Estimating genetic variance contributed by a quantitative trait locus: A random model approach

Abstract

Detecting quantitative trait loci (QTL) and estimating QTL variances (represented by the squared QTL effects) are two main goals of QTL mapping and genome-wide association studies (GWAS). However, there are issues associated with estimated QTL variances and such issues have not attracted much attention from the QTL mapping community. Estimated QTL variances are usually biased upwards due to estimation being associated with significance tests. The phenomenon is called the Beavis effect. However, estimated variances of QTL without significance tests can also be biased upwards, which cannot be explained by the Beavis effect; rather, this bias is due to the fact that QTL variances are often estimated as the squares of the estimated QTL effects. The parameters are the QTL effects and the estimated QTL variances are obtained by squaring the estimated QTL effects. This square transformation failed to incorporate the errors of estimated QTL effects into the transformation. The consequence is biases in estimated QTL variances. To correct the biases, we can either reformulate the QTL model by treating the QTL effect as random and directly estimate the QTL variance (as a variance component) or adjust the bias by taking into account the error of the estimated QTL effect. A moment method of estimation has been proposed to correct the bias. The method has been validated via Monte Carlo simulation studies. The method has been applied to QTL mapping for the 10-week-body-weight trait from an F2 mouse population.

Identification of Fusarium head blight sources of resistance and associated QTLs in historical and modern Canadian spring wheat

“…QFhb.dms-4B.3 was about 5.1 Mb away from the stripe rust resistance QTL ( QYr.dms-4B ). The number of lines and varieties used in two previous studies and the current study varied from 192–198, which agrees with the 150–200 population size widely used in QTL discovery studies ( Wang et al., 2022 ). A few examples include 186 durum wheat association mapping panel ( Ruan et al., 2020 ), an association panel of 171 common wheat cultivars ( Hu et al., 2020 ), 187 spring wheat recombinant inbred lines ( Poudel et al., 2022 ), and 171 bread wheat doubled haploid lines ( Zhu et al., 2021b ).…”

Statistical models and tools for QTL mapping in multi-parent populations

“…, was close to variance that was used to simulate those effects, 𝜎 𝑄𝑇𝐿 𝑠𝑖𝑚 2 = 0.5, while the estimated variance of fixed QTL effects, 𝜎 ̂𝑄𝑇𝐿 𝑓𝑖𝑥𝑒𝑑 2 , was biased to a larger value, which agrees with the assumption that the random model produces an unbiased estimate of the genetic variance (Wang et al 2022b).…”

“…QEI analysis by assessing the stability of QTL effects across families and environments Through the MET&MPP analysis, QEI is detected by testing different types of QTL effects across diverse environments and families by employing IBD-based mixed model approaches. Previous studies have discussed the advantages of using multi-allelic IBDs versus bi-allelic identity-by-state (IBS) markers (Jurcic et al 2021;Li et al 2021) and modeling QTL terms as random versus fixed (Boer et al 2007;Wang et al 2022b). In the current study for MET&MPP analysis, we propose to fit functions of IBD probabilities as genetic predictors to indicate the expected numbers of allele copies originating from each parent, which allows the estimation of multi-allelic QTL effects in relation to parent origins (Wei and Xu 2016;Li et al 2021).…”

“…Beyond detecting QTLs, we also want to estimate QTL effects and variances. For fixed QTL alleles, allelic substitution effects at significant QTLs, as well as the contribution of the allelic variation to the genetic and phenotypic variance, are often overestimated due to undersampling of offspring individuals (known as Beavis effect) of the mapping population (Xu 2003;Beavis 2019;Wang et al 2022b). First, the Beavis effect describes the phenomenon that the variance associated with QTLs is significantly inflated if the offspring population size for identifying those QTLs is not large enough (Xu 2003;Beavis 2019).…”

“…Incorporating the estimation errors into the estimator of genetic variance is one way to adjust the bias. The alternative of directly estimating the genetic variance from the application of a mixed or random model (Wang et al 2022b) is more attractive. Treating QTL effects as random allows the estimation of variance components related to QTLs by restricted maximum likelihood (REML), and it benefits the estimation of unbiased genetic variances.…”