The MendelianRandomization package is a software package written for the R software environment that implements methods for Mendelian randomization based on summarized data. In this manuscript, we describe functions that have been added to the package or updated in recent years. These features can be divided into four categories: robust methods for Mendelian randomization, methods for multivariable Mendelian randomization, functions for data visualization, and the ability to load data into the package seamlessly from the PhenoScanner web-resource. We provide examples of the graphical output produced by the data visualization commands, as well as syntax for obtaining suitable data and performing a Mendelian randomization analysis in a single line of code. The MendelianRandomization package is a software package written for the R software environment3 that implements methods for Mendelian randomization based on summarized data4. Summarized data are genetic associations with risk factors and outcomes taken from regression analyses that have been performed for each genetic variant in turn5. Such data (beta-coefficients and standard errors) are generated in a genome-wide association study, and have been publicly reported for hundreds of thousands of variants by many large studies and consortia6. While the basic functionality and initial features of the package have been discussed previously7, several functions have been added to the package in recent years. These features can be divided into four categories: robust methods for Mendelian randomization, methods for multivariable Mendelian randomization, functions for data visualization, and the ability to load data into the package seamlessly from the PhenoScanner web-resource. We discuss each of these categories in turn, describing the various options available to investigators. A list of functions in the package is provided as8. We also encourage users to consult the package documentation, which describes all the options available for each method in greater detail. The aim of this paper is to provide a broad overview of the package.Mendelian randomization is an epidemiological technique that uses genetic variants to link risk factors to outcomesmr_ivw 9,mr_egger (MR-Egger method)10,mr_median (simple and weighted median methods)11, andmr_maxlik (maximum likelihood method)9. Each of these estimation functions takes anMRInput object as input, created using themr_input command. The syntax is:The initial release of the MendelianRandomization package included four functions for the estimation of causal effects based on summarized genetic data in a univariable  Mendelian randomization framework. These weremr_ivw)ldlc andldlcse are genetic associations with low-density lipoprotein (LDL) cholesterol and their standard errors for 28 genetic variants as previously reported by Waterworthet al.12, andchdlodds andchdloddsse are genetic associations with coronary heart disease risk for the same variants. These data variables are provided with the package. Syntax for the default operation of themr_egger andmr_median commands  is identical, although user-options and the output from each method is different.wherecorrel option. Using correlated variants requires the specification of the correlation matrix between genetic variants, on the assumption that the correlations between the genetic variants are the same as the correlations between the genetic association estimates4. Correlations are typically estimated from reference data, such as those from European-descent participants of the 1000 Genomes Project that can be obtained using theld_matrix command in the TwoSampleMR package13. Care should be taken that entries in the correlation matrix are harmonized to the same effect and reference alleles as the genetic associations14; if the correlation matrix was calculated with the effect and reference alleles reversed, then the positive and negative signs should be flipped for the relevant column and row of the matrix . Exemplar data on genetic associations with calcium and fasting glucose for correlated variants are provided in the package. The IVW method can be applied to these data using the syntax:.Some methods rely on all variants being uncorrelated; others allow correlated variants using themr_ivw)calc.rho is the correlation matrix.wheredistribution = "t-dist") or based on a different significance level . Other options are specific to particular methods; a list of input options for for each method can be found in the package documentation under the subheading “Arguments”; for themr_ivw method, this is accessed by the command?mr_ivw.All methods allow confidence intervals to be calculated using a t-distribution rather than a normal distribution )$Estimatemr_ivw)$StdErrormr_ivw)$CILowermr_ivw)$CIUppermr_ivw method, this is accessed by the command?mr_ivw.A list of output slots for each method can be found in the package documentation under the subheading “Value”; for theThe R software environment runs on a wide variety of UNIX platforms, Windows, and MacOS, and requires minimal computer resources (256 kilobytes of RAM is recommended). The package requires R version 3.0.1 or higher.15.A brief description of each method is given in4. There are two options in themr_ivw method that represent different robust methods. Therobust option performs the IVW method method using robust regression (referred to as MR-Robust)16. Thepenalized option performs the IVW method with penalized weights16. The syntax is:The IVW method is implemented by weighted linear regression of the genetic associations with the outcome on the genetic associations with the risk factormr_ivw, robust=TRUE)mr_ivw, penalized=TRUE)mr_mbe)17, the heterogeneity penalized method (mr_hetpen)18, the lasso method (mr_lasso)16, and the contamination mixture method (mr_conmix)19. As for themr_ivw command, the syntax is:Other methods implemented in the package are the mode-based method )and similarly for the other methods.mr_mbe method has optionsweighting = "weighted" orweighting = "simple", corresponding to weighted and unweighted versions of the method. It also has optionsstderror = "simple" orstderror = "delta" corresponding to first- and second-order standard errors. Themr_hetpen method has options prior to set theprior probability of a genetic variant being a valid instrument (default is 0.5), andCIMin,CIMax, andCIStep to allow feasible and efficient calculation of confidence intervals.Themr_conmix method has optionspsi to set the value of the standard deviation of the distribution of invalid estimands , andCIMin,CIMax, andCIStep as above. Themr_lasso method has the optionlambda to set the tuning parameter in the penalized (lasso) regression model.The21. Typically, it is employed when several risk factors share genetic predictors, and so it is not possible to find genetic variants that are specific predictors of a particular risk factor. In multivariable Mendelian randomization, it is assumed that the genetic variants are specifically associated with any of a set of risk factors, such that any causal pathway from the genetic variants to the outcome passes via one or other of the risk factors. To perform multivariable Mendelian randomization with summarized data, genetic associations are required for each variant with all of the risk factors.Multivariable Mendelian randomization is an extension of the standard Mendelian randomization paradigm to include multiple risk factors in a single analysis modelMRMVInput object as an input, created using themr_mvinput command. Four functions are included for the estimation of causal effects based on summarized genetic data in a multivariable Mendelian randomization framework. These aremr_mvivw (multivariable IVW method)22,mr_mvegger (multivariable MR-Egger method)23,mr_mvmedian (multivariable median-based method)24, andmr_mvlasso (multivariable lasso method). The syntax is:Methods for multivariable Mendelian randomization take anmr_mvivw,   bxse = cbind,   by = chdlodds, byse = chdloddsse))hdlc andhdlcse are genetic associations with high-density lipoprotein (HDL) cholesterol and their standard errors, andtrig andtrigse are genetic associations with triglycerides and their standard errors for the same 28 variants. Again, these data variables are provided with the package. Syntax for themr_mvegger,mr_mvmedian, andmr_mvlasso commands is identical. wheremr_mvivw command can be implemented using robust regression with therobust = TRUE option24. Themr_mvivw andmr_mvegger methods have acorrel option to allow for correlated variants. Themr_mvlasso method has thelambda option to set the penalization parameter as in the univariable case. All methods havedistribution andalpha options as discussed above.The multivariable IVW method is implemented similarly to the univariable IVW method, except using multivariable regression of the genetic associations with the outcome on the genetic associations with the risk factors. As in the univariable case, themr_plot function. Application of themr_plot function to anMRInput object gave an interactive scatter plot of the genetic associations together with a line representing the IVW estimate. Genetic associations with the risk factor are plotted on the horizontal axis, and genetic associations with the outcome on the vertical axis. Application of themr_plot function to anMRAll object plotted a similar  scatter plot of the genetic associations together with lines representing the estimates from various methods. AnMRAll object is created by themr_allmethods function, which returns estimates from various estimation methods.The initial release of the MendelianRandomization package included two options for data visualization, both implemented using themr_plot function can now be applied to anMRMVInput object. In this case, we still plot the estimated genetic associations with the outcome on the vertical axis. On the horizontal axis, we plot predicted genetic associations with the outcome. These are fitted values from the multivariable IVW method, which regresses the genetic associations with the outcome on the genetic associations with the risk factors. Horizontal error bars represent confidence intervals for these fitted values. These refiect uncertainty in the multivariable IVW estimates, but not in the genetic associations with the risk factors, which are assumed to be known without error. A diagonal line is plotted with gradient 1 to help the detection of outliers, which may be pleiotropic variants. The syntax is:We have added functionality so that themr_plot, # Figure 1                   bxse = cbind,                   by = chdlodds, byse = chdloddsse))interactive = FALSE to produce a non-interactive version of this plot.In the example ofmr_forest function plots the variant-specific estimates in a forest plot, with the pooled estimate from the IVW method at the bottom  or Rücker's Q statistic (for the MR-Egger method), which are reported as the “heterogeneity test statistic” by the relevant estimation functions. Themr_forest function can also be used to plot estimates from different methods, either in addition to the variant-specific estimates or without them ) # Figure 2Amr_forest, # Figure 2B    snp_estimates=FALSE,    methods = c)mr_funnel function is similar, except that the variant-specific estimates are plotted against their precision . This plot also enables the user to investigate heterogeneity in the variant-specific estimates  Thetimates :mr_funnel) # Figure 3mr_loo function allows the user to investigate sensitivity of the IVW estimate to individual data points. This is implemented by calculating the IVW estimate omitting each variant from the analysis in turn (loo stands for ‘leave one out’). The IVW estimate based on all the variants is also plotted for reference ) # Figure 4ggplot object, and so basic graphical parameters can be changed using functions from the ggplot2 package26. For example, the horizontal axis can be set to run from −5 to +5 using the following code:Output from each of these commands is alibrary(ggplot2)forest  = mr_forest)forest2 = forest + coord_cartesian)forest2extract.pheno.csv. This function took a .csv file previously downloaded by the user from the PhenoScanner webtool (http://www.phenoscanner.medschl.cam.ac.uk/) and converted the file into anMRInput object, extracting the relevant genetic associations with the risk factor and outcome. PhenoScanner28 is a database of genetic associations that contains over 65 billion associations for over 150 million unique genetic variants, including genetic associations reported by major consortia, as well as those for the UK Biobank study reported by Ben Neale’s team . The initial release of the MendelianRandomization package included a function calledextract.pheno.csv function is no longer maintained; however, it has been superseded by thepheno_input command, which calls PhenoScanner directly from R and creates anMRInput object. Using this command, the entire workflow of a Mendelian randomization analysis can be performed in a single line of code. For example:Themr_ivw, exposure = "Low density lipoprotein", pmidE = "24097068", ancestryE = "European", outcome = "Coronary artery disease", pmidO = "26343387", ancestryO = "Mixed"))MRInput object using the genetic associations with “low density lipoprotein” taken from the study with PubMed ID 2409706829 in individuals of European descent as the summarized associations with the risk factor, and genetic associations with “coronary artery disease” taken from the study with PubMed ID 2634338730 in a mixed ancestry sample as the summarized associations with the outcome. The triplet of trait name, PubMed ID, and ancestry is necessary to uniquely identify the correct dataset for genetic associations, as some publications report associations with multiple traits, or associations with the same trait in different ancestry groups. While the above code then implements the IVW method on thisMRInput object, any other estimation or data visualization command that takes anMRInput object as input could be applied to the output of thepheno_input function.This code first extracts data on eight genetic variants (their ‘rsid’ identifiers are listed above), and creates an7: while this software simplifies the operational aspects of a Mendelian randomization, the truly difficult parts of an analysis are choosing sensible risk factors and outcomes, selecting genetic variants that are plausible instrumental variables, performing a reasonable range of analyses, and interpreting the results with care and caution31. Software code for these aspects of an analysis cannot be written32.In summary, the MendelianRandomization package has added a number of features since its initial release: to implement various robust estimation methods, to implement methods for multivariable Mendelian randomization, to enable a greater range of data visualization options, and to facilitate data entry. We conclude with the same warning that we stated at the end of the manuscript accompanying the initial package releaseAll data used in this article are distributed in the software package described, or can be freely downloaded using commands in the software package that are detailed in the text of the article.The MendelianRandomization package is available via the Comprehensive R Archive Network (CRAN)https://cran.r-project.org/web/packages/MendelianRandomization/index.html. The software package is available here:https://github.com/sb452/MendelianRandomization/tree/v0.5.0Source code is available from GitHub:http://doi.org/10.5281/zenodo.408867233Archived source code at time of publication:GPL-2 |GPL-3. Software license: The authors have addressed my concerns.Are the conclusions about the tool and its performance adequately supported by the findings presented in the article?YesIs the rationale for developing the new software tool clearly explained?YesIs the description of the software tool technically sound?YesAre sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others?YesIs sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool?YesReviewer Expertise:genetic epidemiology, nutrition, cardiometabolic traits, aging traits, coffee, caffeine, metabolomicsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. et al. summarize updates made to their MendelianRandomization R package. The package is widely used and thus a detailed description of updates is justified and warranted. I have only very minor suggestions.The R package manual  details all functions described in this paper. The introduction or summary should briefly mention what the current paper adds above and beyond the R package manual.The paper can use some minor re-organizing or heading revisions. Currently, “Introduction”, “Methods”, “Use cases”, “Summary”, “Data availability” and “Software availability” are the major sections. The “Use cases” is well written and describes features in four categories which the authors introduce in the beginning and constitutes the key/main section of the paper. The “Methods” section, however, seems out of place or mislabeled for this descriptive paper. Perhaps use “Software overview”?Table 1. Please annotate functions that are new and not discussed in reference 5.BroadbentAre the conclusions about the tool and its performance adequately supported by the findings presented in the article?YesIs the rationale for developing the new software tool clearly explained?YesIs the description of the software tool technically sound?YesAre sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others?YesIs sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool?YesReviewer Expertise:genetic epidemiology, nutrition, cardiometabolic traits, aging traits, coffee, caffeine, metabolomicsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Reviewer 3: Marilyn C. CornelisC0. Broadbent et al. summarize updates made to their MendelianRandomization R package. The package is widely used and thus a detailed description of updates is justified and warranted. I have only very minor suggestions. - We thank the reviewer for their positive view of this submission. C1.    The R package manual  details all functions described in this paper. The introduction or summary should briefly mention what the current paper adds above and beyond the R package manual. - The reviewer is correct that all of the material in the current paper is also available through the R package manual. However, there are reasons why we believe that a publication is worthwhile. First, this paper presents the contents of the package in a clearer and more holistic way than the manual. Secondly, it provides examples of usage and interpretation of the output. Thirdly, it creates a citation in the scientific literature so that we can track usage of the package. - We have added text to the introduction to more clearly define the scope of this paper. We have also referenced the manual more clearly within the text, for example to obtain lists of the input options and output slots for each method. C2.    The paper can use some minor re-organizing or heading revisions. Currently, “Introduction”, “Methods”, “Use cases”, “Summary”, “Data availability” and “Software availability” are the major sections. The “Use cases” is well written and describes features in four categories which the authors introduce in the beginning and constitutes the key/main section of the paper. The “Methods” section, however, seems out of place or mislabeled for this descriptive paper. Perhaps use “Software overview”? - Thank you for the suggestion. However, the format of the article is set by the journal to ensure homogeneity of papers across this article class. Hence we do not have complete freedom to determine the structure of the article. We have reviewed the guidelines and re-arranged where possible according to the journal guidelines, but the original structure largely remains. C3.    Table 1. Please annotate functions that are new and not discussed in reference 5. - We have added annotation of those functions that are new and those that are updated since the publication of Yavorska and Burgess 2017 (now reference 7). This article demonstrates how a range of valuable Mendelian randomization approaches can be easily implemented using the MendelianRandomization R Package. It describes substantial additions to the existing software, which I believe would be of great value to researchers. This is especially true of integrating data from the PhenoScanner web-resource, which can be invaluable in identifying avenues for pleiotropic bias.In the methods section, some of the wording is at times confusing, for example: “simple and weighted method methods)”.Use cases section, the details provided at times read like the help file for various functions when using R. This shifts from providing insufficient detail overall for using such methods  with confidence, to providing at times a puzzling focus on elements such as the standard error options for the modal estimator. If these options are important enough to be included in the manuscript, then this would warrant more description of their usage.There is an understandably difficult balance between summarising methods previously described, and providing sufficient detail so as for researchers to understand how options relate to methods implemented. For example, while the correl option is referenced several times, there is no indication of appropriate usage (such as providing a suitable correlation matrix). Especially in theA brief overview of multivariable MR would potentially be helpful, as there is often confusion over whether only SNPs correlated with all exposures should be used, or a set of SNPs where each SNP is correlated with at least one exposure included in the model. I appreciate this has been explained in previous publications, but the clarification would be welcome. The material presented in the article is technically sound, though I believe it could be improved with minor revisions. Having performed an example analysis using this software as part of the review process, I commend the authors on providing helpful vignettes and documentation guiding the analysis process in the R package itself. It is also very encouraging to see issues surrounding the appropriate selection of exposures and outcomes, as well as interpretation of results, afforded attention at times lacking in software showcasing novel statistical approaches. With the above comments in mind, I believe the MendelianRandomization R package represents a valuable addition to a growing body of MR software ensuring emerging methods are easily implemented in applied research.Are the conclusions about the tool and its performance adequately supported by the findings presented in the article?YesIs the rationale for developing the new software tool clearly explained?YesIs the description of the software tool technically sound?YesAre sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others?PartlyIs sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool?NoReviewer Expertise:Genetic Epidemiology, Applied Statistics, Mendelian Randomization, Transethnic MRI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Reviewer 2: Wes SpillerB0. This article demonstrates how a range of valuable Mendelian randomization approaches can be easily implemented using the MendelianRandomization R Package. It describes substantial additions to the existing software, which I believe would be of great value to researchers. This is especially true of integrating data from the PhenoScanner web-resource, which can be invaluable in identifying avenues for pleiotropic bias. - We thank the reviewer for their positive view of this submission. The material presented in the article is technically sound, though I believe it could be improved with minor revisions.B1.    In the methods section, some of the wording is at times confusing, for example: “simple and weighted method methods)”. - Thank you for pointing out that error. The text should read “simple and weighted median methods”. B2.    There is an understandably difficult balance between summarising methods previously described, and providing sufficient detail so as for researchers to understand how options relate to methods implemented. For example, while the correl option is referenced several times, there is no indication of appropriate usage (such as providing a suitable correlation matrix). Especially in the Use cases section, the details provided at times read like the help file for various functions when using R. This shifts from providing insufficient detail overall for using such methods  with confidence, to providing at times a puzzling focus on elements such as the standard error options for the modal estimator. If these options are important enough to be included in the manuscript, then this would warrant more description of their usage. - We appreciate the sentiment of the reviewer’s comment. As per the response to A3, our preference is for this paper to be brief and to illustrate the options available rather than to wade into deep discussions about the properties of the various methods or the reasoning for choosing between the different options available. Hence, we are happy to provide the various options that can be chosen, but we would rather not discuss the merits and demerits of the options at length – these are already addressed elsewhere. This is now explicitly stated in the Introduction. - If there are other specific examples where the reviewer feels that additional detail is required, then we would be happy to consider adding these. As for the specific examples that the reviewer calls out: 1) we are not aware of any novel options that are provided in the package – all the methods and options have been introduced elsewhere (see citations in the new Table 2); 2) we have added explanation and an example of the “correl” option; 3) the discussion of standard errors for the mode-based estimation method is one sentence. We do not think this is excessive. The original version of the mode-based estimation method provided by the authors gave 12 different estimates based on different options for the method : we have condensed these down into the three options discussed in the submission. B3.    A brief overview of multivariable MR would potentially be helpful, as there is often confusion over whether only SNPs correlated with all exposures should be used, or a set of SNPs where each SNP is correlated with at least one exposure included in the model. I appreciate this has been explained in previous publications, but the clarification would be welcome. - As per the response to A4, we have added a short description of multivariable MR to the manuscript. In particular, we clarify that genetic associations are required for all variants with each risk factor. B4. Having performed an example analysis using this software as part of the review process, I commend the authors on providing helpful vignettes and documentation guiding the analysis process in the R package itself. - We thank the reviewer for his positive feedback on the vignettes and documentation. B5. It is also very encouraging to see issues surrounding the appropriate selection of exposures and outcomes, as well as interpretation of results, afforded attention at times lacking in software showcasing novel statistical approaches. - We thank the reviewer for his positive feedback on our discussion of practical implementation of the methods and interpretation of the results. B6. With the above comments in mind, I believe the MendelianRandomization R package represents a valuable addition to a growing body of MR software ensuring emerging methods are easily implemented in applied research. - We thank the reviewer for his comments, which have strengthened and clarified this manuscript. This article describes an invaluable addition to the set of tools facilitating MR analyses, and provides a more up-to-date suite of methods.  In the introduction I advise the authors to amend the specification that MR is used on ‘modifiable’ risk factors and ‘clinical’ outcomes as MR can and often is conducted for risk factors that are not clearly modifiable, such as proteins, and similarly MR may be run on non-clinical outcomes.Additionally, I would provide greater clarity for ‘summarised data’; perhaps, summary level data for the association of SNPs with a trait, or facilitate a two-sample MR design. For the description of methods, I would firstly comment that the degree of customisability of these methods , is rather impressive and to be lauded. However, I would perhaps add one or two sentences to each of the method paragraphs further clarifying the use of these options. For example, the description of the priors of SNPs with causal effects may be quite unclear for those coming new to these methods. While I acknowledge that ultimately the papers behind each method should be read by users of the software, one or two extra helper sentences for each method would be an easy way to improve the ease of use for your software.Similarly, it would be useful to add some extra description to the MVMR introduction to explicitly specify what is going on; for example that the basic MVMR is just a regression with first order weights (y ~ x1 +x2) to make it less intimidating for users.Is there a facility to report Cochran’s or ruckers Q within the software? The authors discuss the value of visually inspecting plots for heterogeneity but it would wonderful if it were possible to return the statistics for this. I also note that it is enjoyable that the plots can be directly edited as ggplot objects.Finally, it would be excellent to have a brief paragraph explaining the format of the data frame of results being reported. It can be quite frustrating when using a package to have to manually explore the data object to try and sleuth out what exactly is present and what it means. I expect this is in the vignette in R but I recommend a summary of this here, perhaps, even only for the components reported in common for all MR methods. I believe the paper, however, would benefit from some minor revisions: In general, this is a welcome update that is described in a clear manner. With the minor updates I suggest above it will be a very useful tool for genetic epidemiology.Are the conclusions about the tool and its performance adequately supported by the findings presented in the article?YesIs the rationale for developing the new software tool clearly explained?YesIs the description of the software tool technically sound?YesAre sufficient details of the code, methods and analysis (if applicable) provided to allow replication of the software development and its use by others?PartlyIs sufficient information provided to allow interpretation of the expected output datasets and any results generated using the tool?NoReviewer Expertise:Genetic and Molecular Cancer EpidemiologyI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above. Reviewer 1: Karl Smith ByrneA0. This article describes an invaluable addition to the set of tools facilitating MR analyses, and provides a more up-to-date suite of methods.  - We thank the reviewer for their positive view of this submission. I believe the paper, however, would benefit from some minor revisions:A1.    In the introduction I advise the authors to amend the specification that MR is used on ‘modifiable’ risk factors and ‘clinical’ outcomes as MR can and often is conducted for risk factors that are not clearly modifiable, such as proteins, and similarly MR may be run on non-clinical outcomes. - We have modified the language as suggested. A2.    Additionally, I would provide greater clarity for ‘summarised data’; perhaps, summary level data for the association of SNPs with a trait, or facilitate a two-sample MR design. - We have added a brief description of what is meant by “summarized data”. A3.    For the description of methods, I would firstly comment that the degree of customisability of these methods , is rather impressive and to be lauded. However, I would perhaps add one or two sentences to each of the method paragraphs further clarifying the use of these options. For example, the description of the priors of SNPs with causal effects may be quite unclear for those coming new to these methods. While I acknowledge that ultimately the papers behind each method should be read by users of the software, one or two extra helper sentences for each method would be an easy way to improve the ease of use for your software. - We appreciate the sentiment of the reviewer. However, as the reviewer states, detailed descriptions of these methods are already available in the literature, and a paper reviewing the methods has already been written . Our strong preference is that this paper remains short and focuses on the software package, rather than deviating too strongly into technical detail. To this end, we have included a brief description of the methods in a separate table (Table 2), so that this information is available to the interested reader, but it does not add to the length of the text. The aim of this paper is now more clearly stated in the introduction. A4.    Similarly, it would be useful to add some extra description to the MVMR introduction to explicitly specify what is going on; for example that the basic MVMR is just a regression with first order weights (y ~ x1 +x2) to make it less intimidating for users. - We have added a brief description of multivariable Mendelian randomization (MVMR), and describe how the multivariable IVW method is implemented using multivariable regression. A5.    Is there a facility to report Cochran’s or ruckers Q within the software? The authors discuss the value of visually inspecting plots for heterogeneity but it would wonderful if it were possible to return the statistics for this. - The mr_ivw and mr_egger functions provide the “Heterogeneity test statistic” as part of the outcome. This is the same as Cochrane’s Q statistic for the IVW method and Rücker’s Q statistics for the MR-Egger method. This is clarified in the help files for the mr_ivw and mr_egger functions, and now in the manuscript. A6.    I also note that it is enjoyable that the plots can be directly edited as ggplot objects. - That is wonderful! A7.    Finally, it would be excellent to have a brief paragraph explaining the format of the data frame of results being reported. It can be quite frustrating when using a package to have to manually explore the data object to try and sleuth out what exactly is present and what it means. I expect this is in the vignette in R but I recommend a summary of this here, perhaps, even only for the components reported in common for all MR methods. - We understand the reviewer’s request, and sympathize with this problem. As suggested, we have provided details of some key outputs that are common to all  methods. A full description of the output of each method is readily available in the package documentation. - For example, typing ?mr_ivw opens the description of the mr_ivw function. Under the subheading “Value”, there is a clear list of the output for the IVW method. In this case, there are 15 slots: Model, Exposure, Outcome, Correlation, Robust, Penalized, Estimate, StdError, CILower, CIUpper, Alpha, Pvalue, SNPs, RSE, and Heter.Stat. We do not think it would be helpful to the reader to provide a detailed list of every slot for every method in this manuscript, but have added an explanation of how to access this information. A8. In general, this is a welcome update that is described in a clear manner. With the minor updates I suggest above it will be a very useful tool for genetic epidemiology. - We thank the reviewer for his comments, which have strengthened and clarified this manuscript.


Genomic selection is a new technology in animal breeding after the selection according to the best linear unbiased prediction (BLUP) value and marker assisted selection. Genomic selection has gradually been used in practical applications over recent years following the advent of high-density single nucleotide polymorphism (SNP) chips for livestock and poultry. Yak are a critical species on the Qinghai–Tibet Plateau, which is of great significance to herders. The early selection of yak could save feeding costs and shorten the generation interval. In the present study, we estimated the accuracy of genomic prediction compared with different classical models for yak early growth traits. The results of cross-validation indicated that the average predictive accuracy ranged from 0.147 to 0.391. The average correlation coefficient between prediction and true phenotype was 0.4.Genomic selection is a promising breeding strategy that has been used in considerable numbers of breeding projects due to its highly accurate results. Yak are rare mammals that are remarkable because of their ability to survive in the extreme and harsh conditions predominantly at the so-called “roof of the world”—the Qinghai–Tibetan Plateau. In the current study, we conducted an exploration of the feasibility of genomic evaluation and compared the predictive accuracy of early growth traits with five different approaches. In total, four growth traits were measured in 354 yaks, including body weight, withers height, body length, and chest girth in two early stages of development (weaning and yearling). Genotyping was implemented using the Illumina BovineHD BeadChip. The predictive accuracy was calculated through five-fold cross-validation in five classical statistical methods including genomic best linear unbiased prediction (GBLUP) and four Bayesian methods. Body weights at 30 months in the same yak population were also measured to evaluate the prediction at 6 months. The results indicated that the predictive accuracy for the early growth traits of yak ranged from 0.147 to 0.391. Similar performance was found for the GBLUP and Bayesian methods for most growth traits. Among the Bayesian methods, Bayes B outperformed Bayes A in the majority of traits. The average correlation coefficient between the prediction at 6 months using different methods and observations at 30 months was 0.4. These results indicate that genomic prediction is feasible for early growth traits in yak. Considering that genomic selection is necessary in yak breeding projects, the present study provides promising reference for future applications. Animal breeding has been traditionally conducted through conventional phenotypic selection followed by the evaluation of estimated breeding values (EBVs), using best linear unbiased prediction (BLUP) . In the The use of genomic selection in dairy cattle breeding has been widely implemented in many countries, such as the USA , AustralThe yak, an indispensable but rare member of the Bovidae family living on the Qinghai–Tibet Plateau, supplies meat, milk, transportation, and fur to local herdsmen. The Asidan yak is a new variety bred by Chinese scientists, characterized by its notably docile temperament and outstanding performance. Increasingly, the mode of grazing in yak is changing into intensive farming, along with a transformation of the lifestyle of herdsmen. Therefore, it is desirable to apply genomic selection to the yak population in order to facilitate gains in the overall level of production. To take full advantage of genomic selection, we have placed emphasis on selection for early growth traits compared to a previous study concerning the preliminary exploration of genomic prediction in yak . FurtherThe procedures for yak blood sample collection and body measurements were consistent with the guidelines approved by the Lanzhou Institute of Husbandry and Pharmaceutical Sciences (No. LIHPS-CAAS-2017-115).A total of 354 female Ashidan yaks were randomly selected from the Datong yak farm located in Datong county, Qinghai province, China. All animals were born between March and May 2017 and grazed freely on natural pasture with ad libitum drinking water.Yak growth traits were measured at weaning (6 months), yearling (12 months) and adult (30 months), respectively. A total of four traits were examined and analyzed: body weight , withers height , body length , and chest girth . The summary statistics of animal phenotypes are presented in p-values < 10−6 for the Hardy–Weinberg Equilibrium test and minor allele frequency < 0.01 were removed before subsequent analysis. Individuals were retained where the genotype call rate >0.90. Plink v1.90 software (http://www.cog-genomics.org/plink2) was used for the quality control of data. A total of 642,021 variants were removed due to failing to pass the minor allele threshold. The distribution of minor allele frequency of SNPs after quality control is displayed in Blood was sampled from the jugular vein for genomic DNA extraction. An EasyPure Blood Genomic DNA kit  was used to extract genomic DNA. Quantified DNA samples were stored at −20 °C. All animals were genotyped using an Illumina BovineHD BeadChip . A total of 777,962 variants were included in this chip at an average spacing of 3.43 kb. The SNPs with call rate ≤ 0.90, 2h) was calculated by dividing additive genetic variance by total variance, as follows:Variance component estimation and heritability calculations were performed using the restricted maximum likelihood method using BLUPF90 software . A relatThe accuracy of the predictive capability of five approaches, including genomic best linear unbiased prediction (GBLUP) and four Bayesian methods was compared. Furthermore, only additive effects, and not fixed effects, were considered in the present study.G matrix was substituted for the traditional A matrix normally constructed using a pedigree. The G matrix—constructed using SNP data—was used for estimating the relationships between animals [y, Z, g, and e denote the phenotype vector, the overall constant, incidence matrix that links g, the GEBV vector, and residual vector, respectively. It was assumed that e was represented by the normal distribution e~N  . For theThe Bayesian formulae can thus be represented as follows:te GBLUP . Bayesia:σg2~Expλ}BLUPF90y was the observed phenotype, and Five-fold cross-validation was implemented to assess the accuracy of the predictions. The 354 individual animals were randomly allocated into five groups, of which four groups had genotypes and phenotypes considered to be the reference population whereas phenotypes in the validation population were recorded as unknown. Predictive ability was calculated as the correlation between phenotype and GEBV. Additionally, to avoid any influence of heritability, the following formula was used to evaluate the accuracy of prediction :(5)r=CorFor further testing and verifying the feasibility of genomic prediction, a Pearson correlation test was performed between phenotypes estimated at BW6 with different approaches and observations at BW30. Analyses were conducted using IBM SPSS Statistics software .As shown in For predictive accuracy, the means were 0.253, 0.246, 0.275, 0.258, and 0.278 corresponding to GBLUP, Bayes A, Bayes B, Bayes C, and Bayes Lasso methods for different traits, respectively. The integral of predictive accuracy ranged from 0.147 to 0.391. It should be noted that the predictive accuracy of GBLUP was similar to that of the Bayesian methods. In particular, Bayes B outperformed Bayes A for the majority of traits. Additionally, GBLUP exhibited the worst performance for BW6, BL6 and CG6. Conversely, GBLUP displayed the greatest accuracy for WH6 and BL12 in comparison with the Bayesian methods.The correlation coefficient for the prediction using different models at BW6 and observations at BW30 are presented in The superiority of genomic selection represents an acceleration of genetic progression and a shortening of the generation interval compared with traditional breeding. Growth traits, as a representation of important economic traits, are key indicators in the breeding programs of livestock. In a previous study, Saatchi et al. reported that the accuracy of genomic prediction for weaning and yearling weight was 0.33 and 0.36 in Angus cattle . It has The particular statistical model used in genomic prediction has been demonstrated to be critical in the identification of superior livestock . Direct A number of studies that have compared the accuracy of GBLUP and Bayesian methods have been previously reported. Sun et al., using simulated data, reported that Bayesian regression approaches are superior to GBLUP . SimilarHeritability is defined as the proportion of genetic variance or additive genetic variance that contributes to the variance of phenotype. Studies have shown that traits with higher heritability often display considerably more genomic predictive accuracy than those traits with lower heritability ,36,37. AIn addition, we primarily focused on the trait of body weight, considered a major indicator of production in the yak. Correlation analysis was conducted between the prediction of BW6 and observations at BW30. The results verify that reliable genomic evaluation is feasible and necessary in the early period in yak. Weaning and yearling weights embody the growing potential of livestock and represent common criteria for the assessment of bulls in beef cattle in many countries. There are additional challenges for the implementation of genomic selection in yak due to environmental constraints and outdated breeding technology. Nevertheless, with the attention of grassland ecological conservation, intensive feeding will progressively substitute for smallholder farming. Not only that, the government have created policies that provide governance and support for the industrialization of yak which is a pillar industry in Tibet. The difficulty in data collection will improve little-by-little. In this regard, considering that the yak is an essential species for herdsmen on the plateau, we performed genomic prediction using a number of basic methods in a limited population size and discussed the factors that may influence its predictive accuracy. The results prove that genomic prediction can be exploited in yak selection programs.The feasibility of genomic prediction of early growth traits in the yak population was explored in the present study. To estimate breeding values, five different approaches were conducted and individually compared in 354 Ashidan yaks for four traits in weaning and yearling animals. The results indicate the accuracy of prediction ranged from 0.147 to 0.391. For the majority of traits, the accuracy of Bayesian methods was similar to that of GBLUP. However, additional investigation, using alternative predictive approaches, with a greater marker density, and/or a larger training population size might be warranted in the future for yak genomic selection.


Genome-wide studies often exclude family members, even though they are a valuable source of information. We identified parent–offspring pairs, siblings and couples in the UK Biobank and implemented a family-based DNA-derived heritability method to capture additional genetic effects and multiple sources of environmental influence on neuroticism and years of education. Compared to estimates from unrelated individuals, total heritability increased from 10 to 27% and from 17 to 56% for neuroticism and education respectively by including family-based genetic effects. We detected no family environmental influences on neuroticism. The couple similarity variance component explained 35% of the variation in years of education, probably reflecting assortative mating. Overall, our genetic and environmental estimates closely replicate previous findings from an independent sample. However, more research is required to dissect contributions to the additional heritability by rare and structural genetic effects, assortative mating, and residual environmental confounding. The latter is especially relevant for years of education, a highly socially contingent variable, for which our heritability estimate is at the upper end of twin estimates in the literature. Family-based genetic effects could be harnessed to improve polygenic prediction.The online version of this article (10.1007/s10519-019-09984-5) contains supplementary material, which is available to authorized users. Heritability measures the proportion of individual differences in a trait explained by inherited genetic variation, and is traditionally estimated by comparing the resemblance of identical and non-identical twins , takes advantage of small genetic differences among many unrelated individuals to predict trait similarity  received with the UK Biobank data. Relatedness between two individuals is summarised by a kinship coefficient, which is defined as the probability that a random allele from an individual is identical by descent (IBD) with an allele at the same locus from the other individual . For example, in parent–offspring duos, kinship is ~ 0.25, as it is the probability that a random allele in a child is from one specific parent (0.5 since humans are diploid) multiplied by the probability that the parental allele from that parent is passed to the child . To allow for normal variation in within-pair similarity, first-degree relatives are therefore defined as pairs that have a pairwise kinship coefficient of ≥ 0.177 and ≤ 0.354.zero identity-by-state (IBS0) within the kinship bounds of 0.177–0.354  in all positions on autosomes. In other words, an individual is unlikely to share zero variants with one of their parents, unless for example both copies come from the other parent , or unless there are genotyping errors meaning that shared variation is not called. In contrast, siblings have a higher pairwise IBS0.To distinguish parent–offspring pairs from sibling pairs, we plotted the proportion of SNPs with Couples were identified as pairs of unrelated opposite-sex individuals matching exactly on a string of household variables: social deprivation (Townsend Deprivation Index), assessment centre, income, time at address, smoker in household, type of accommodation, relatives in household, number in household. This approach of matching on household variables was used in a recent study of assortative mating in the UK Biobank ; S = siblings; C = couples. For the G matrix, we calculated genetic similarity for all possible pairs of individuals across all genotyped SNPs. As GREML-KIN allows for effects of the family environment, no relatedness cut-off was applied to the G matrix . The K matrix is a modified G matrix, containing only information on relatives (cut-off > 0.025), since values for unrelated pairs are set to 0. Family, sibling and couple  similarity matrices were created in the format required for GCTA. Elements in the genomic relatedness matrix were replaced by 0 if a pair did not have the specific relationship; and 1 if a pair do have the relationship, or for elements representing individuals’ relatedness to themselves.Importantly, the variance components are not purely ‘genetic’ and ‘environmental’. The sibling and couple environment sharing matrices likely pick up variance due to other processes that inflate covariance between relatives, including dominance and assortative mating, respectively.Assortative mating refers to greater similarity between partners than is expected by chance. This can result from multiple mechanisms, including direct choice based on phenotype, social homogamy, and convergence over time due to shared environments. Assortative mating amongst couples in the UK Biobank sample will be captured by fitting the couple similarity matrix (C). However, to the extent that phenotypic similarity among the parents of the UK Biobank participants reflects their genetic similarity, it is also likely that assortative mating in their parents will contribute to the additive genetic variance in our estimates (G + K). This is because assortative mating induces a positive correlation between trait-increasing alleles (‘gametic phase disequilbrium’), which elevates trait-specific genetic and phenotypic variance  and error.To identify the best-fitting model for each trait, we ran a model for every possible combination of variance components (31 models), and compared them with backwards stepwise likelihood ratio testing, starting with the full model and dropping non-significant parameters.We compared GREML-KIN results against those from a standard GREML model in a subset of unrelated individuals from the family-based analyses. The standard GREML model uses a single genomic relatedness matrix with a cut-off to exclude one from each pair of related individuals (cut-off > 0.025). This approach therefore only detects population-level additive genetic effects tagged by common genotyped SNPs, plus potential confounding, for example from gene-environment correlation and population stratification. The residual component contains other sources of variance: gene–environment interaction, error, plus all of the environmental influence, rare variant effects that are not captured when using an unrelated population sample, and non-additive genetic effects.In our GREML-LDMS-I analyses, we started with whole genome data imputed from the HRC panel , using a script from the Broad Institute, which is available online: We note that the number of relationships per individual in the UK Biobank is lower than in Generation Scotland. Their sample was selected to capture dense kinships, where many individuals have siblings, parents and spouses who are also study participants. This may result in lower power in the UK Biobank to detect influences of family similarity, especially if small in magnitude, and reduces power to separate confounding factors, as in biometric designs .Columns 2–4 of Table The discrepancies between the numbers of individuals, families and nuclear pairs reflects that most people only have one family member in the study. This contrasts to samples with dense kinship networks such as Generation Scotland, where many individuals have siblings, parents and spouses who are also study participants. As described in the Methods, we distinguished parent–offspring and sibling pairs according to their IBS0 Fig. . We chosPhenotypic correlations for neuroticism were 0.03 for couples, 0.14 for siblings, and 0.13 for parent–offspring pairs. Phenotypic correlations for years of education were 0.38 for couples, 0.30 for siblings, and 0.26 for parent–offspring pairs.Figure Figure See Supplementary Tables 1–3 for full model-fitting results, including all sub-models and fit statistics. As noted above, we ran two sets of GREML-KIN models in independent samples to reduce the computational burden. The first used the same matrices as in analyses of neuroticism. The second used new matrices including individuals who have education data and at least one family member, and who were not included in the neuroticism matrices. In defining these groups, we ensured that individuals in the same family were kept together.Supplementary Fig. 1 gives GREML-KIN results for alternative education phenotypes . Estimates differed only slightly, and the conclusions remain the same.Table Checksum analyses indicated that there were no family members with phenotype data in the UK Biobank who were also in Generation Scotland. We can therefore be confident that our results are independent of the previous study . Simulations in an Icelandic dataset suggest that although GREML-KIN gives unbiased heritability estimates when family environmental influences are present, it over-estimates heritability if phenotypes are also substantially influenced by passive gene-environment correlation  above and beyond other controls for population stratification  give mixed support for the notion that the contribution of family-associated genetic influence is explained by rarer variants. For education, some effects of low allele frequency, low LD variants are captured by our partitioned genomic relatedness matrices. For neuroticism, the same GREML-LDMS-I heritability analyses indicated less rare genetic influence than expected based on the large kin-genetic component from the GREML-KIN model-fitting. For neuroticism, the gain in heritability from GREML-KIN despite the lack of variance in the 0.001-0.01 frequency bins is perplexing but may be partly explained by poor imputation,very rare and structural variation, and population stratification. With regard to imputation quality, the rarest SNPs were more likely to be dropped prior to analysis (see Supplementary Table 4). Since rare SNPs tag other rare SNPs poorly, dropping rare ones would lead to more dramatic underestimation of their effects.Evidence from other studies suggests an important role for rarer variants, which will be further elucidated with the increasing availability of whole genome sequence data. Multifactorial traits such as personality and educational attainment are thought to have complex genetic aetiologies, consisting of interplay between common and rare variation. Recent exome sequencing work has demonstrated rare coding variant effects on many psychiatric traits [that are closely related to neuroticism; Below is the link to the electronic supplementary material.


Understanding the genetic underpinnings of fitness trade-offs across spatially variable environments remains a major challenge in evolutionary biology. In Mediterranean gilthead sea bream, first-year juveniles use various marine and brackish lagoon nursery habitats characterized by a trade-off between food availability and environmental disturbance. Phenotypic differences among juveniles foraging in different habitats rapidly appear after larval settlement, but the relative role of local selection and plasticity in phenotypic variation remains unclear. Here, we combine phenotypic and genetic data to address this question. We first report correlations of opposite signs between growth and condition depending on juvenile habitat type. Then, we use single nucleotide polymorphism (SNP) data obtained by Restriction Associated DNA (RAD) sequencing to search for allele frequency changes caused by a single generation of spatially varying selection between habitats. We found evidence for moderate selection operating at multiple loci showing subtle allele frequency shifts between groups of marine and brackish juveniles. We identified subsets of candidate outlier SNPs that, in interaction with habitat type, additively explain up to 3.8% of the variance in juvenile growth and 8.7% in juvenile condition; these SNPs also explained significant fraction of growth rate in an independent larval sample. Our results indicate that selective mortality across environments during early-life stages involves complex trade-offs between alternative growth strategies. Understanding how species adapt to heterogeneous environments is a central objective in evolutionary biology and ecology ,2,3,4. TThe main obstacle to establishing such connections occurs when selection affects complex quantitative traits that are themselves encoded by many genes ,13. In tPolygenic selection may however generate heterogeneous patterns with both subtle and large allele frequency changes ,18,19, iSparus aurata L.), is a seasonal migratory fish which uses highly heterogeneous habitats throughout its life cycle. Adults reproduce at sea during winter and the 3–4-month-long larval duration ensures efficient mixing of drifting larvae before they recruit to coastal juvenile habitats [Our model, the gilthead sea bream  lagoon environments. We developed a test to detect allele frequency shifts caused by a single generation of selection and evaluated the extent to which outlier loci additively contribute to survival probability in each environment. Furthermore, we used polygenic scores to test whether spatially varying selection affecting multiple loci partly explains the observed environment-dependent correlation between growth and condition, and the larval growth rate. Our study illustrates how spatially varying selection acting on complex traits involved in alternative growth strategies can help maintain variation at loci affecting survival in different environments. N = 44), (ii) young juveniles (0+) from the Mauguio brackish lagoon (N = 106) and (iii) young juveniles (0+) from the Thau marine lagoon (N = 106), which represent the main nursery habitats in the region. Postlarvae were collected at the entrance of Thau lagoon in early spring, and juveniles were collected at different points in both lagoons during summer and fall of the same year (a concentration of 56.1 µg L−1) and provides suitable conditions for rapid growth. However, it also shows important temporal variations of physicochemical parameters  due to its shallow depth (<1 m) and inputs from continental waters. By contrast, the Thau lagoon provides a stable marine-like habitat, which is less physiologically stressful but also less nutritive (mean Chl a concentration of 1.6 µg L−1). Its water characteristics are close to seawater, as illustrated by its marine-like community of macrophyte species [Wild sea bream were sampled from two different nursery habitats of a single population in the northern part of the Gulf of Lion, Southern France a. We col species . K) was calculated as the ratio of its measured weight to the predicted weight obtained from the log–log linear regression of weight against length based on all juvenile samples [vs. marine) for the condition factor response using an analysis of covariance (ANCOVA) in R, which allows fitting different slopes and intercepts in each habitat using lm(formula = Condition ~ Habitat × Std length).We collected two phenotypic traits, condition factor and growth, which are generally considered as good indicators of fitness in fish . Each ju samples . Total lThe predictive accuracy of the standardized index as a surrogate for individual somatic growth rate was evaluated using otolith age reading in 40 juveniles. Twenty fish from each lagoon were prepared following the protocol of  to obtaitpsDig 2.17 [geomorph [vegan [Shape ~ Sampling date + Habitat + Std length + Condition. The significance of each factor was tested using a redundancy analysis (RDA) marginal effects permutation test (1000 permutations). Finally, we analyzed the influence of growth and condition on shape independently from temporal effects using a partial RDA under the model Shape ~ Std length + Condition, removing the effect of Sampling date.A picture of the left lateral side of 145 randomly selected juveniles was used to perform morphometric measurements in Dig 2.17 . Photogrgeomorph , and alih [vegan  to estim−1 and digested with the restriction enzyme SbfI-HF. Eight Restriction Associated DNA (RAD) libraries were constructed by multiplexing 32 uniquely barcoded individuals per library, following a protocol adapted from previous studies [Genomic DNA was isolated from each of the 256 individuals (larvae and juveniles) using the NucleoSpin Tissue Kit (Macherey-Nagel), standardized to 25 ng µL studies ,38. Eachprocess_radtags in Stacks [ustacks using a minimum read depth (−m) of 5 × per individual per allele and allowing at most three mismatches (−M) between two alleles for a same locus. We used the ‘bounded error rate’ model with a maximal error rate of 1% for SNP calling. These parameters were optimized in preliminary runs using different individuals  between alleles within loci. Each individual was finally matched back to the catalog of loci using sstacks, and the program populations was used to export genotypes using a minimum call rate of 70% in at least two of the three samples and a minor allele frequency (maf) threshold of 1%. Individual genotypes were exported as biallelic SNPs as well as multiallelic haplotypes defined by reads at the scale of single RAD-tags. Illumina reads were demultiplexed and quality filtered using n Stacks ,40 and sividuals . A catalP-value threshold of 10−3 in PLINK [t-test, P-value threshold of 0.05) were excluded from the datasets.The two polymorphism datasets (SNPs and haplotypes) were further filtered to include only loci with no missing data in at least 90% of the individuals within each of the three samples . We then excluded markers showing significant deviation from Hardy–Weinberg equilibrium within at least one sample using a in PLINK . This fiin PLINK . Finallyadegenet [FST for each polymorphism dataset (SNPs and haplotypes).The overall genetic structure among all individuals was examined using a principal component analysis (PCA) in the R package adegenet . GeneticIn order to detect within-generation allele frequency changes that are unlikely to occur by random chance alone, we developed a statistical test based on a previous method that detects selective changes occurring within a single generation . Our appThe power of the test was evaluated using simulations and compared to Fisher’s exact test, which is classically used to test for genetic differentiation. We considered a finite panmictic population s values .N = 105) versus marine (N = 102) juveniles, using 10,000 iterations to estimate P-values. The test for detecting single-generation selection (SGS) was finally applied to the SNP dataset to compare brackish  to perform a PCA using all individuals. The distribution of larval genotypes in the plane defined by the first two PC axes was used as a representation of the initial genetic composition within the larval pool before postsettlement selection. This multilocus diversity was then compared to that observed in each juvenile sample in order to estimate the relative enrichment or depletion of genotypes after selection over the genotypic space. For each of the three samples, individual coordinates on the first two PCs were used to perform two-dimensional kernel density estimation using the kde2D function in the R package MASS. We then calculated the difference between juvenile and larval density estimates to estimate a relative survival probability surface within each habitat. The genotype of each individual was then projected on this surface to get individual survival probability scores in each habitat.We used the subset of outlier loci detected with the SGS test  and the interaction term P-value for the third model . The genome-wide significance threshold was adjusted using Bonferroni correction by taking within-RAD-tag linkage disequilibrium into account. Quantile–quantile (Q–Q) plots and Manhattan plots were drawn using the R package qqman. Genome-wide association (GWA) study was used to identify RAD markers linked with causative variants underlying variation in standardized length and condition. Quantitative-trait association analysis was performed using three different models in PLINK : (i) a slm(formula = Std length ~ Habitat × Polygenic Score) and condition using lm(formula = Condition ~ Habitat × Polygenic Score). Individual polygenic scores were obtained by summing over all significant SNPs the number of alleles that are favored in a given environment. We thus obtained a marine polygenic score and a brackish polygenic score that measure the cumulative effects of alleles that were inferred to be advantageous in the marine and brackish habitat, respectively. Because of the low amount of missing genotypes per individual (3.7%), we did not correct for missing data in the calculation of individual polygenic scores. Therefore, marine and brackish polygenic scores (that sum to 2 times the number of loci in the absence of missing data) were computed separately for each individual and separately tested in the ANCOVA. Individual polygenic scores were computed for different sets of loci that were detected at different P-value cutoffs in the SGS test to determine the nominal significance threshold maximizing the amount of total phenotypic variance explained by the ANCOVA for each trait [In order to test whether selected genes collectively contribute to phenotypic variation in interaction with the environment, we performed ANCOVA based on individual polygenic scores for both growth using ch trait .The genotype-by-environment interaction for growth was then tested using the juvenile summer otolith growth rate measured as the average daily width increment (in μm per day) during 60 days in June–July. Although this strongly decreased the power of the tests due to data availability for otolith growth rates in only 40 samples, it provided a better estimation of summer growth as compared to the standardized length. lm. Finally, we evaluated the genotype–phenotype relationships using an independent sample of larvae that were not used for outlier SNP detection. Mean otolith growth rate from 30 larvae during the 60 first days of larval life were used to test for association between larval growth and polygenic scores using the linear model t-test P = 0.2). However, the ANCOVA model for the condition response was significant . Condition tended to be positively correlated with standardized length in the brackish habitat, but negatively correlated in the marine habitat. Otolith daily increments and age readings in 40 juveniles confirmed that the standardized length provides a good substitute measure for both individual somatic growth rate (The average condition factor did not differ significantly between brackish and marine juveniles (marine P < 0.001). On average, brackish juveniles displayed a larger body height between first dorsal spine and anterior pectoral-fin insertion compared with marine juveniles. All factors had significant marginal effects in the RDA of body shape (P < 0.001). The effect of standardized length and condition remained significant (P < 0.001) after controlling for sampling date. The two axes of the partial RDA constrained by standardized length and condition after removing the sampling date effect explained 7.8% of the total morphological variance, and partly separated brackish and marine juveniles  was almost zero in all pairwise sample comparisons  were retained after filtering for genotype quality. We detected no evidence of population structure from each of these two datasets (SNPs and haplotypes). Genetic differentiation  outperformed Fisher’s exact test for genetic differentiation in most simulations . Applyin−3 . For mosP = 2.8 × 10−10, P = 6.6 × 10−11).The PCA based on the 67 outlier loci partly distinguished brackish and marine juveniles along the first axis, whereas larvae occupied mostly intermediate positions . The estP < 2.88 × 10−5) in the GWA study performed for standardized length and condition using three different models. Overlaid Q–Q plots for the three models showed that smaller P-values were generally obtained with the model including genotype-by-environment interaction . A similar trend was obtained using measures of mean summer otolith growth rate from 40 juveniles and a nominal significance threshold of P = 0.01 to detect candidate selected SNPs. However, the significance of the interaction between the marine polygenic score and habitat was only suggestive (interaction term: P = 0.077) due to a lack of power.The proportion of phenotypic variance cumulatively explained by nominally significant variants detected by the SGS test first increased with decreasing nominal significance thresholds and then decreased a,c. The P = 0.001), with 8.71% of phenotypic variation explained using the brackish polygenic score in interaction with habitat . The amount of explained variance for condition was maximized for 67 outlier loci  and the larval growth rate calculated during the first 60 days of life . This clearly rejects the matching habitat choice hypothesis, which was already dismissed in earlier works in sea bream . TherefoOur next objective was to evaluate the extent to which candidate SNPs for spatially varying selection explained phenotypic variation among individuals and environments. GWA analyses revealed that individual variants explain at most a small and usually insignificant fraction of phenotypic variance. Therefore, there is a limited overlap between the list of candidate SNPs for spatially varying selection and candidate loci detected in our GWA study. To compensate for this lack of power, we used additive polygenic scores to estimate the joint contribution of candidate variants to phenotypic variation. This approach has already provided informative assessments of polygenic gene action on fitness-related traits ,24. It iOverall, our results provide empirical support that selected variants with moderate to small individual effects on fitness traits can cumulatively explain several percent of the phenotypic variance among individuals living in contrasted environments. More generally, they support the view that selected mutations with antagonistic pleiotropic effects partly underlie the environment-dependent correlations between growth and condition in juvenile sea bream.Antagonistic pleiotropy between environments likely involves complex allocation trade-offs that emerge due to compromises between growth and stress regulation ,58. JuveReduced genome representation methods such as RAD-Seq have been criticized as providing insufficiently dense genome-scans for detecting local adaptation genes when linkage disequilibrium extends over small chromosomal distances around selected loci ,61,62. WTo conclude, the molecular footprint of local polygenic selection acting within a single generation was found at multiple SNPs, which will need to be further validated using a recently developed high-density SNP array in the gilthead sea bream. Our results imply that fitness-related traits such as juvenile growth and condition are encoded by multiple small-effect genes with antagonistic pleiotropic effects across environments. They also support the view that different life-history strategies, which are partly genetically encoded, segregate in sea bream as a response to different optimal growth trajectories across juvenile habitats.


Picea glauca). Trees were phenotyped for growth and wood quality traits, and genotyped for 4092 SNPs representing as many gene loci distributed across the 12 spruce chromosomes. For the polycross progeny test, heritability estimates were smaller, but more precise using the genomic BLUP (GBLUP) model as compared with pedigree-based models accounting for the maternal pedigree or for the reconstructed full pedigree. Cross-validations showed that GBLUP predictions were 22–52% more accurate than predictions based on the maternal pedigree, and 5–7% more accurate than predictions using the reconstructed full pedigree. The accuracies of GBLUP predictions were high and in the same range for most traits between the polycross (0.61–0.70) and full-sib progeny tests (0.61–0.74). However, higher genetic gains per time unit were expected from the polycross mating design given the shorter time needed to conduct crosses. Considering the operational advantages of the polycross design in terms of easier handling of crosses and lower associated costs for test establishment, we believe that this mating scheme offers great opportunities for the development and operational application of forward GS.Genomic selection (GS) has a large potential for improving the prediction accuracy of breeding values and significantly reducing the length of breeding cycles. In this context, the choice of mating designs becomes critical to improve the efficiency of breeding operations and to obtain the largest genetic gains per time unit. Polycross mating designs have been traditionally used in tree and plant breeding to perform backward selection of the female parents. The possibility to use genetic markers for paternity identification and for building genomic prediction models should allow for a broader use of polycross tests in forward selection schemes. We compared the accuracies of genomic predictions of offspring’s breeding values from a polycross and a full-sib  mating design with similar genetic background in white spruce ( Eucalyptus , also called genomic prediction, relies on genome-wide dense marker maps to model the entire complement of QTL effects across the genome , despite relatively imprecise estimation of offspring’s breeding values when the male parents are unknown. The use of genetic markers to recover paternity identity as a means of improving the accuracy of forward selections’ breeding values and to better manage inbreeding was first proposed by Lambeth et al.  is one of the most commercially important conifer species and one of the most planted forest trees in Canada. Breeding programs have been active in most of the Canadian provinces since the 1960s  to recover the paternity identity of white spruce polycross progeny and estimate the variation in the number of offspring for each pollen donor, (2) evaluate the bias in the additive genetic variance estimates when no differential male reproductive success is assumed in the polycross progeny test, that is, using the known maternal pedigree as compared with using the reconstructed full pedigree or the genomic relationship matrix, (3) build GS models for growth and wood quality traits using progeny tests from two different mating designs, that is polycross and full-sib  mating designs, to estimate offspring’s breeding values in the context of forward selection, (4) compare the prediction accuracy of conventional pedigree-based models versus GS models in the polycross progeny test, and (5) compare the accuracy of GS models from polycross versus full-sib progeny tests, as well as the genetic gains that can be obtained from both designs.In 1995, white spruce polycross progeny tests were initiated and replicated in several regions in the province of Quebec, Canada, to estimate the general combining ability of parental material forming the first-generation breeding population. These parent trees had been previously selected in provenance trials established in the 1950s and 1960s on various sites representative of the ecological conditions corresponding to white spruce reforestation zones in Quebec. Crosses for the next cycle were carried out using an equal volume of the pollen of the 19 males implicated in the polymix.o 55′ N, Long. 71o 30′ W, Elev. 208 m) until plantation. For the present study, trees were sampled from three polycross progeny test sites: the first one in Valcartier  located in the sugar maple-basswood bioclimatic domain, the second in Normandin  located in the balsam fir-yellow birch bioclimatic domain, and the third in the Watford Township  located in the sugar maple-yellow birch bioclimatic domain  until June 1995 and then moved to the Valcartier Forest Experiment Station nursery  was calculated from height (m) and DBH (cm) following Prégent et al.  located in the balsam fir-yellow birch bioclimatic domain, and in St. Casimir  located in the sugar maple-basswood bioclimatic domain  from 54 full-sib families involving 42 parents Fig. . These fTable DNA samples for genotyping were isolated from needles and terminal buds by using the Qiagen DNeasy Plant Kit  and quantified using the PicoGreen fluorescent dye . For genotyping purposes, an Infinium iSelect SNP array  containing 5308 correctly manufactured type II SNPs (one bead per SNP) was used Appendix . The arrFe| ≥ 0.50. Valid SNPs had an average call rate of 99.8%, average MAF of 0.222, and average Fe of 0.020. For the second set of 1513 full-sib progeny trees, 4661 SNPs were deemed valid following the same criteria as above. Valid SNPs had an average call rate of 99.6%, average MAF of 0.222, and average Fe of −0.019. Less SNPs were retained for the population of full-sibs due to DNA samples being in suboptimal concentration for a subset of trees.Of the 5308 correctly manufactured SNPs, 5252 were deemed valid on the first set of 892 trees from the polycross population: 56 SNPs were discarded because they had low or null signal, or average call rate < 85%, or minimum allele frequency (MAF) <0.01, or potentially erroneous/paralogous SNPs with absolute value of fixation index |p value < 0.05) were discarded. After all above SNP quality control filters, all retained trees in polycross and full-sib datasets had call rates ≥87%, with 99.5% of the trees having call rates ≥95% . Rare missing genotypes  were imputed using a k-nearest neighbour method based on linkage disequilibrium (LD-kNNi) with the software LinkImpute  using high quality SNPs for both full-sib and polycross data, a restricted set of 4092 SNPs was delimited from the set of 4661 SNPs described above, following the verification of Mendelian segregation of each SNP using 2700 progeny trees from a larger set of 80 full-sib crosses for which we had parent genotypes for the full set of 5308 correctly manufactured SNPs. SNPs with ≥5% of genotyping errors, that is, incompatible offspring genotypes according to parent genotypes, or for which offspring genotype frequencies departed significantly from Mendelian expectations in more than 25% of families , and 2 outliers for tree height and acoustic velocity after checking GS model residuals (see below), a total of 856 trees were kept for further analyses of the polycross progeny test data.Ns reported in Table θ is the group coancestry estimated from the reconstructed full pedigree , and offspring that did not belong to their expected full-sib cross were discarded so that no pedigree errors remained for the final set of 1513 full-sib offspring retained for GS analyses. Genetic diversity of the polycross and full-sib progeny tests was estimated with the status number (A) was computed using the function “asreml.Ainverse” of the R package ASReml-R v.3.0  the matrix computed from the partial polycross pedigree with known mothers, but unknown fathers ; and (2) the matrix computed from the full polycross pedigree with known mothers and retrieved fathers using the paternity assignment analysis (ABLUP full pedigree). For the GBLUP method, the realized additive genomic relationship matrix (G) and its inverse were computed from the marker data using the “A.mat” function of the R package rrBLUP , the site, and the block within site; a is the random additive genetic effect, with sa is the random interaction of site with additive genetic effects, with e is the residual term, with X and Z matrices are incidence matrices of their corresponding effects, and Ix is an identity matrix of its proper dimension. The symbol ⊗ refers to the Kronecker product. To test the hypothesis of greater than zero variance for each random effect , we performed a likelihood ratio test with one degree of freedom between the full model in Eq.  in ASReml-R v.3.0 of the form:The amplitude of genotype-by-environment interaction (G × E), or type-B correlation . The theoretical accuracy  was obtained from the diagonal elements of the G matrix. For the calculation of the theoretical accuracy of EBVs and make it comparable across models , we fixed the variance parameters For all models, estimated breeding values  of parents and offspring were obtained from the best linear unbiased predictions (BLUPs) of the random additive effect  or using the dominance genomic relationship matrix  scheme combining data across sites . Adjusted phenotypes were obtained by taking the residuals (y* = e) of a model that included an overall mean and the fixed effects (β) of the breeding group (full-sib test), the site, and the block within site: y = Xβ + e. The predictive accuracy (PACC) of models was estimated from PA as The predictive ability (PA) of the models was evaluated as the Pearson correlation coefficient between the predicted breeding values of the validation trees and adjusted phenotypes  of the validation trees (i.e. prediction without phenotypes) as estimated from the CV procedure of the GBLUP analysis in Eq.  and for We first verified the identity of each maternal parent and assigned paternity using the software CERVUS and COLONY. Eleven offspring (1.2%) could not be assigned to any of the 38 candidate mothers using both software. The two software fully agreed on maternal assignments for the remaining 881 offspring. CERVUS and COLONY also fully agreed for paternity assignments of 361 offspring (41%) to the 11 known genotyped candidate paternal trees forming the polymix Fig. .Fig. 2a The remaining 520 offspring (59%) could not be assigned to candidate parents by CERVUS . The maternal family sizes varied from 11 to 25 (mean = 22.5) and the paternal family sizes varied from 14 to 103 (mean = 45.1). The polycross resulted in 443 realized biparental crosses and small full-sib family sizes  with the conventional pedigree-based models using either the partial pedigree with known mothers only  or using the fully reconstructed pedigree with recovered fathers (full pedigree ABLUP model). Using ABLUP with the partial pedigree, the wood quality traits acoustic velocity and average wood density were the most heritable  the theoretical accuracy that is based on the standard errors of breeding values; and (2) the predictive accuracy of breeding values (PACC) that is based on repetitive prediction of offspring’s breeding values in cross validation (CV). The average theoretical accuracy of parental breeding values for the 38 maternal trees was high for growth traits  and was even higher for wood quality traits (0.83–0.84) . Heritability estimates (We compared the accuracies obtained using GS models (GBLUP) for the polycross mating design to those obtained for the full-sib  mating design of the same parental breeding population and using the same training population size  and that of offspring’s breeding values were lower for the full-sib progeny test as compared with the polycross progeny test  mating design in terms of expected genetic gains. Therefore, GS based on polycross mating appears as a valuable approach to especially enhance the gain output of early cycles in conifer breeding.Using a relatively small set of 657 SNPs, we could recover the maternal and paternal contributions of polycross offspring with a high level of confidence. COLONY and CERVUS fully agreed on maternal assignments (881 offspring) as well as on paternal assignments when the father was genotyped (356 offspring). These results suggest a very high accuracy of assignments given that the two software work very differently: CERVUS is a pairwise likelihood method whereas COLONY is a full pedigree likelihood method that searches for the most likely sibship configuration. None of the software assigned the correct mother for a small portion of offspring (1.2%), which could be caused by miss-assignments, but also errors in handling of crosses or in field test establishment may occur in tree breeding operations  by 22–52% in CVs. Still, genomic prediction (GBLUP) increased theoretical accuracies values by an additional 4–7% and PACC values by another 5–7%. This trend may be due to the better estimation of Mendelian sampling in GS models by using the realized relationship matrix  for accurate pedigree reconstruction, while Vidal et al.  performeNs = 38.46) than the partial diallel mating design . In the partial diallel, each parent must be crossed at least twice, and ideally four to six times  mating and testing designs. Estimates of total genetic gain were also similar between both designs, except for DBH and volume. Nevertheless, genetic gain per unit time was higher for the polycross progeny test because crosses can be conducted more quickly and the time needed to deploy the selected material can thus be further shortened by about 2 years, compared with the partial diallel mating design. It is challenging to compare different mating designs based on empirical data because of the slightly different levels of genetic diversity, heritability, and predictive accuracy of breeding values. Using simulations and pedigree reconstruction, Bouffier et al.  found loIn conifer breeding, polycross mating was traditionally used under a backward selection scheme to evaluate the general combining ability of female trees to be propagated in seed orchards or to plan further controlled crosses of superior genotypes to augment genetic gain. In the present study, the theoretical accuracy of parental breeding values indicated a small advantage of pedigree-based methods over GS in the case of backward selection, but the accuracy of breeding values in forward selection was higher for GS.Figure Operationally, the use of pollen mixtures demands less effort and the reduced risk of male-female incompatibility in a polymix crossing design will shorten the time needed for completing the breeding cycle by 2 years compared with full-sib crosses. But despite the application of genomic prediction, the entire breeding cycle in white spruce will request nearly 15 years Fig. , given tBesides the ease and cost-effective implementation of polycross mating design compared with partial diallel mating design, the large number of realized mating for both females and males allows for a more reliable estimation of additive effects and breeding values, and provides good opportunities for genetic gain  mating design based on the same parents. In the polycross, the recovery of full pedigree indicated a very variable number of offspring for each pollen donor which, when neglected, led to overestimated genetic parameters and inexact predictions of genetic merit. GS models using a few thousand SNPs representative of as many gene loci distributed across the 12 spruce chromosomes led to improved prediction accuracies of genetic merit of offspring and thereby, offered a more precise approach compared with simple pedigree reconstruction. We did not find any advantage to use operationally more demanding and cost-intensive full-sib crosses. The accuracy of genomic predictions in the full-sib versus the polycross progeny test was significantly higher for wood density, but was in a similar range for all other traits. However, the polycross mating design allowed for higher genetic gains per unit time while maintaining genetic diversity and incurring reduced breeding costs.Besides optimizing genetic gain as the economic motivation, breeders need to manage coancestry in each selection and deployment decision. Genomic prediction in association with polycross mating design appears especially suitable for early breeding cycles of outcrossed conifers where this approach allows for rather high selection intensities while testing a large number of realized matings. The full potential of GS was observed in forward selection schemes while no particular advantage to increase gain or accuracy of predictions was found for backward selection. Decreasing genotyping costs make it affordable to genotype accurately hundreds or thousands of individuals and include GS into advanced tree breeding programs, allowing to hasten breeding cycles and increase selection intensity


Incorporating mate choice into conservation breeding programs can improve reproduction and the retention of natural behaviors. However, different types of genetic‐based mate choice can have varied consequences for genetic diversity management. As a result, it is important to examine mechanisms of mate choice in captivity to assess its costs and benefits. Most research in this area has focused on experimental pairing trials; however, this resource‐intensive approach is not always feasible in captive settings and can interfere with other management constraints. We used generalized linear mixed models and permutation approaches to investigate overall breeding success in group‐housed Tasmanian devils at three nonmutually exclusive mate choice hypotheses: (a) advantage of heterozygous individuals, (b) advantage of dissimilar mates, and (c) optimum genetic distance, using both 1,948 genome‐wide SNPs and 12 MHC‐linked microsatellites. The managed devil insurance population is the largest such breeding program in Australia and is known to have high variance in reproductive success. We found that nongenetic factors such as age were the best predictors of breeding success in a competitive breeding scenario, with younger females and older males being more successful. We found no evidence of mate choice under the hypotheses tested. Mate choice varies among species and across environments, so we advocate for more studies in realistic captive management contexts as experimental or wild studies may not apply. Conservation managers must weigh up the need to wait for adequate sample sizes to detect mate choice with the risk that genetic changes may occur during this time in captivity. Our study shows that examining and integrating mate choice into the captive management of species housed in realistic, semi‐natural group‐based contexts may be more difficult than previously considered. We use seven years of data from the largest managed captive breeding program in Australia , heterozygosity (‐‐max_obs_het 0.70), minor allele frequency (‐‐min_maf 0.01), and linkage equilibrium (‐‐write_random_snp). Within R, we further filtered on minimum average allelic depth , coverage difference (<80%), reproducibility between technical replicates (>90%), and minor allele frequency (>5%) to obtain 1,948 SNPs across the samples relevant to this analysis to calculate diversity metrics.A reduced representation sequencing (RRS) approach was used to genotype genome‐wide SNPs by Diversity Arrays Technology Pty Ltd  as our measure of genome‐wide diversity, calculated as the total number of heterozygous loci in a sample divided by the sum of the average observed heterozygosities for all samples at the same genotyped loci, using the "inbreedR" package in R  for which we had sufficient DNA at 12 MHC‐linked microsatellite loci Table  developeHGW, we standardized MHC‐based heterozygosity (HMHC) for each individual. Our two measures of genetic diversity, HMHC and HGW, were weakly correlated across the dataset  using our entire dataset. Modeling both sexes together would require multiple interaction terms to be fitted to account for age and weight differences between the sexes, which was not feasible given our sample sizes. Males and females were therefore analyzed in separate models containing age, average weight, and the two standardized genetic diversity metrics, SD following Gelman  or unsuccessful (0) breeders, were estimated with the "glmer" function from the "lme4" package in R. Model averaging and model selection using an information theoretic approach following Grueber, Nakagawa, Laws, and Jamieson  were useg Gelman . Sub‐modg Gelman , and modAdditionally, for successful breeders, we modeled the number of offspring produced using the same four factors of interest. As this reduced the sample size, for males a generalized linear model was used , with a Poisson error distribution. For females that are biologically limited to producing a maximum of four offspring, a two‐column vector of successes (number of offspring) and failures (4—number of offspring) was used as the binomial response.2.6HGW, and HMHC within each enclosure and sex. Predictors were standardized by calculating the difference from the group mean and dividing by 2 SD of the group values; male and female models were rerun as above for both breeding success and number of offspring responses. Models were specified as above, but using the relative measures of heterozygosity, weight, and age instead of absolute measures.We tested relative effects  by standardizing all four predictors, age, weight, 2.7DAB=2×FAB/(FA+FB), where FA is the total alleles of female A, FB is the total alleles of male B, and FAB is the total number of unique alleles shared by female A and male B , we calculated pairwise genetic similarity as2.8Observed pairwise genetic similarities below the expected range  may indicate increased fitness of dissimilar mates. In contrast, observing a high proportion of pairwise similarities falling within the expected range is also predicted under the optimum genetic distance hypothesis, if the optimum heterozygosity is close to the mean heterozygosity. If animals that mate with individuals at an optimal genetic distance to themselves are more likely to successfully breed than other pairings, we would expect the standard deviation of the observed pairwise dissimilarities to be lower than that of the expected standard deviation of successful pairings that would occur under random mating. We therefore compared the observed standard deviation in pairwise similarities of the observed successful breeders to the standard deviation under simulated random mating, similar to the approach of Forsberg et al.  and Lenz33.1HGW and HMHC, had low model selection certainty (RI < 1) as predictors of overall breeding success for both females and males. Examining successful breeders only, average weight had a negative relationship with the number of offspring produced in females, but there were no strong predictors for males . Age showed a negative relationship with breeding success for females in competitive environments as per the overall breeding success model. The youngest female relative to the average age of the other females in the enclosure had a 73% fitted probability of breeding success compared to 17% for the oldest female in the enclosure. Conversely, age had a positive relationship with breeding success for males in competitive environments. The youngest male relative to the average age of the other males in the enclosure had a 17% fitted probability of breeding success compared to 65% in the oldest male. However, absolute age was not an important predictor for overall male breeding success  for both genome‐wide SNPs and MHC‐linked microsatellites Figure , providi4Mate choice is often touted as a reason to group‐house individuals in captivity , where dominance rank was positively correlated with age but there was no age effect on reproductive behavior after controlling for dominance , Gooley, Hogg, Belov, and Grueber  found thA genetic study by Russell et al.  found thSeveral authors have called for empirical studies of mate choice in conservation breeding programs  (Farquharson, Hogg, Belov, & Grueber, The data and code underlying this study are available from the public database Dryad (Supplementary MaterialClick here for additional data file.