Genomic Heritability: A Ragged Diagonal Between Bias and Variance

Many important traits in plants, animals, and microbes are polygenic and are therefore difficult to improve through traditional marker?assisted selection. Genomic prediction addresses this by enabling the inclusion of all genetic data in a mixed model framework. The main method for predicting breeding values is genomic best linear unbiased prediction (GBLUP), which uses the realized genomic relationship or kinship matrix (K) to connect genotype to phenotype. The use of relationship matrices allows information to be shared for estimating the genetic values for observed entries and predicting genetic values for unobserved entries. One of the key parameters of such models is genomic heritability (h2g), or the variance of a trait associated with a genome-wide sample of DNA polymorphisms. Here we discuss the relationship between several common methods for calculating the genomic relationship matrix and propose a new matrix based on the average semivariance that yields accurate estimates of genomic variance in the observed population regardless of the focal population quality as well as accurate breeding value predictions in unobserved samples. Notably, our proposed method is highly similar to the approach presented by Legarra (2016) despite different mathematical derivations and statistical perspectives and only deviates from the classic approach presented in VanRaden (2008) by a scaling factor. With current approaches, we found that the genomic heritability tends to be either over- or underestimated depending on the scaling and centering applied to the marker matrix (Z), the value of the average diagonal element of K, and the assortment of alleles and heterozygosity (H) in the observed population and that, unlike its predecessors, our newly proposed kinship matrix KASV yields accurate estimates of h2g in the observed population, generalizes to larger populations, and produces BLUPs equivalent to common methods in plants and animals.

Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

The Kinship Matrix: Inferring the Kinship Structure of a Population From Its Demography

The familial structure of a population and the relatedness of its individuals are determined by its demography. There is, however, no general method to infer kinship directly from the life-cycle of a structured population. Yet this question is central to fields such as ecology, evolution and conservation, especially in contexts where there is a strong interdependence between familial structure and population dynamics. Here, we give a general formula to compute, from any matrix population model, the expected number of arbitrary kin (sisters, nieces, cousins, etc) of a focal individual ego, structured by the class of ego and of its kin. Central to our approach are classic but little-used tools known as genealogical matrices, which we combine in a new way. Our method can be used to obtain both individual-based and population-wide metrics of kinship, as we illustrate. It also makes it possible to analyze the sensitivity of the kinship structure to the traits implemented in the model.

Effects of kinship correction on inflation of genetic interaction statistics in commonly used mouse populations

It is well understood that variation in relatedness among individuals, or kinship, can lead to false genetic associations. Multiple methods have been developed to adjust for kinship while maintaining power to detect true associations. However, relatively unstudied, are the effects of kinship on genetic interaction test statistics. Here we performed a survey of kinship effects on studies of six commonly used mouse populations. We measured inflation of main effect test statistics, genetic interaction test statistics, and interaction test statistics reparametrized by the Combined Analysis of Pleiotropy and Epistasis (CAPE). We also performed linear mixed model (LMM) kinship corrections using two types of kinship matrix: an overall kinship matrix calculated from the full set of genotyped markers, and a reduced kinship matrix, which left out markers on the chromosome(s) being tested. We found that test statistic inflation varied across populations and was driven largely by linkage disequilibrium. In contrast, there was no observable inflation in the genetic interaction test statistics. CAPE statistics were inflated at a level in between that of the main effects and the interaction effects. The overall kinship matrix overcorrected the inflation of main effect statistics relative to the reduced kinship matrix. The two types of kinship matrices had similar effects on the interaction statistics and CAPE statistics, although the overall kinship matrix trended toward a more severe correction. In conclusion, we recommend using a LMM kinship correction for both main effects and genetic interactions and further recommend that the kinship matrix be calculated from a reduced set of markers in which the chromosomes being tested are omitted from the calculation. This is particularly important in populations with substantial population structure, such as recombinant inbred lines in which genomic replicates are used.

Pedigree and Molecular Analyses in the Assessment of Genetic Variability of the Polish Greyhound

The aim of the study was to assess the genetic variability of the Polish Greyhound population based on pedigree analysis and molecular DNA testing and to determine the degree of relatedness among individuals in the population. Pedigree data of 912 Polish Greyhounds recorded in pedigree books since they were opened for this breed were analyzed. For molecular testing, DNA was obtained from cheek swabs taken from 235 dogs of the tested breed. A panel of 21 markers (Short Tandem Repeat—STR) was used. The mean inbreeding determined for the Polish Greyhound population based on pedigree analyses was low and amounted to 11.8%, but as many as 872 individuals of the 912 dogs in the studied population were inbred. A total of 83 founders (at least one unknown parent) were identified, among which 27 founders had both unknown parents. Full-sibling groups consisted of 130 individuals, with a minimum and maximum litter size of 2 and 16, respectively. The average litter size was 5.969. Gene diversity calculated based on the mean kinship matrix was 0.862 and the population mean kinship was 0.138. The founder genome equivalent based on the mean kinship matrix was 3.61; the founder genome surviving level was 12.34; the mean Ne was estimated at 21.76; and the Ne/N ratio was 0.135. The FIS inbreeding coefficient for 21 STR was negative, and the mean FIS value for all loci had a low negative value (−0.018). These values suggest a low level of inbreeding in the examined breed as well as the avoidance of mating related animals.

“May Her Memory Be a Revolution”

This essay explores the ways in which queer kinships are manifold through mourning. Using an autoethnographic methodology accounting the suicide of DanVeg, a transwoman and queer activist from Israel/Palestine and a member of the author’s chosen family, the article aims to question the different affects of queer kinships as they unravel through mourning, as well as the challenges trans death pose to them. Examining different mourning practices and subversive political actions following DanVeg’s death, through the lens of critical kinship studies, queer and trans theories of necropolitics, and spectrality theories, it is claimed that eventually queer kinships are a precarious haunting ghost on the nuclear, biological heterosexual family, always in danger of being deconstructed but nevertheless always lingers and posing a threat to the normative kinship matrix.

High throughput genotyping of structural variations in a complex plant genome using an original Affymetrix® axiom® array

Background Insertions/deletions (InDels) and more specifically presence/absence variations (PAVs) are pervasive in several species and have strong functional and phenotypic effect by removing or drastically modifying genes. Genotyping of such variants on large panels remains poorly addressed, while necessary for approaches such as association mapping or genomic selection. Results We have developed, as a proof of concept, a new high-throughput and affordable approach to genotype InDels. We first identified 141,000 InDels by aligning reads from the B73 line against the genome of three temperate maize inbred lines (F2, PH207, and C103) and reciprocally. Next, we designed an Affymetrix® Axiom® array to target these InDels, with a combination of probes selected at breakpoint sites (13%) or within the InDel sequence, either at polymorphic (25%) or non-polymorphic sites (63%) sites. The final array design is composed of 662,772 probes and targets 105,927 InDels, including PAVs ranging from 35 bp to 129kbp. After Affymetrix® quality control, we successfully genotyped 86,648 polymorphic InDels (82% of all InDels interrogated by the array) on 445 maize DNA samples with 422,369 probes. Genotyping InDels using this approach produced a highly reliable dataset, with low genotyping error (~ 3%), high call rate (~ 98%), and high reproducibility (> 95%). This reliability can be further increased by combining genotyping of several probes calling the same InDels (< 0.1% error rate and > 99.9% of call rate for 5 probes). This “proof of concept” tool was used to estimate the kinship matrix between 362 maize lines with 57,824 polymorphic InDels. This InDels kinship matrix was highly correlated with kinship estimated using SNPs from Illumina 50 K SNP arrays. Conclusions We efficiently genotyped thousands of small to large InDels on a sizeable number of individuals using a new Affymetrix® Axiom® array. This powerful approach opens the way to studying the contribution of InDels to trait variation and heterosis in maize. The approach is easily extendable to other species and should contribute to decipher the biological impact of InDels at a larger scale.

GPU empowered pipelines for calculating genome-wide kinship matrices with ultra-high dimensional genetic variants and facilitating 1D and 2D GWAS

Genome-wide association study (GWAS) is a powerful approach that has revolutionized the field of quantitative genetics. Two-dimensional GWAS that accounts for epistatic genetic effects needs to consider the effects of marker pairs, thus quadratic genetic variants, compared to one-dimensional GWAS that accounts for individual genetic variants. Calculating genome-wide kinship matrices in GWAS that account for relationships among individuals represented by ultra-high dimensional genetic variants is computationally challenging. Fortunately, kinship matrix calculation involves pure matrix operations and the algorithms can be parallelized, particular on graphics processing unit (GPU)-empowered high-performance computing (HPC) architectures. We have devised a new method and two pipelines: KMC1D and KMC2D for kinship matrix calculation with high-dimensional genetic variants, respectively, facilitating 1D and 2D GWAS analyses. We first divide the ultra-high-dimensional markers and marker pairs into successive blocks. We then calculate the kinship matrix for each block and merge together the block-wise kinship matrices to form the genome-wide kinship matrix. All the matrix operations have been parallelized using GPU kernels on our NVIDIA GPU-accelerated server platform. The performance analyses show that the calculation speed of KMC1D and KMC2D can be accelerated by 100–400 times over the conventional CPU-based computing.