomic selection increased rates of genetic gain. Many studies have shown the negative relationships between milk production traits and female fertility. Phenotypic and genetic changes for female fertility and production traits in the Israeli dairy cattle population over the last three decades were studied in order to determine if long-term selection has resulted in reduced heritability and increased negative genetic correlations. Heritabilities were 0.4 for protein production and 0.05 for conception status. The genetic correlation between conception status and protein yield was −0.38. Heritabilities decreased with increase in parity for protein but remained the same for conception status. For milk, fat, and protein production and female fertility, heritabilities increased or stayed the same over the entire period of 30 years. There is no indication that a selection plateau is imminent for dairy cattle.Phenotypic and genetic changes for female fertility and production traits in the Israeli Holstein population over the last three decades were studied in order to determine if long term selection has resulted in reduced heritability and negative genetic correlations. Annual means for conception status, defined as the inverse of the number of inseminations to conception in percent, decreased from 55.6 for cows born in 1983 to 46.5 for cows born in 2018. Mean estimated breeding values increased by 1.8% for cow born in 1981 to cows born in 2018. Phenotypic records from 1988 to 2016 for the nine Israeli breeding index traits were divided into three time periods for multi-trait REML analysis by the individual animal model. For all traits, heritabilities increased or stayed the same for the later time periods. Heritability for conception status was 0.05. The first parity genetic correlation between conception status and protein yield was −0.38. Heritabilities decreased with the increase in parity for protein but remained the same for conception status. Realized genetic trends were greater than expected for cows born from 2008 through 2016 for somatic cell score, conception status and herd-life, and lower than expected for the production traits. In 1960 Falconer  by simulGenomic selection based on genotypes for thousands of genetic markers has been incorporated into nearly all commercial dairy cattle breeding programs over the last decade . In all Female fertility traits were first included in national breeding indexes by the Scandinavian countries in the 1970s. Female fertility was included in the total merit index for Norwegian dairy cattle since 1972 by considering the 56-d nonreturn rate in virgin heifers, that is, the fraction of cows with a first insemination that were not re-inseminated . GenomicMuch has been written about both the phenotypic and genetic economically negative correlation between milk production traits and female fertility, reviewed by ,11. NumeOne major problem with these studies, as noted by , is thatInsemination data in Israel is unique in that nearly all cows that are inseminated are vet-checked for pregnancy after 60 days . RoutineIn order to determine if long-term selection for fertility and production has in fact resulted in reduced heritability and more negative genetic correlations, we estimated the phenotypic and genetic changes for CS over the last three decades, and the environmental and genetic correlations among the traits included in the Israeli breeding index by the individual animal model, including CS and milk, fat, and protein production. Genetic and environmental variance components were computed for first parity for the nine index traits over the last 30 years, and for protein and CS for the first three parities over the last eight years. Genetic trends over the last decade were computed for all traits included in the Israeli breeding index, and the realized values were compared to the expected values derived from the principles of selection index. Finally, genome-wide association studies (GWAS) were performed for both protein production and CS, and correlations were computed between the marker effects.The seven data sets analyzed are described in The second data set included phenotypic records of cows born between 2008 and 2015 with valid first parity records for protein and CS. This data set was used to estimate variance components and genetic parameters by REML for protein and CS for parities 1 through 3. Genetic and environmental correlations were computed among the three parities for both traits. Both data sets were analyzed by the multi-trait individual animal model (IAM).The third and fourth data sets were used to compute genetic evaluations for the three milk production traits and CS, respectively, for all cows with valid records born from 1983 through 2018 by the multi-trait IAM, including valid records for parities 1 through 5. Data set 3 included only parities with valid records for all three milk production traits. Data set 5 included estimated breeding values (EBV) for the nine index traits from cows born between 2009 and 2018 and was used to compute realized genetic trends in the Israeli Holstein population. Data sets 6 and 7 included bulls with reliabilities >0.5 for protein and CS respectively, from the analyses of data sets 3 and 4, and genotypes for >40,000 SNPs. These two data sets were used for the GWAS analyses.Edits applied for all traits included in PD19 prior to genetic evaluation were as described previously ,16. All Variance components were estimated for data set 1 with the MTC program  and the Data sets 3 and 4, which included all valid records for cows born between 1983 and 2018, were analyzed by the multi-trait IAM. These models included fixed parity and HYS effects, as defined previously, in addition to the random additive genetic and residual effects. Records were pre-adjusted for birth and calving month and days open as described previously ,16. The jc) was computed as proposed by [jb = the index coefficient for trait j, jg = the genetic standard deviation for trait j, J = 9, the total number of traits, and “abs” denotes “absolute value”. The values of jb were derived from jg were derived from the REML analysis of data set 1 for cows born between 2008 and 2016.The contribution of each of the nine traits included in the PD19 selection index (posed by :(1)cj=abΦ) were computed using the following equation [b = the vector of breeding index coefficients for PD19, G = the genetic variance matrix among the 9 traits, and P = the phenotypic variance matrix, computed as the sum of the genetic and residual variance matrices. The G and P matrices were derived from the REML analysis of data set 1 for cows born between 2008 and 2016. The index coefficients for the Israeli breeding index are given in Φ replaced by the vector of realized gains, as derived from the analysis of data set 5. The selection intensity in equation [Realized genetic gains for the nine index traits were estimated from data set 5 as the linear regressions of the cows’ EBV for each trait on their birth dates. The vector of expected genetic changes over 10 years of selection on PD19 (equation :Φ = ibG/(b′Pb)0.5where i The genomic analysis included all Israeli Holstein bulls with genotypes born from 1991 with reliabilities >0.5 from the analyses of data sets 3 and 4. Of the 1749 Israeli Holstein bulls genotyped, 1663 were born since 1991 and had genetic evaluations for protein with reliabilities >0.5, and 1610 had genetic evaluations for CS. As genotyping of these bulls was performed using several SNP chip platforms, we included only those markers that were genotyped in >90% of the tested cohort. A total of 40,498 SNPs were retained. GWAS files were prepared and formatted as described ,25 usingFirst parity phenotypic annual means for CS for cows born from 1983 through 2018 and annual means of EBV for CS of cows born from 1981 through 2018 are given in Annual genetic means for the EBV of the three milk production traits are given in Genetic parameters derived from the REML analysis of data set 1 are given in Genetic parameters for protein and CS ± standard errors in the first three parities as derived from the REML analysis of data set 2 are given in Genetic and environmental variance components from the analysis of data set 1 for cows born from 2008–2016 are given in Genetic standard deviations (SD), fraction of the Israeli breeding index, PD19 as computed by equation , and reaThe EMMAX G-REML results for CS and protein were 0.63 and 0.87. That is, the cumulative effects of all the markers explained 63% and 87% of the variance among the sire evaluations for these traits. After the Bonferroni correction for multiple comparisons, none of the markers for CS were significant at the 5% experiment-wise level, and only three markers met this criterion for protein.−4. The scatter plot of the 10 markers with the lowest probability values for protein as a function of the effects of these markers on CS is given in The scatter plot of the allele substitution effects of 31,744 SNPs with minor allele frequencies (MAF) >0.10 on protein as a function of their effects on CS is given in “Cow conception rate” in the US dairy cattle population is defined as the percentage of inseminated cows that become pregnant at each service, and “daughter pregnancy rate” is defined as the percentage of nonpregnant cows that become pregnant during each 21-day period . HeritabThere is an apparent contradiction between the major phenotypic reduction in CS over the last 30 years, and the fact that the environmental correlations between CS and the milk production traits were all very low. It should be noted, however, that the HYS effect was considered fixed in the variance component analyses. Thus, changes in management factors detrimental to fertility would be excluded from the environmental correlations.The genetic trend for CS in the Israeli Holstein population became positive in 2001, the year after this trait was included in the Israeli breeding index. Genetic trends in the UK and Ireland for calving interval were negative until 2004 and then positive since then, corresponding to the changes in the selection indices of these countries . GeneticIn the current study, changes in heritability and genetic correlations were investigated for close to 30 years, or approximately six generations. In long-term selection experiments, the selection response usually ends after 20 to 30 generations , althougCurrent methods applied for genomic evaluation in nearly all populations are based on the evaluation of bull EBV separately for each trait . These mAnnual means for CS decreased from 55.6 for cows born in 1983 to 46.5 for cows born in 2018, while mean estimated breeding values increased from −1.9 for cows born in 1981 to −0.1 for cows born in 2018. Heritability for CS increased from 0.04 to 0.05 from the first through the third time periods. For all traits, heritabilities increased or stayed the same for the later time periods. The first parity genetic correlation between conception status and protein was −0.38. Environmental correlations between CS and the milk production traits were all close to zero. Heritabilities decreased with an increase in parity for protein but remained the same for CS. Realized trends were greater than expected for cows born from 2008 through 2016 for SCS, CS and herd-life, and were lower than expected for the production traits. No correlation was found for the effects on protein and conception status of the 31,744 SNPs with minor allele frequency >0.1 included in the GWAS analysis, or for the 10 markers with the lowest probability values for the substitution effect on protein. Thus, there is no apparent reason to change the current procedures that compute genomic evaluations separately for each trait.