FPED) and genomic measures using segment based (FROH) and marker-by-marker (FGRM) based approaches.Phenotypic performances of livestock animals decline with increasing levels of inbreeding, however, the noticeable decline known as inbreeding depression, may not be due only to the total level of inbreeding, but rather could be distinctly associated with more recent or more ancient inbreeding. Therefore, splitting inbreeding into different age classes could help in assessing detrimental effects of different ages of inbreeding. Hence, this study sought to investigate the effect of recent and ancient inbreeding on production and fertility traits in Canadian Holstein cattle with both pedigree and genomic records. Furthermore, inbreeding coefficients were estimated using traditional pedigree measure , respectively. Similarly, an extension in first service to conception (FSTC) of 0.29, 0.24 and 0.31 day in heifers was found for every 1% increase in FPED, FROH and FGRM, respectively. Fertility traits that did not show significant depression were observed to move in an unfavorable direction over time. Splitting both pedigree and genomic inbreeding into age classes resulted in recent age classes showing more detrimental inbreeding effects, while more distant age classes caused more favorable effects. For example, a − 1.56 kg loss in 305-day protein yield (PY) was observed for every 1% increase in the most recent pedigree age class, whereas a 1.33 kg gain was found per 1% increase in the most distant pedigree age class.Inbreeding depression was found for all production and most fertility traits, for example, every 1% increase in Inbreeding depression was observed for production and fertility traits. In general, recent inbreeding had unfavorable effects, while ancestral inbreeding had favorable effects. Given that more negative effects were estimated from recent inbreeding when compared to ancient inbreeding suggests that recent inbreeding should be the primary focus of selection programs. Also, further work to identify specific recent homozygous regions negatively associated with phenotypic traits could be investigated. Over the past decade, Canadian Holstein cattle populations have experienced an increase in the annual rate of inbreeding from 0.08 to 0.23%, which were observed from 2000 to 2010 and 2010–2018, respectively . In the Before the availability and popularity of genomic data, estimation of inbreeding depression was predominantly done by calculating inbreeding coefficients from pedigree data and regressing any trait of economic interest on the inbreeding coefficients , 10. MorIdeally, the aim of the genetic selection being practised in livestock species is to increase the frequency of favorable alleles, thus, increasing the level of homozygosity. In essence, inbreeding could result in the depression or enhancement of any trait of economic interest, therefore not all inbreeding is detrimental. Inbreeding increases the expression of deleterious recessive alleles, which are naturally or artificially selected against in a process called genetic purging , 20. Witg centiMorgans (cM), where g is the number of generations to a common ancestor [The partitioning of inbreeding into recent and ancient inbreeding can be examined with pedigree and genomic data. For pedigree data, recent inbreeding can be estimated by tracing the pedigree back relatively few generations to the common ancestor, while ancient inbreeding traces back the pedigree to a more distant common ancestor . In addiancestor .The objectives of this study were to 1) estimate the effect of inbreeding on production and fertility traits in Canadian Holsteins using pedigree and genomic information; 2) assess the effect of recent and ancient inbreeding on production and fertility traits in Canadian Holsteins.The basic descriptive statistics of the phenotypic data are presented in Table FPED and FROH and 0.61 for FPED and FGRM. A correlation of 0.97 was estimated for FROH and FGRM , respectively, whereas, a correlation with a more distant pedigree age of inbreeding (FPED7 − 6) was equal to − 0.12, − 0.13 and − 0.12, respectively. Similarly, correlations between FPED, FROH and FGRM with FROH > 16 were estimated to be 0.51, 0.77 and 0.76, respectively, in contrast to − 0.10, − 0.06 and − 0.08 for FROH2 − 4, respectively. For the model-based age of genomic inbreeding, the correlations ranged from 0.44 to 0.65 for the most recent age and − 0.01 to 0.00 for the most distant age of genomic inbreeding with the classical inbreeding measures. The movement in different directions of the correlations with the different classes of the age of inbreeding was notable, with correlations ranging from − 0.45 to 0.11 for the pedigree classes, − 0.17 to 0.17 for the ROH classes and − 0.48 to 0.06 for the model-based classes  was observed for all production traits based on FPED, FROH and FGRM  increase of 0.29, 0.24 and 0.31 days in FSTC for every 1% increase in inbreeding coefficients based on FPED, FROH and FGRM, respectively, which represents 1.50, 1.24 and 1.60% of the phenotypic means. Despite the statistically non-significant effects (P < 0.44) for cows, a 1% increase in inbreeding coefficients based on FPED, FROH and FGRM resulted in an extension of 0.16, 0.19 and 0.19 days, respectively, for FSTC. In addition, both heifers and cows showed genomic inbreeding depression for number of services (NS). For instance, a 1% increase in FROH resulted in a 0.78 and 0.83 chance of getting re-inseminated after the first insemination for heifers and cows, respectively. An inbreeding depression of 0.96 was observed in NS (P < 0.01) for a 1% increase in FPED for heifers, while a statistically non-significant (P < 0.51) effect of 0.45 was observed for a 1% increase in FPED for cows. To further support the effect of inbreeding, differences in the phenotypic means of animals with low inbreeding levels (5th percentile) and high inbreeding levels (95th percentile) were estimated and are presented in Table FPED, FROH and FGRM, respectively. In a similar fashion, animals with low inbreeding coefficients had 3.26, 5.04 and 7.10 kg more FY based on FPED, FROH and FGRM, respectively, when compared to animals with high inbreeding coefficients. For fertility traits, heifers with high inbreeding levels had on average 6.40, 6.71 and 5.39 more days to age at first insemination (AFS) based on FPED, FROH and FGRM, respectively. Likewise, 2.83, 4.12 and 3.87 less days for FSTC was estimated based on FPED, FROH and FGRM, respectively, for heifers with low inbreeding compared to heifers with high inbreeding. For cows, a more evident increase in NS of 3.56, 1.04 and 1.82% based on FPED, FROH and FGRM, respectively, was estimated for highly inbred cows in comparison to lowly inbred cows.Statistically significant inbreeding depression , which showed a 0.42 increase in days for a 1% increase in FPED4 − 3 (P < 0.05).Splitting the pedigree inbreeding coefficients into different age (generation) classes showed varying effects on phenotypes. Interestingly, inbreeding occurring within the most recent five generations resulted in unfavorable and statistically significant depressing effects on phenotypic traits, however, more distant generations showed favorable, but a statistically non-significant effects on phenotypic traits Fig. . A 1% inP < 0.05  was not statistically significant for all ROH classes, however, shorter segments (ROH < 4 Mb) showed favorable effects while longer segments (ROH > 4 Mb) had unfavorable effects. For AFS in heifers, unfavorable inbreeding effects for all classes of ROH were observed, but only ROH > 8 Mb showed statistical significance (P < 0.05). Additionally, a statistically significant and unfavorable effect of 0.62 and 0.96 was obtained for a 1% increase in FROH8 − 16 and FROH > 16 for NS, respectively, whereas a statistically non-significant, but favorable effect of − 2.26 and − 0.07 was obtained for, FROH1 − 2 and FROH2 − 4, respectively. For fertility traits in cows, only an unfavorable and statistically significant (P < 0.05) effect on NRR for ROH >16 Mb was observed. In general, cow traits follow a similar pattern with shorter segments tending to have favorable effects, while longer segments tending to be unfavorable.ROH was split into age classes with longer ROH indicating more recent inbreeding and shorter ROH suggesting more remote inbreeding. Although the effect of all ROH classes were unfavorable for production traits, only ROH classes with segments longer than 4 Mb were significant at .05 Fig. . For exaFHBD1, FHBD2 and FHBD3 corresponded to a − 40.79, − 33.76 and − 30.53 kg loss in MY, respectively. In contrast, a 1% increase in FHBD4 and FHBD5 was related to 10.06 and 15.65 kg gain in MY, respectively. For fertility traits, a 1% increase in FHBD1 and FHBD2 in heifers prolonged FSTC by 0.28 and 0.28 days, respectively. Conversely, a 1% increase in FHBD5 reduced FSTC by 0.42 days, although, this was statistically non-significant. In addition, a statistically significant increase of 0.83 in NS for cows with a 1% increase in FHBD1 and a statistically non-significant decrease of 0.22 for every 1% increase in FHBD4 in NS in cows was estimated.The age of inbreeding estimated using the model-based approach provided varying effects on phenotypes. Based on this approach, more recent age of inbreeding had statistically significant and unfavorable effects on production traits and more distant ages had statistically non-significant and favorable inbreeding effects Fig. . A 1% inFk _ NEW and Fk _ ANC  by 0.27 and 0.42 days, respectively [FROH and FGRM, respectively. Using genomic inbreeding, Martikainen et al. [FROH and FGRM, respectively. This is in line with the 301 and 315 kg difference between lowly and highly inbred cows reported by Doekes et al. [FROH and FGRM, respectively. Despite FPED having a higher estimated effect of inbreeding on phenotypes compared to FROH, FROH accounted for a larger difference in phenotypic means between lowly and highly inbred animals. These results are similar to those reported in Doekes et al. [FROH over FPED.As with other studies, a 1% increase in pedigree inbreeding has been shown to have a significantly negative effect on production traits –36, whicectively . This trn et al.  also fous et al.  and 161 s et al.  using FRs et al.  and is mFPED5). In addition, Doekes et al. [FPED7 − 6 on MY, FY, PY, IFL and calving interval (CI). These findings are in line with the favorable, but non-significant effects of FPED7 − 6 and FPED8 − 7 on production traits, AFS and FSTC in the present study. The consistency between these studies suggest that recent inbreeding is more detrimental than ancient inbreeding. Previous researchers have found effects of different ROH length classes on phenotypes [Few studies have investigated the effect of pedigree and genomic inbreeding age classes on phenotypes , 23. Thes et al.  reportedenotypes , 38. In enotypes  found thenotypes . Generalenotypes , 40. In enotypes . In an aenotypes , 42. To enotypes , the modFNEW and − 5.52 to 15.51 per unit increase in FANC for the number of pups in first litter. Thus, indicating that new inbreeding causes more deteriorating effects, whereas old inbreeding causes lesser deteriorating effects and sometimes favorable effects. Using Kalinowski’s [FK _ NEW and old FK _ ANC inbreeding, Mc Parland et al. [FK _ NEW. In addition, they observed a significant, but less unfavorable effect of − 8.8 kg and 0.52 day for MY and AFC, respectively, per 1% increase in FK _ ANC. In Dutch Holstein-Friesian cattle, Doekes et al. [FK _ NEW and a non-significant, but favorable effect of 0.03 kg for 305-day FY per 1% increase in FK _ ANC. Those authors mentioned evidence of purging due to favorable effects found with FK _ ANC. In the present study, no significant effects were observed for production traits, however, estimates for FK _ ANC were favorable for MY and PY, whereas FK _ NEW showed unfavorable effects for MY and PY. Conversely, a favorable effect was detected for FY when using estimates from FK _ NEW and FK _ ANC. For fertility traits, significant effects were found only for AFS and CTFS. A favorable effect of − 0.77 and − 0.94 days for AFS and CTFS, respectively, per 1% increase in FK _ ANC, while an unfavorable effect of 1.58 and 1.00 days for AFS and CTFS, respectively, was found for every 1% increase in FK _ NEW. The varying results among these studies could be due to the differences in the populations used, which are subjected to different selection criteria. In the present study, there seems to be no evidence of purging and given the rate at which inbreeding is increasing following the implementation of genomic selection [Some studies have evaluated the effect of new and ancestral inbreeding on phenotypic traits , 43, 44.nowski’s  approachs et al.  found a election , 20. In election , 46. Theelection , 47 and election .A significant and unfavorable effect of classical inbreeding on all production traits and some fertility traits was found. Genomic inbreeding measures seemed to capture more phenotypic differences between lowly and highly inbred animals. Recent inbreeding was found to show more detrimental effects on both fertility and production traits than ancient inbreeding. However, no substantial evidence of purging was uncovered with ancestral inbreeding. The model-based approach of classifying inbreeding into age classes provided similar results to the pedigree age of inbreeding, hence, in the absence of pedigree records, genomic measures could be used. Overall, heterogeneity of inbreeding depression was observed with recent and ancestral inbreeding. In future studies, the molecular architecture of inbreeding could be investigated to identify regions negatively associated with phenotypic traits.Pedigree records for all available animals with genotype and phenotype data were provided by Canadian Dairy Network . The pedigree information consisted of a total of 259,871 individuals that trace back to 1950 as the base year. To ensure that inbreeding estimates were not severely underestimated, pedigree completeness index (PCI) going back five generations and the number of complete generation equivalence (CGE) were estimated using EVA software . AnimalsA total of 50,575 genotyped Holstein cows were available with birth year ranging from 1999 to 2017. Cows were genotyped with the Illumina BovineSNP50 Chip (50 K)  and lower density array panels (10 K - 30 K). Animals with lower density genotypes were imputed to medium density (50 K) using FImpute software . After qPhenotypic records of 46,430 cows with first calving date that ranged from 2008 to 2018 were available for production and fertility traits. For production traits, a total number of 21,194 cows had first lactation records on a 305-day basis for milk yield in kg (MY), fat yield in kg (FY) and protein yield in kg (PY). Fertility traits had a total of 52,948 records and these were split up into heifer (first parity) and cow (second parity) traits. Of these records, 33,610 were for heifers and 19,338 were for cows and all animals with cow records also had heifer records. The following fertility traits were considered in this study: age at first service in days (AFS); days from calving to first service (CTFS); number of services (NS); first service non-return rate to 56 days (NRR); days from first service to conception (FSTC). All traits recorded before and during the first parity are termed heifer traits and traits recorded after the first parity were cow traits. NRR was coded as 1 when no subsequent service took place between 15 and 56 days following the first service and coded 0 if otherwise. NS was coded from 1 to 10 and animals with more than 10 services were assigned as 10. AFS was measured in days and considered to be a heifer trait. CTFS was measured in days and considered to be a cow trait. FSTC was measured in days and considered to be both a heifer and cow trait.Pedigree and genomic data were both used in calculating inbreeding coefficients. With pedigree data, inbreeding measures were divided into three categories: 1) classical pedigree inbreeding measure; 2) pedigree age of inbreeding measure and; 3) ancestral pedigree inbreeding measure. For genomic data, inbreeding measures were divided in two categories namely 1) classical genomic inbreeding measure and 2) genomic age of inbreeding measure. A detailed explanation of these categories follows below.FPED) was estimated for all individuals with phenotypic records by tracing back the pedigree to the founder generation using the algorithm proposed by Meuwissen and Luo [n generation ago to common ancestors, where n represent the specific number of generations to the common ancestors. More specifically, the inbreeding age classes attributable to ancestors from a specific generation is the difference between two successive generations. For example, inbreeding coefficients that occurred due to ancestors in generation seven (FPED7 − 6) can be calculated as the difference between inbreeding coefficients obtained tracing back to seven generations ago FPED7 and coefficients obtained tracing back to six generations ago FPED6 . This procedure was performed to categorize inbreeding into age classes from most recent to ancient inbreeding. The most recent age traced back was three generations ago (FPED3) because the number of inbred animals in generation two were less than 0.02% of the sample size, while the most ancient age was traced back to generation eight (FPED8) due to having similar inbreeding coefficients with older generations. Pedigree age of inbreeding was estimated using the vanrad.f function implemented in PEDIG software [FPED into new inbreeding (Fk _ NEW) and ancient inbreeding (Fk _ ANC), therefore, FPED = Fk _ NEW + Fk _ ANC. The difference between Fk _ NEW and Fk _ ANC is that Fk _ NEW is the probability that alleles in IBD state of a given individual is occurring for the first time in the pedigree of the individual, while Fk _ ANC is the probability that IBD alleles in an individual have occurred previously in at least one ancestor. Kalinowski ancestral pedigree inbreeding was calculated using a gene dropping approach with 106 replications as implemented in GRAIN [Classical inbreeding coefficient ( and Luo  as imple and Luo . Pedigresoftware . Ancestrsoftware  with thesoftware  further software  by splitin GRAIN .FROH) and 2) marker-by-marker based approach (FGRM). Runs of homozygosity were identified with the deterministic sliding window approach implemented in PLINK using the following criteria: a minimum physical length of 1 Mb; a maximum gap of 500 kb between two successive SNP; a minimum of 20 consecutive homozygous SNP and a minimum density of one SNP per 100 kb. The following formula was used for calculating individual segment based genomic inbreeding:ith individual, jth ROH segment in bp, n is the total number of detected ROH and LAUTO is the total length of the autosomes covered by the SNP in bp.Two approaches were used in estimating the classical genomic inbreeding: 1) segment-based approach (runs of homozygosity (ROH); G) following the proposition of VanRaden [ith individual and Gii is the diagonal element of the genomic relationship matrix.Inbreeding in the marker-by-marker based approach was calculated by subtracting one from the diagonal of the genomic relationship matrix  1–2 Mb; 2) 2–4 Mb; 3) 4–8 Mb; 4) 8–16 Mb; and 5) > 16 Mb length classes. These length classes indicate inbreeding resulting from ancient to most recent ancestors. Additionally, genomic age of inbreeding was estimated using the model-based method that uses a Hidden Markov Model (HMM) approach to identify homozygous by descent (HBD) segments [Rk is the rate specific to the kth class. Thus, the length of an HBD segment of any kth class is exponentially distributed with rate Rk. In the current study, a model with 5 HBD classes was defined following predefined default rates as implemented in the R statistical package “RZooRoH” [The genomic age of inbreeding was estimated by classifying already identified ROH length into five different length classes to specify the approximate age or generation in which they occur. As mentioned earlier, deducing the age of inbreeding from ROH length is an expectation that follows an exponential distribution with a mean of 100/2 segments . With thRZooRoH” , 42.a); and error term (e). Inbreeding depression was estimated separately for each trait using the following linear mixed model:y is a vector of phenotypic measurement for MY, FY, PY, AFS, CTFS, NS, NRR and FSTC, b is a vector of systematic effects, β is the coefficient of the linear regression on F, F is a vector of inbreeding coefficients from pedigree or genomic data , a is a vector of random additive genetic effects, cj is a vector of jth non-genetic random effects  and e is a vector of random residual effects, n is the number of non-genetic random effects, X, Z and Wj are incidence matrices that link the fixed effects, random additive genetic effects and jth non-genetic random effects to the phenotypes, respectively. The assumptions for the random effects include: A is the numerator relationship matrix and I is an identity matrix. For age of inbreeding and ancestral inbreeding, inbreeding depression was estimated using the following linear mixed model:βk is the coefficient of the linear regression on inbreeding coefficients within the kth class of inbreeding (Fk), m is the number of inbreeding classes, and all other parameters are the same as mentioned in model I.To estimate the effect of inbreeding on phenotypes, the same models used in the national genetic evaluation for Canadian Holsteins were adapted from Jamrozik et al. , with thAll linear models in this study were fitted using the restricted maximum likelihood procedure implemented in ASReml 4.1 .


Manihot esculenta Crantz)fortifies cassava with β-carotene by breeding for carotene-rich tubers(yellow cassava). However, a negative correlation between yellowness and drymatter (DM) content has been identified. We investigated the genetic control ofDM in white and yellow cassava. We used regional heritability mapping (RHM) toassociate DM with genomic segments in both subpopulations. Significant segmentswere subjected to candidate gene analysis and candidates were validated withprediction accuracies. The RHM procedure was validated via a simulation approachand revealed significant hits for white cassava on chromosomes 1, 4, 5, 10, 17,and 18, whereas hits for the yellow were on chromosome 1. Candidate geneanalysis revealed genes in the carbohydrate biosynthesis pathway including plantserine–threonine protein kinases (SnRKs), UDP (uridinediphosphate)-glycosyltransferases, UDP-sugar transporters, invertases,pectinases, and regulons. Validation using 1252 unique identifiers from the SnRKgene family genome-wide recovered 50% of the predictive accuracy of whole-genomesingle nucleotide polymorphisms for DM, whereas validation using 53 likely genes(extracted from the literature) from significant segments recovered 32%. Genesincluding an acid invertase, a neutral or alkaline invertase, and aglucose-6-phosphate isomerase were validated on the basis of an a priori listfor the cassava starch pathway, and also a fructose-biphosphate aldolase fromthe Calvin cycle pathway. The power of the RHM procedure was estimated as 47%when the causal quantitative trait loci generated 10% of the phenotypic variance(sample size = 451). Cassava DM genetics are complex and RHM may be useful forcomplex traits.The HarvestPlus program for cassava ( Regional heritability mapping (RHM) is effective for understanding thegenetic architecture of complex traits in cassava.Prediction accuracies can reflect the impact of genomic segments on cassavadry matter (DM) content.Serine–threonine protein kinases (SnRKs) are candidates positionallyassociated with cassava DM.The prediction accuracy of SnRKs for cassava DM was 50% of the total accuracyfrom genome-wide single nucleotide polymorphisms.Cassava currently ranks as the sixth world staple crop consumed by morethan 500 million people in Africa, Asia, and South America  Lam.], maize(Zea mays L.), rice (Oryza sativa L.), andwheat (Triticum aestivum L.). Biofortification of cassava is gearedtoward breeding varieties containing increased levels of Provitamin A, orβ-carotene, a precursor for Vitamin A. The so-called ‘yellowcassava’ ” procedure.–1) ; the percentage of DM ofstorage roots, which measures root dry weight as the percentage of the rootfresh weight; and pulp color a binary trait rated on a scale from 1 (white tolight cream root flesh) to 2 (deep cream to yellow root flesh). The DM trait wasmeasured via the oven method: 100 g of grated root sample (with thorough mixingof 10–15 randomly selected roots from a plot) were collected peraccession and oven-dried. Dry matter content was then measured as residualweight after oven drying. We further divided the GG population (713 clones) intotwo subpopulations of white (451 clones) and yellow (262 clones) cassava withthe pulp color trait where clones with a score of 1 for this trait were groupedinto the white population and those with score 2 into the yellow population.We used phenotypic data collected from the Genetic Gain (GG) population trialsconducted by the cassava breeding program at the IITA, Ibadan, Nigeria for ouranalysis. The GG population (713 clones) is an elite population bred from the1970s to 2007 by the cassava breeding program at the IITA . These trialswere planted with an augmented design consisting of 20 to 30 blocks with 22 to24 clones and two checks in each block. Plots were a single row of five-plantstands (1 by 1m spacing) without borders and without replication, and trialswere planted during 2014 and 2015. Cassava trait measurements for thispopulation were as described earlier, except that no strict distinction betweenyellow and white flesh color was used because the GS-C1 plants were mostly whiteand cream clones; thus we performed validation analysis with all clones.ApeKI libraries were constructed and sequenced on an IlluminaHiSeq  , with one lane per library. Single nucleotidepolymorphisms were called from the sequence data using the TASSEL pipelineVersion 4.0  from713 clones from the 2013 Genetic Gain trial at IITA and was quantified withPicoGreen . Genotyping-by-sequencing wasused for genotyping ,X is a known incidence matrix for fixed effectsβ , Z is a known incidencematrix for the clonal additive genomic effects 1u for the target genomic segment and 2u for the whole-genome SNPs. u1K and u2K are the genomic relationship matrices calculated from theSNPs with the procedure of VanRaden and the total genomic variance for the whole genome(σu22);σe2 is thegenomic error variance and e indicates theresiduals from the model. Model 1 was fitted using the R EMMREMLpackage  above, the genomic heritabilityfor each target genomic segment was computed as follows:h2 is genomic heritability for atarget genomic segment and the variance components are as describedabove.where y = X β +Zu2 + e .This model was also fitted with the EMMREML package  was estimated with the R qvaluepackage . We extracted all markers within 2.5kb of the start and end of each gene model with the Bedtools intersectfunction , Z is known incidence matrix for clonaladditive candidate genomic effects s and whole-genomiceffects g. For sK and gK, we used the candidate SNPs andthe remaining SNPs from the whole genome excluding the candidate SNPs,respectively, to generate genomic relationship matrices for the 1651 clonesof the GS-C1 population as above. A third kinship matrix,Krand, was generated as a control from 7203SNPs anchored to 2000 randomly selected genes from the cassava genome andused in Model 2 in place of Ks, whereas wecalculated gK by using SNPs from the whole genome excluding those inKrand. Other components of the model includethe SnRK candidates’ genetic variance(σs2) and the geneticvariance from other parts of the genome(σg2),σe2 is the errorvariance, and e represents the residuals from the model.Model 2 was fitted with the EMMREML package. To assess predictionaccuracies, we fitted another model as follows ; (ii) we calculatedgK with SNPs from the whole genomeexcluding the likely candidate SNPs; (iii) randKwas also calculated as above (as a control) from 402 SNPs anchored to 53randomly selected genes from the cassava genome (with 7.5 kb flanking thestart and end of these genes); (iv) unlikelyK was calculated from the 395 unlikely candidate SNPs. These werealso used in place of sK in Model 2 with theirappropriate gK being calculated as other SNPs inthe genome excluding those in randK andunlikelyK. Other components of the modelwere as described for Model 2 and prediction accuracies were obtained in thesame way. To assess the prediction accuracy of the whole-genome SNPs, wealso fitted a model analogous to Model 3 with the covariance ofu coming from a genomic relationship matrix withwhole-genome SNPs. We term this the predictive accuracy of the whole-genomeSNPs.We performed a second procedure to validate the 53 candidate genes identifiedin significant hit regions in the RHM analysis based on plant physiologyliterature . Using thttp://bedtools.readthedocs.io/en/latest/, accessed 20 Nov.2017), resulting in 2297 SNPs from 650 unique genes. We refer to these SNPsas the RHM-region SNPs. In addition, we extracted the SNPs anchored to 123unique genes in the cassava starch pathway compiled by Saithong et al. to (e) were repeated twelve times,resulting in 216 tests.Subsequently, Steps (b) to (d) of the RHM procedure above wereperformed, resulting in P-value from the RHM analysison our data that corresponded to the LFDR threshold of 0.05 and usedthis as the significance threshold.We then calculated the P-values weresignificant, given the significance threshold from Step (f)above.The power of the RHM analysis was then calculated as the number oftimes any of the five segment M. esculenta genome for asignificant segment in the RHM analysis, the number of times eitherthe first or fifth segment’s P-values weresignificant, conditional on the third segment having a higherP-value, was also calculated. This reflectedhow far away adjacent segments captured causal variants.To make a decision on the bounds set for extracting adjacentcandidate genes from the The genomic heritabilities for DM in white and yellow cassava, based onwhole-genome SNPs, were 0.57 and 0.48, respectively. These heritabilities aresomewhat higher than those found by Ly et al. , presumaSignificant genomic segments for the white cassava DM were observed onchromosomes 1, 4, 5, 10, 17, and 18; for the yellow cassava, a significantsegment was only observed on chromosome 1 . BecauseBy using information from the estimates of the mean linkage disequilibriumbetween genomic segments per chromosome , the disphosphofructokinase, was associated with the nonsignificantpeak on chromosome 9, which was more pronounced in the yellow cassavagermplasm.For the top RHM hits in both cassava gene pools, we identified possible candidategenes and transcriptional regulators adjacent to these hits based on theirinvolvement in the carbohydrate biosynthesis pathway, including members of theSnRKs family, members of the UDP-glycosyltransferase family (including starchand sucrose synthases), and UDP-sugar transporters; specific planttranscriptional factors including members of the β helix-loop-helix(bHLH) family and mini-zinc fingers; and other genes involved in cell wallprocesses, root storage, and development including pectinases andβ-vacuolar processing enzymes. We show a list of these genes in The predictive accuracy of the whole-genome SNPs was 0.54 . With the set of candidate SnRK SNPs, theprediction accuracies from the cross-validation with Model 2 were 0.26  and 0.12  for the candidate and random SNPs, respectively. Thepredictive ability of the genome-wide SnRK candidates (7203 SNPs) had~50% of the total prediction accuracy from our set of genome-wide SNPs for the GS-C1 population.With the likely candidate SNPs from the genes identified for all the top hittinggenomic segments genome-wide shown in , predictManes.01G076500), aglucose-6-phosphate isomerase (Manes.18G060600), and a neutralor alkaline invertase (Manes.04G006900). However, in the Calvincycle pathway list, we found one RHM-region gene, namely fructose-biphosphatealdolase (Manes.04G007900). These genes are known to play keyroles in starch biosynthesis and storage , 0.18 (SD = 0.03), and 0.03 (SD = 0.01), respectively. Based on two apriori lists compiled by Saithong et al. , includi Junker, .To asse Junker,  and diviP-values were significant. TheP-value from the RHM analysis on our data that correspondedto the LFDR threshold of 0.05 was 0.00024, which became our significancethreshold for this analysis. We found that 102 tests were significant out of atotal of 216, representing 47% statistical power to detect the simulated causalregion. To set the bounds for how far in the genome to cover when extractingcandidate genes from a significant RHM segment, we also calculated the number oftimes the P-values from the first or fifth genomic segmentswere significant, conditional on the third segment’sP-value being higher. With a total of 216 analyses, 27 caseshad significant P-values on Segment 3 and 15 cases hadsignificant P-values from Segments 1 or 5 when theP-values from Segment 3 were higher. This represents 15%coverage further away from the causal segment. With this information, we chosean adjacent span of 500,000 kb pairs flanking a significant RHM segment as thebounds for extracting adjacent candidate genes. A summary of the predictionaccuracies from validated candidates are shown in Table 2We calculated the statistical power of the RHM procedure to detect simulatedcausal effects from 216 analyses as the number of times any of the fivesegments’ The RHM results in the high DM and white cassava populations clearly demonstrate thepolygenic nature of the DM trait. Dry matter is composed of carbohydrates (mostlystarch), cell wall components, and fiber, as well as other nonstarchypolysaccharides. Thus it is not surprising that this trait is complex and controlledby many genes. In addition, the RHM procedure in this study showed a 47% power fordetecting association with a sample size of less than 500, given the polygenicnature of this trait.Pisum sativum L.)  and wheat, SnRK1phosphorylates and inactivates key enzymes in the sugar and starch biosynthesispathway, affecting sucrose synthase, trehalose phosphate synthase, andα-amylase  Heynh. root tips  fruits showed altered pectin composition and decreased starch accumulation hadminiature seeds caused by arrested endosperm development  have also foundconsistent phenotypes with cytosolic neutral invertase  . Interestingly, transgenic studiesoverexpressing 6-phosphofructokinase in potato found no changes in thetransgenic tuber phenotype compared with the controls but had an increased fluxof cytosolic 3-phosphoglycerate that did not affect the amount of starch thataccumulated in the tubers , is known to play a key role incarbohydrate biosynthesis. Changes in FDA activity have marked consequences forphotosynthesis, C partitioning, growth, yield, and improved uniformity of solidsin potato and other plants , and other crops] that expressed theEscherichia coli FDA gene in their chloroplasts hadsignificantly higher root mass, leaf phenotypes with significantly higher starchaccumulation, and lower leaf sucrose than control plants expressing the nullvector , a candidate from the Calvin cycle pathway for SnRKs onFYLD, 0.02 (SD = 0.02) for 53 likely candidates, 0.006 (SD = 0.03) for 53unlikely candidates, 0.03 (SD = 0.02) for RHM-region genes, and -0.009 (SD =0.02)for cassava starch pathway genes. These results suggest no singlebiological pathway that controls DM and FYLD. This is not surprising, sincethere is little genetic correlation between DM and FYLD (Kawano et al., In this paper, we have used candidate gene analysis in an attempt to understandthe function of the genes or gene families positionally associated with the RHMhits. We do not make the claim that these candidates are causal genes detectedby the RHM hits but rather we have shown, by using prediction accuracies, thatthese RHM hit loci were positionally associated with the DM trait in cassava thus resBy using RHM analysis, we demonstrate the complex genetic architecture of DM contentin high-DM white African cassava. Candidate gene analysis revealed the possibleroles of SnRKs, vacuolar and neutral invertases, phosphoglucose isomerase, and FDAin the regulation of sugar and starch biosynthesis in cassava. The RHM analysisindicated that inheritance of DM content in the high-DM white cassava population ismore polygenic than that in the low-DM yellow cassava population. We examined theutility of models based on the genome-wide candidate genes found in this study withprediction accuracies in a different but related population and found appreciablepredictive ability compared with what is obtained when whole-genome markers wereused. Transcriptional regulators such as bHLH may be involved in flesh root colorand sugar biosynthesis in cassava, as shown in potato. We recommend further studiesusing genome editing or transgenic technology to better understand these mechanismsand to inform and accelerate breeding efforts for cassava.Click here for additional data file.Click here for additional data file.


Mixed linear models (MLM) have been widely used to account for population structure in case-control genome-wide association studies, the status being analyzed as a quantitative phenotype. Chen et al. proved in 2016 that this method is inappropriate in some situations and proposed GMMAT, a score test for the mixed logistic regression (MLR). However, this test does not produces an estimation of the variants’ effects. We propose two computationally efficient methods to estimate the variants’ effects. Their properties and those of other methods  are evaluated using both simulated and real genomic data from a recent GWAS in two geographically close population in West Africa.p values inflation or deflation when population strata are not clearly identified in the sample.We show that, when the disease prevalence differs between population strata, MLM is inappropriate to analyze binary traits. MLR performs the best in all circumstances. The variants’ effects are well evaluated by our methods, with a moderate bias when the effect sizes are large. Additionally, we propose a stratified QQ-plot, enhancing the diagnosis of milorGWAS available on the CRAN. Both methods scale up to at least 10,000 individuals. The same computational strategies could be applied to other models .The two proposed methods are implemented in the R package  Population stratification has long been known to be at the origin of spurious associations in genetic association studies : if the Methods adapted to large scale population studies have thus been proposed, among which the Genomic Control  and StruA major breakthrough was achieved in 2006 with EIGENSTRAT , also knp values is well corrected by this method, it leads to conservatives p values for some SNPs and to anti-conservative p values for others. This behavior was made evident by the mean of quantile-quantile plots (QQ-plots) in which SNPs were categorized according to their allele frequencies in the different population strata. In order to address this issue, Chen et al. proposed GMMAT, a score test for the MLR, which is feasible in GWAS. The p values obtained with this test were shown to be well distributed in all SNP categories.The analogue of MLM for case-control studies is the mixed logistic regression (MLR). However, fitting the MLR with the Penalized Quasi-Likelihood (PQL)  is compuWhile the score test has a reduced computational burden, its drawback is the absence of an estimation of the variants’ effects. When only the effects of genome-wide significant SNPs are needed, an obvious solution is to fit MLR models including each of these SNPs. When the SNPs’ effects are needed for the whole genome, e.g. for meta-analysis purposes, it is desirable to have a computationally efficient method to estimate these effects. We propose two such methods in this paper.p values with no estimate of the variant’s effects, the methods proposed here give such estimates.The strategy to reduce the computational burden is to fit the MLR only once for a “null model”. This null model may incorporate relevant covariates, but no SNP. The SNPs are then tested one by one. Roughly speaking, this is done by using an appropriate method to confront a vector of genotypes with the residues of the null model. This stragegy is shared by the score test (GMMAT) and by the two proposed methods; but while the score test provides association One of the proposed method, named hereafter Approximate Maximum Likelihood Estimate (AMLE), is based on a first-order approximation of the MLR, which leads to an approximation of the SNPs effect. The association is tested by a Wald test, which is identical to the score test of . A similThe other method, named the Offset method, which bears similarities with the methods of , consistIn the sequel, we evaluate the capacity of logistic regression (LR), MLM, and MLR (using either the score test or the methods mentioned above) to properly take into account population structure associated with heterogeneous prevalence. While Chen et al. were interested in geographically distant populations, spanning several countries in South America, part of our work focuses two geographically very close populations in West Africa, using real genotype data from a recent GWAS . We alsoAdditionally, we propose to generalize the categorization of SNPs in QQ-plots presented in  to variaAll methods are implemented in the R package milorGWAS (for mixed logistic regression in GWAS), freely available on the Comprehensive R Archive Network (CRAN).n varying from 1000 to 10, 000. The results are reported in Fig. We measured the running times of GMMAT and of the methods AMLE and Offset, implemented in our package milorGWAS, for a sample size O(n) while the AMLE and GMMAT are in The Offset method is in e needed .We analyzed two data sets with a simulated binary phenotype. Simulations were based either on real genotype data from a recent GWAS , or on lThe first simulated set uses genotypes of 800 individuals from South Benin, ascertained in two sites distant of 20 km from each other, forming the two population strata in which we set different prevalences for simulating the phenotypes. These data were analyzed using the logistic regression (LR), the mixed logistic regression (MLR)  and the mixed linear model (MLM) , with or without the top 10 principal components (PCs) in the model.p values, the 1, 847, 505 SNPs being split in three categories according to their allelic frequencies as described in the methods , statistic inflation is observed for LR (When 10 PCs are included in the models (second row of the figure), this difference of behavior between SNPs categories persists for MLM. However, both logistic regression and MLR show an adequate correction for all categories of SNPs.The second simulation set consists in 10, 000 individuals simulated on a Both data sets were also analyzed using the Offset method for MLR. Figure We extended the stratified QQ-plot proposed in  to the cFigure Figure In all situations, the PQL displays no bias, or a very small bias . The two proposed methods tend to have a negative bias. For data simulated with a moderate SNP effect For larger SNPs effects , but AMLE produces slightly higher p values for the most associated SNPs. Consistently, the largest The two methods give similar p values for some SNPs, and to anti-conservative p values for others, depending on the ratio of expected genotype variance in the two strata. The motivation of Chen et al. was a genome-wide association study of asthma including individuals from different Caribbean and Latin American backgrounds, with in particular ca.ca. 20 km apart) from South Benin , and Z is the indicator variable of the strata, One of the contributions of Chen et al. was to show that a QQ-plot of log a logistic regression model (LR)a mixed linear model (MLM)a mixed logistic regression model, using Chen et al. score test GMMAT, identical to AMLE Wald test (MLR)a mixed logistic regression model, using the offset method (Offset)All analyses were repeated with the top ten PCs included as fixed effects in the model. We assessed the capacity of each test procedure to control type I error rates using Chen’s stratified QQ-plot. Moreover, to gauge the interest of our extension, we compared Chen’s QQ-plot to the stratified QQ-plot obtained using the first PC instead of the cohort indicator.We performed two sets of simulations, based on the simulations performed in , to assementclass2pt{minimWe used genotype data from a GWAS on mild malaria susceptibility performed on two cohorts in South Benin . The pari of being a case was calculated as:Z is an indicator variable for belonging to the second cohort, and K is the Genomic Relationship Matrix (GRM) calculated from all the SNPs. We set We simulated a binary phenotype with a difference of disease prevalence between the two cohorts, and a random effect modeling both population stratification and relatedness. Specifically, the probability on an individual We also performed coalescent simulations, reproducing closely the simulations described in , to obtan Europe . We simumentclass2pt{minimmentclass2pt{minimTo obtain related individuals, we first simulated the genotypes for 8000 founders (20 on each of the 400 cells). We then sampled 10 pairs of individuals in each cell, forming 4000 couples, and simulated two offsprings by gene dropping. Thus we obtained 16,000 individuals (founders and offspring) from which 10,000 individuals were randomly selected to obtain the cohort.The phenotype was simulated as before using Eq. , where \G, a genotype picked at random in the data, and Z and AModerate cohort effect (respective prevalence BModerate cohort effect (respective prevalence CLarge cohort effect (respective prevalence The coefficients G is centered to ensure that the expected prevalence is as prescribed. For each scenario, we considered SNPs with MAF in intervals (0.05; 0.10], (0.20; 0.25] and (0.45; 0.50], and SNP effect Simulations including a SNP effect were performed using the South Benin data set, using the modelTo compare the power of the methods that have shown a correct type I error, we performed additional simulations in a similar setting as in the previous section, with a large random effect (To illustrate the method, we applied it on the data from the GWAS in South Benin described in . We usedAdditional file 1. Including details on the AMLE and Offset methods, commands used for the simulations with the coalescent model and supplementary figures.


Genomic prediction (GP) is a method whereby DNA polymorphism information is used to predict breeding values for complex traits. Although GP can significantly enhance predictive accuracy, it can be expensive and difficult to implement. To help design optimum breeding programs and experiments, including genome-wide association studies and genomic selection experiments, we have developed SeqBreed, a generic and flexible forward simulator programmed in python3.SeqBreed accommodates sex and mitochondrion chromosomes as well as autopolyploidy. It can simulate any number of complex phenotypes that are determined by any number of causal loci. SeqBreed implements several GP methods, including genomic best linear unbiased prediction (GBLUP), single-step GBLUP, pedigree-based BLUP, and mass selection. We illustrate its functionality with Drosophila genome reference panel (DGRP) sequence data and with tetraploid potato genotype data.https://github.com/miguelperezenciso/SeqBreed.SeqBreed is a flexible and easy to use tool that can be used to optimize GP or genome-wide association studies. It incorporates some of the most popular GP methods and includes several visualization tools. Code is open and can be freely modified. Software, documentation, and examples are available at  Genomic prediction (GP) is a method whereby DNA polymorphism information is used to predict the breeding value of individuals for complex traits. The availability of high-throughput single nucleotide polymorphism (SNP) genotyping in a cost-effective manner has led GP to become a standard tool in the analysis and improvement of complex traits . GP has https://numpy.org/) or ‘pandas’ (https://pandas.pydata.org/), are wrappers on compiled languages, such that careful programming significantly alleviates the limited speed of native python. Thus, SeqBreed is much more versatile than pSBVB and incorporates many new options, such as genome-wide association studies (GWAS) and principal component analysis (PCA). Most importantly, it allows automatic implementation of standard genomic selection procedures. Usage details and the main features of SeqBreed are described in the following and in the accompanying GitHub site https://github.com/miguelperezenciso/SeqBreed.Here, we present a versatile python3 forward simulation tool, SeqBreed, to evaluate GP performance in generic scenarios and with any genetic architecture . The purpose of SeqBreed is to generate phenotype and genotype data of individuals under different (genomic) selection strategies. SeqBreed is inspired by a previous pSBVB fortran software program , but thehttps://github.com/miguelperezenciso/SeqBreed/blob/master/SeqBreed_tutorial.ipynb and in the python script https://github.com/miguelperezenciso/SeqBreed/blob/master/main.py.Broadly, SeqBreed takes genotype/sequence data from a founder population and simulates phenotypes according to a predetermined genetic architecture. Offspring genomes and phenotypes can be simulated under selection or random drift. By default, selection is simulated across a predetermined number of generations and selection intensities. SeqBreed offers extensive flexibility to the user. For example, accuracy of GP with several SNP arrays can be simultaneously compared using the same data; offspring of specific pairs of parents can be generated; and dihaploid offspring can be simulated. SeqBreed can be run using scripts or interactively, where the user can, say, obtain plots for each generation or generate genotype data of a given set of individuals. Examples of the program’s usage are in the GitHub’s jupyter notebook Upload founder sequence genotypes in vcf or plink format. The program automatically determines ploidy and the number of chromosomes and SNPs.Specify genome characteristics. Sex-linked SNPs and/or recombination rates can be specified.Specify desired heritabilities and causal SNPs (QTN) and their effects for every trait. Environmental variances are inferred given founder genomes, QTN effects and heritabilities.Offspring genomes and phenotypes are simulated by gene-dropping along a predetermined pedigree or by implementing selection.SeqBreed is programmed in python3 using an object-oriented paradigm. The generic SeqBreed flowchart is visualized in Fig. Population: This class contains the main attributes for running selection experiments and is a container for Individual objects. It includes methods to add new individuals generated by mating two parents or randomly shuffling founder genomes in order to increase the number of base population animals (see ). It alsIndividual: It allows generation, manipulation, and printing of the genotypes and phenotypes of individuals. Internally, an individual’s genome is represented by contiguous non recombining blocks rather than by the list of all SNP alleles, which allows dramatic savings in memory and increases in efficiency .Genome: All genome characteristics are stored and can be accessed by methods in this class. It specifies ploidy, number and class of chromosomes, and recombination rates or SNP positions.GFounder: SeqBreed requires as minimum input the genotypes of the so-called ‘founder population’, which comprises the parents of the rest of the individuals to be generated. This class stores these genotypes and automatically retrieves main genome features such as SNP positions, number of chromosomes, etc. Initial genotypes can be filtered by minimum allele frequency (MAF).QTN: This class determines the genetic architecture for each trait simulated. It has methods to determine the environmental variance given a desired heritability, and to plot variance components for QTN. In its current version, SeqBreed allows for dominance and additive actions, but not epistasis.Chip: This class is basically a container for the list of SNPs that are included in a genotyping array. It allows easy comparison of different genotyping strategies in genomic selection.PCA plots or GWAS options are also implemented. The main python classes are:For each chromosome id, homologs are randomly paired.Within each pair of homologs, cross-over events are generated as for diploids, i.e., no interaction between homologous chromosomes is modeled and the number of cross-over events is simulated following a Poisson distribution with a rate equal to chromosome length in Morgans.Sex chromosomes are modeled with a maximum ploidy of 2.By default, SeqBreed assumes that all loci are autosomal and a recombination rate of 1 cM = 1 Mb throughout the genome. It includes options to specify sex or mitochondrial chromosomes, and local and sex specific recombination maps. A pseudo-autosomal region (PAR) is not accommodated for sex chromosomes, i.e., the whole Y chromosome is assumed to be non-recombining. A mitochondrial chromosome is a non-recombining chromosome that is transmitted maternally. SeqBreed allows for autopolyploidy of any level, which is automatically detected from vcf files. Accurate modeling of meiosis in polyploids is notoriously difficult , 12 and Therefore, our algorithm does not fully model the interaction of preferential pairing of homologous chromosomes and double reduction arising from multivalent formation . For thehttps://github.com/miguelperezenciso/SeqBreed#3-specifying-genetic-architecture): (i) a random number of QTN positions are sampled genome-wide and additive effects are sampled from a gamma distribution SeqBreed allows the simulation of any number of phenotypic traits, regardless of ploidy. For each trait, broad-sense heritability must be specified. There are three options to specify the number of QTN and their effects . SeqBrehttps://github.com/miguelperezenciso/SeqBreed#3-specifying-genetic-architecture). There is no specific assumption on genetic correlations between traits. To simulate no pleiotropy, QTN for each trait have zero effects for all other traits. Note that this does not prevent a non-zero genetic correlation arising from linkage disequilibrium. The program does not automatically adjust desired genetic correlations and, thus, different QTN values may need to be tested to fit desired correlations. Environmental correlations are always zero.For multiple traits, the user needs to specify additive and dominant QTN effects separately for each trait. This is done via an external text file, where additive and dominant QTN effects are specified for each trait (option 3 in https://github.com/miguelperezenciso/SeqBreed/blob/master/README.md#breeding-population).It is typically difficult to find real sequence data to generate a reasonably sized founder population. To accommodate this, SeqBreed can generate ‘dummy’ founder individuals by randomly combining recombinant haplotypes. This can be done in two ways, either by generating a random pedigree and simulating a new founder individual by gene-dropping along this pedigree, or by directly simulating a number of recombining breakpoints and assigning random founder genotypes to each block between recombination breakpoints . It is also possible to generate new individuals interactively, including dihaploids. To speed up computations and avoid unnecessary memory usage, only recombination breaks and ancestor haplotype ids are stored for each individual .SeqBreed allows computing estimated breeding values using several GP methods. It also allows several lists of SNPs (SNP chips) to be defined, such that GP performance can be easily compared across chips. From a methodological point of view, most GP implementations are based on penalized linear methods . SeqBreVanRaden  as:\docuhttps://github.com/miguelperezenciso/SeqBreed). Running a selection scheme requires specifying the number of generations, the numbers of females and males to be selected, and the number of offspring per female. SeqBreed splits the selection process in three steps, which allows a fine control over the breeding program. First, breeding values are predicted using the chosen evaluation method and marker information. By default, the data from all individuals across the current and previous generations are used, but this can be changed by specifying the subset of individuals to be used. Second, a function is used to generate offspring from selected parents. This function requires specifying the candidates for selection , selection intensity, family size, and either assortative or random mating between selected parents. Hierarchical mating between females and males is employed by default (https://github.com/miguelperezenciso/SeqBreed#7-implementing-selection). Assortative and random mating schemes are implemented; more sophisticated mating schemes, such as those based on optimal contributions [https://github.com/miguelperezenciso/SeqBreed/blob/master/src/selection.py).Selection can be automatically configured and run, as documented in the GitHub examples , shows the basic commands to run SeqBreed and import the required modules. First, SeqBreed modules are imported as:The basic functioning of SeqBreed is illustrated by the main.py script that is available at Founder population genotypes are uploaded from the vcf file, using the command:which generates a GFounder object that contains founder genotypes, vcffile is the file containing genotypes and seqfile is generated by the program and contains information about SNP positions, which are used in the next step.Next, the main genome features are specified. The following command creates a Genome object that assumes that the ‘X’ chromosome is the sex X chromosome, while SNPs on the chromosome named ‘MT’ are mitochondrial.Genetic architecture can be specified in different ways. The simplest is to generate nqtn QTN randomly distributed along the genome with effects sampled from a gamma distribution, where h2 is the desired heritability.Selection is implemented in cycles, the number of generations, the numbers of males and females selected, and family size must be specified. The following is an example with GBLUP selection, random mating, and continuous generations.https://github.com/miguelperezenciso/SeqBreed/tree/master/DGRP and in https://github.com/miguelperezenciso/SeqBreed/tree/master/POTATO for the Drosophila and potato examples, respectively. The DGRP scripts illustrate the specific recombination map of Drosophila, where males do not recombine, as shown in the ‘dgrp.map’ file. The example provided in GitHub consists of a small experiment to compare genomic and mass selection. Plots in the jupyter notebook are implemented to track phenotypic changes by generation. The potato scripts illustrate how to generate an F2 cross between extreme lines and to perform a GWAS experiment in polyploids. GWAS results using PCA corrected phenotypes are also shown.We illustrate the software with sequence data from the Drosophila genome reference panel , parsedhttps://alphagenes.roslin.ed.ac.uk/wp/software-2/alphasimr/), PedigreeSim [Several other programs have been developed for similar purposes as SeqBreed, including our own pSBVB , AlphaSiigreeSim , simuPOPigreeSim , and QMSigreeSim . HoweverNote that SeqBreed was designed to evaluate the performance of GP or GWAS over a short time horizon, i.e., new mutations are not generated. SeqBreed is not designed to investigate the long-term effects of demography or selection on DNA variability because new mutations are not generated. For these purposes, Slim  or similPlans for further development of SeqBreed include additional features to generalize available genetic architectures , integration with machine-learning tools  for genetic evaluation, development of an educational tool with an html-based interface, and improving output and plotting features.


P < 1×10−8), respectively. High genetic correlations are observed between sedentary behaviours and neurological traits, including education and body mass index (BMI). Two-sample Mendelian randomization (MR) analysis estimates a causal effect between 1.5 hour increase in television watching and CAD , that is partially independent of education and BMI in multivariable MR analyses. This study finds independent observational and genetic support for the hypothesis that increased sedentary behaviour by leisure television watching is a risk factor for CAD.Leisure sedentary behaviours are associated with increased risk of cardiovascular disease, but whether this relationship is causal is unknown. The aim of this study is to identify genetic determinants associated with leisure sedentary behaviours and to estimate the potential causal effect on coronary artery disease (CAD). Genome wide association analyses of leisure television watching, leisure computer use and driving behaviour in the UK Biobank identify 145, 36 and 4 genetic loci  and Mendelian randomization analyses to explore potential causal relationships with coronary artery disease.Epidemiological studies have shown an association between sedentary behaviours and cardiovascular disease risk. Here, van de Vegte  In the United Kingdom, each adult spends an average 5 h sedentary per day2. Observational studies have previously shown that prolonged time spent on sedentary behaviours are associated with increased risk of cardiovascular disease and all-cause mortality6. Sedentary behaviours represent a major public health problem considering their high prevalence2. In addition, they pose a large economic burden on national level, with an estimated cost of cardiovascular disease caused by a sedentary lifestyle to be 424 million pounds sterling annually in the United Kingdom alone7.The association between sedentary behaviours and coronary artery disease (CAD) is less clear. Three studies that investigated the association between total sedentary behaviour and CAD found contrasting results10, whereas one study focused on domain-specific sedentary behaviour and found a clear association between television watching and CAD11.Sedentary behaviours are defined as any waking behaviour characterized by an energy expenditure ≤1.5 metabolic equivalents, while in a sitting, reclining or lying posture5, cancer5 and cardiovascular mortality5, television watching seems most strongly associated with CAD. In fact, television watching is often used as proxy for total leisure sedentary behaviour in observational studies, as television watching is almost solely performed in occupational setting, modifiable by intervention14 and shows higher validity than total sedentary behaviour as it is easier to recall15. Several hypotheses can be put forward as to why television watching seems to be the most important sedentary behaviour associated with risk of CAD. An epidemiological explanation is that leisure television time is associated with less and shorter breaks, lower total energy expenditure and different snacking behaviours than other sedentary traits, possibly increasing adverse effects of prolonged sitting19. A statistical explanation is that observational studies are possibly hampered by reverse causation or confounding through a broad range of determinants known to affect sedentary behaviours20. One recent study examined the causal nature of the association between leisure television watching and CAD by using a negative control outcome and found the association mirrored by the association with accidental death, indicating confounding to likely be a driver of the association between sedentary behaviours and CAD21.In line with the previous literature on the association between sedentary behaviours and all-cause23. Genetic variants are randomly assigned when passed from parents to offspring and are therefore mostly unrelated to the presence of confounders. However, little is known regarding the genetic variants accounting for the heritable component to domain-specific sedentary behaviours26.Another way to study causality of an association is by using a Mendelian randomization (MR) approach, which uses genetic variants as proxy for risk factors to minimize confounding and reversed causation in observational dataP < 1 × 10−8), respectively. We find observational evidence that increased time spent watching television is associated with risk of CAD and find evidence for a similar causal estimate by using a MR approach. Considering the complex nature of behavioural traits and the broad range of determinants known to affect sedentary behaviours, we estimate the genetic correlation with other traits and find especially high correlations with educational and obesity traits. However, multivariable MR shows that the effect of television watching on CAD is at least partially independent of education and likely mediated by traditional cardiovascular risk factors as body mass index (BMI). These results support conclusions from traditional observational epidemiology that policy guidelines aiming to reduce sedentary behaviours may help to prevent CAD.To extend our knowledge of how genetics might affect sedentariness and to investigate whether sedentary behaviours are a causal risk factor for CAD, we perform a genome-wide association study (GWAS) of three phenotypes of sedentary behaviours: (1) leisure television watching, (2) leisure computer use and (3) driving and identify 145, 36 and 4 genetic loci  and driving , while leisure computer use and driving had a weak positive correlation  , while computer use was not  after extensive adjustment for cardiovascular risk factors , followed by leisure computer use , and driving . Television watching and computer use showed a negative genetic correlation , similar to the observational analyses. Driving was positively associated with television watching , but not with computer use . Television watching and computer use showed a positive genetic correlation with objectively measured sedentary behaviour , while driving did not . Genetic correlations with other traits can be found in Supplementary Data R2 > 0.1) with the newly discovered variants. Of the 193 variants, 21 genetic variants were in linkage disequilibrium (R2 > 0.8) with previously established variants for years of education and 46 variants with any trait surpassing P < 1 × 10−5 , as well as between driving and CAD . However, this was not true for leisure computer use . Television watching remained significantly associated with CAD in all univariable pleiotropy and sensitivity analyses, except weighted mode, which had wider confidence intervals but a similar effect estimate  had F-statistics ranging from 29 to 164 for television watching, from 31 to 83 for computer use and from 35 to 46 for driving  analyses are shown in Supplementary Table Instruments used for the two-sample univariable MR analyses between sedentary behaviours and CAD can be found in Supplementary Data I2 index and Cochran’s Q for MR-IVW analyses and Rucker’s Q for MR-Egger analyses (Supplementary Table P = 5.63 × 10−07). Rucker’s Q was not significantly lower than Cochran’s Q for television watching, computer use and driving . Please see Supplementary Tables a indicated remaining heterogeneity and thus potential pleiotropy in the estimates between television watching, education and CAD (Supplementary Table P = 0.01), low density lipid protein levels , a history of diabetes  and hypertension . Please see Supplementary Table Using the multivariable MR approach correcting for education, we found the direct effect of television watching on CAD to be attenuated compared with the total effect due to a wider confidence interval. However, a causal effect between 1 SD increase in leisure time watching television was still estimated to increase CAD risk when corrected for education  have been performed to understand the biology of domain-specific sedentary behaviours33. However, none of these genes or variants were brought forward in our analysis. One recent GWAS on blood pressure34 performed a phenome scan and reported locus rs13107325 to be related to leisure television watching, which is confirmed in the current study.Only three candidate gene studies  between 2006 and 2010. All study participants provided informed consent and the North West Multi-centre Research Ethics Committee approved the studyDuring the first visit, participants were asked three questions, “In a typical DAY, how many hours do you spend watching TV?”, “In a typical DAY, how many hours do you spend using the computer? (Do not include using a computer at work)” and “In a typical DAY, how many hours do you spend driving?”. Participants outside a 99.5% range on the right side of the normal distribution were excluded on a per-phenotype basis, since the sedentary phenotypes were right-skewed.44. Three Cox regression models were used to investigate the association of leisure sedentary television watching, leisure computer use and driving with CAD; potential confounders were selected per prior epidemiological analyses8. These models included (1) univariable analysis (2) a multivariable model correcting for age and sex (3) a multivariable model correcting for important CAD risk factors. These risk factors included age, sex, BMI, smoking status, hypertension, diabetes, Townsend deprivation index as proxy for income, physical activity levels, alcohol use per weak and years of education. Associations between sedentary behaviours and potential confounders were assessed using linear regressions analyses or logistic regression analyses in case of binary outcomes. We considered two-sided P < 0.05 statistically significant. Analyses were performed using statistical software STATA 15 (StataCorp LP).The associations between sedentary phenotypes were assessed by performing Spearman’s rank correlation. Cox regression analysis was performed to investigate the association between different sedentary behaviours and new-onset CAD events. CAD was defined based on ICD-9 and ICD-10 codes, together with operation codes and self-reported data on myocardial infarction, other ischaemic heart disease and history of coronary artery bypass grafting or percutaneous coronary intervention as performed previously45. We single-inverse normalized the Townsend deprivation index, in line with previous studies’ methodologies46. Sex, smoking status, hypertension, diabetes and years of education were ordinal data. Smoking status was defined as ideal (never smoked or quit >12 months ago), intermediate (quit smoking ≤12 months ago) or poor (current smoker). Physical activity was based on questionnaires concerning do-it-yourself and exercise activities using guidelines for ideal cardiovascular health and according to previous research44. In short, physical activity was defined as ideal if participants had ≥150 min/week moderate or ≥75 min/week vigorous or 150 min/week mixed (moderate and vigorous) activity. Intermediate physical activity was more than 1 min/week of moderate or vigorous exercise without achieving ideal physical activity guidelines. Poor physical activity was defined as not performing any moderate or vigorous activity. Duration and intensity of physical activity was ascertained using the answers provided by participants on a range of questions based on the validated International Physical Activity Questionnaire47. Do-it-yourself activity examples included pruning or lawn watering for light activities, and lifting heavy objects, using heavy tools or digging for heavy activities. Years of education were based on the standardized 1997 international standard classification of education (ISCED) according to previously published guidelines48.The covariates age, BMI, Townsend deprivation index and alcohol use were treated as continuous variables. The Townsend deprivation index is a measure of material deprivation within a population based on unemployment, non-car ownership, non-home ownership and household overcrowding49. Minor Allele Frequency of 0.5% and INFO-score of more than 0.3 was used in post-GWAS analysis.The Wellcome Trust Centre for Human Genetics performed genotyping, quality control before imputation and imputed to HRC v1.1 panel. Analysis has been restricted to variants that are in the HRC v1.1. Quality control of samples and variants, and imputation was performed by the Wellcome Trust Centre for Human Genetics, as described in more detail elsewhere50. Leisure television watching, leisure computer use and driving were adjusted for age-squared, age, sex, age-sex interaction, the first 30 principal components to correct for population stratification and genotyping array (Affymetrix UK Biobank Axiom array or Affymetrix UK BiLEVE Axiom array). Participants were excluded if they were of non-European ancestries  in order to reduce non-polygenetic signals.All three sedentary phenotypes were inverse rank normalized in order to obtain normally distributed data. Genome-wide association analysis in UK Biobank was performed using BOLT-LMM v2.3beta2, employing a mixed linear model that corrects for population structure and cryptic relatednessR2 < 0.005 within a five megabase window into a set of independently associated variants. Genetic loci were determined by assessing the highest associated variants in a one megabase region at either side of the independent variants. We combined all loci of the sedentary phenotypes and again searched within a one megabase region at either side to obtain the highest associated locus in order to receive a set of independent genetic loci associated with sedentary behaviour in general (Supplementary Data We used the PLINK clumping procedure for each sedentary phenotype separately to prune genetic variants at a stringent linkage disequilibrium (LD) of P < 1 × 10−8 were taken forward, in order to account for multiple independent traits in line with other multi phenotype studies52.Since the current study is the only population-based study of sedentary behaviours, independent cohorts that matched this study in size and availability of variables (specific questions assessing different subtypes of sedentary behaviour combined with genetics) were unavailable for replication purposes. Therefore, only loci that reached a stringent (two-sided) genome-wide significant threshold of 53 indicated polygenicity, not population stratification, to be the main driver of the observed inflation of test statistics for television watching (0.0697 ± 0.0104). QQ-plots for the three independent GWAS traits can be found in Supplementary Figs. The genomic inflation lambda was 1.37 for watching television, 1.20 for computer use and 1.10 for time spent driving. LD score regression intercepts showed no genomic inflation due to non-polygenic signals for computer use (1.049 ± 0.0092) and time spent driving (1.0083 ± 0.0076). Attenuation ratio statistic54. In addition, genetic correlations with other traits were assessed using LD score regression software (v1.0.0)56 and the LD hub platform (v1.9.3)57. Genetic correlations were considered significant if they achieved a Bonferroni-corrected significance of P < 0.05/696 = 7.18 × 10−5.Genetic correlations between the three sedentary phenotypes were assessed using BOLT-REML variance components analysis using BOLT v2.3.1R2 > 0.8; 3) eQTL genes in LD (R2 > 0.8) with sedentary behaviour variants (described below); and (4) DEPICT gene mapping using variants that achieved P < 1 × 10−6 (described below).For all independent genetic variants that were genome-wide significantly associated with a sedentary behaviour, candidate causal genes were prioritized as follows: (1) by proximity, the nearest gene or any gene within 10 kb; (2) genes containing coding variants in LD with sedentary variants at 58 analysis (version 0.710) in data repositories from GTEx V759, GTEx brain60, Brain-eMeta eQTL60 and blood eQTL from Westra61 and CAGE62. EQTL genes were considered as a candidate causal gene if they achieved a Bonferroni-corrected significance of P < 0.05/187,747 = 2.66 × 10−7, passed the HEIDI test of P > 0.05 and if the lead variants of the eQTL genes were in LD (R2 > 0.8) with the queried variants.To search for evidence of the functional effects of genetic variants associated with any of the three sedentary traits, we used multiple functional eQTL mapping. This was done using summary data based Mendelian randomization (SMR)https://data.broadinstitute.org/mpg/depict/) was used to perform integrated gene function analyses. DEPICT was run using all genetic variants that achieved P < 1 × 10−6. We opted for a more conservative approach than suggested because the signal was highly polygenic63.Identification of genes associated with identified variants, enriched gene sets and tissues in which these genes are highly expressed, was performed using DEPICT. DEPICT.v1.beta version rel137 , MR-PRESSO (version 1.0)64 and MVMR (version 0.1)65.All 1000G imputed independent lead variants associated with sedentary behaviours at 66 1000 genomes-based meta-analysis was used. This cohort included data from individuals of mostly European, but also Hispanic, African American, and South and East Asian ancestry. In total, there were 60,801 cases of CAD and 123,504 control subjects66. CAD events were defined as a documented diagnosis of CAD, such as acute coronary syndrome (including MI), chronic stable angina, or >50% stenosis of at least one coronary vessel, as well as those who had undergone percutaneous coronary revascularization or coronary artery bypass grafting66.For CAD, the Coronary Artery Disease Genome-Wide Replication and Meta-Analysis plus Coronary Artery Disease Genetics Consortium’s (CARDIoGRAMplusC4D)48. We used information of the cohort which included 293,723 individuals of European ancestry, as this cohort did not include the UK Biobank. Educational years were standardized using the 1997 ISCED of the United Nations Educational, Scientific and Cultural Organization48. Proxies were not searched for in case requested lead variants of sedentary behaviours were not found in the GWAS of CAD or educational years.For educational years, the Social Science Genetic Association Consortium (SSGAC) GWAS meta-analysis of years of schooling was usedF-statistic, calculated using the equation F = R2(n − 2)/(1 − R2)67. In this formula, R2 is the proportion of the variability in sedentary behaviours explained by the SNP and n is the sample size67. An F-statistic of >10 indicates a relatively low risk of weak instrument bias in MR analyses67, which is essential prevent violation of the ‘NO Measurement Error’ assumption. In addition, potential weak instrument bias in MR-Egger regression analysis was assessed by calculating the variation between individual genetic variant estimates for each exposure (I2GX)68. An I2GX of >95% was considered low risk of measurement error.The strength of the instruments was assessed using the I2- index69 and Cochran’s Q70 statistics were calculated to test for heterogeneity produced by different genetic variants in the fixed-effect variance weighted analyses. Heterogeneity statistics provide useful information on pleiotropy, since low heterogeneity indicates that estimates between genetic variants should vary by chance only, which is only possible in case of absence of pleiotropic effects. An I2 index > 25% and Cochran’s Q P value of <0.05 were considered as an indication of heterogeneity and, as a consequence, of pleiotropy. In case Cochran’s Q indicated potential pleiotropy, we moved from the inverse-variance-weighted fixed to random-effects model70.Pleiotropy in the context of MR analyses refers to genetic variants exerting multiple effects. In other words, pleiotropic genetic variants may affect the outcome independently of the exposure. This can lead to confounding and bias of MR estimates and investigation of pleiotropy is therefore essential. First, 23. The MR-Egger regressions allows for a variable intercept as a consequence of allowing genetic variants to be invalid. Large deviations from the non-zero intercept represent large average horizontal pleiotropic effect across the genetic variants23. An MR-Egger’s intercept of zero, tested using a P value threshold of >0.05, was considered to provide evidence for absence of pleiotropic bias. The MR-Egger assumes that the association of genetic variants with the exposure are independent of the direct effects of the genetic variants on the outcome (InSIDE assumption)23. In case the InSIDE assumption is not violated, the slope coefficient from the MR-Egger regression is a consistent estimate of the causal effect. In addition, heterogeneity within the MR-Egger analysis was assessed by calculating Rucker’s Q70. A significant difference (P < 0.05) between the Cochran’s Q and Rucker’s Q (Q-Q’)70 indicates the MR-Egger test to be a better method to study the genetic association between the particular exposure and outcome. MR-PRESSO was used to detect pleiotropy as well71. MR-PRESSO compares the difference between the residuals for each genetic variant in the variable, non-zero intercept of the genetic variant-outcome estimate with the genetic variant-exposure estimate in case pleiotropy is absent71. By doing so, pleiotropic effects can be detected and outliers can be identified. MR-PRESSO then re-analysis the association without the outliers, correcting for possible pleiotropic effects. Next, we excluded genetic variants with potential pleiotropic effects through education and through all traits  and secondary exposures (education). When both Qx1 and Qx2 are larger than the critical value for a the χ2 distribution, there is little evidence of weak instrument bias. We estimated the critical value for the χ2 distribution using the amount of SNPs minus two degrees of freedom at a P value of 0.05. Qa was assessed to test for heterogeneity and thus potential pleiotropy in the multivariable two-sample MR setting. In case Qa is larger than the critical value on the χ2 distribution, there is evidence for heterogeneity and thus potential pleiotropy even when corrected for education. The critical value for the χ2 distribution was assessed using the amount of SNPs minus three degrees of freedom at a P value of 0.05. For the results, please see Supplementary Table 11. Before multivariable MR analyses, we explored the association between years of education and sedentary behaviours using the inverse-variance-weighted fixed-effect method  are estimated in the same cohort of the UK Biobank and thus covariance in this setting could be reintroduced. However, as the effect of the secondary exposure can be overestimated when tested within the same cohort, this would likely results in a stricter correction within the multivariable MR. Lastly, MR-Steiger filtering was applied in the main analyses to remove variants that are more strongly associated with CAD than with sedentary behaviours73. MR-Steiger filtering calculates the R2 for the exposure and outcome and removes variants if the R2 of the exposure is significantly lower than R2 of the outcome73.Next, MR-Egger test was performed. The MR-Egger test, in contrast to the inverse-variance-weighted method, does not assume all genetic variants to be valid74. In addition, we performed weighted mode-based estimator MR analyses which allows even the majority of all variants to be invalid in case the largest number of that produce similar MR results are valid. Weighted mode-based MR generates causal effect estimates based on these valid instruments75. To investigate whether the results were robust to P value thresholds, we determined the relationship between sedentary traits with CAD. This was done by adding genetic variants with higher P values for sedentary behaviours  and then repeated the MR analyses stated above. Lowering the P value thresholds increases the chance of weak instrument bias and therefore instrument strength for all variants were assessed using the F-statistic (Supplementary Data Several sensitivity analysis were performed. Weighted median analysis was performed, which allows up to 50% of information from variants to violate MR assumptions, in contrast to regular inverse-variance-weighted analysis in which absence of pleiotropic effects for all included genetic variants is assumedFurther information on research design is available in the Supplementary InformationPeer Review FileSupplementary Dataset 1Supplementary Dataset 2Supplementary Dataset 3Supplementary Dataset 4Supplementary Dataset 5Supplementary Dataset 6Supplementary Dataset 7Supplementary Dataset 8Supplementary Dataset 9Supplementary Dataset 10Supplementary Dataset 11Supplementary Dataset 12Supplementary Dataset 13Reporting SummaryDescription of Additional Supplementary Files