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The Beavis effect in quantitative trait locus (QTL) mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners' curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners' curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated noncentral Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated noncentral Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300 k single nucleotide polymorphism markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction., (© The Author(s) 2021. Published by Oxford University Press on behalf of Genetics Society of America. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

Identification of functional markers (FMs) provides information about the genetic architecture underlying complex traits. An approach that combines the strengths of linkage and association mapping, referred to as nested association mapping (NAM), has been proposed to identify FMs in many plant species. The ability to identify and resolve FMs for complex traits depends upon a number of factors including frequency of FM alleles, magnitudes of their genetic effects, disequilibrium among functional and nonfunctional markers, statistical analysis methods, and mating design. The statistical characteristics of power, accuracy, and precision to identify FMs with a NAM population were investigated using three simulation studies. The simulated data sets utilized publicly available genetic sequences and simulated FMs were identified using least-squares variable selection methods. Results indicate that FMs with simple additive genetic effects that contribute at least 5% to the phenotypic variability in at least five segregating families of a NAM population consisting of recombinant inbred progeny derived from 28 matings with a single reference inbred will have adequate power to accurately and precisely identify FMs. This resolution and power are possible even for genetic architectures consisting of disequilibrium among multiple functional and nonfunctional markers in the same genomic region, although the resolution of FMs will deteriorate rapidly if more than two FMs are tightly linked within the same amplicon. Finally, nested mating designs involving several reference parents will have a greater likelihood of resolving FMs than single reference designs.

The effects of intermating on recombination and the development of linkage maps were assessed in maize. Progeny derived from a common population (B73 x Mo17) before and after five generations of intermating were genotyped at the same set of 190 RFLP loci. Intermating resulted in nearly a four-fold increase in the genetic map distance and increased the potential for improved genetic resolution in 91% of the intervals evaluated. This mapping population and related information should connect research involving dense genetic maps, physical mapping, gene isolation, comparative genomics, analysis of quantitative trait loci and investigations of heterosis.