Optimizing the interplay between sinks and sources is of crucial importance for breeding progress in winter wheat. However, the physiological limitations of yield from source  and sink (e.g. grain number) are still unclear. Furthermore, there is little information on how the source traits have been modified during the breeding history of winter wheat. This study analyzed the breeding progress of sink and source components and their relationships to yield components. Field trials were conducted over three years with 220 cultivars representing the German breeding history of the past five decades. In addition, genetic associations of QTL for the traits were assessed with genome-wide association studies. Breeding progress mainly resulted from an increase in grain numbers per spike, a sink component, whose variations were largely explained by the photosynthetic activity around anthesis, a source component. Surprisingly, despite significant breeding progress in GCD and other source components, they showed no direct influence on thousand grain weights, indicating that grain filling was not limited by the source strength. Our results suggest that, 1) the potential longevity of the green canopy is predetermined at the time point that the number of grains is fixed; 2) a co-evolution of source and sink strength during the breeding history contribute to the yield formation of the modern cultivars. For future breeding we suggest to choose parental lines with high grain numbers per spike on the sink side, and high photosynthetic activity around anthesis and canopy duration on the source side, and to place emphasis on these traits throughout selection. The final grain yield of winter wheat is the result of the number of grains and the grain weight which are determined by the primary yield components: spike number per unit area, grain number per spike, and thousand grain weight (TGW) . The forThe interplay between sinks and sources has an impact on yield formation which becomes apparent from double ridge stage (first spikelet ridges visible) to the end of grain filling. In the very early phase, from double ridge to terminal spikelet stages, a source limitation may result in a reduced spikelet number . Around An ongoing debate is whether grain yield is sink or source limited. Complementary crosses between genotypes with high sink capacity and those with high source capacity resulted in progeny with substantial yield improvement , suggestThe co-limitation of sink and source implies that breeding progress of them should be achieved parallelly. However, the concrete interactions of source characteristics with the sink traits and thereby its role in breeding progress of winter wheat is unclear, especially for the capacity of the canopy to stay green . Since sThe present study aims to decipher the source-sink interdependencies between the yield components during grain filling and to evaluate the contributions of German breeding progress on the sink and source characteristics after anthesis. We used 220 cultivars, 174 of which were released in Germany between 1966 and 2013, representing the breeding history of the last five decades. All cultivars were grown over three consecutive seasons (2014–2017) to study the breeding progress of the source strength  and the sink strength . We hypothesized that high yield of modern wheat cultivars is realized by both a higher grain number and higher TGW with the first being associated with the photosynthetic capacity and leaf area at flowering, whereas the latter is linked to the increase in canopy longevity to assure the source for grain filling. Furthermore, a genome wide association study (GWAS) was conducted to identify the significant quantitative trait loci (QTL) to facilitate marker-assisted selection.https://gbis.ipk-gatersleben.de) were included to enlarge the genetic diversity and improve the reliability of the genome-wide association study (see later section). In total, 220 cultivars were used in this study and the complete list of cultivar names, year, and country of registration, breeder, quality classification, and the assignment to the subsets is provided in Breeding history of German winter wheat was represented by a collection of 174 wheat cultivars released between 1966 and 2013. These cultivars, including 5 hybrids and 169 pure lines, are recommended for conventional production and represent all baking quality classes “E,” “A,” “B,” and “C” . They were selected based on their economical importance in Germany. Each decade in the breeding history was represented by more than 20 cultivars and 66% of the collection were released in the last two decades (2 and in 15 rows in 2 m plot width (13.33 cm row spacing). The plot sizes were 12 m², 10 m², and 9.4 m² in the three consecutive years, respectively. Plots were arranged in a randomized block design with two replications and cultivars were randomized within four sub-groups according to the flowering time and plant height  based on previous knowledge . The plots were treated according to standard agrochemical application in intensive wheat production in Germany (min) measured at the beginning of the growing season in the root zone  at the research station in Ruthe near Hannover . All 220 cultivars were sown in plots with 330 viable seeds moot zone . In each-2) to total dry biomass (g m-2). Numbers of spikes and TGW (g) of these samples were used to determine spikes per m² and grains per spike and m². Plot grain yield and TGW were determined by harvesting the complete plots with a combine harvester. Plot biomass was calculated by dividing the grain yield by the harvest index.Shortly before harvesting the plots, a sample of one row (50 cm in length) was cut to determine the harvest index (HI) by the ratio of grain yield  was visually scored every one to two weeks. Around the heading date (approx. 230 days after sowing), the leaf area index was maximal and was measured by a plant canopy analyzer .Heading date  was recTo quantify the dynamics in the senescence pattern, a logistic power function with two parameters was used to describe the relationships between the fraction of green leaf area  and the thermal time :50 is the temperature sum (°Cd), at which the green leaf area drops to 50% and s describes the steepness of the curve :GLAmax) and duration of it, namely the integral of the logistic curve from heading to harvest:In addition, leaf area duration (LAD) was defined as the product of the maximal leaf area index (LAImax is a measure for the canopy development until heading and a proxy of the biomass accumulation prior to grain filling. GCD is defined as the duration of the availability of photosynthetic leaves from heading to 50% leaf senescence (max), in other words the product of the integrated canopy duration and the canopy size. The photosynthetic activity is difficult to assess in a large scale field experiment. Therefore, the SPAD values of the flag-leaf were measured as a proxy for the photosynthetic activity in 2016 and 2017. For each genotype and replication, five flag leaves were measured at the widest section around the heading dates of that genotype (±10 days).LAIThe phenotypic data collected in the field experiment was evaluated with the following mixed modelijklP was the phenotypic observation of the ith cultivar  in the jthyear  in the kth complete replication and the lth incomplete sub-group . Fixed factors are indicated by lowercase letters, capital letters indicate random effects. The observation was dissected into the general mean, μ, the genetic effect of the ith cultivar ic, the effect of the jth season jy, the interaction of the cultivar and the season ijcy, the interaction of the sub-group, the replication and the season jklGRY, the interaction of the replication and the season jlRY and the residual ijkle. The model was fit to the data with the lmer function of the lme4 package in the R environment (anova function. The best linear unbiased estimators (BLUE) for each cultivar and cultivar within each year were calculated using the lsmean function from the lsmeans package  was the slope of the linear regression line between the year of release and the parameter of interest. The linear regressions were calculated based on sliding window means, where the window for mean calculation is moving on the scale of the year of release with a constant window size of 10 cultivars with cultivars ordered by the year of release. Means and standard deviation of the parameters in each window were calculated. Using the linear regression equation of the absolute breeding progress, the relative four-decades breeding progress (%) of the parameters was described by the ratio between the trait values of 2010 and 1970. It is an estimate for the superiority of the modern cultivar in percent (in the following referred to as relative breeding progress). The breeding progress was investigated for each experimental year separately  and on average .The population of 174 cultivars was used to quantify the breeding progress in winter wheat. The adegenet  was performed to identify marker-trait-associations of the single nucleotide polymorphisms (SNPs) associated with the parameters which were putatively improved with breeding. Leaf DNA samples of the total collection of 220 accessions were genotyped with the 135K Affymetrix TGWEXCAP Array carrying a total of 136,780 SNP markers . The results were filtered with the following criteria 1) uniquely mapped, 2) no gap, and 3) minimum 1 base mismatch, to obtain a total of 92,464 anchored SNP markers. After quality control by filtering monomorphic markers with >10% missing values or a minor allele frequency <5%, a selection of 45,370 high-quality, polymorphic SNPs remained in the data set for further analyses. On average 2,130 markers per chromosome were applied for the genome-wide scan for marker-trait assassinations. The size of the area on the chromosome covered with markers ranged from 473 Mbp (chromosome 6D) to 829 Mbp (chromosome 3B) and hence the marker density lied between one marker per 1.6 Mbp (chromosome 4D) and one marker per 0.2 Mpb (chromosome 5B). The minor allele frequency ranged from 0.19 (chromosome 3D) to 0.28 (chromosome 6A). The allelic associations were calculated for genotypic trait values  of yield, HI, biomass, grains per spike, SPAD, LAImax, and GCD with the polygenic function in the R package genABEL by implementing the population structure and the genome wide kinship matrix (p < 0.05) and the false discovery rate (FDR 10%) were considered as thresholds for significant marker-trait-associations.To anchor the SNP markers to physical positions, 136,780 SNP probes were aligned to the  version ] using B version . Markersp matrix . The Bonp < 0.05). Between the growing seasons all parameter values differed significantly except TGW , SPAD, and the canopy longevity parameters, including green canopy duration  and leaf area duration , were taken as the parameters describing source capacity. All parameters showed significant cultivar and cultivar by year effects, and, except for SPAD, significant differences between years  and these yield parameters indicate that both, the photosynthetic activity (SPAD) and the longevity of the canopy (GCD) are of importance for yield formation.HI and biomass explain variations in grain yield with high accuracies, indicated by the high correlation values on average  of assimilate production around anthesis (r) of up to 0.54 averaged over all seasons  showed on average a significant correlation with GCD with The absolute breeding progress in yield between 1970 and 2010 was clearly linear and was nearly twice as high in 2015 than in 2016 and 2017 (Grain yield can be expressed as the product of biomass and harvest index (HI). The relative breeding progress in yield from 1970 to 2010 may be considered as the result of changes in biomass and HI:With approx. 12 % the relative breeding progress in biomass was similar in all three experimental years  and is improved by breeding with a relative breeding progress of 13% = 5.96), one significant marker was detected for biomass on chromosome 3A (1.93 Mbp) and considering the FDR < 0.1, one additional significant association appears on chromosome 6A for GCD (441.4 Mbp)  by applying high-throughput phenotyping techniques. Aerial imaging is proposed as a promising strategy to estimate the canopy photosynthesis and thereby light utilization on a spatial and temporal scale by multispectral-sensing. The advancement of these techniques will, together with genomics, facilitate a more efficient selection of source parameters and thereby accelerate progress in the final yield .Previous studies on the genetics of stay-green traits in winter wheat were exclusively designed to investigate genetic variation with experiments under different drought and heat stress conditions. A prolongation of the available photosynthetic tissue is known to facilitate yield formation under post-anthesis abiotic stress conditions without detrimental impact under non-stress conditions . The preQTLs of GCD explained up to 22% of the phenotypic variance and at only one single location the SNP markers exceeded the significance threshold (chromosome 6A). Nevertheless, this dataset showed the progress of GCD during breeding history genetically, in parallel to previous findings demonstrating a shift in haplotype blocks with detrimental effects on stay-green through breeding . The conTo our knowledge, there are only two chromosomes, on which no one ever detected a significant marker trait association with a stay-green trait in wheat: 5D and 6D. All other 19 chromosomes have been mentioned to carry some genetic regions relevant for the stay-green trait expression but unfortunately, there is no chromosome, which was conspicuous in all genomic marker association reports. This indicates the great complexity of the trait. Regions on chromosomes 1B and 3B are most prominent as in summary four further groups of researchers detected relevant signals . ContrarThe present study identified the photosynthetic activity around anthesis and the longevity of the green canopy as the relevant source traits ensuring the supply to the increased number of sink organs in the course of wheat breeding. The linkage between duration and capacity of the source and grain number suggests a predetermined longevity of green leaf area around anthesis when the grain number is fixed. Our results suggest placing emphasis on a balanced improvement of floret fertility and canopy longevity during the development of wheat cultivars. Furthermore, combining and selecting the most promising components of sink and source traits may further increase grain yield. The genome wide association study underpinned the association of breeding progress in canopy longevity. Further analyses of allele frequencies and associations with known genes involved in plant development will reveal in depth insights in the interdependencies of the yield relevant traits and whether the theory of unintentional selection can be confirmed.The BLUE-values of the genotypes used in this manuscript are available in ZENODO data repository . The 135The study was conceived by CL and HS. The phenotypic data was generated by CL and T-WC. CL performed the analyses, drafted the manuscript and discussed with T-WC, AS, and HS. All authors have read and approved the final manuscript.This research was funded by the German Federal Ministry of Education and Research (BMBF) grant 031A354 provided to HS within the project Breeding Innovations in Wheat for Resilient Cropping Systems (BRIWECS) as part of the funding initiative Innovative Plant Breeding in the Production Systems (IPAS). We thank Leibniz Open Access Publishing Fund for covering the publication cost.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Feather pecking is a behavior frequently occurring in commercial layer flocks. It often leads to skin injuries and cannibalism. Besides economic losses, severe animal welfare problems cannot be ignored. Previous research has shown that the trait is heritable. Thus breeding against feather pecking is possible, but phenotyping in a commercial environment is economically unfeasible at the moment because of the lack of proper techniques. Therefore, understanding the genetic background of the trait is mandatory to establish a genomic breeding program. This would require genotypic information of the hens, which is feasible under practical conditions. In the present study, we used different methods to identify regions in the genome that influence feather pecking and extreme feather pecking. We found one trait associated with the genomic region. The use of genotypic information from this region in terms of selection against the undesired behavior may help to improve animal welfare in layer flocks.ST approach. In addition, the existence of an extreme subgroup of FP hens (EFP) across both selected lines has been demonstrated by fitting a mixture of negative binomial distributions to the data and calculating the posterior probability of belonging to the extreme subgroup (pEFP) for each hen. A genomewide association study (GWAS) was performed for the traits pEFP and FP delivered (FPD) with a subsequent post GWAS analysis. Mapping of selection signatures revealed no clear regions under selection. GWAS revealed a region on Chromosome 1, where the existence of a QTL influencing FP is likely. The candidate genes found in this region are a part of the GABAergic system, which has already been linked to FP in previous studies. Despite the polygenic nature of FP, selection on these candidate genes may reduce FP.Feather pecking (FP) is a longstanding serious problem in commercial flocks of laying hens. It is a highly polygenic trait and the genetic background is still not completely understood. In order to find genomic regions influencing FP, selection signatures between laying hen lines divergently selected for high and low feather pecking were mapped using the intra-population iHS and the inter-population F Feather pecking is a long known and still existing problem in commercial flocks of laying hens. It causes feather damages and skin lesions often resulting in cannibalism, which is an animal welfare issue and leads to economic losses. For years it has been a topic of intensive research and many aspects influencing feather pecking have already been revealed like stocking density, light intensity, nutrition, or litter . BesidesST index [One approach to identify candidate regions in the genome is to map selection signatures in selected lines. As selection increases the frequency of an advantageous allele, nearby variants in linkage disequilibrium (LD) with the superior allele will also increase in frequency, termed as “hitch-hiking” alleles. At the beginning of selection, this results in long haplotype segments that are surrounding the advantageous alleles. Their increase in frequency in the population is called a “selective sweep” which leads to a reduced genetic diversity in the vicinity of advantageous alleles ,8. HenceST index ,11. ChroFeather pecking is not homogenous within groups of laying hens and several studies reported the presence of a subgroup of extreme feather peckers (EFP), i.e., showing an exceptional high severe feather pecking activity compared to group mates ,13,14,15The aim of the present study was to map selection signatures in lines that were divergently selected for feather pecking. In a second step, we identified extreme feather pecking hens by fitting a mixture of two negative binomial distributions to feather pecking data and calculated the new trait pEFP. Finally, genomic regions associated with feather pecking were identified by conducting a GWAS for the traits feather pecks delivered (FPD) and pEFP. Those regions were further analyzed to reveal the putative candidate genes.Based on a founder line of a White Leghorn layer strain established in 1970 as a control population in the Scandinavian selection and cross-breeding experiment of Liljedahl et al. , divergeThree hatches were produced in two week intervals. The hens of the first two hatches took part in the first experimental run at the age of 33 and 31 weeks, respectively and hatch three in the second run at the age of 32 weeks. One week before behavioral observations, the hens were marked with numbered plastic tags on their back for individual identification and then transferred to observation pens in a ratio of 1:1 of LFP to HFP hens and around 42 individuals per pen in at total seven pens in the first run.Because of less total hens and a lower number of LFP in the second run, six groups each of about 40 hens were used with a ratio of 1:2 LFP to HFP. A 14 hours’ light program was provided by incandescent bulbs from 3 am to 5 pm. There was additional natural light through transparent plastic material at the upper part of the side walls. Depending on the fluctuation of the natural light, light intensity increased occasionally from 20 up to 2500 lux.Observations were done in two sessions each day, starting at 10 am on four consecutive days. In order to ensure a balanced observation scheme, the number of observers corresponded with the number of observation pens (7 in the first and 6 in the second run). Each pen was observed by each observer on each day in 20 min sessions. The observers changed the compartments in a rotational system. This resulted in at total 560 min of observation time in the first run and 480 min in the second. To gain compatibility with data from an F2 design of these lines, observation time was standardized to 420 min . FPD as FPD was recorded as non-aggressive severe pecks or pulls directed to the plumage of group members with sometimes resulting in pulled out feathers and a recipient which tolerates or moves away ,19. A seiy is the number of bpb of each hen i and tiy is the transformed observation. The power parameter −0.2 was used according to Lutz et al. [For the GWAS, FPD was Box-Cox transformed to reduce the deviation of the distribution from a normal distribution. After adding 1 to the FPD recordings the following transformation was applied: z et al.  and Su ez et al.  showing Blood was collected from the hens to extract the DNA and to perform genotyping with the Illumina 60 K chicken Infinium iSelect chip. SNPs with a call frequency lower than 0.95 and a minor allele frequency of zero were filtered out. Additionally, SNPs located on the sex chromosomes as well as SNPs that were not allocated to a specific chromosome according to positional information of the chicken genome assembly GRCg6a were excluded. This filtering resulted in 29,020 SNPs and 494 hens (270 HFP and 219 LFP) with sufficient genotype information. Sporadic missing genotypes were imputed and the genotypes were phased with Beagle 5.0 . The totThe research protocol was approved by the German Ethical Commission of Animal Welfare of the Provincial Government of Baden-Wuerttemberg, Germany .In order to visualize the genetic distance between the divergently selected feather pecking lines, a multidimensional scaling was performed. In the first step, using R package “optiSel” , the segg denotes the number of generations after the base population has been established, which is 15 in our case. It needs to be ensured that the number of SNPs that remained in the dataset after filtering is enough to deliver segments which are sufficiently long. This can be seen as follows. Under the assumption of equally spaced SNPs, The 20 markers per segment are considered to be enough to ensure that two segments with identical marker alleles are not identical by chance . In acco markers . This isThe kinship between individuals The individuals were arranged on a two-dimensional plane such that their distances correspond to their genetic dissimilarities as good as possible by performing multidimensional scaling with R package “smacof” .t with Selection signatures within each line were mapped with the iHS statistic of R package “rehh” ,29. The If the value is smaller than 0, then haplotypes that carry the derived allele are on average longer than the haplotypes that carry the ancestral allele, so it might be expected that the derived allele has swept up in frequency. A large positive value, however, can also indicate a selective sweep. This is the case when ancestral alleles hitchhike with the selected site. Therefore, a two-sided test was carried out. The standardized iHS value was used as the test statistic. The standardization was done conditionally on the allele frequency, which removed the effect of the allele frequency on the distribution of the test statistic. The “rehh” package assumes that the standardized iHS value has a normal distribution . For thiIn order to increase the power of the iHS test, the test was also carried out for both populations simultaneously. First, the standardized iHS values were calculated separately for the two divergently selected lines. The standardized difference of both iHS values was then used as the test statistic, i.e.,Thereby, the mad is the scaled median absolute deviation, which is a robust estimate for the standard deviation of a normal distribution. The test statistic has therefore a standard normal distribution under FST. Similar allele frequencies in the two subpopulations are represented by small FST values whereas different allele frequencies lead to large FST values and thus indicate regions under selection [FST index was already calculated in Grams et al. [FST indices were computed using Equation (8) of Weir and Cockerham [Selection signatures between the HFP and LFP lines were mapped using the genetic differentiation index election . The FSTs et al.  for dataockerham :(6)FST=σFST-values under the null-hypothesis that an allele is neutral was obtained by simulation. Each allele was given a starting allele frequency of 0.5 in the base population. The allele frequencies for the two populations were simulated for 15 generations. For the first 11 generations, the effective population size (Ne) was the same as in Grams et al. [FST values. This revealed the distribution of FST indices under the null hypothesis of genetic drift but without selection. Finally, the p-value for each real SNP  was computed as the proportion of simulated SNPs that showed a greater FST index than the SNP under consideration. FST computations were performed using an own written R script.To account for differences in allele frequencies because of genetic drift, a statistical test was developed by Grams et al. . The diss et al. . From gepgenomewide was set to ≤ 0.05. The other two additional levels of significance were set to pnominal ≤ 5 × 10−4 and pnominal ≤ 5 × 10−5 as well due to the very conservative approach of the Bonferroni correction. False discovery rates (FDR) for every pnominal value were calculated with the R package “qvalue” [The correction for multiple testing was done by applying a Bonferroni correction as “qvalue”  to estimp-values of the combined iHS test and the FST test. This was done as follows using Fisher’s combined probability test [p-value for the In a final step, a meta-analysis was performed by combining the ity test :(7)χ2k2~j (j = EFP or FP) and Iffland et al.  introducmixdist” .k-th time. These values can be estimated from the results of the fit of the mixture of negative binomial distributions as follows [If a hen belongs to subgroup  follows (9)E(Nj)Hence, the separation into pecking motivation periods and number of pecks within pecking motivation periods was not part of the applied ethogram, but is our interpretation of the parameters of the mixture distributions. In a second step, using the estimated parameters of the fit of the mixture distributions, the posterior probability for each hen to belong to the EFP subgroup (pEFP) is calculated as follows:G. For each of the two traits, the following model was applied:y is a vector of observations of the corresponding trait, b is a vector containing the fixed effect of the line as well as a fixed combinational effect consisting of the experimental run and pen. X is the corresponding design matrix, u is a vector of the fixed SNP effects to be tested, and W is the standardized genotype matrix. The random vector g contains the additive animal effects with G is the genomic relationship matrix. The vector e residual effects has distribution I being the identity matrix. For GWAS computation, the minor allele frequency (MAF) was set to 0.01, which resulted in 28,525 remaining SNPs.To analyze the genetic background of pEFP and FPD, a single-marker GWAS was carried out using the software GCTA . The chrThe variance components were also estimated with GCTA , where tA prevalence of 0.24 was specified for pEFP to transform the heritability estimated on the observed scale within a case-control threshold model on the liability scale. The prevalence was estimated from the data.p ≤ 0.05) were used as stated out in Huang et al. [In regions of the genome where QTL are likely according to the GWAS results of pEFP and FPD, screening for positional candidate genes was done going from significant Peak-SNP 1.5 Mb up- and downstream using the NCBI  genome data viewer. The positional candidate genes were then analyzed with the database for annotation, visualization and integrated discovery (DAVID) version 6.8 ,36 to peThe multidimensional scaling plot can be seen in p ≤ 10−5) SNPs on Chromosome 4  with an FDR of 0.021. With the relaxed level of significance , another 92 SNPs on in total 22 chromosomes reached significance (FDR 0.056). The most significant SNPs  were found (in descending order) on Chromosomes 2, 3, 1, 8 and 11. No genomewide significant SNPs could be revealed because SNPs did not reach genomewide significance.Results of Fp-values of the combined iHS statistic and the FST indices is plotted in The meta-analysis of the combination of the In p ≤ 5 × 10−5) SNPs on Chromosome 1 for FPD  on Chromosomes 4 and 3 using a sliding window approach. In the current study as well, Chromosome 3 harbored the second most significant SNPs. The mean FST index in Grams et al. [Nevertheless, Grams et al.  mapped ss et al.  over alls et al. , in the s et al.  versus 2ST indices with the p-values of the combined iHS statistics in the meta-analysis, no more selection signatures reaching nominal significance could be found. A reason why no selection signatures could be detected might be that feather pecking is a highly polygenic trait influenced by many genes with small effects. During selection, selection pressure is distributed on those many genes leading to a slow accumulation of low to medium allele frequencies. Hence, there might be divergent selection but it is not detectable for us with the current study design .After combining the p-values of the FAnother reason for the lack of selection signatures might be as follows. At the beginning of the divergent selection, breeding was successful and the two lines differed recognizably from each other. Over the past generations, the lines remained divergent in the trait because it was still the basis of selection but no more breeding progress could be gained and thus only the status quo was maintained  Figure . A thresThe fit of the mixture distributions revealed the existence of FP and EFP subgroups. The results are confirmed by a previous study where the mixture distributions were fitted to F2 cross FPD data . The prop-values for pEFP were found in one region on Chromosome 1. This indicates the presence of a QTL. Hence, screening of positional candidate genes was done in this window. The terms in the significant cluster of the functional annotation clustering are linked to neurotransmitter-gated ion-channels, particularly gamma-aminobutyric acid receptor A (GABAA). These receptors are made up of five subunits with several isoforms, which can be divided into the following classes: α (1–6), β (1–4), γ (1–3), δ, ε, θ, π, and ρ (1–3) [A receptors are mainly located in the central nervous system. They act as inhibitory ion channels representing an important antagonist to excitatory forces regarding the transmission of axon potentials and thus neuronal activity in the brain [A receptors resulting in a loss of inhibitory processes for feather pecking. Further research is needed to get more detailed information on the role of GABAA in this regard, for example via eQTL studies. Iffland et al. [A receptors on behavior patterns. Bennewitz et al. [2 receptors inhibits GABAA receptor currents [Significantly associated SNPs for both traits with highly significant  ρ 1–3) . The thrhe brain . These fd et al.  already d et al.  it has b . The thz et al.  found a ses: α 1–, β (1–4)currents . As revicurrents  it was rcurrents  identifiDirect observations by several observers for measuring FP behavior, as was used in this study, leads to some limitations. Although our observers were trained to differentiate between severe FP, gentle FP and aggressive pecking, a bias due to subjectivity cannot be completely excluded. In order to minimize this, we used as many observers as we had pens and hence all groups were observed by all observers at the same day in a rotational scheme. Thus, an inter-observer reliability was not calculated. The calculation of the intra-observer reliability requires video-records in order to provide the same feather pecking pattern repeatedly to the same observer. This technique, however, was not applicable in our study because of the relatively large groups with about 40 individually tagged hens. As reviewed by Ellen et al. , it coulMapping of selection signatures in lines of laying hens divergently selected for feather pecking behavior revealed no clear regions under selection indicating that they are either not detectable with the current study design because of the polygenic nature of the trait or that there are no selection signatures because of the lack of stringent selection response over the last generations. A GWAS for the traits feather pecks delivered and the posterior probability of a hen belonging to the extreme feather peckers revealed a region on Chromosome 1 where the existence of QTL influencing the feather pecking phenomenon is likely. The candidate genes found in this region are a part of the GABAergic system which is related to the serotonergic system. Both systems were frequently linked to feather pecking which is confirmed by the current study as well. The candidate genes found in the present study may play an important role in the occurrence of the phenomenon. However, feather pecking is a quantitative trait influenced by many genes with more or less small effects.


We investigated how the COVID-19 crisis and the extraordinary experience of lockdown affected young adults in England and Wales psychologically. One month after lockdown commenced (T2), we assessed 30 psychological and behavioural traits in more than 4000 twins in their mid-twenties and compared their responses to the same traits assessed in 2018 (T1). Mean changes from T1 to T2 were modest and inconsistent. Contrary to the hypothesis that major environmental changes related to COVID-19 would result in increased variance in psychological and behavioural traits, we found that the magnitude of individual differences did not change from T1 to T2. Twin analyses revealed that while genetic factors accounted for about half of the reliable variance at T1 and T2, they only accounted for ~ 15% of individual differences in change from T1 to T2, and that nonshared environmental factors played a major role in psychological and behavioural changes. Shared environmental influences had negligible impact on T1, T2 or T2 change. Genetic factors correlated on average .86 between T1 and T2 and accounted for over half of the phenotypic stability, as would be expected for a 2-year interval even without the major disruption of lockdown. We conclude that the first month of lockdown has not resulted in major psychological or attitudinal shifts in young adults, nor in major changes in the genetic and environmental origins of these traits. Genetic influences on the modest psychological and behavioural changes are likely to be the result of gene–environment correlation not interaction.The online version contains supplementary material available at 10.1007/s10519-021-10050-2. It is rare for such massive and abrupt social change to occur as the world has experienced with the COVID-19 pandemic and lockdown. COVID-19 disease can be a life or death issue for those infected with the virus, but the psychological responses of those infected and of the many more people in lockdown who have not contracted the disease are also of concern. For example, a recent review of 24 studies on the effects of quarantine concluded that ‘the psychological impact of quarantine is wide-ranging, substantial, and can be long lasting’  and one month after lockdown had commenced in the UK (T2). In addition to asking participants how they think the crisis affected them, we compared the same psychological and behavioural traits obtained at T1 and T2 on the same individuals with data at both T1 and T2. To assess the aetiology of individual differences, we used the classical twin design based on the resemblance of identical and non-identical twins. From 17 April to 4 May 2020, we collected online data from 4000 twins in our Twins Early Development Study . However, our focus is on individual differences and their genetic and environmental origins at T1 and T2 and in changes from T1 to T2. On the assumption that the COVID-19 crisis affected people differently, we hypothesised that variance will be greater at T2 than T1 (Hypothesis 2). We predicted that phenotypic correlations will be substantial between T1 and T2 (Hypothesis 3), indicating the stability of psychological traits across the 2-year period.Our overall hypothesis is that genetics, by which we mean inherited DNA differences, is the major systematic force governing how people respond psychologically to the COVID-19 crisis. Specifically, we expected that all traits will show substantial genetic influence at T1, as indicated by a large body of genetic research on psychological traits . That is, most of the genetic effects on T2 scores will be accounted for by genetic effects in common with T1, although there will be some novel genetic effects at T2 independent of T1, possibly due to gene–environment interplay. Environmental effects due to shared rearing or living circumstances during lockdown will be negligible.Finally, we predicted that these results for T2 change will not interact significantly with potential moderators (Hypothesis 8). Lockdown presents a quasi-experimental test of contemporary shared environments by comparing results for twins living together during lockdown and those living apart. If such shared experiences were important, twins locked down together should be more similar than twins living apart during lockdown. On the basis of the generally weak effects of shared rearing environment, we predicted that environmental effects due to living together during lockdown will be negligible. We also investigated other possible moderators of genetic and environmental influences on individual differences in psychological traits before and during the COVID-19 crisis, such as conditions of lockdown, having COVID-19 symptoms, socioeconomic status and gender. However, our power to detect moderation is limited to large GxE effects  In summary, they were:Mean changes from T1 to T2 will be modest and inconsistent.Variance will be greater at T2 than T1.Phenotypic correlations will be substantial between T1 and T2.Heritability of individual differences will be substantial for all traits at T1 and T2. Heritability will be lower for T1 to T2 change scores.For all traits, genetic correlations between T1 and T2 will be high.Environmental influences due to shared rearing or current living circumstances will be negligible for all traits at T1 and T2 as well as for T2 change scores.Similar results will be obtained from a bivariate model-fitting analysis across T1 and T2.These results for T2 change will not interact significantly with potential moderators.All of our hypotheses were preregistered prior to analysis with Open Science Framework: Figure d statistic, which is the ratio of the mean difference to the standard deviation , which seems likely to be due to less opportunity for volunteering during lockdown.Cohen  proposedd of 0.5, considered a medium effect size, accounts for about 9% of the variance. Medium-sized mean differences in the negative direction emerged for three variables. Prosocial Behaviour declined (0.44), which, like Volunteering, might be due in part to reduced opportunity. Achievement Motivation decreased (0.47), which is worrying because emerging adults are our next generation of workers. Verbal Victimisation declined (0.58), which again could be explained by decrease in social interactions, particularly in person, during the lockdown. Hyperactivity-Inattention increased (0.42), which seems to fit with reports that people feel less able to concentrate. Other effect sizes were modest (d = 0.20).A lower than at T1 (1.79). Out of 30 variables, variance decreased in 17 measures and increased in 13 measures (Supplementary Table 3). Many of these variance differences are significant even after correcting for multiple testing, however, the effect size as indexed by F value (ratio between variance at T1 and T2) is small , and the effect sizes were smaller when variance increased from T1 to T2 than when variance decreased. These variance differences were similar for males and females .These mean differences mask a wide range of individual differences. If the COVID-19 crisis affected people in more extreme ways, we would expect to see increased variance at T2. The standard deviations (Supplementary Tables 1 and 2) do not support this hypothesis. The average standard deviation at T2 (1.71) was slightly For these analyses and the following analyses of individual differences, we focused on variables that showed sufficient variability and approached normal distributions, including Achievement motivation, Alcohol use (measured by multiplying the frequency with quantity), Community satisfaction, Conduct problems, Depression, Emotional problems, General anxiety, Healthcare, Hyperactivity/inattention, Importance of relationships, Love and relationships, Media use, Money attitudes, Peer problems, Physical activity, Prosocial behaviour, Purpose in life and Volunteering.If the COVID-crisis re-shuffled the rank order of individual differences, we would expect to see little stability from T1 to T2. Pearson correlations from T1 to T2 are shown in Fig. total variance of the measures was stable from T1 to T2. Taking test–retest reliability into account (through dividing the correlation estimate by the test–retest coefficient) suggests that 68% of the reliable variance of the measures was stable from T1 to T2. This finding indicates that there is still some change between T1 and T2 across the range of psychological and behavioural measures studied here.Reliability of the measures represents a ceiling for stability. In TEDS, we obtained two-week test–retest reliability from TEDS twins on most measures as part of our preparatory work for the 2018 (T1) assessment (Supplementary Table 12). The average test–retest reliability was 0.71, ranging from 0.47 for Importance of Healthcare to 0.84 for Volunteering. The average stability correlation of 0.48 implies that 48% of the Despite the substantial stability from T1 to T2, T2 change scores revealed some individuals who changed dramatically in positive as well as negative directions, as illustrated in Supplementary Fig. 1.Although phenotypic moderation of the psychological response to the COVID crisis revealed many significant interactions between moderators and outcome variables, these interactions did not survive correction for multiple testing using Bonferroni corrections. Moreover, the effect sizes of the interaction terms were small, explaining less than 1% of the variance in all cases (See Supplementary Tables 13–33).Figure At T1, the average twin correlations for identical and non-identical twins were 0.35 and 0.16, respectively. Because identical twins are identical genetically whereas non-identical twins are only share 50% of their segregating genes, the difference in their correlations indexes genetic influence on individual differences, called heritability. Doubling the difference between these correlations suggests a rough estimate of heritability of 35% at T1 because heritability cannot exceed the identical twin correlation. At T2, the average twin correlations for identical and non-identical twins were similar, 0.31 and 0.16, as was the average heritability of 30%, despite the COVID-19 crisis and lockdown.Twin resemblance not explained by zygosity can be attributed to shared environment (C). In other words, the extent to which heritability does not account for the identical twin correlation is a rough index of C. On average, C was negligible at T1 (2%) and T2 (4%).The rest of the variance is attributed to a residual component of variance (E) that includes non-shared environment plus unreliability of measurement. The average E was 63% at T1 and 66% at T2. Test–retest reliabilities suggest that non-shared environment accounted for about half of E at T1 and T2.reliable variance at T1 and T2 can be attributed to inherited DNA differences. In other words, of the total variance at T1 and T2, about 40% can, on average across the measures, be attributed to genetic factors, about 30% to non-shared environmental factors, and about 30% to unreliability of measurement. Shared environmental influence has negligible impact.Deducting the component of variance due to unreliability indicates that about half of the T2 change scores show lower heritabilities, 16% on average. Because T2 change is a residualised score independent of scores at T1, stable genetic influence from T1 to T2 is removed from T2 change scores. Thus, heritability of T2 change scores represents novel genetic influence at T2 that does not affect T1. This new genetic influence could be due to gene–environment interplay: gene–environment correlation, that is where environments young adults chose or were exposed to did not simply happen at random but were correlated with their genotypes; or gene–environment interaction, that is young adults responded differently to the environment (e.g. COVID-19 and associated lockdown) based on their genotypes; alternatively, the new genetic influence can be explained by maturation over the 2-year period. Shared environment, which includes not only shared rearing environment (the twin pairs grew up together in the same family) but also shared experiences during the COVID-19 crisis, has negligible effects on T2 change, 3% on average. Most of the variance of T2 change scores is due to the E component of variance, 81% on average. We cannot separate E of T2 change scores into non-shared environment and unreliability of measurement because test–retest reliability at T1 cannot be assumed to represent the reliability of T2 change scores.These results about variance and covariance gleaned from the twin correlations are highly similar to the results of univariate model-fitting analyses of variance for T1, T2 and T2 change measures, as shown in Fig. The Cholesky Decomposition bivariate model-fitting model separates A, C and E components of variance at T2 into variance in common with variance at T1 and variance at T2 independent of variance at T1. As explained in Methods, the model yields estimates of the extent to which the phenotypic correlation between T1 and T2 is accounted for by A, C and E. The genetic correlations are shown in the top panel of Fig. The Cholesky model also estimates A, C and E components of variance at T2 independent of their respective A, C and E components of variance at T1. These A, C and E estimates at T2 independent of those at T1 (Supplementary Tables 38–43) are, as expected, similar to the A, C and E estimates for T2 change shown in Fig. Figure Finally, we investigated possible moderators of the univariate results. The most novel moderator is whether the twins were locked down together or living apart during lockdown. Lockdown presents a quasi-experimental test of contemporary shared environments by comparing results for the 28% of twins living together during lockdown and those living apart. If shared lockdown experiences were important, twins locked down together should be more similar than twins living apart during lockdown. On the basis of the generally weak effects of shared environment, we predicted that environmental effects due to living together during lockdown are negligible.At first this prediction seemed wrong because the average twin correlation for twin pairs locked down together (0.30) was higher than the correlation for twin pairs living apart during lockdown (0.23), although this difference was not significant (p = 0.051). However, this possible effect of shared environments might be a genetic effect in disguise because identical twins locked down together more often than non-identical twins (32% vs 25%). Results of univariate model-fitting separately for twins locked down together vs apart Fig.  are consPower to detect significant differences for such small effects is negligible. Nonetheless, further support for the hypothesis that the apparent C effect of being locked down together is not really C comes from finding nearly identical A and C estimates pre-existing at T1: A and C are 0.33 and 0.06 for twins together and 0.30 and 0.03 for twins apart. Results of T2 change scores provides additional confirmation in that a similar pattern emerged: A and C are 0.19 and 0.04, respectively, for twins together and 0.14 and 0.02 for twins apart.We also considered other potential moderators. For example, similar to being locked down together or apart, gender is a dichotomous variable that is the same for both members of a twin pair . Separate univariate analyses for male and female twins yielded similar results. These model-fitting results are presented in Supplementary Tables 50 and 51.For the continuous moderator of family SES and for moderators that can be discordant for members of a twin pair , we corrected T2 and T2 change scores for these moderators and repeated the analyses. ACE estimates were similar when we compared estimates before and after correction for these moderators. These model-fitting results are included in Supplementary Tables 52–66.d of 0.24. Importantly, while the average effects on young adults after a month of lockdown were small, it is possible that the effects of the crisis will hit harder later or that longer lockdown or the economic aftermath of the crisis will have a greater effect. We hope to investigate these possibilities with follow-up surveys during 2020–2021.How much has the COVID-19 crisis changed young adults psychologically following the unprecedented COVID-19 pandemic and one month of lockdown? As expected, the 30 measures in our study yielded many statistically significant changes in means. The largest changes in the negative direction were reduced volunteering and achievement motivation and increased hyperactivity-inattention. However, there were as many changes in the positive direction, most notably, reduced verbal peer victimisation. Changes were similar in direction and magnitude for males and females, with the single exception of general anxiety, which increased more for females than males. However, most of these mean changes have modest effect sizes, with an average Why do these young adults in Great Britain show modest negative effects on average after being in lockdown for one month when it is generally assumed that the psychological effects will be substantial? Part of the answer is that research often focuses on statistical significance and mean differences rather than considering effect size and individual differences. With our large sample size, nearly all variables show significant mean differences, but they accounted for less than two percent of the variance on average. Another reason might be methodological. In the present study we did not focus on participants’ subjective reports of how the COVID-19 crisis changed them. Instead, at T2, we asked participants to report, for example, how depressed they felt during the month following lockdown, which we compared to their reports of depression on the same measures in 2018. We found no difference in depression on average.Other reasons why we found few negative effects of the COVID-19 crisis could be that the lockdown was so widespread  or that they are young adults (resilience? insouciance?). Concerning the insouciance hypothesis, we asked participants at T2 how much they were worried about their physical health and mental health during the month since lockdown. The frequency of those reporting that they were moderately, very, or extremely worried was 38% for physical health and 57% for mental health. In other words, they were, quite reasonably, worried, although on average they did not change psychologically, including their symptoms of general anxiety. This can be viewed as a hopeful message that young people on average, are resilient psychologically to an experience as seismic as COVID-19 and lockdown, although these mean differences mask individual differences to COVID-19 and lockdown. It remains to be seen if similar results emerge in other countries, at other ages and after longer exposure to the crisis and its aftermath.The focus of our study was on individual differences rather than mean differences. How much has COVID-19 shuffled the deck of individual differences? The rank order of individual differences was largely stable from T1 to T2, with stability accounting for about 70% of the reliable variance at T1 and T2 on average across the measures. We predicted increased variance in all outcomes if the COVID-19 crisis had a major impact on individual differences, but the variance remained roughly the same. In fact, the stability of all these diverse traits was similar to what we would have predicted after a 2-year period without pandemic , although we cannot be sure that this change in psychological traits happened because of the lockdown or because of various other events that happened over the 2-year period, or alternatively, because of maturation during the 2 years; we hope to address this with further follow-up studies. We also note that present analyses are based on a sample drawn from the population of England and Wales, and the results could differ in countries that implemented lockdown sooner or where lockdown was stricter.We conclude that inherited DNA differences are the major systematic force shaping individual differences in psychological traits at T2 as well as at T1. Genetic effects account for about half of the reliable psychological differences between people at T1 and T2. The environment accounts for the rest of the variance, but it is not the systematic effect of environmental factors often assumed to be important, such as shared family environment. Environmental factors of this systematic sort had negligible effects on variance at T1 and T2 and for T2 change. The environmental effects that make a difference are those that are not shared by twin siblings growing up in the same family or, in our study, by twins locked down together. These idiosyncratic ‘non-shared’ environmental factors are likely to be unsystematic, chance experiences Plomin .https://osf.io/r58be/) hypotheses. This speaks to the replicability of findings from behavioural genetic research on which these hypotheses were based, which is noteworthy given the replication crisis in science in general and in psychology in particular  and data collected 17 April–4 May 2020, approximately one month after the lockdown in response to the COVID-19 pandemic had started (T2). For the COVID-19 assessment, we only invited the subsample of twins for whom we had email addresses, which included many unpaired twins as well as pairs. The twins were invited by email and given a link and code to use to log on to the survey, a platform created and supported by Quodit Ltd. The survey began with an information sheet and consent mechanism. Incentives included a prize draw for iPads and shopping vouchers. Ethical approval was received from King’s College London Research Ethics Committee (Reference number PNM/09/10-104). Although 4 May was the cut-off used for the present analyses, we continued to collect data, which will be used in future papers.For our analyses for this paper, we selected twin pairs in which either one or both twins had at least some T2 data plus at least some T1 data. Of the total sample 5355 individuals had responded at T1, 4052 individuals had responded at T2, and 4000 individuals had responded at both T1 and T2. Sample sizes for each measure at T1 and T2 are reported in Supplementary Tables 1 and 2. All available data were used in the analyses. The total sample size of individuals was 5714, which includes ‘unpaired’ twins in which data from only one member of a twin pair was available. The total number of twin pairs in which both members of a twin pair responded at both T1 and T2 was 1133. Of these twin pairs, 537 were pairs of identical twins, 365 were pairs of same-sex non-identical twins and 231 were pairs of opposite-sex non-identical twins. In order to increase the power of our twin analyses, we combined the two groups of non-identical twins using sex-corrected data, as described later.The sample for the current data collection at T2 for whom we also have data at T1 remains reasonably representative of the population in England and Wales for some key demographic characteristics. For example, our sample was similar to UK equivalents .Our statistical analysis plan was registered in the Open Science Framework, prior to creation of the dataset and prior to analysis . Change scores were calculated by correcting T2 scores for T1 scores using the regression method . Descriptive statistics were calculated for the entire sample, and separately for males and females. Cohen’s d was used to obtain an estimate of the effect sizes of the mean differences Cohen . UnivariPhenotypic correlations were calculated between T1 and T2 scores for the whole sample and for males and females separately as an index of stability. We then compared the stability to test–retest reliability that was obtained in 2018 prior to T1 data collection (Supplementary Table 11). In all phenotypic analyses, we included one, randomly selected, twin from each pair to account for the non-independence of observations in the sample (i.e. twin pairs). The results remained consistent when we examined the other randomly selected half of the sample (Supplementary Tables 7–9).Phenotypic moderation was tested using regression models. We adjusted the significance threshold for multiple testing using Bonferroni correction, therefore, all p values below 0.000007  were considered to be significant.The twin design was used for univariate and bivariate genetic analyses. The twin method offers a natural experiment capitalising on the known genetic relatedness of identical  and non-identical  twin pairs. MZ twins are genetically identical and share 100% of their genes, while DZ twins share on average 50% of their segregating genes. Both MZ and DZ twins are assumed to share 100% of their shared environmental influences growing up in the same family. Non-shared environmental influences are unique to individuals, not contributing to similarity between twins. Using these known family relatedness coefficients, it is possible to estimate the relative contribution of additive genetic (A), shared environmental (C), and non-shared environmental (E) effects on the variance and covariance of the phenotypes, by comparing MZ correlations to DZ correlations. Heritability can be roughly calculated by doubling the difference between MZ and DZ correlations, C can be calculated by deducting heritability from MZ correlation and E can be estimated by deducting MZ correlation from unity  , non-additive (or dominant) genetic (D) and non-shared environmental (E) effects. This model is fitted in cases when intraclass correlations for DZ twins are below 50% of the MZ intraclass correlation—indicating non-additive genetic influences. Although for a few traits the DZ correlation suggested the possibility of non-additive genetic effects, we opted for running ACE models across all variables for three key reasons: first, despite our large sample size, we lacked power to detect non-additive variance reliably; second, conducting the same models across all traits allowed us to meaningfully compare the results across all measures; third, even in studies equipped with the necessary power to detect non-additive genetic effects, it is rare to find a significant contribution of D (and C) for self-reported psychological traits measured in adulthood , indicating the extent to which the same genetic variants influence two traits or measures of the same trait at two times. The shared environmental correlation (rC) and non-shared environmental correlation (rE) are estimated in a similar manner , shared environmental (C), and non-shared environmental (E) components by comparing the cross-trait cross-twin correlations between MZ and DZ twin pairs. This method also enables estimation of the genetic correlation , we calculated ACE estimates separately for each group and compared the univariate ACE estimates between groups. For continuous moderators (SES) and for moderators that were mostly discordant for members of twin pairs , we corrected the trait scores for the moderator using the regression method and repeated the analyses. We then compared the univariate ACE estimates before and after the correction.The Cholesky decomposition  allows for examination of common and independent genetic (A), shared environmental (C) and non-shared environmental (E) effects on the covariance of two or more traits Below is the link to the electronic supplementary material.


Tribolium castaneum. We used artificial selection to generate lines with either high or low dispersal tendency. Our populations responded quickly in the first generations of selection and almost all replicates had higher dispersal tendency in males than in females. These selection lines were used to create a total of 6 additional lines: F1 and reciprocal F1, as well as 4 types of backcrosses. We estimated the composite genetic effects that contribute to divergence in dispersal tendency among lines using line cross-analysis. We found variation in the dispersal tendency of our lines was best explained by autosomal additive and 3 epistatic components. Our results indicate that dispersal tendency is heritable, but much of the divergence in our selection lines was due to epistatic effects. These results are consistent with other life-history traits that are predicted to maintain more epistatic variance than additive variance and highlight the potential for epistatic variation to act as an adaptive reserve that may become visible to selection when a population is subdivided.The genetic underpinnings of traits are rarely simple. Most traits of interest are instead the product of multiple genes acting in concert to determine the phenotype. This is particularly true for behavioral traits, like dispersal. Our investigation focuses on the genetic architecture of dispersal tendency in the red flour beetle,  Drosophila melanogaster is associated with 192 genes, indicating a polygenic pattern.Complex traits are notoriously difficult to study, and dispersal behavior, which plays a significant role in life history, gene flow, and invasive species dynamics is no exception . The genTribolium castaneum is an ideal system for understanding the genetic architecture of dispersal behavior. Tribolium castaneum is a cosmopolitan human commensal stored product pest. These beetles live in a variety of processed grains and frequently disperse to find new mates and resources. Previous studies have shown that dispersal behavior responds rapidly to selection and that males are more likely to disperse than females  are often found to underly complex traits. Epistatic effects describe a case where the contribution of an allele at one locus is dependent on the genotype at a second locus. Maternal effects are common and describe a case where an individual’s phenotype is influenced by the mother’s genotype or condition. The genetic architecture of traits can be investigated using a variety of methods. Genome-wide association studies (GWAS) and quantitative trait locus (QTL) analyses have become particularly popular in the last decade. GWAS and QTL studies are infamous for inferring an oligogenic genetic architecture for complex traits . HoweverT. castaneum. We found that dispersal tendency has both additive and epistatic components that are important in determining variation in the dispersal tendency.We chose to apply LCA which offers a fundamentally different approach to understanding the genetic underpinnings of traits. Rather than focusing on locus identification as GWAS and QTL do, LCA focuses on understanding the mode of gene action that is responsible for variation in the trait of interest. For instance, the genes responsible for variation in a trait could act in an additive fashion, through dominance, or epistasis, or even more complex modes of gene action like additive by sex interactions . Using aT. castaneum was collected from a feed store in Hereford, Texas  in 2014 . The beetles were housed in glass jars with 200 mL of standard media (95% whole wheat flour and 5% brewer’s yeast) in an incubator at 30°C with 60% humidity. Prior to the start of this study, these beetles were maintained by starting a new generation every 45 days by collecting approximately 200 adult beetles from an existing population jar and placing them in a new jar with fresh media. This 5-year period of acclimation to lab conditions ensures that the beetles were not impacted by adaptation to a lab environment during the present study.A population of To measure the dispersal tendency and perform artificial selection, we created a dispersal chamber inspired by previous work  Arnold . This diSelection lines were initiated by collecting 1200 male and 1200 female pupae from the source population. These were subdivided into 3 replicates for the high selection lines and 3 replicates for the low selection lines (for each sex). Each of the 12 groups of 200 sexed pupae were kept isolated in 250 mL fly jars with standard media for up to 1 week to ensure that all of the pupae had become adults.To perform selection, we placed 200 virgin beetles of the same sex in the conditioned media , jar 1 aAfter the 24-hour test period, the selected males and females (approximately 80 to 100 each) from a replicate were combined and allowed to randomly mate. Parents were removed from the mating jar after 14 days and pupae for the next generation of selection were collected beginning on or about 25 days after the initiation of mating. This process was repeated for a total of 5 generations.After 3 generations of selection 100 males and 100 females were drawn from each replicate selection line to act as our high dispersal line (P2) and low dispersal line (P1). When mating beetles for our line crosses we allowed adults to mate for 14 days after which adults were removed and larvae were allowed to develop. The offspring of each cross were sexed as pupae and kept isolated until all beetles had eclosed and then had dispersal tendency measured as described above. Parental lines (P1 and P2) were used to create both F1 and reciprocal F1 lines. F1s were then mated to both parental lines to generate a total of 8 lines. For each cross, both males and females were measured for dispersal tendency. All crosses are depicted in An LCA approach was used to infer the relative contribution of possible composite genetic effects  on divergence in dispersal tendency among our 2 selected lines. This method requires both a mean and standard error for each line included in the study. For each line, we used the 3 replicates to estimate the mean and standard error for a line.Since each line will have different proportions of the parental genome and different levels of heterozygosity, the phenotype for each line has different opportunities to be impacted by possible composite genetic effects. For instance, the phenotype measured in the selected lines P1 and P2 should not be strongly impacted by dominance since they have undergone selection for alleles that contribute to either low or high dispersal tendency respectively. In contrast, the F1 line is expected to be strongly impacted by dominance since it is heterozygous at all loci that carry fixed differences in the parental lines. This characteristic allows us to construct a matrix of coefficients (C-matrix) that describes the opportunity for each possible genetic effect to impact dispersal tendency in each of our 8 lines . Based oUsing this information, we performed an LCA which is a weighted least squares model that allows us to represent a model of genetic architecture as a linear model (1)Where Here We used the software SAGA 2.0 to evaluate all possible models for the genetic architecture of our trait . BecauseTo investigate the veracity of our LCA findings, we performed a forward time diploid, 20 loci, biallelic simulation. We assumed that dispersal tendency could be impacted by up to 20 unlinked loci . To maximize the opportunity for transgressive segregation, we made all dispersal alleles dominant to non-dispersal alleles. Each locus could increase dispersal by 5% if it carried 1 or 2 copies of the dispersal allele. Under this model, a line fixed for all dispersal alleles would have 100% dispersal, and 1 fixed for all alternative alleles would have 0% dispersal.To perform the simulation, we first generated a genome for the high dispersal line (P2) by randomly choosing 12 loci and fixing these sites for the dispersal alleles while the remaining 8 were fixed for the non-dispersal alleles. The low dispersal line (P1) genome was created similarly, but only 1 site was chosen at random and fixed for the dispersal alleles while all other sites were fixed for the non-dispersal alleles. Thus, our simulated P1 and P2 will have a dispersal tendency equal to what we observed in our empirical P1 and P2 lines.https://github.com/coleoguy/dispersal.Using these simulated genomes, we can draw gametes from the P1 and P2 lines . These gametes were combined to generate 100 F1 and rF1 offspring. These F1 genomes were used to generate 100 offspring of each of the 4 backcrosses that we created in our experiment. We then calculated the mean and standard error for the dispersal phenotype for each of the 8 simulated lines. This data was, then, used to perform an LCA in the same fashion as described for the empirical data. This process was repeated 100 times to evaluate the impact of dispersion in an experiment like ours. All analyses and simulations were completed using R, version 3.6.3 . Code anT. castaneum appears to increase with time at least under our experimental conditions. One possible explanation is that we held beetles in single-sex populations and perhaps this leads to increased attempts to disperse when no mate has been located.Our selection lines showed an immediate but short-lived response to selection . The basP-value = 0.018, T = 2.48, df = 37; In accordance with previous research, we found a consistent but weak effect of sex on dispersal tendency. To test the significance of this observation, we used the R package LME4 to fit a mixed model . DispersT. castaneum, we find that a group of just 10 models is necessary to construct a 95% confidence set . These pseudo R2 values ranged from just 0.39 for the autosomal additive only model to 0.99 for the 4-parameter model given the highest weight in our confidence set. When we plotted the observed mean phenotypes and the expected mean phenotypes under this 4-parameter model . Within these 70 datasets, 30, also, were inferred to have a significant epistatic composite effect. However, these simulated epistatic effects were an order of magnitude smaller than inferred with the empirical data . To compT. castaneum dispersal (The present study joins a host of others that concludes that dispersal is polygenic and has epistatic interactions . Our finispersal . HoweverOne assumption of LCA is that there is no dispersion—all alleles that contribute to a higher phenotype are fixed in the high line, and all alleles contributing to a lower phenotype are fixed in the low line. In a short-term artificial selection experiment like ours, this assumption may not be satisfied. In our experiment, we observe transgressive segregation and epistatic composite genetic effects. Both of these characteristics can be due to the dispersion of alleles among the selection lines . To inveResults from our simulation study showed that as expected dispersion can lead to false inferences of epistasis. Out of the 100 simulated line cross experiments, 31 supported a role for epistasis. However, the magnitude of epistasis that we infer in these simulated datasets is strikingly small compared to what we infer from our empirical data. Furthermore, the contribution of epistasis relative to additive variance is remarkably different in the empirical dataset relative to the simulated datasets. We suggest that these findings show that it is unlikely that the large role of epistasis that we infer is simply from dispersion among our parental lines. Furthermore, the relatively small role of epistasis that we infer from dispersion points to an added strength of accounting for model selection uncertainty during LCA not previously documented .The rapid response to selection that we observed in our P1 and P2 lines suggests that there is an additive genetic variance that can be selected upon for dispersal tendency. However, the results of our LCA support a large role for epistatic interactions as the explanation for the total divergence in our 2 parental lines. Though these results may appear to conflict with one another initially, they are not at odds with previous analyses or theory concerning the expected standing genetic variation for traits, like dispersal, that may have a strong link to fitness (Mousseau and If a trait is directly linked to fitness, then, the additive genetic variance should erode relatively quickly as the fittest allele is fixed in the population . In contT. castaneum has shown a positive correlation between fitness and dispersal (Previous work in ispersal . Therefoispersal . This woUnder many circumstances, the additive variation in a trait will determine the outcome of selection . The altOur results show that even for a trait with little contribution from additive genetic effects, epistatic variance may be abundant and may contribute more to divergence in dispersal tendency. Because the conversion of epistatic variance to additive variance is made more likely when populations are small , it seemesaa030_suppl_Supplementary_MaterialClick here for additional data file.


In this study, we proposed two estimators, which can estimate tr(KTK) with greatly reduced sampling variance compared to the existing method under the same computational complexity. We applied this method to 81 traits in UK Biobank data and compared the chromosome-wise partition heritability with the whole-genome heritability, also as an approach for testing polygenicity.The estimation of heritability has been an important question in statistical genetics. Due to the clear mathematical properties, the modified Haseman–Elston regression has been found a bridge that connects and develops various parallel heritability estimation methods. With the increasing sample size, estimating heritability for biobank-scale data poses a challenge for statistical computation, in particular that the calculation of the genetic relationship matrix is a huge challenge in statistical computation. Using the Haseman–Elston framework, in this study we explicitly analyzed the mathematical structure of the key term  K and the mathematical expression can be seen in section Materials and Methods, with its computational cost MN2)] and (ii) the estimation of heritability using linear mixed model [N3)] are computationally expensive ], but the construction of GRM is still needed  constructing the genetic relationship matrix [GRM, denoted as ed Chen, . Using sed Chen, , if not tr(KTK), the trace of the multiplication of GRM with its transpose. Direct computation of tr(KTK) can be time-consuming, at the time cost of N2M), but in RHE the numerical evaluation of tr(KTK) can be realized via a randomization method expressed in quadric form. However, we found that the sampling variance of RHE in the original report is incorrect because of their wrong derivation . In this study, we further investigate the statistical property of RHE, in particular the term about tr(KTK), and its relevant extensions.Even under the HE framework, given the availability of biobank-scale data, such as UK Biobank (UKB) data  is correct but with its sampling variance, which is proportional to tr(KTKKTK), not properly treated in Wu and Sankararaman's original report. We derived and numerically validated the sampling variance of tr(KTK). Second, recently a hybrid routine that can use either individual-level data and summary statistics has also been found ; however, its sampling variance was not available. We provided a similar method as subsampling but with availability of its analytical sampling variance. Third, we partitioned the heritability based on the effective number of markersand applied them in the partitioning of heritability for some complex traits in UKB.This report was written for three purposes. First, we found that the provided nd Zhou, , in whicX, a matrix of N rows—individuals, and M columns—coding the count of the reference allele for a biallelic locus. After standardization for each genotype pl is the allele frequency and K, we can easily derive some characters of K. Denote Ko as the off-diagonal elements, and it is easy to see that N − 1. var (Ko) is the sampling variance of the all off-diagonal elements.For a homogenous unrelated sample, its genotypic matrix can be written as var (Ko) relates to the concept, so-called effective number of markers, denoted as Me thereafter. As noticed, Me is defined as the reciprocal of var (Ko). l1l2) is the expected Pearson's correlation between the Me is a constant genetic parameter. The definition of Me in this report allows researchers to calculate Me based on a reference population of the same origin to the population in question. Similarly, Me.c represents the averaged LD for any pair of markers on the cth chromosomes.Of note, Me. As Me is a critical parameter in many genetic applications, a conceptional parameter is its involvement in genetic prediction  has been initially proposed for the linkage analysis ; in contrast, a method of moment (MoM) can provide equivalent estimation for the heritability for complex traits.We assume thaty is the standardized phenotype for a trait of interest, N individuals and M the biallelic markers, β is the additive effect associated with each marker, e is the residual, h2 is the SNP heritability, and in which Consequently, we extend the work by Wu and Sankararaman ; the momh2 and By taking the differentiation in terms of After algebra, we have the normal equations below:ĥ2 can be written asThe estimator for yTKy can be decomposed as jth marker and y that can be computed via simple linear regression, or multivariate linear regression if covariates are included. It is easy to recognize that N, and a possible non-central parameter related to the heritability of the trait. Alternatively, we derive the mathematical expectation However, different computational strategies deal with the computational expensive part for both the numerator and the denominator. In particular, for the numerator, KTK, a high-order function for GRM. Alternatively, according to the property of the trace of a matrix, it can be calculated that K. From the first glance, it seems inevitable to compute K, the computational cost of which is tr(KTK) but reduce computation cost, three methods are proposed for estimating tr(KTK).The denominator involves the trace of tr(KTK). Sampling method I has been proposed by Wu and Sankararaman, but we provide its correct sampling variance, which was incorrectly given in their original report  and estimates it in a reference population with the similar genetic origin of the population of question. Sampling method III slightly modifies method II if the reference population is big and yields smaller sampling variance of tr(KTK) than that of method II.We present three methods in estimating LB is employed to estimate tr(KTK) in RHE . As LB can be plugged into a normal equation (Equation 2).In each iteration, a vector LB was given as In Wu and Sankararaman's original report, the sampling variance of LB is proportional to tr(KTKKTK), the computational cost of which is likely to be infeasible for biobank-scale data. However, its practical sampling variance can be estimated from B iterations above The derivation of the penultimate step uses the quadratic variance calculation formula. The sampling variance of tr(KTK). It is shown that N is the sample size, a known parameter; we only need to estimate Me. As noted above, Me can be estimated by subsampling a proportion of the study population . We define a new LS estimator: s, there are s2/2 off-diagonal elements and it takes s2M/2) time to calculate LS is, using the Delta method, LS and In an alternative route, we bypass the direct computation of ples see . N is thpulation  or by a pulation . Thus, wmate see . Supposes times in the estimation of variance. With slightly modification, we developed a new estimator LT (lower triangle shotgun sampling estimator) to estimate tr(KTK) in RHE. The difference in sampling schemes between methods II and III can be visualized as s × s after rearrangement and calculates half elements, whereas method III randomly samples n = s2/2 elements in the whole GRM without replacement so as to reduce overlapping of samples /2}, we defineGiven a random subset of LT is an unbiased estimator of tr(KTK) with its sampling variance tr(KTK) and its sampling variance at the same time in one step. It does not need to calculate all the elements in Ko but the corresponding pairs of the individuals, and to calculate the mean of the product of all their genetic values. Therefore, each item in the summation can be computed in M), and the total running time is nM).It can be proved that 2)/n see . Therefotr (KTK) with its subsampling estimators, we can get the synthesized estimator for heritabilityIf we replace ĥ2 can be formulated aswhere and each item in the above formula is estimable, then we can get the variance estimator of the variance componentĥ2, all other parts involved are independent to the phenotype, so given a specific sample of question, the estimator has a linear relationship with the square of the estimated heritability.Except for Yang et al.  estimatecth chromosome and cth chromosome. Under the assumption of polygenicity, in which K in Equation (1) into the GRMs for 22 autosomes, we can also estimate the chromosome heritability jointly in one model. This method has to inverse a 23 × 23 matrix. Under the assumption that the genotype of each chromosome contains the same N individuals, the inversed matrix is completely upon N and Me.c, so a computation cost linear to 23, without bothering the conventional matrix inversion procedure, a computation cost of 233, can be written down analytically. In particular, the cth diagonal element of the inverse matrix is By breaking the GRM of the whole genome Given the definition of the weighted GRMwe can get an estimator of the weighted heritability as well as its variance estimator based on weighted GRM through a similar derivationMe for Kw, and lth SNP with or without the adjustment of covariates. The weighted chromosome-wise partition heritability can be expressed aswhere Me for the cth chromosome and Mc is the number of SNP of the cth chromosome.where P is the number of iterations for convergence. In the LT estimator, the subsample size n ≪ N1.5, so our calculation time is less than BOLT-LMM in theory. In terms of actual calculation, the LB estimator used less calculation time to get an accuracy similar to BOLT-LMM , while the memory of our subsampling estimators is proportional to M and the subsample size s in the LS estimator, which generally does not exceed 10% of the total sample size.The BOLT-LMM method   strength were set as 0–0.2 (weak LD) and 0.6–0.8 (strong LD) with the SNP number M = 2,000, 5,000 and sample size N = 500, 1,000, and 2,000, respectively. (2) The real genotype data consisted of 12,980 adjacent markers on chromosome 22 of 2,000 randomly sampled unrelated white British individuals in UKB. B was set from 5 to 50 and repeated 100 times for each to assess the mean and variance of the three estimators.In the simulation and in the real data, we compared the mean and variance of the three estimators tr(KTK). We chose M = N = 2,000 and strong LD for detailed presentation, and the rest were shown in B. The real sampling variance of LB was several times larger than the analytical incorrect result given in Wu and Sankararaman's study  but was consistent with 2tr (KTKKTK)/B, just the corrected one as derived in this study (Equation 3). The sampling variance of LT was about an order of magnitude smaller than that of LB. The simulation results in the real data shown in Across different parameter settings , it yielded a similar pattern for the evaluated results of LB, LS, and LT in UKB. After quality control, 525,460 autosome SNPs with MAF > 0.01 for 278,788 unrelated British white individuals, whose pairwise genetic relationship coefficient <0.0125, were included for analysis. We set B = 5, 10, 20, 40, 60, 80, and 100, and calculated each of the three estimators 100 times to get the mean and the variance for each B. We compared the means of the three estimators with the expected value of tr (KTK) was expected to be 1,168,573 for each of the three estimators.We compared the performance of the three estimators NMB). The variances of the three estimators LB, LS, and LT for tr(KTK) are listed in LB was large, while the sampling variances of the other two estimators were smaller and the variance of LT was about half that of LS. The variances of each of the three estimators decreased with the increasing B, consistent with the simulation.The calculation was performed on an Intel(R) Xeon(R) Bronze 3104 CPU @ 1.70-GHz server cluster, and about 30 threads were allocated for each calculation. The actual calculation time of the three estimators were basically the same see  and confMe.c for each chromosome (Equation (2) presents how heritability is estimated using all 22 autosomes, and Equation (5) offers an alternative method by summation of chromosome-wise estimation for heritability. For ease of comparison, we only estimated heritability for 81 traits as demonstrated by Ge et al. . We usedromosome , and theN = 270,000). Although the variances of the The estimated heritability of some selected UKB traits is listed in In the comparison of the two kinds of heritability for each trait, all the chromosome-wise partition heritability was higher than the whole-genome heritability except for the trait of the age diabetes diagnosed (the explanation of this exception is given below). For a certain polygenic trait, the heritability attributed to each chromosome was proportional to N for the whole genome in Equation (5), but smaller N were taken in the equation for estimating the heritability of each chromosome singly, as fewer individuals met the quality control standards for a single chromosome. We mentioned in Method that the fast estimation of joint heritability should meet the precondition that N of each chromosome are equal. The heritability estimated by the two methods will be strictly equal if this precondition holds , which was the most time-consuming term in RHE /B could also be derived by the subsampling method (beyond the scope of this study), its time complexity greatly exceeded the calculation of tr (KTK) as far as we know.We also gave the sampling variance of the subsampling estimator, which could be calculated by one sampling without additional calculation. As a result, the variance estimator of the heritability could be easily derived. Although the variance of the LS was always slightly larger than that of LT. This was because LT randomly extracted nearly uncorrelated elements in the lower triangular matrix Ko, while LS extracted all elements in a triangle of Ko . Although their sampling variance was approximately equal to the population variance var(Ko), the sampling variance of LT was relatively smaller because it uses less related individuals.The variance of LT estimator relies on a much larger reference population than that of LS. When the reference sample size is small, it is obvious that LT becomes LS. Therefore, the LT estimator can make full use of large sample size, such as that of UKB. Although the difference between the variances of these two estimators is small, and the difference in the final heritability estimation is even slight, we still provide a novel and simple subsampling idea, which can be used in many situations involving large samples.One possible drawback of the N = 410,638, of various possible relatedness with the 278,788 unrelated samples and reestimated the heritability. The results are listed in In the early analysis of heritability, both GRM and Haseman–Elston regression were applied to related individuals under the context of linkage analysis using sibling data. Under linkage, relatedness is actually related to the concept of identity by descent (IBD). However, with the increasing amount of data, the significance and application range of GRM and HE have been expanded. The unrelated individuals we emphasize here are mainly to distinguish from the linkage analysis of pedigree data. There is no problem in the estimation of heritability with related individuals, as demonstrated below. The expression ples see , which wples see . We haveMe, the effective number of independent SNPs, which is also a critical concept in quantitative genetics. We found that Me plays a pivotal role in the estimation of variance components and heritability. As long as we get the estimation of Me, we can easily get the estimation of its corresponding variance components.Using modified Haseman–Elston regression to estimate heritability is becoming more and more popular in summary statistics. We further explored an important connection between Haseman–Elston regression and Me allows researchers to estimate heritability based on a reference population of the same origin to the population in meta-analysis. However, the existence of family structure will make Me shrink (see Me), and different family structures make it shrink differently, leading to inaccurate meta-analysis. Therefore, we do not recommend using our method in samples with various related individuals, but it raises a very interesting question for the estimation theory using mega-scale family trees (Kaplanis et al., Although we used only individual-level data to estimate heritability in this report, the nature of Me, we can easily extend Me to the dominant model and use the same method to obtain both additive and dominant heritability, as long as their codes for the count of the reference allele are orthogonal, as discussed (Vitezica et al., Me to estimate a genetic correlation for a pair of traits, in which No is the overlap sample size between a pair of cohorts, which have N1 and N2 individuals, respectively.Due to the statistical property of URLs: The related source code, https://github.com/GuoanQi1996/LT-Estimator.https://biobank.ctsu.ox.ac.uk/.Publicly available datasets were analyzed in this study. This data can be found at: Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study.TX developed the method and wrote the manuscript. G-AQ analyzed the data. JZ and H-MX revised the manuscript. G-BC designed the study and improved the manuscript. All authors read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.