A framework for modeling epistatic interaction

Motivation Recently, various tools for detecting single nucleotide polymorphisms (SNPs) involved in epistasis have been developed. However, no studies evaluate the employed statistical epistasis models such as the χ2-test or quadratic regression independently of the tools that use them. Such an independent evaluation is crucial for developing improved epistasis detection tools, for it allows to decide if a tool’s performance should be attributed to the epistasis model or to the optimization strategy run on top of it. Results We present a protocol for evaluating epistasis models independently of the tools they are used in and generalize existing models designed for dichotomous phenotypes to the categorical and quantitative case. Additionally, we propose a new model which scores candidate SNP sets by computing maximum likelihood distributions for the observed phenotypes in the cells of their penetrance tables. Extensive experiments show that the proposed maximum likelihood model outperforms three widely used epistasis models in most cases. The experiments also provide valuable insights into the properties of existing models, for instance, that quadratic regression perform particularly well on instances with quantitative phenotypes. Availability and implementation The evaluation protocol and all compared models are implemented in C ++ and are supported under Linux and macOS. They are available at https://github.com/baumbachlab/genepiseeker/, along with test datasets and scripts to reproduce the experiments. Supplementary information Supplementary information is available at Bioinformatics online.

Homeologous Epistasis in Wheat: The Search for an Immortal Hybrid

Hybridization between related species results in the formation of an allopolyploid with multiple subgenomes. These subgenomes will each contain complete, yet evolutionarily divergent, sets of genes. Like a diploid hybrid, allopolyploids will have two versions, or homeoalleles, for every gene. Partial functional redundancy between homeologous genes should result in a deviation from additivity. These epistatic interactions between homeoalleles are analogous to dominance effects, but are fixed across subgenomes through self pollination. An allopolyploid can be viewed as an immortalized hybrid, with the opportunity to select and fix favorable homeoallelic interactions within inbred varieties. We present a subfunctionalization epistasis model to estimate the degree of functional redundancy between homeoallelic loci and a statistical framework to determine their importance within a population. We provide an example using the homeologous dwarfing genes of allohexaploid wheat, Rht-1, and search for genome-wide patterns indicative of homeoallelic subfunctionalization in a breeding population. Using the IWGSC RefSeq v1.0 sequence, 23,796 homeoallelic gene sets were identified and anchored to the nearest DNA marker to form 10,172 homeologous marker sets. Interaction predictors constructed from products of marker scores were used to fit the homeologous main and interaction effects, as well as estimate whole genome genetic values. Some traits displayed a pattern indicative of homeoallelic subfunctionalization, while other traits showed a less clear pattern or were not affected. Using genomic prediction accuracy to evaluate importance of marker interactions, we show that homeologous interactions explain a portion of the nonadditive genetic signal, but are less important than other epistatic interactions.

A subfunctionalization epistasis model to evaluate homeologous gene interactions in allopolyploid wheat

1AbstractHybridization between related species results in the formation of an allopolyploid with multiple subgenomes. These subgenomes will each contain complete, yet evolutionarily divergent, sets of genes. Like a diploid hybrid, allopolyploids will have two versions, or homeoalleles, for every gene. Partial functional redundancy between homeologous genes should result in a deviation from additivity. These epistatic interactions between homeoalleles are analogous to dominance effects, but are fixed across subgenomes through self pollination. An allopolyploid can be viewed as an immortalized hybrid, with the opportunity to select and fix favorable homeoallelic interactions within inbred varieties. We present a subfunctionalization epistasis model to estimate the degree of functional redundancy between homeoallelic loci and a statistical framework to determine their importance within a population. We provide an example using the homeologous dwarfing genes of allohexaploid wheat, Rht-1, and search for genome-wide patterns indicative of homeoallelic subfunctionalization in a breeding population. Using the IWGSC RefSeq vl.0 sequence, 23,796 homeoallelic gene sets were identified and anchored to the nearest DNA marker to form 10,172 homeologous marker sets. Interaction predictors constructed from products of marker scores were used to fit the homeologous main and interaction effects, as well as estimate whole genome genetic values. Some traits displayed a pattern indicative of homeoallelic subfunctionalization, while other traits showed a less clear pattern or were not affected. Using genomic prediction accuracy to evaluate importance of marker interactions, we show that homeologous interactions explain a portion of the non-additive genetic signal, but are less important than other epistatic interactions.

Detecting High-Order Epistasis in Nonlinear Genotype-Phenotype Maps

High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the "scale" of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this paper, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2% to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.

A Two-State Epistasis Model Reduces Missing Heritability of Complex Traits

ABSTRACTDespite decade-long efforts, the genetic underpinnings of many complex traits and diseases remain largely elusive. It is increasingly recognized that a purely additive model, upon which most genome-wide association studies (GWAS) rely, is insufficient. Although thousands of significant trait-associated loci have been identified, purely additive models leave much of the inferred genetic variance unexplained. Several factors have been invoked to explain the ‘missing heritability’, including epistasis. Accounting for all possible epistatic interactions is computationally complex and requires very large samples. Here, we propose a simple two-state epistasis model, in which individuals show either high or low variant penetrance with respect to a certain trait. The use of this model increases the power to detect additive trait-associated loci. We show that this model is consistent with current GWAS results and improves fit with heritability observations based on twin studies. We suggest that accounting for variant penetrance will significantly increase our power to identify underlying additive loci.

Inheritance of Major Spathe Colors in Anthurium andraeanum Hort. Is Determined by Three Major Genes

The inheritance of spathe color in anthurium (Anthurium andraeanum Hort.) was studied in 77 crosses involving 59 parental genotypes. The progeny segregation into “colored : white” did not fit the genetic model proposed by Kamemoto et al. (1988), but fit a duplicate recessive epistasis model involving genes O and R, in which either O or R or both in the recessive form would result in white-spathed progeny. The progeny segregation into red or orange group was in agreement with the Kamemoto et al. (1988) model and is determined by the status of the M gene. The dosage effect of particularly the R gene accounted for the differentiation of reds from pinks and oranges from corals. Putative roles for the three genes (M, O, and R) in the flavonoid biosynthetic pathway are postulated.