The increasing availability of genotype data in longitudinal population‐ and family‐based samples provides opportunities for using polygenic scores (PGS) to study developmental questions in child and adolescent psychology and psychiatry. Here, we aim to provide a comprehensive overview of how PGS can be generated and implemented in developmental psycho(patho)logy, with a focus on longitudinal designs. As such, the paper is organized into three parts: First, we provide a formal definition of polygenic scores and related concepts, focusing on assumptions and limitations. Second, we give a general overview of the methods used to compute polygenic scores, ranging from the classic approach to more advanced methods. We include recommendations and reference resources available to researchers aiming to conduct PGS analyses. Finally, we focus on the practical applications of PGS in the analysis of longitudinal data. We describe how PGS have been used to research developmental outcomes, and how they can be applied to longitudinal data to address developmental questions. Since their conception and first application in human studies , obtained  from external GWAS summary statistics.A basic stepwise process for calculating PGS is presented in Figure PGS^=snp11⋯snp1p⋮⋮⋮snpn1⋯snpnpβ1⋮βp=snp11∗β1+⋯+snp1p∗βp⋮⋮⋮snpn1∗β1+⋯+snpnp∗βp=PGS1⋮PGSnPGS^i=∑j=1p(xijβj), where xij∈0,1,2 effect alleles for the jth SNP of the ith individual, that is, one row of the PGS^ matrix above (snp11∗β1+⋯+snp1p∗βp).That is, in their simplest form PGS are formulated as the weighted sum of trait‐associated alleles for a number of SNPs within an individual, Box 1Single nucleotide polymorphism (SNP): Common variation between individuals at a single position in the genetic code happening in at least 1% of the population.Cryptic relatedness: Distant relationships between individuals that make people genetically similar, confounding associations in observational studies such as GWAS.Dominance: Interaction between alleles within a genetic locus, that is, deviation from additivity within a locus.Epistasis: Interaction of alleles across different genetic loci, that is, SNP–SNP interactions.Linkage disequilibrium: the correlation between nearby variants on the same chromosome.Clumping: Pruning of variants in linkage disequilibrium above a certain threshold (e.g. a correlation r > .1), prioritizing variants depending on a statistic of interest, typically p‐values in GWAS.Overfitting: When a statistical model matches the data too closely modelling noise instead of the actual signal. This makes the model too optimistic and thus not generalizable well to independent data.Cross‐validation: Resampling method used to evaluate a model within a unique dataset. The model parameters are learned in part of the dataset and performance is tested in a hold‐out set (e.g. with a 9 to 1 split for training and testing respectively).2)SNP‐heritability , usually in the order of millions. For an n × p mean‐centered genotype matrix X containing genotype vectors of individual SNPs (x) for each person, the regression equation can be expressed as follows:xj is a vector of genotype values for individuals at the jth SNP, βj is the marginal effect for the jth SNP and ε the error term. This relationship is usually adjusted for demographic covariates such as age and sex, and a number of genetic principal components, to account for confounders such as population stratification and cryptic relatedness. In addition, depending on the cohort, technical confounders are accounted for, such as the version of genotyping chip used if different chip arrays were used to screen the cohort.SNP weights used to derive PGS are typically obtained from external GWAS (discovery) samples. In GWAS, a phenotype vector xjty/n=cov and xjtxj/n=var(xj). Additive genetic variance at each locus is defined as a2=2pqβj2, where 2pq is the variance of the genetic locus , and βj is the effect size obtained from the regression of the phenotype on the genotype as stated above. The proportion of variance explained in the phenotype can be calculated as R2=2pqβj2/ys2, where ys2 is the variance of the phenotype (R2=2pqβ2 for a standardized phenotype). Hence, the power to detect single SNP effects is a function of both the average genetic effect, and allele frequencies . LD refers to the nonrandom association between nearby SNPs on a chromosome and is the reason for the typical association peaks in a ‘Manhattan plot’ Figure , which d−8  approach. It consists of performing an informed LD‐pruning (clumping) using N > 1000; Vilhjálmsson et al., The reason to perform clumping is that if SNPs in LD are included in the PGS without accounting for their correlation, the individual contribution of the specific loci included will be overestimated  could also be suboptimal due to added noise across many false positives SNPs included.The standard GWAS threshold to select SNPs is often too restrictive for the purpose of PGS construction, and typically more lenient thresholds for SNPs inclusion in the score will lead to higher predictive power, depending on genetic architecture. This is often the case with highly polygenic traits, where a more liberal inclusion of SNPs in the score improves prediction. However, a PGS derived from all SNPs  should be performed to maximise accuracy. This, however, cannot be performed on the same sample where PGS effects are evaluated (i.e. the target set) because of overfitting. That is, the selected score will result in a prediction that will be too optimistic and will tend to underperform if applied to an external independent sample. Instead, an independent validation set  target set as the gold standard  a priori. This can be done either based on previous evidence in a similar sample, or on prior assumptions such as the polygenicity of a trait . However, in practice, the optimal threshold is often not known a priori, and using a preselected threshold is likely to lead to underperformance of the PGS.p‐value thresholds. However, interpretation based on the optimal PGS will be biased upwards and correction for multiple testing will need to be performed. One solution implemented in PRSice2 is to perform permutation tests and to use empirical p‐values as evidence for association. While this is appropriate to establish if an association exists, it will not correct for the aforementioned bias in effect sizes. Therefore, for PGS studies that involve interpretation of coefficients or assessing predictive accuracy, an independent out‐of‐sample or hold‐out set is recommended. An alternative solution consists of taking the first principal component out of a number of calculated PGS thresholds weighting of SNP effect sizes from GWAS summary statistics is performed along with some form of shrinkage . More generally, methods can be divided into Bayesian and frequentist approaches that differ in terms of how they attempt to model genetic architecture to improve prediction accuracy.In practice, this translates into shrinking parameter estimates which typically improves predictions over marginal effects from GWAS because it reduces the total variance/noise in the estimates of the summed‐up SNPs. For example, thresholding in C + T can be thought of as a type of shrinkage, where certain effect sizes are shrunk exactly to 0. Different methods apply different types of shrinkage, and they will tend to perform favourably compared to others depending on the true underlying mixture of distributions of the trait of interest , or elastic net penalty, is applied on GWAS effect sizes. Frequentist penalization methods can be likened to Bayesian priors. For example, the lasso penalty can be likened to drawing effect sizes from a double exponential distribution effectively introducing sparsity, retaining only one effect size from a set of correlated SNPs, and shrinking the rest towards or exactly to 0 , including major depressive disorder (MDD) and Schizophrenia (SCZ)  in the UKbiobank, extending PGS comparisons to different settings including cross‐ancestry performance  the PGI Repository provides already calculated single and multitrait scores based on GWAS including data from 23andMe, which is typically excluded from most PGS studies due to access restrictions.There are also repositories of already developed PGS which allow researchers to construct PGS within a reproducible framework. For example, the PGS catalog  with childhood BMI, it is possible to infer genetic continuity of risk across the lifespan. However, the adult BMI PGS will likely become more predictive of the BMI phenotype at later stages in life, likely because the target trait becomes closer to the phenotype assessed in the original GWAS used to construct the PGS. Another plausible and nonmutually exclusive reason for this is (active) gene–environment correlation Plomin, . HoweverStability and change across development can be investigated with latent growth curve (LGC) modelling techniques, by which we attempt to model between‐person  differences and within‐person  changes over time . We can in turn ask whether PGS associate with some trait of interest via systematic developmental processes  or age‐specific processes  Figure . It is iAs discussed, an alternative approach is to conduct repeated measures GWAS across development and in turn, construct PGS for specific developmental stages. These can be implemented as time‐varying covariates in longitudinal models such as LGC models, as shown in Figure This framework can be extended to examine the association between PGS and joint trajectories, using a multivariate LGC Figure . SimilarPolygenic scores can also be used to examine the specificity of genetic influences on developmental outcomes. That is, do PGS effects vary depending on particular domains, such as the age of assessment? A multivariate metaanalysis can answer such questions by testing for heterogeneity of effects across different domains. For example, Nivard et al.  implemenh2 (Appendix P), as well as substantial genetic stability of P across time  psychopathology  phenotypes where the power of PGS is typically reduced, given that large GWASs are generally based on adult outcomes. Performance of different methods is variable, especially depending on the trait of interest if misspecification of underlying architecture occurs, but often not dramatic. Workflows, and atlases benchmarking performance of PGS and PGS methods across an array of traits, have an important role to guide researchers in the choice of methods.Finally, the rapid advancement of the behavioral genetics field, both in terms of methods and (GWAS) results, is one challenge faced by repositories and other open resources, such as online tools, which, if not continuously maintained, run the risk of becoming rapidly outdated. One solution is afforded by community‐based repositories , and platforms , which can rely on users to stay up to date. Capitalizing on these advances will enable powerful and novel research applications to better integrate polygenic scores in child developmental psychology and psychopathology.Appendix S1. Assessing the predictive power of PGS.Table S1. PGS methods and related tutorials.Table S2. General resources for PGS workflow.Click here for additional data file.


Abies alba). Drought-induced dieback had been previously explored in this conifer, although the role played by tree-level genetic diversity and its relationship with growth patterns and soil microsite conditions remained elusive. We used double digest restriction-site-associated DNA sequencing (ddRADseq) to describe different genetic characteristics of five silver fir forests in the Spanish Pyrenees, including declining and non-declining trees. Single nucleotide polymorphisms (SNPs) were used to investigate the relationships between genetics, dieback, intraspecific trait variation , local bioclimatic conditions, and rhizosphere soil properties. While there were no noticeable genetic differences between declining and non-declining trees, genome–environment associations with selection signatures were abundant, suggesting a strong influence of climate, soil physicochemical properties, and soil microbial diversity on local adaptation. These results provide novel insights into how genetics and diverse environmental factors are interrelated and highlight the need to incorporate genetic data into silver fir forest dieback studies to gain a better understanding of local adaptation.Ongoing climatic change is threatening the survival of drought-sensitive tree species, such as silver fir ( Climate-change-induced disturbances are increasing in frequency and severity, threatening the persistence of numerous tree species, as well as the diversity and dynamics of forest ecosystems worldwide . TogetheTree populations can follow two main strategies to cope with major changes in climatic conditions: migration and adaptation . MigratiRegarding genomic information, single nucleotide polymorphism (SNP) genotyping allows one to make extensive use of genetic markers, as they are found at a high frequency across genomes . GenotypThe combination of genetic data with environmental factors and dendrochronology can help provide a comprehensive vision of how genomes are shaped by their interactions with the environment, and how much of an impact they make on functional traits and growth patterns .Genome–environment associations look for statistical associations between allele frequencies and ecological variations with the aim of identifying genes involved in local adaptation . With clloci [While genome–environment associations can help identify putatively adaptive loci , genotyploci . Leaf fuloci , just liloci ,30.Abies alba Mill.), which is among the tree species affected by extensive dieback and increased mortality rates [In this context, this study focuses on silver fir  to describe and compare the genetic characteristics of declining and non-declining stands, as well as declining and non-declining trees, (ii) to detect genomic regions under selection in such trees, and (iii) to identify genetic markers (SNPs) associated with environmental and phenotypic variables potentially involved in responses to climate stress. This information could help gain a better insight into this conifer’s declining process.Consequently, the main objective of this study was to identify molecular markers (SNPs) in the After trimming, an average of 96.87% of the reads were retained . An average of 68.74% of those reads were successfully mapped to the reference genome . A total of 55,803 SNPs were identified in the 266 sequenced samples, of which 3958 SNPs and 254 individuals were retained after the filtering step .loci of 99.44, 88.53, 99.62, 99.72, and 98.79 in the five studied stands , were detected between all population pairs  showed, in agreement with the Ftogether . CO was together . The twoSelection signatures were found in 41 SNPs taking into account the five genetically different populations . The resGenome–environment associations were found between 47 different SNPs and the five bioclimatic variables, giving a total of 71 associations . Of thesGenome–environment associations were found between 35 different SNPs and the eight abiotic soil variables, giving a total of 80 associations . Of thesRegarding the eight biotic soil variables, 33 different SNPs were significantly associated with them, giving a total of 81 associations . Of thesA high proportion of SNPs were found to be associated with several types of environmental variables and/or to be under selective pressure , showingGenotype–phenotype associations were found between 19 SNPs and 2 functional traits (out of 5) and 7 dendrophenotypic traits (out of 46) related to response to past drought events, with resilience to the 1998 drought (Rs98) as the variable with the highest number of associations . Of thesRegarding the 2005–2006 drought, there were two proteins with functions involved in drought response associated with resistance and resilience to this extreme climatic period. One of them was a zinc finger transcription factor which has been linked to drought and heat response multiple times, e.g., ,49,50. HAlso associated with resilience, but to the 1998 drought period, there was an aluminum-activated malate transporter, which influences the cellular gamma-aminobutyric acid (GABA) concentration . This amThis study aimed to gain a better understanding of how genetics could be involved in tree decline and mortality, determining local variability in healthy trees and neighboring individuals showing a declining process towards death. Furthermore, we provide information about the genetic characteristics of contrasting Pyrenean populations of silver fir and their relationship with the environment and phenotypic traits, finding climate and soil microsite conditions as the main factors affecting their local adaptation.loci (QTL), which tend to be scattered across the genome [A. alba [Previously, microsatellites were the most widely employed method to study genetic diversity, structure, and adaptation in silver fir populations, e.g., ,55,56. Me genome , rather e genome , stressi[A. alba , and ourHowever, genome-wide identification of SNPs in conifers, although possible, remains a complex process hindered by the lack of reference genomes and their quality. For instance, 70% of the reads used in this study mapped to the silver fir reference genome, possibly due to the highly fragmented nature of this assembly. This means 30% of the generated information was lost. It is clear that efforts must be made to improve the existing references and sequence new species.A. alba is known to have high phenotypic plasticity, mainly attributed to the effect of environmental factors rather than genetic variability [To our knowledge, this is the first study comparing the genetics of declining or non-declining silver fir individuals. Our results showed that there were no genetic differences between them within their respective populations. iability . Thus, eiability ,18. The Regarding the comparison between populations and considering that they are placed in regions with different environmental conditions, it is not surprising that several SNPs showed signs of selection. Some of these could be used as molecular markers of nearby genes that are involved in stress responses, mainly related to ABA signaling pathways. Whole-genome scans in other coniferous species have demonstrated that genes under selection are often involved in responses to abiotic stress and are rapidly evolving to enable trees to cope with such demanding conditions ,63. TherA. alba [Temperature and precipitation had a similar number of associated SNPs whose allele frequencies changed between populations in line with the variable’s variation. Precipitation seasonality (BIO15) had the highest number of associations, including an aquaporin, which has been directly linked to drought stress in A. alba . AdditioA. alba , revealiA. alba . On the A. alba .Soil variables also had a high number of associations, with a large percentage of SNPs associated with both biotic and abiotic parameters. Vegetation, microbial community, and physicochemical properties of soil are closely linked to each other, interacting in a process known as plant–soil feedback . It has In addition, it has been described that forest management affects soil microbial composition, increasing soil microbial stress  and affeFinally, the genotype–phenotype associations were fewer and almost unique for each variable. While genome–environment associations identify general trends due to their population-level nature, phenotype data can produce much more finely tuned results, as they consider tree-level information. Thus, a strong genetic signal related to growth traits is less likely to be found ,77,78.In accordance with this, only 7 out of the 46 dendrophenotypic variables related to growth patterns were associated with genetic markers. More specifically, these traits define how each tree responded to past drought periods. Survival to one-time extreme events, such as extended drought periods, might not be driven as much by adaptation as by each tree’s genetic variability, which could be key to increasing its chances of carrying a variant that could help it cope with the adverse climatic situation . Thus, tTwo traits related to leaf characteristics also showed a low number of associated SNPs, in line with a weak differentiation in leaf morphology between individuals . Lastly,In summary, integrative studies incorporating genetic, phenotypic, and environmental data represent a powerful tool for the uncovering adaptation mechanisms of natural tree populations, as demonstrated by the growing number of publications following this approach, e.g., ,27,58.loci, they would pave the way for the accurate identification of epigenomic marks [In this regard, improved reference genomes for conifer species are of utmost importance in the pursuit of understanding their genetic vulnerability to climate change. In addition to allowing more efficient genome-wide identification of molecular markers and adaptive candidate ic marks . Epigeneic marks , which wAbies alba Mill.) is a large conifer distributed in montane areas in Europe (Fagus sylvatica L.) or Scots pine (Pinus sylvestris L.), with the understory vegetation dominated by several shrubs such as European box (Buxus sempervirens L.) [Silver fir (n Europe . It can rens L.) .A. alba stands included in a previous study [The study sites were the four us study  plus an us study , consideus study .A. alba individuals. In total, 100 mg of each sample was lyophilized and used for total genomic DNA extraction with DNeasy Plant Mini Kit . DNA yield and purity were determined using a NanoDropTM spectrophotometer and visually inspected after electrophoresis on agarose gels. Paired-End (PE) libraries for ddRADseq [ApeKI and PstI restriction enzymes and sequenced by LGC Genomics , with a sequencing depth of 1M. Quality of raw reads was assessed using FastQC v0.11.9 [A. alba reference genome  [Fresh leaf samples were collected from 266 ddRADseq  were con v0.11.9 . They we v0.11.9  to removbal.1_1)  using ipbal.1_1) . This rebal.1_1)  to retailoci and allele frequencies of relevant SNPs in each population. Genodive v3.06 [ST [Different descriptive statistics were calculated. GenAlEx v6.5 ,91 was uve v3.06  was used3.06 [ST ) and to 3.06 [ST ,95) with3.06 [ST  was usedq-values < 0.05 were considered to be under selective pressure. Different configurations of groups were tested looking for significant differences in allele frequency measured by their FST coefficient: sampling points as groups, condition as groups (non-declining vs. declining), condition as groups within each population, age as groups (adult vs. young), and age as groups within each population.Detection of selection signatures was performed using BayeScan 2.1  with defThree types of environmental variables were considered for genome–environment associations (GEA): (1) bioclimatic variables, (2) abiotic soil variables, and (3) biotic soil variables . The associations were identified using BayEnv2  with 100For each sampling point’s location, 19 bioclimatic variables were obtained from the WorldClim database , with a The 8 abiotic soil variables were obtained at individual-level  and thenFinally, the 8 biotic soil variables  were basq-values < 0.05 after FDR correction were considered to be associated.Two types of tree-level phenotypic data were considered for genotype–phenotype associations (GPA): (1) functional traits related to leaf characteristics, and (2) dendrophenotypic traits related to growth patterns, climate sensitivity, and response to past drought events. Only adult trees were used for this analysis as saplings were not big enough to sample wood cores from their logs. The associations were determined using the R package rrBLUP v4.6.1 ,103, inc2), which was measured while needles were fresh, and leaf mass per area , which was calculated after they were dried [−1) [The 4 functional traits  includedre dried . Leaf dried [−1) .Abies alba forests, and a near-to-present period when this fir dieback was widely reported [The 46 dendrophenotypic traits were obtained from dendrochronological studies carried out using data obtained from sampled cores . For thereported .For the 21 dendrophenotypic traits  related For the 12 dendrophenotypic traits  related The sampled stands of silver fir in the central-western Spanish Pyrenees showed genetic differences among them. However, no significant genetic differentiation was obtained between declining and non-declining trees within populations. Associations between genome and environment were abundant, linking tree genetics, climate, and soil composition and microbial communities. A high percentage of them also showed signs of selection, supporting a strong impact of environmental factors on this species’ genome. Genotype–phenotype associations were scarce, indicating that growth patterns might be shaped by mechanisms beyond the tree’s genotype itself, such as phenotypic plasticity in response to extreme climatic events. All in all, we provide an integrative vision of how the silver fir genome, the environment, and its phenotype are interrelated, which could be a valuable source of information in the context of climate change.


Plant height, anthesis to silking interval, and grain yield were collected from high and low N conditions in three environments for both per se and testcross trials. We used three GWAS models, namely, general linear model (GLM), mixed linear model (MLM), and Fixed and Random model Circulating Probability Unification (FarmCPU) model. We observed significant genetic variation among the DH lines and their derived testcrosses. Interestingly, some testcrosses of exotic introgression lines were superior under high and low N conditions compared to the check hybrid, PHB47/PHZ51. We detected multiple SNPs associated with agronomic traits under high and low N, some of which co-localized with gene models associated with stress response and N metabolism. The BGEM panel is, thus, a promising source of allelic diversity for genes controlling agronomic traits under different N conditions.Nitrogen (N) limits crop production, yet more than half of N fertilizer inputs are lost to the environment. Developing maize hybrids with improved N use efficiency can help minimize N losses and in turn reduce adverse ecological, economical, and health consequences. This study aimed to identify single nucleotide polymorphisms (SNPs) associated with agronomic traits  under high and low N conditions. A genome-wide association study (GWAS) was conducted using 181 doubled haploid (DH) lines derived from crosses between landraces from the Germplasm Enhancement of Maize (BGEM lines) project and two inbreds, PHB47 and PHZ51. These DH lines were genotyped using 62,077 SNP markers. The same lines from the  In cereals such as maize, the application of N fertilizers is an essential agronomic practice . AlthougImproving NUE in maize would not only help to reduce N fertilization in the field but may also increase productivity in N-deficient environments. However, NUE is a complex trait in which interactions between genetic and environmental factors are involved. Traits such as anthesis-silking interval, plant height, and grain yield have the potential to be used as parameters for NUE screening, since they play an essential role in N acquisition and N utilization in maize, the two main components of NUE . NUE-relIn US elite germplasm, only a small fraction of the total available genetic diversity in maize (<10 out of 300 maize races) is currently used . The Gerper se, and their testcrosses, were evaluated in field trials under low and high  N conditions for agronomic traits related to NUE. GWAS analyses for the agronomic traits under low (LN) and high N (HN) conditions were conducted. The main objective was to identify novel alleles associated with agronomic traits under low N conditions, which can aid in improving NUE in maize. The specific objectives were to (i) determine the extent of variation of agronomic traits for the BGEM panel grown under HN and LN conditions, (ii) establish correlations among the agronomic traits, (iii) identify associations between SNP markers and agronomic traits grown under HN and LN conditions, and (iv) evaluate the co-localization of these SNPs with putative candidate genes and/or previously identified QTL for traits related to NUE in the inbred and testcross populations.In this study, BGEM lines 22.11 seeds were backcrossed once with PHB47 and PHZ51, respectively, to produce the BC1F1 generation as described in per se field trials. The DH lines were produced using the protocol described by 1F1 or F1-derived crosses between GEM accessions and PHB47 or PHZ51 were crossed with the inducer hybrid RWS 9 × RWK-76 , and each group was planted in separate isolation plots in Ames during the summer of 2014. Two rows and two ranges of pollen parent surrounded each isolation plot. Inside, for every two rows of female, there was one row of male. There were three replications or rows of each DH line, randomly distributed per isolation plot. In one isolation plot, all lines belonging to the stiff-stalk group  that were used as female parents were detasseled before anthesis, and PHZ51 was used as pollen parent. In the other isolation plot, all non-stiff stalk lines  were detasseled and crossed with PHB47. In total, 74 and 105 testcrosses obtained from the cross with PHZ51 and PHB47, respectively, were evaluated.The same lines from the 2.2−1 was applied in the form of 32% urea–ammonium nitrate (UAN) fertilizer before planting via liquid broadcast and immediately incorporated with tillage. Three environments were used for the per se trials: at Iowa State University Agricultural Engineering and Agronomy Farm  in Ames, IA, during the summers of 2014 (Ames 2014) and 2015 (Ames 2015), and at the Iowa State University Northeast Research and Demonstration Farm  in Nashua, IA, during the summer of 2015 (Nashua 2015).In this study, a combination of location and year was considered as an environment. Within each environment, two N conditions were evaluated: HN and LN. No fertilizer was applied within the LN condition in all environments. For the HN condition, 261.60 kg N haTwo environments were used for the testcross trials, which were performed at the same farms from Ames and Nashua during the summer of 2015. No N fertilizer was applied to the Nashua LN location in 2014, and oats were planted in that area before, in order to deplete the soil N content. For the testcross evaluation in Ames 2015, two LN locations were used. One has historically been planted with maize, and no fertilizer has been applied in that location for several years. The other LN location in Ames 2015 did not receive any fertilizer treatment and was planted with non-nodulating soybeans in the previous year (2014). Therefore, for the testcrosses trials, the maize–maize location was referred to as Ames 2015A, and the soybean–maize location was referred to as Ames 2015B. Only one HN location was used for testcrosses trials in Ames 2015 environment.Soil samples were collected right before sowing, and the samples were analyzed in the Ames trial plots in 2015. Using a probe, 10 samples per location were collected in the top 30 cm of the soil at randomly selected areas, and samples for each trial were bulked, thoroughly mixed, and submitted to the ISU Soil and Plant Analysis Laboratory at the Department of Agronomy to determine total N and carbon (C) content . The res−1.All trials were planted following a randomized complete block design (RCBD), in two-row plots. Two ranges of filler were planted at the front and back and four rows at the left and right sides of each trial. Each row was 5.64 m long, and the rows were spaced 0.76 m apart. Planting density was 65,323 plants ha2.3maxT is the maximum daily temperature which is set to 30°C when maxT exceed 30°C, and minT is the minimum temperature and is set to 10°C when minT falls below 10°C. PHT in centimeters was taken from the ground surface to the topmost end of the central tassel spike. GY was obtained from two-row plots using a harvesting combine, where grain weight and moisture content were measured. Yield in tons per hectare was computed after moisture content was adjusted to 15.50%.Plant height (PHT) and grain yield (GY) were measured in all trials, while anthesis to silking interval (ASI) data were only collected at the Ames trials. ASI was calculated using the difference in growing degree units (GDUs) between anthesis and silking times. Days to anthesis was recorded as the number of days from sowing to the day when 50% of the plants in the plot had anthers extruded outside the glumes. Days to silking were recorded as the number of days from sowing to the day when 50% of the plants in the plot had silks emerging from the ears. Days to anthesis and silking were converted to growing degree units (GDUs), which were calculated according to the following equation: 2.4per se and testcross trials fitting the following linear model: ijklY is the observation in the thk genotype in the thj replication in the thi environment and thl N rate; μ is the overall mean; iE is the effect of the thi environment; R(E)ij is the effect of thj replication nested within the thi environment; lN is the effect of the thl N rate; ilEN is the interaction effect of the thi environment and thl N rate; kG is the effect of the thk genotype; ikEG is the effect of the interaction of the thi environment with the thk genotype; lkEG is the effect of the interaction of the thl N rate with the thk genotype; iklENG is the effect of the interaction of the thi environment and thl N rate with the thk genotype; and ijklε is the residual error.Data analysis was performed separately for the h2) on an entry mean basis for each trait under each N condition and in the combined analysis were estimated as follows  was used to perform the analysis of mixed model, where N rate was fixed, and the other factors were random. Variance components,  follows : h2=σg2For each N condition, best linear unbiased predictions (BLUPs) from all inbred lines and testcrosses across the environments were estimated for all measurements. This was also implemented using PROC MIXED in SAS 9.3 . The BLU2.5The BGEM lines were genotyped using 955,690 genotyping-by-sequencing (GBS) markers . GBS datper se, PHB47 and PHZ51.The average number of recombination events per line was substantially greater than expected. Therefore, the genotypic data were corrected for monomorphic markers that were located between flanking markers displaying donor parent genotypes. The correction was based on Bayes theorem, with an underlying assumption that very short distances of a marker with recurrent parent (RP) genotype to flanking markers with donor genotype are more likely due to identity of marker alleles for that particular SNP between RP and donor, instead of a rare double recombination event. These short RP segments interspersed within donor segments were tested for the null hypothesis that a double recombination occurred and were either corrected or kept as original genotype, accordingly, based on p-values from the Bayes theorem . After c2.6per se and testcross trials, were used for GWAS. In order to balance false-positives and false-negatives in detecting significantly associated SNPs, three statistical models were implemented, namely, (1) General Linear Model (GLM) + PCA (Q), where the PCA output from GAPIT was used as a covariate to account for fixed effects due to population structure; (2) Mixed Linear Model  was divided by the eff_GM (α/eff_GM). For this study, based on the α level of 0.05, the multiple testing threshold level was set at 8.10 × 10−7.Multiple testing in GWAS was accounted for using the statistical program simpleM , which chttp://www.maizegdb.org; http://www.ncbi.nlm.nih.gov/gene) and were also compared to previously published candidate genes.The available maize genome sequence  was used as the reference genome for candidate gene identification. Candidate genes were identified using the Ensembl Biomart tool . Genes w33.1According to the soil chemical analysis  by the likelihood ratio test for all traits in the per se trials . On the other extreme, DH lines BGEM-0223-N, BGEM-0225-N, BGEM-0247-N, BGEM-0237-N, and BGEM-0165-S performed poorly with yields ranging from 1.19 t ha−1 to 1.30 t ha−1.Variance components due to genotype were highly significant , except for PHT in the combined analysis. Variance components due to genotypes × N rates interaction were highly significant (p< 0.01) for GY in all environments, while for ASI and PHT, the significance depended on the environment where they were evaluated. In relation to the heritability estimates within environments, we observed that PHT had the highest estimates among the three traits, ranging from 0.41 to 0.72 under LN and from 0.58 to 0.68 under HN. The heritability estimates for GY ranged from 0.09 to 0.56 under LN and from 0.37 to 0.62 under HN , and GY (r = 0.69) and ASI  and LN (r = 0.52). Testcross PHT under LN also correlated well with per se PHT under both HN (r = 0.49) and LN (r = 0.52). According to the correlation coefficients, there is no possibility to use any trait from the per se performance to predict the performance of testcross hybrids under neither N condition.Weak to moderate (r< 0.60) correlation coefficients were observed between the performance of testcross and 3.4To reduce the impact of environmental variability, BLUP values across the three environments  were used for association study. No SNPs were found when performing GWAS with MLM model. A total of seven significant SNPs were found by applying FarmCPU and GLM models  had PVE >30%. This SNP is within the gene model GRMZM2G414252, located between 190,556,326 and 190,557,054 bp on Chromosome 2. The SNP marker S1_13685600  was also significantly associated with ASI under HN conditions. The associated gene model GRMZM2G037912  was identified as a putative vesicle-associated membrane protein  with a PVE equal to 24.8%. This SNP is located within the gene model GRMZM2G158976 , and encodes a VQ motif-containing protein. GRMZM2G070271 is 308,612 bp away from GRMZM2G158976 and encodes a xyloglucan endotransglucosylase/hydrolase protein. For PHT under HN conditions, one SNP marker had a PVE higher than 10% (S3_179633217). This SNP marker is within the gene model GRMZM2G087619 , identified as sister chromatid cohesion protein on Chromosome 3. S2_209927372 was significantly associated with GY under HN . It is worth noting that this SNP marker explained more than 40% of phenotypic variance. The gene model GRMZM2G311187  co-locates with this SNP, which encodes for a phosphatase protein. Other putative gene models identified by significant associations are listed in For testcross data, three significant SNP markers each were found for PHT under both LN and HN, but did not overlap. None of the SNPs affected more than one trait. The SNP marker S1_104874404 on Chromosome 1 was significantly associated with PHT under LN  to 0.32 (GY in Ames 2015A) in the testcross trials. Decrease in heritability under stress conditions was also observed in previous studies in both maize inbred lines per se  to 0.52 (GY in Ames 2014) in the s per se  and tests per se . Reasonss per se  and highs per se . The sig4.2per se trials, the GY correlation between HN and LN was close to 0.70, the correlation was<0.50 in the testcross trials. This reveals how critical it is to evaluate genotypes under the target environment, for both stress and optimal N conditions. Indirect selection for GY under LN through performances obtained from HN conditions was found to be inefficient in a study conducted by Indirect selection for GY based on secondary traits is a cheaper approach compared to direct selection for GY due to relatively high heritability of secondary traits and high genetic correlation between secondary traits and GY under LN conditions. As heritability estimates for GY were low to moderate in our study, significant and close correlations between GY and traits with higher heritability, such as PHT and ASI, would be useful for indirect selection. Moreover, correlations between GY under HN and LN would be useful to predict GY under LN based on HN trials. However, the efficiency of indirect selection depends on the strength of the genetic correlation between the environments or traits. In this context, despite positive correlation between HN and LN conditions for GY, the magnitude of the correlation coefficients in our study was small and non-significant in most cases. While in the per se trials, while these were not significant in the testcross trials. per se and testcrosses trials, which indicates a possibility to evaluate PHT under only one N condition.In our study, significant and moderately negative correlations were observed between GY and ASI in the per se and testcrosses, weak to non-significant correlations were observed between per se and testcross data. Therefore, the prediction of testcross performance based on per se information does not seem to be feasible for BGEM materials. This prediction is even more difficult for traits showing high heterotic effect, such as GY. Therefore, while the BGEM per se lines are mainly under additive genetic control, their testcrosses have the effect of dominance and, potentially, epistasis effects. According to per se performance is economically advantageous, but it is only feasible with a high positive correlation between per se and testcross performance.In terms of correlation between traits in BGEM lines 4.3bHLH (Zm00001d005841) displayed a subset of stress-responsive genes in Arabidopsis , which is the main transport channel between cytoplasm and nucleoplasm and plays an important role in stress response. According to nup58 in maize significantly promoted both chlorophyll content and activities antioxidant enzymes under drought and salt conditions. In addition, the expression patterns of the VQ genes (Zm00001d030098) have been analyzed in stress response in maize. According to cdpk (Zm00001d006479) is one of the well-known Ca2+ sensor protein kinases involved in environmental stress resistance  with over 40% of PEV. Although the literature reports few cases of total PEV higher than 30% for GY , the ideOur derived DH lines may be promising materials for further studies on NUE or developing lines with improved NUE. SNPs significantly associated with agronomic traits under LN conditions, which can aid in improving NUE in maize. These SNPs can also be used to select for donor lines or superior breeding lines, after validating these putative SNPs by developing near-isogenic lines for linkage or expression analysis, or through transgenic methods. Our study shows that exotic germplasm from the GEM project are, therefore, useful sources of novel genes to select for yield and other agronomic traits under low N to improve NUE in maize.https://doi.org/10.25380/iastate.24009039.v1.The original contributions presented in the study are publicly available. This data can be found here: DS: Data curation, Formal Analysis, Methodology, Writing – original draft, Writing – review & editing. AS: Formal Analysis, Writing – original draft, Writing – review & editing. PM: Writing – original draft, Writing – review & editing. EP: Methodology, Writing – original draft, Writing – review & editing. GD: Supervision, Validation, Writing – review & editing. MC: Funding acquisition, Validation, Writing – review & editing. MB: Funding acquisition, Writing – review & editing. TL: Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Writing – review & editing.


This paper highlights the relationships between economic weights, genetic progress, and phenotypic progress in genomic breeding programs that aim at generating genetic progress in complex, i.e., multi-trait, breeding objectives via a combination of estimated breeding values for different trait complexes.Based on classical selection index theory in combination with quantitative genetic models, we provide a methodological framework for calculating expected genetic and phenotypic progress for all components of a complex breeding objective. We further provide an approach to study the sensitivity of the system to modifications, e.g. to changes in the economic weights. We propose a novel approach to derive the covariance structure of the stochastic errors of estimated breeding values from the observed correlations of estimated breeding values. We define ‘realized economic weights’ as those weights that would coincide with the observed composition of the genetic trend and show, how they can be calculated. The suggested methodology is illustrated with an index that aims at achieving a breeding goal composed of six trait complexes, that was applied in German Holstein cattle breeding until 2021.Based on the presented results, the main conclusions are (i) the composition of the observed genetic progress matches the expectations well, with predictions being slightly better when the covariance of estimation errors is taken into account; (ii) the composition of the expected phenotypic trend deviates significantly from the expected genetic trend due to the differences in trait heritabilities; and (iii) the realized economic weights derived from the observed genetic trend deviate substantially from the predefined ones, in one case even with a reversed sign. Further results highlight the implications of the change to a modified breeding goal based on the example of a new index comprising eight, partly new, trait complexes, which is used since 2021 in the German Holstein breeding program. The proposed framework and the analytical tools and software provided will be useful to define more rational and generally accepted breeding objectives in the future. Modern livestock breeding programs aim at improving several traits at the same time. Typically, the considered traits have a polygenic background and, with few exceptions (see e.g. ), the aiFollowing , the defIn this contribution, we will consider the case of genomic selection in dairy cattle breeding, where genetic progress is mainly driven by the selection of young bulls based on their genomic breeding values. All candidate bulls have genomic breeding values for the same set of traits and with very similar reliability, because most of the information stems from genomic sources which is uniform among genotyped individuals. The reliability of genomic breeding values is primarily a function of population parameters and technical parameters of the genomic breeding value estimation scheme, like training set size and marker density , and depGiven a certain index, and assuming that genetic progress is primarily due to the selection of young bulls based on this index, which composition of genetic and phenotypic progress do we expect ?Given an observed pattern of genetic progress for a set of traits, what are the ‘realized’ economic weights that would coincide with the observed composition of the genetic trend?How sensitive is the composition of the genetic trend to variations in the composition of the index?What are the consequences of a change in the breeding goal?The main questions, which we want to address here are:We will study this problem with a classical selection index approach, in which we assume that each individual has two sets of traits: for s theory . With thWe consider the case where we have For the To provide a general approach to select Estimated breeding values have a reliability lower than 1, which must be taken into account . To do ttion see .The reliability of a breeding value is defined as the squared correlation between true and estimated breeding values, i.e., Note that with this, the mean , the varThis can be achieved by re-scaling the estimated breeding values in the form Then, With this, the total genetic merit can be defined as x theory , 15 suggWith Note that the matrices resulting from this derivation are identical to those suggested by Miesenberger , which, Remember that it was assumed that the residuals of the estimated genomic breeding values are uncorrelated, i.e., that y argued , 13, 17 m index traits for an unselected sample of contemporary breeding animals. The variance–covariance-matrix of these breeding values Let us assume that we have an empirical set of estimated breeding values The matrix mentclass2pt{minimNote that due to this modification, the resulting index weights in ented by .Following classical selection index theory, the variance of the index is:Applying the general rule in matrix algebra Here A further aspect of practical relevance is how the expected genetic trend translates into a phenotypic trend, i.e., what changes in phenotypes can actually be expected for the different traits and what is the overall composition of the phenotypic trend. The expected genetic trend in trait from Eq. , and sinWe might also be interested in the question of how a change in the economic weight of some traits would affect the composition of the genetic trend. In principle, this could be studied by taking the first derivative of Thus, we propose to calculate an approximate empirical derivation by contrasting the genetic trend obtained with a modified weight vector and the optimal genetic trend for each trait separately. For trait By using  in Eqs. , 4) and and\docu in Eqs. , respectIn an ongoing breeding program, we can measure the empirical genetic progress in the set of relevant traits, i.e., those traits that have a non-zero economic weight in essed in ). Again,For the case of matrix Based on the equation:Putting these realized index weights in Eq.  we can sSince we have dropped the scalar factor n et al.  and laten et al.  or to don et al. , but theRemember that a unique solution for  in Eqs.  and 8)  \documenhttps://github.com/johannesgeibel/IndexWizard) and will be submitted to CRAN soon. This allows researchers and professionals to easily explore the expected outcome of potential changes of the economic weights of an index and to post-hoc analyze whether the expected trend matches the observed trend.The described framework was implemented in the R package “IndexWizard”, which can be accessed from GitHub , which in most cases are composed of several traits. Details can be found in the respective documentation . The traFour of the trait complexes  are present in both indices, albeit with different weights, conformation traits appear in both indices, but with a slightly modified trait complex definition (RZEn vs. RZEo), and three new trait complexes, mainly providing a better representation of health and welfare related traits, have been added in the new index. The former trait complex RZS, representing somatic cell score as an auxiliary trait for udder health, is now included directly in the trait complex ‘Health’ (RZH). The change of index weights reflects the increased emphasis on health and welfare in the breeding goal: while in the old index, milk yield (RZM) had a weight of 45%, it now has a weight of 36% and much of this weight has been relocated to welfare related trait complexes, especially by assigning 18% of the total weight to the new health trait complex (RZH).We first apply the suggested methodology in detail to the old index, and later analyze the expected effects of the change from the old to the new index.The old index with six trait complexes was continuously used since August 2010, when genomic breeding value estimation was officially implemented for the Holstein breed in Germany, with only minor modifications in trait complex definitions and technical details of the trait-specific evaluation procedures since then. For these six trait complexes, we calculated observed genetic trends by regressing the average breeding values of bulls used in a certain year on the average birth year of those bulls, interpreting the slope of this regression as the genetic trend. This was done with data from 2010 to 2020, comprising bulls of the average birth years 2003 to 2016. The composition of the observed trend is displayed in the right column of Fig. We estimated the variance–covariance matrix of the residual errors entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaWe used Eq.  to calcuThe main assumption underlying the calculation of the expected genetic progress is that all selection decisions are made based on the combined index. However, in real life, other criteria can be used: for each bull, not only the estimated breeding value for the combined index is published, but also estimated breeding values for each trait category as well as average daughter performances. Hence, breeders may decide to use a certain bull based on such detailed information, e.g. they may strive to focus on a specific trait complex, or they may prefer bulls from a certain line or origin, regardless of their actual breeding values.In mating software, breeders can configure their own overall index, whereby the official total merit index is preset. Internal evaluations of breeders' individual total indices in such mating software have shown that breeders give on average a greater weight to conformation traits (RZE) in their own index than in the official total merit index RZG.Furthermore, not all genetic progress comes from the selection of young bulls. In modern dairy cattle breeding programs, a small proportion of the overall genetic progress comes from the selection of cows , 24. ThiWe can even assume some effect of natural selection in fitness-related traits , especiaFinally, the expected values are derived under the assumption that the assumed parameters are correct; if this is not the case, the predictions may be biased . This coThere are several possible reasons that explain these differences between the expected and the observed composition of the genetic trend:However, it is very clear that there is no immediate link between the predefined weights in When designing an index, it may be of interest to see what effect it has on the composition of the genetic trend if a particular trait complex is weighted more or less. Obviously, we would expect a greater share of the genetic trend in a given trait complex if we assign more weight to it. However, due to the covariance structure and to the fact that assigning more weight to one trait reduces the relative weight of the other traits, we also expect a correlated response in other trait complexes. Tables Interestingly, on average across all trait complexes, just about half . Note that changes in the economic composition of an index can have a negative effect on the overall efficiency of a breeding program, especially, if important trait complexes are omitted or unimportant trait complexes are given importance, or when the direction of selection is reversed for an important trait complex .The composition of the genetic trend cannot be directly converted into the composition of the phenotypic trend, because genetic progress by one genetic standard deviation has a smaller effect on the phenotypic trend for a trait complex with a low heritability than for a trait complex with a high heritability. The composition of the expected phenotypic trend, scaled in phenotypic standard deviations and resulting from the application of Eq.  is displThe empirically observed genetic trend in the six traits of the index applied over the last 10 years can be used to derive the realized economic weights t}ω [Eq. ], which Finally, the suggested methodology was applied to assess the impact of modifications in the construction of an index. Starting in April 2021, a new total merit index was introduced, which comprises eight trait complexes  loses importance (from 25.4 to 17.5% of expected genetic gain), which presumably is mainly due to the lower economic weight. The new fitness-related traits, RZH, RZKd and RZC, gain importance in the new index since they are directly observed and have been assigned an economic weight. Expected genetic gain in both RZN and RZR increase in spite of the fact that their relative economic weight has been reduced compared to the old index. Presumably, this is due to the inclusion of the health trait RZH, which shows a strong positive genetic correlation both with RZN (+ 0.78) and RZR (+ 0.41). As shown in Table We present a general framework for analyzing the effects of setting an overall breeding objective in genomic selection in complex breeding programs. The proposed approach is based entirely on classical selection index theory , but ado


The aim of this study was to estimate genetic parameters for the reproductive traits of boars based on single-nucleotide polymorphism data. A total of 109,836 semen samples from 2249 boars were collected between 2010 and 2022. Five basic traits were assessed: sperm volume, sperm concentration, motility, number of abnormal sperm, and, for the first time for the local population, libido. In addition, two derived traits were assessed: total sperm count and number of functional sperm. Genetic parameters were estimated using the single-step genomic best linear unbiased prediction method (ssGBLUP). Dam and sire breeds were evaluated separately. The five basic traits were evaluated using five-trait models, while the two derived traits were evaluated using single-trait models. The heritability coefficients had lower values for all sperm quality traits with both methods. For the basic traits, the heritability ranged from 0.099 to 0.342. The greatest difference between dam and sire breeds was observed for the heritability of the sperm concentration trait . The heritability of the libido trait was twice as high for boars of sire breeds as it was for boars of dam breeds. The genetic parameters estimated with ssGBLUP can be used in routine genetic evaluations to improve the pig breeding process. The insemination of sows has become a very useful technique that is widely used in swine production. In addition to the classical productive and reproductive traits of sows and boars, their sperm characteristics and libido also play an important role. An emphasis on improved sperm quality and quantity can be beneficial in terms of the economics of insemination stations , as wellSperm characteristics and libido form the mainstay of the reproductive evaluation of breeding boars. According to Knecht et al. , the maiThe estimation of the breeding values of sperm characteristics and libido is intended to reflect the genetic potential of animals through these traits. The estimated parameters can provide useful information for the establishment of a comprehensive breeding scheme in purebred sire ,12 and dA general task at present is the implementation of molecular information into routine breeding processes to enhance the genetic progress of such traits. The detection and application of novel candidate genes for sperm characteristics through marker-assisted selection is generally considered  to proviEven though semen traits have not yet taken a place among the breeding goals for the Czech pig population , they haThe data, which were provided by the Czech Pig Breeders’ Association, were routinely collected from twelve insemination stations between 2010 and 2022 for genetic evaluation as part of CzePig . Altogether, 109,836 semen samples were collected within the evaluation period. The data included the ejaculates and sexual behavior of boars from two dam breeds  and three sire breeds . The dam breeds are used in the Czech national breeding scheme in the maternal position as they are carriers of excellent female reproductive traits such as numbers of piglets born and weaned, and milk yield. On the other hand, sire breeds are characterized by excellent meat-quality parameters. The design of the study was based on a routine genetic evaluation in the Czech national pig breeding program. In this scheme, a joined genetic evaluation for two dam breeds is used, and separately a joined evaluation for three sire breeds is applied. The reason for this is, on the one hand, the relatively close similarity of the maternal breeds bred in the Czech Republic and, on the other hand, the small population of individual sire breeds. Therefore, two groups (D and S) were formed from the original dataset for animals of dam and sire breeds, respectively. Semen volume (SV)—measured in milliliters per ejaculate;3 cells per mm3;Sperm concentration (SC)—measured as 10Motility (MO)—measured as the proportion of sperm moving in a straight line (as a percentage);Abnormal sperm (AB)—measured as the proportion of deformed or otherwise defective sperm;Libido (LI)—expressing the willingness to mount a phantom sow; this was measured subjectively on a five-point scale, where one was the worst and five was the best expression of libido ; 0 = did not mount.A total of seven traits describing the reproduction of boars were analyzed. The following were assumed as the basic traits:Two other traits were derived from the basic traits:9 sperm:The total number of sperm per boar collection (TNS) in 109 sperm:The number of functional sperm per boar collection (NFS) in 10In total, reproductive traits were available for 2249 boars. The analyses of variances for the evaluated traits and factors were performed in R-project [p-value of Hardy–Weinberg equilibrium of >0.0001, and a minor allele frequency (MAF) of >0.05 were included in the SNP analyses. After the quality-control analysis of all SNPs, the data from 1681 animals containing 32,345 SNPs were used for further investigation. All of the genotypes were stored in TheSNPpit database [Genome-wide data were available for 1763 individuals  born between 2005 and 2022. Bristles, frozen blood samples, ear tissue samples, and used insemination dose samples were employed as the sources of DNA. All DNA analyses were performed at the laboratory of genetics of the Czech–Moravian Breeders’ Corporation . DNA was isolated using the magnetic bead method and the silicate column method for the bristles and insemination samples, respectively. DNA from the blood samples was isolated using the GeneAll Eugene DNA micro isolation kit . First, an evaluation of the quality of the DNA isolates  was performed. The selected DNA isolates were applied to two different arrays. The PorcineSNP60 v2 BeadChip array  and the GGP Porcine 50 k array  were used for 658 and 1105 animals, respectively. The average call rates were 0.99, 0.97, and 0.94 for the bristles, blood samples, and insemination samples, respectively. Animals with a call rate higher than 0.89 were used in the subsequent analyses. Only the SNPs that were present on both arrays were considered for further evaluation . Only SNPs mapped on autosomal chromosomes were considered in this study. PLINK v. 1.9 software  was useddatabase , a perfon represents a permanent environmental effect on the boar; an is an additive genetic effect on the boar; and eijklmno represents a residual effect. The genetic parameters were estimated using the VCE method, and airemlf90 was run for the estimation of the variance components as implemented in [−12 or reached a convergence criterion (at a maximum of 2000 iterations) . The standard errors of estimates were assessed with an approximation method described in the tutorial for the BLUPF90 program [The genetic parameters were estimated with the single-step genomic best linear unbiased prediction method (ssGBLUP) using the phenotypes, pedigree information, and genotypes. Two main datasets were established. The first dataset (D) consisted of information from dam breeds , and the second dataset (S) contained information from sire breeds . The basic boar reproductive traits were evaluated together using a five-trait animal model. Single-trait models were applied for the derived sperm-quality traits . For each method and dataset, a statistical model was formed as follows:ented in . The cal program . Breedin program . The cal program .Collection was started at 313 days of age on average for boars of dam breeds; 54.79 collections were made over a period of 412 days, and the boars produced sperm in 1.15 insemination stations on average. The sire-breed boars were characterized as males that started production at an average age of 338 days and stayed at an insemination station for 489.31 days on average. During this period, an average of 65.00 collections were made, and 1.10 inseminations were performed. The greatest number of collections took place in the months of March and April for both groups of boars. The shortest intervals between collections were also recorded in March and April, again for both groups of boars. Basic information on the evaluated datasets and traits is summarized in The average monthly trends for the evaluated traits in this recent period (2010–2022) are summarized in The coefficients of heritability  and the genetic  and phenotypic  correlations between the evaluated traits in the five-trait ssGBLUP animal models are summarized in The heritability coefficients had lower values for all sperm-quality traits. For the basic traits, the heritability ranged from 0.099 (for SC in dam-breed boars) to 0.280 (for SV in dam-breed boars). Some of the heritability coefficients found for the dam and sire breeds even showed significant differences between the populations. The greatest difference was observed for the SC trait; for dam breeds, it reached a value of 0.099, whereas for sire breeds, it was 0.276. Slightly higher values of the heritability coefficients were obtained in the dam breeds for SV, MO, and AB. The opposite trend was observed for the LI trait (higher heritability in sire breeds). The coefficient of heritability for libido was twice as high for boars of the sire breeds as it was for boars of the dam breeds.Similarly, for the derived traits, which were evaluated separately with single-trait models, lower heritability coefficients were obtained. There were basically no differences when comparing the heritability values between the evaluated populations. Although a small difference was observed for TNS, where the heritability value for the dam breeds was 0.149, for the sire boar population it was 0.123. The heritability coefficient for NFS reached values of 0.153 and 0.152 for the dam and sire breeds, respectively. The variance caused by the permanent effects of derived traits reached values from 0.235 (for TNS in sire-breed boars) to 0.287 (for TNS in dam-breed boars).The genetic correlations among the sperm-quality traits ranged widely from moderately negative to moderately positive. According to the results, libido did not seem to have a negligible genetic influence on some of the evaluated reproductive traits. Moderately positive correlations were found among libido, SV, and MO, whereas a moderately negative relationship was detected with AB when boars of dam breeds were evaluated. A weak negative genetic relationship was observed between LI and SC.In our study, unlike many with a similar focus ,12,18,30The heritability coefficients for the sperm characteristics found in the present study ranged from 0.099 to 0.342. Comparable results were attained by the authors of the studies summarized in The genetic potential of the evaluated sperm characteristics appeared to be similar for the sire and dam breeds. The heritability coefficients summarized in In contrast to our findings, the authors of  obtainedThe genetic relationships between traits, which were expressed as correlation coefficients, reached low to intermediate values in both the positive and negative directions in our study. The strongest appeared to be a relationship between SV and SC . This negative relationship has also been well documented in other studies ,32. Li eThe effects of the insemination station and the year of collection were the main sources of the explained variability in the evaluated semen characteristics and libido of boars of both dam and sire breeds. The heritability of traits in both groups of breeds showed similar values, except for sperm concentration, which, in the case of dam breeds, had a significantly lower heritability. The genetic correlations between most of the semen characteristics and libido were found to be desirable, indicating that common selection would lead to joint improvement. Assessments are essential to ensure an effective genetic-evaluation system for boars in the context of economic consequences for AI stations and integrated production systems. We anticipate that the incorporation of genomic information on an individual basis can enhance the selection accuracy and, thus, selection progress of animals. Other studies should be oriented toward detecting some novel candidate genes for sperm characteristics and genomic evaluation of further traits that are included as selection criteria in boar populations.


The issue of whether increasing inbreeding may be associated with a decrease in the trait values used to select sheep was investigated in all sheep breeds in Germany to obtain a picture of all populations in this country. We analyzed heritabilities and inbreeding depression for the three traits of wool quality, muscling conformation and exterior, for which all sheep intended for breeding are evaluated and upon which breeding decisions in Germany are based. All sheep breeds with sufficient data were included, resulting in 30 different breeds representing all breeding directions in different ecosystems. Heritabilities were across all breeds of moderate size. We estimated the degree of inbreeding depression by animal models and employing linear regressions of the phenotypic trait on inbreeding coefficients calculated from pedigree data. Linear regression slopes were estimated for the individual rate of inbreeding and new and ancestral inbreeding. Inbreeding depression was significant for all three traits when averaged across all 30 sheep breeds and was associated with a reduction in the mean value of the phenotypic trait by 0.33% standard deviation units. Positive effects through ancestral inbreeding seem to have an impact on the exterior of sheep. The results of this study should help to determine the effects of inbreeding on breeding objective traits in sheep breeds.This study provides comprehensive results on the current status of inbreeding depression for traits upon which sheep are selected for the herdbook in Germany. A total of 30 sheep breeds from the OviCap national database met the inclusion criteria for the present analysis regarding the depth and completeness of pedigrees and the number of animals with phenotypic data. We analyzed heritabilities and inbreeding depression for the three breeding objective traits of wool quality, muscling conformation and exterior. Heritabilities were across all breeds of moderate size, with estimates of 0.18 for wool quality and muscling conformation and of 0.14 for exterior. The models employed to estimate linear regression slopes for individual and ancestral inbreeding rates also account for non-genetic effects and the additive genetic effect of the animal. Inbreeding depression was obvious for all three traits when we averaged the estimates across all 30 sheep breeds. Inbreeding depression was significant for wool quality for only a few breeds, whereas for muscling conformation, 14/30 breeds achieved significant estimates. A 1% increase in inbreeding decreased the mean of all three traits across all sheep breeds by 0.33% of their standard deviation. Positive effects due to ancestral inbreeding were only significant in very few breeds in the different traits. Across all 30 sheep breeds, there were indications that purging effects (a reduction in negative effects of inbreeding depression due to selection for heterozygotes) may play a role for the exterior. The results of this study should help for reviewing breeding programs, particularly for sheep breeds with critical effective population sizes and increasing rates of inbreeding, with regard to the selection policy and selection intensity applied. During the long history of domestication of livestock, breeds were developed to meet the needs for the human food supply and to be adapted to the local environmental and climatic conditions. Among livestock species, most breeds can be considered as populations of limited size, because a limited number of reproductive partners contribute unequally to the next generation, and the selected reproductive partners are likely to be related in a quantitative scheme . InbreedUnlike Doekes’ comparative study  on inbreDespite breeding objectives to further improve performance, breed-typical traits and genetic diversity should be maintained at the same time. The results of our last study encouraged us to perform a follow-up study on inbreeding depression in sheep breeds in Germany, particularly as many sheep breeds with different breeding and utilization directions have developed due to the diverse environmental and climatic conditions. For each of the 30 breeds in this follow-up study, results were available on the traits of wool quality, muscling and exterior, so our results again reflect a picture of the situation in German sheep breeding.There is a need for studies that investigate the issue of inbreeding purging and the effects of inbreeding on the adaptability of livestock species . Since iThe main objectives of the present study were to estimate genetic parameters for wool quality, muscle conformation and exterior  and to quantify the extent of inbreeding depression. In addition, we examine whether negative variants may be eliminated through selection, resulting in positive effects associated with ancestral inbreeding coefficients. The present work thus allows for an overall assessment of the influence of the breeding management style practiced in the different sheep breeds from Germany and the resulting consequences with regard to inbreeding depression and purging.As a follow-up study to the earlier work, the data sets used in this paper were extracted from serv.it OviCap by Vit/Verden, Germany. Vit is the leading information service provider for animal husbandry and breeding. With OviCap, the service company Vit makes data from one source available to livestock farmers and breeders. The sheep breeds studied here were selected according to the depth of the pedigrees, resulting from the number of complete equivalent generations (GE), and the number of phenotypic records available. Only breeds with a GE > 3.5 and more than 2000 phenotypic records per trait were considered, resulting in 30 sheep breeds . As amoua_Bal) captures the proportion of the genome of an individual previously exposed to ancestral inbreeding [a_Bal compared to F over generations implies an increase in inbred ancestors in the pedigrees, but not necessarily an increase in the individual inbreeding coefficient.According to Ballou, the ancestral inbreeding coefficient  means that homozygous alleles have already met in former generations, whereas new inbreeding (Fa_New) is caused by alleles that are identical-by-descent (IBD) for the first time in this pedigree. Fa_Kal is zero if classical inbreeding is zero, because common ancestors have to be present on both sides of the pedigree to be able to calculate an ancestral inbreeding coefficient Fa_Kal.According to Kalinowski et al. , ancestra_Bal with an inbred ancestor in each generation of a pedigree. A faster increase in Fa_Bal compared to F across generations indicates an accumulation of inbred ancestors in the pedigrees, but these inbred ancestors do not necessarily contribute to the individual inbreeding coefficient.Ballou’s concept of inbreeding regards all ancestors in the pedigree, unlike its contribution to the individual inbreeding, which results in an increase in FPurging reduces the negative effects of inbreeding depression, because many deleterious alleles express their harmful effects only when homozygous. Reducing the frequency of deleterious alleles in ancestral generations by natural or artificial selection after exposing them to inbreeding leads to purging. Purging is quantified by estimating the linear regression slope of ancestral inbreeding coefficients on the phenotypic trait. Positive estimates for ancestral inbreeding coefficients indicate the presence of purging.The responsibility for the performance tests of German herdbook animals lies with the breeding association and is carried out as a field test, either compulsory or voluntary depending on the breed, by trained personnel  of the respective association. Overall scores for each of the three traits of wool quality, muscling conformation and exterior are recorded for all breeds, for both male and female animals intended for breeding, within the framework of the herdbook entry according to the regulations in the herdbook. The scores awarded by the commission, on a scale from 1 to 9, are valid for the whole life and serve as the basis for the classification of animals by their breeding value and the decision for herdbook entry. A minimum score of 4 must be achieved for each trait for herdbook admission. A score of 9 for wool quality, muscling and exterior is the optimum for an animal of each breed and corresponds best to the breeding objectives. The final scores of all three breeding objective traits and all animals presented at the field test are recorded in OviCap. Therefore, the whole variation in these final scores from 1 to 9 is captured for each breed. The final scores for wool quality, muscling conformation and partly for exterior  are breed-specific. They are thus centered on the breed average and are therefore not comparable between breeds. The evaluation takes place in selected locations for a group of animals from different farms. For the assessment of wool quality, a score from 1 to 9 is given for the assessed criteria including fineness, color, length, density, balance and growth at the shoulder, chest and haunches. It is then summarized with equal weights in a final score. In the case of typical wool defects such as stalky, matted or yellow-sweaty wool, twist, color defects or stitch hairs, the final score is downgraded to 1–4 depending on the grade and extension of the wool abnormality. Instead of the wool quality, the shedding behavior during molting and the coat quality  of hair sheep are evaluated; just as the wool quality, a score from 1 to 9 is given and combined for a final score . The evaFor muscling conformation, the flesh-bearing parts of the chest, shoulder, back and haunch are evaluated and then combined into a final muscling score, with the back and haunch weighted higher. The most important single criteria for exterior include head shape, dentition, horn status, head pigmentation and breed-typical appearance; pigmentation of the wool, legs and head; height at the withers, body length, rump depth and width of the breast; conformation of the neck and shoulder; backline and conformation of the back; length, width and inclination of the pelvis; angle and position of the carpal and hock joints; angle at the pasterns, spread of the claws and movement. The scores of the single criteria are summarized with equal weights in a final score if no defects in the body conformation are observed. In the case of severe defects in body conformation such as underbite, kyphosis, lordosis, broken pasterns or steep ankle posture or signs of disorders of sexual development like testicles that are too small or split, the final score is downgraded to less than 4 in order to exclude animals from breeding.ijklm = overall score for wool quality, muscling conformation and exterior; LOC-YEARi is the ith location by year effect for each breed, with different numbers of levels for each breed; SEX-MULTIPLESj is the jth class of the sex of the animal by number of animals born per lambing for j = 1–2 (sex) by 1–4 ; AGEk = age at scoring in days by six classes for k = 1 (60–129), 2 (130–159), 3 (160–189), 4 (190–365), 5 (360–729) and 6 (730–1095); SEASONl is the lth class of the lambing season for l =1 (December–May) and 2 (June–November) for seasonal breeds otherwise omitted; animalm = random animal effect; and eijklm = random error term.In order to further investigate breeds with similar breeding objectives, we assigned the 30 sheep breeds to seven different breeding directions  with mer1 to b5) on the respective inbreeding coefficients. We employed three differently parameterized models for analyzing the effects of inbreeding coefficients. Model 2 regarded the individual rate of inbreeding (ΔF):The effects of the different inbreeding coefficients were calculated by extending model 1 with linear regressions  and new inbreeding coefficient (FNew) according to Kalinowski et al. (2000) [In model 3, the effects of the ancestral (F. (2000)  were sima_Bal with F, as suggested by Ballou (1997) [a_Bal:In model 4, the classical inbreeding coefficient (F) and the interaction of Fu (1997) , were siVariance and covariance components were estimated with model 1 and using VCE 6.0.2 . For modWe analyzed overall scores for the wool quality, muscling conformation and exterior of 30 sheep breeds . For eacThe mean (median) heritability for wool quality was 0.18 on average across all breeds . The valThe mean heritability of muscling conformation across all breeds was also 0.18, and we found two outliers: Ouessant, with a maximum value of 0.34 ± 0.07, and Carinthian, with a minimum value of 0.02 ± 0.09 . The 25%2 = 0.18) contained 22/30 breeds.The mean heritability for the exterior trait was 0.14, and all but two values were in the range between the upper and the lower quartile. The breed with the lowest estimate was Swifter, with an estimate of 0.02 ± 0.03. The highest value was achieved by Berrichon du Cher, with 0.27 ± 0.08 . The firp-value of 0.0505 for the estimate of −1.59 ± 0.97.A significant negative regression was found for GGH (−6.19 ± 1.74), SKU (−5.17 ± 1.84), MLW (−4.16 ± 1.73), WKF (−3.24 ± 1.52) and CHA (−2.82 ± 1.21), and a significant positive regression was found for NOL (8.58 ± 3.38) . The RHOa_Kal on wool quality were significantly negative for BDC (−19.14 ± 11.05) and LES (−2.59 ± 1.35). MLS showed a positive value of 1.31 ± 0.82, and this result was close to the significance threshold. For the new inbreeding coefficient Fa_New, significant negative results could be detected for CHA (−2.24 ± 0.82), SKU (−2.22 ± 0.70), MLW (−1.29 ± 0.50) and WAD (−1.09 ± 0.41), and an almost significant negative value was found for AST (−0.87 ± 0.54). Nolana was the only breed with a significant positive regression coefficient (3.00 ± 1.68)  .a_Bal was significantly negative for BDC, MFS and LES . The WAD, SKF and OMS breeds showed significant positive results  . The interaction of F × F ± 4.47) .For the individual rate of inbreeding, 14/30 breeds  showed significant negative regression coefficients .a_Kal, only TEX (−2.38 ± 0.93) reached a significant negative value, and only WHH (2.34 ± 1.18) a significant positive value. For Fa_New, all but two breeds  had a negative regression coefficient, and it was significantly negative in 7/30 breeds  (For Fand SKF) .a_Bal was significantly negative for TEX (−6.08 ± 3.69), and WHH was the only breed with a significant positive regression (5.20 ± 2.99)  being significantly negative. The across-breed average was significantly negative. The interaction of F × F ± 2.99) .i (−1.72 to −3.03) , significant negative estimates were obtained for ΔFo −3.03) .a_Kal showed a significant negative regression coefficient in only 2/30 breeds . MLW was the only breed with a significant positive estimate. For Fa_New, 12/30 breeds  had significantly negative estimates  and TEX (−7.62 ± 4.55). A significant positive regression coefficient was obtained for OMS (6.34 ± 3.38).Significant negative regression coefficients for F were estimated in 11/30 breeds  . The intThus, a further objective of the present study was to quantify the degree of inbreeding depression across all 30 sheep breeds and, in addition, to examine whether negative variants may be eliminated through selection, resulting in positive effects associated with ancestral inbreeding coefficients .i, F and Fa_New, whereas significant positive effects on ancestral inbreeding Fa_Kal, F × Fa_Bal were not found. In order to be able to compare the present results with previous reports, estimates of regression coefficients were scaled to the respective phenotypic (bσp) and additive genetic standard deviations (bσa) of the traits using variance components from model 1. For wool quality, muscle conformation and exterior, median per 1% increase in F was −0.33% , −0.33%  and −0.33% , respectively.Overall means for all 30 breeds under study showed significant negative slopes for the regression of wool quality, muscle conformation and exterior on ΔFσp for F were largest among the breeding directions with values of −1.21% (CI25–75%: −1.51 to −0.48), −1.19% (CI25–75%: −1.51 to −0.47) and −1.19% (CI25–75%: −1.54 to −0.48) for wool quality, muscle conformation and exterior, respectively. Using the median decrease scaled to the standard deviation (bσp) of the wool quality, muscle conformation and exterior score per 1% increase in ΔFi, the resulting estimates across all breeds were −1.29% , −1.29%  and −1.25% , respectively.Differences between the breeding directions for the decrease per 1% increase in inbreeding were not significantly different for any of the three traits. However, for heath sheep, the median decreases due to inbreeding depression expressed with bi, Fa_New and F. These significant differences are due to the breeding directions HEA and EXO.We compared the estimates for the regression coefficients between breeding directions and found significant differences for ΔFCompared in the different breeding groups, three of six  showed significant negative regression coefficients .a_New  showed a significant result for Fa_New .Significant negative results for F were estimated for CON and MON .Significant differences between breeding directions were not found.For four of six breed groups , significant negative regression coefficients were obtained .a_Kal, only meat sheep (MEA) achieved a significant negative estimate. Meanwhile, the breeding directions MEA, CON and MON showed significant negative values for Fa_New  for bor sheep , as wellOur data seemed only very slightly or not skewed and not so widely distributed in comparison to the meta-analysis of Doekes . A reasoWe employed linear regressions in agreement with other authors ,34, becaSince the method of phenotype assessment for the selection of breeding animals presented in this study is not comparable with previously published reports, it is difficult to compare the estimated values with those of other breeds. Just as the number of studies for production traits far exceeds that of type traits, this is analogous to the situation of estimating heritabilities, for which far more work was performed than for traits such as wool quality and conformation. For example, Safari has performed studies on genetic correlations and heritabilities of wool parameters , growth  and reproductive traits in merino sheep ,36. For Inbreeding depression is particularly important for traits under selection in breeding . The quep-Value < 0.001) for each of the linear body measurements at all ages studied, and the variation between the three crossbred types was also significant. In agreement with this work [The present work is the first to investigate inbreeding effects in traits upon which the decision to breed directly depends on. Although a number of papers have been published on the subject of inbreeding depression and production traits in sheep breeding, none of the authors have yet investigated all traits used for breeding decisions. For example, Ercanbrack and Knight observed a decrease in fleece weight and body weight as a significant effect of inbreeding in the Targhee and Rambouillet breeds . Similarhis work , a signia_Kal. Thus, purging effects cannot be generally excluded in sheep breeds. Considering the definition of Ballou (1997) [a_Bal would be evidence for the occurrence of purging. Significant beneficial effects were found in more breeds compared to Fa_Kal, with 3/30, 1/30 and 2/30 sheep breeds for wool quality, muscle conformation and exterior, respectively. In managed populations, minimizing inbreeding or kinships are the main approaches for minimizing inbreeding depression, based primarily on genealogical information, but possibly also based on detailed genomic data when available [Recent inbreeding across all sheep breeds was more damaging than ancestral inbreeding in our data. However, a few breeds  had significant positive estimates for Fu (1997) , a signivailable . Eliminavailable ,42. Thenvailable ,44,45,46Inbreeding depression across all 30 sheep breeds was obvious for the individual rate of inbreeding, new inbreeding and classical inbreeding coefficients. Effects of inbreeding depression, expressed as a 1% increase in inbreeding per the trait’s standard deviation, were of very similar size for the traits of wool quality, muscle conformation and exterior. Favorable effects through alleles that were identical-by-descent in ancestral generations seem to play a role in the exterior in sheep breeding, and significant effects have been shown in a few breeds. Efforts to maintain genetic diversity in sheep can be made more efficient by taking inbreeding depression into account, particularly in sheep breeds with increasing trends in individual rates of inbreeding. The results of the present study should be useful in evaluating breeding programs and selection intensity, particularly for sheep breeds classified as threatened.