A unified model for functional and statistical epistasis and its application in quantitative trait Loci analysis

Interaction between genes, or epistasis, is found to be common and it is a key concept for understanding adaptation and evolution of natural populations, response to selection in breeding programs, and determination of complex disease. Currently, two independent classes of models are used to study epistasis. Statistical models focus on maintaining desired statistical properties for detection and estimation of genetic effects and for the decomposition of genetic variance using average effects of allele substitutions in populations as parameters. Functional models focus on the evolutionary consequences of the attributes of the genotype-phenotype map using natural effects of allele substitutions as parameters. Here we provide a new, general and unified model framework: the natural and orthogonal interactions (NOIA) model. NOIA implements tools for transforming genetic effects measured in one population to the ones of other populations (e.g., between two experimental designs for QTL) and parameters of statistical and functional epistasis into each other (thus enabling us to obtain functional estimates of QTL), as demonstrated numerically. We develop graphical interpretations of functional and statistical models as regressions of the genotypic values on the gene content, which illustrates the difference between the models--the constraint on the slope of the functional regression--and when the models are equivalent. Furthermore, we use our theoretical foundations to conceptually clarify functional and statistical epistasis, discuss the advantages of NOIA over previous theory, and stress the importance of linking functional and statistical models.     

Natural and orthogonal interaction framework for modeling gene-environment interactions with application to lung cancer

Objectives: We aimed at extending the Natural and Orthogonal Interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data. Methods: The NOIA statistical models are developed for additive, dominant, and recessive genetic models as well as for a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data. Results: Our simulations showed that power for testing associations while allowing for interaction using the NOIA statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to lung cancer data, much smaller p values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested. Conclusion: The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.     

Multiallelic models of genetic effects and variance decomposition in non-equilibrium populations

Quantitative genetics stems from the theoretical models of genetic effects, which are re-parameterizations of the genotypic values into parameters of biological (genetic) relevance. Different formulations of genetic effects are adequate to address different subjects. We thus need to generalize and unify them under a common framework for enabling researchers to easily transform genetic effects between different biological meanings. The Natural and Orthogonal Interactions (NOIA) model of genetic effects has been developed to achieve this aim. Here, we further implement the statistical formulation of NOIA with multiple alleles under Hardy–Weinberg departures (HWD). We show that our developments are straightforwardly connected to the decomposition of the genetic variance and we point out several emergent properties of multiallelic quantitative genetic models, as compared to the biallelic ones. Further, NOIA entails a natural extension of one-locus developments to multiple epistatic loci under linkage equilibrium. Therefore, we present an extension of the orthogonal decomposition of the genetic variance to multiple epistatic, multiallelic loci under HWD. We illustrate this theory with a graphical interpretation and an analysis of published data on the human acid phosphatase (ACP1) polymorphism.     

How to perform meaningful estimates of genetic effects

Although the genotype-phenotype map plays a central role both in Quantitative and Evolutionary Genetics, the formalization of a completely general and satisfactory model of genetic effects, particularly accounting for epistasis, remains a theoretical challenge. Here, we use a two-locus genetic system in simulated populations with epistasis to show the convenience of using a recently developed model, NOIA, to perform estimates of genetic effects and the decomposition of the genetic variance that are orthogonal even under deviations from the Hardy-Weinberg proportions. We develop the theory for how to use this model in interval mapping of quantitative trait loci using Halley-Knott regressions, and we analyze a real data set to illustrate the advantage of using this approach in practice. In this example, we show that departures from the Hardy-Weinberg proportions that are expected by sampling alone substantially alter the orthogonal estimates of genetic effects when other statistical models, like F₂ or G2A, are used instead of NOIA. Finally, for the first time from real data, we provide estimates of functional genetic effects as sets of effects of natural allele substitutions in a particular genotype, which enriches the debate on the interpretation of genetic effects as implemented both in functional and in statistical models. We also discuss further implementations leading to a completely general genotype-phenotype map.     

Genetic characterization of a newly discovered Finnish Arctic charr (Salvelinus alpinus; Salmoniformes) population: Stocked or natural?

Like many salmonid species, Arctic charr (Salvelinus alpinus) is currently threatened by human-induced perturbations. From a conservation perspective, it is important to characterize the genetic diversity of populations so that genetically distinct units worthy of conservation effort can be identified. Here, we used microsatellite markers to assess whether a recently discovered Finnish population of lacustrine charr found in Lake Karhunpesälampi is of natural origin. We also aimed to reveal the colonization history of this lake. To this end, we quantified genetic diversity and distance of this population to other charr populations inhabiting Fennoscandia including all sources used in official Finnish stocking programs. The population was found to be genetically differentiated from all other populations analysed. This, together with the remote location of the lake and other population genetic information, indicates that the population is likely of natural origin. The population deserves to be acknowledged as a genetically distinct unit worthy of conservation.     

长江流域野生拟南芥种群QTL作图平台的建立

对模式植物的研究不仅能揭示众多具有普遍规律的生物现象,而且能为其它植物物种,特别是与人类生活紧密相关的经济植物提供具有借鉴与参考意义的研究方法。QTL遗传作图是寻找那些影响不同地域植物自然变异等位基因的传统且有效的工作方法。对不同分化时长和不同遗传背景的植物种群,有针对性地开发特异的分子标记,一直是QTL遗传作图工作的重要内容。该研究利用二代测序技术得到的全基因组重测序结果,根据其中鉴定到的结构变异(SV)多态性设计引物,开发了针对分化时间短、多态性位点少的中国长江流域野生拟南芥(Arabidopsis thaliana)种群的QTL作图分子标记平台,得到了有效适用的结果,该方法不仅在模式植物拟南芥中适用,而且也适用于其它植物。     

An improved method for quantitative trait loci detection and identification of within-line segregation in F2 intercross designs

We present a new flexible, simple, and powerful genome-scan method (flexible intercross analysis, FIA) for detecting quantitative trait loci (QTL) in experimental line crosses. The method is based on a pure random-effects model that simultaneously models between- and within-line QTL variation for single as well as epistatic QTL. It utilizes the score statistic and thereby facilitates computationally efficient significance testing based on empirical significance thresholds obtained by means of permutations. The properties of the method are explored using simulations and analyses of experimental data. The simulations showed that the power of FIA was as good as, or better than, Haley-Knott regression and that FIA was rather insensitive to the level of allelic fixation in the founders, especially for pedigrees with few founders. A chromosome scan was conducted for a meat quality trait in an F(2) intercross in pigs where a mutation in the halothane (Ryanodine receptor, RYR1) gene with a large effect on meat quality was known to segregate in one founder line. FIA obtained significant support for the halothane-associated QTL and identified the base generation allele with the mutated allele. A genome scan was also performed in a previously analyzed chicken F(2) intercross. In the chicken intercross analysis, four previously detected QTL were confirmed at a 5% genomewide significance level, and FIA gave strong evidence (P < 0.01) for two of these QTL to be segregating within the founder lines. FIA was also extended to account for epistasis and using simulations we show that the method provides good estimates of epistatic QTL variance even for segregating QTL. Extensions of FIA and its applications on other intercross populations including backcrosses, advanced intercross lines, and heterogeneous stocks are also discussed.     

CONNECTING QTLS TO THE G-MATRIX OF EVOLUTIONARY QUANTITATIVE GENETICS

Evolutionary quantitative genetics has recently advanced in two distinct streams. Many biologists address evolutionary questions by estimating phenotypic selection and genetic (co)variances ( G matrices). Simultaneously, an increasing number of studies have applied quantitative trait locus (QTL) mapping methods to dissect variation. Both conceptual and practical difficulties have isolated these two foci of quantitative genetics. A conceptual integration follows from the recognition that QTL allele frequencies are the essential variables relating the G -matrix to marker-based mapping experiments. Breeding designs initiated from randomly selected parental genotypes can be used to estimate QTL-specific genetic (co)variances. These statistics appropriately distill allelic variation and provide an explicit population context for QTL mapping estimates. Within this framework, one can parse the G -matrix into a set of mutually exclusive genomic components and ask whether these parts are similar or dissimilar in their respective features, for example the magnitude of phenotypic effects and the extent and nature of pleiotropy. As these features are critical determinants of sustained response to selection, the integration of QTL mapping methods into G -matrix estimation can provide a concrete, genetically based experimental program to investigate the evolutionary potential of natural populations.     

Genetic analysis of populations of threatened snake species using RAPD markers

Snakes are a particularly threatened vertebrate taxon, with distributions of many species and populations becoming increasingly fragmented. At present, little is known about the degree of genetic differentiation that exists between isolated populations even though such information may be critical to their survival and conservation. As an example of how recently developed RAPD genetic markers can be used in conservation genetics, we present preliminary results from a study which used these DNA-based markers to assess population divergence in two threatened Canadian snakes, the black rat snake ( Elaphe o. obsoleta ) and the eastern massasauga rattlesnake ( Sistrurus c. catenatus ). We present information on the levels of variation and reliability of amplification for fragments generated from five primers. We then use a recently developed analytical technique to estimate levels of nucleotide diversity within populations and sequence divergence between populations. Our results show that intrapopulation levels of divergence as estimated by the methods of Clark & Lanigan ( Molecular Biology and Evolution 1993, 10 , 1096–1111) approximate those found for mtDNA in vertebrates and that diversity between snake populations is small and non-significant when tested using randomization procedures. Thus, our study provides an example of how RAPDs can be applied to conservation genetic studies of vertebrates and suggest that the snake populations we examined have only recently become isolated and maybe considered genetically equivalent from a conservation perspective, although this conclusion needs to be confirmed with other DNA-based markers.     

Durability of marker-quantitative trait loci haplotypes in structured populations

Given the relative ease of identifying genetic markers linked to QTL (compared to finding the loci themselves), it is natural to ask whether linked markers can be used to address questions concerning the contemporary dynamics and recent history of the QTL. In particular, can a marker allele found associated with a QTL allele in a QTL mapping study be used to track population dynamics or the history of the QTL allele? For this strategy to succeed, the marker-QTL haplotype must persist in the face of recombination over the relevant time frame. Here we investigate the dynamics of marker-QTL haplotype frequencies under recombination, population structure, and divergent selection to assess the potential utility of linked markers for a population genetic study of QTL. For two scenarios, described as "secondary contact" and "novel allele," we use both deterministic and stochastic methods to describe the influence of gene flow between habitats, the strength of divergent selection, and the genetic distance between a marker and the QTL on the persistence of marker-QTL haplotypes. We find that for most reasonable values of selection on a locus (s < or = 0.5) and migration (m > 1%) between differentially selected populations, haplotypes of typically spaced markers (5 cM) and QTL do not persist long enough (>100 generations) to provide accurate inference of the allelic state at the QTL.     

Group-structured genetic models in analyses of the population and behavioral ecology of poikilothermic vertebrates

Estimates of gene correlations among individuals within and among populations are frequently derived from statistical analyses of genetic data (e.g., F statistics). These measures can be important tools in molecular ecology and conservation, and offer important insights into population breeding structure. Using recently derived theory developed for group-structured populations, we show that fixation indices, when combined with basic population ecological and demographic data can be used to investigate population mating systems and to predict dispersal rates, trajectories and asymptotic levels of fixation indices, and effective population size. Four case studies of poikilothermic vertebrates are used to demonstrate the broad utility of evolutionary and ecological inferences afforded by group-structured models.     

Quantitative trait locus mapping in natural populations: progress, caveats and future directions

Over the last 15 years quantitative trait locus (QTL) mapping has become a popular method for understanding the genetic basis of continuous variation in a variety of systems. For example, the technique is now an integral tool in medical genetics, livestock production, plant breeding and population genetics of model organisms. Ten years ago, it was suggested that the method could be used to understand continuous variation in natural populations. In this review I: (i) clarify what is meant by natural population in the QTL context, (ii) discuss whether evolutionary biologists have successfully mapped QTL in natural populations, (iii) highlight some of the questions that have been addressed by QTL mapping in natural populations, (iv) describe how QTL mapping can be conducted in unmanipulated natural populations, (v) highlight some of the limitations of QTL mapping and (vi) try to predict some future directions for QTL mapping in natural populations.     

Natural and orthogonal model for estimating gene–gene interactions applied to cutaneous melanoma

Epistasis, or gene–gene interaction, results from joint effects of genes on a trait; thus, the same alleles of one gene may display different genetic effects in different genetic backgrounds. In this study, we generalized the coding technique of a natural and orthogonal interaction (NOIA) model for association studies along with gene–gene interactions for dichotomous traits and human complex diseases. The NOIA model which has non-correlated estimators for genetic effects is important for estimating influence from multiple loci. We conducted simulations and data analyses to evaluate the performance of the NOIA model. Both simulation and real data analyses revealed that the NOIA statistical model had higher power for detecting main genetic effects and usually had higher power for some interaction effects than the usual model. Although associated genes have been identified for predisposing people to melanoma risk: HERC2 at 15q13.1, MC1R at 16q24.3 and CDKN2A at 9p21.3, no gene–gene interaction study has been fully explored for melanoma. By applying the NOIA statistical model to a genome-wide melanoma dataset, we confirmed the previously identified significantly associated genes and found potential regions at chromosomes 5 and 4 that may interact with the HERC2 and MC1R genes, respectively. Our study not only generalized the orthogonal NOIA model but also provided useful insights for understanding the influence of interactions on melanoma risk.     

Six new recombinant inbred populations for the study of quantitative traits in Arabidopsis thaliana

Quantitative approaches are now widely used to study the genetic architecture of complex traits. However, most studies have been conducted in single mapping populations, which sample only a fraction of the natural allelic variation available within a gene pool and can identify only a subset of the loci controlling the traits. To enable the progress towards an understanding of the global genetic architecture of a broad range of complex traits, we have developed and characterised six new Arabidopsis thaliana recombinant inbred populations. To evaluate the utility of these populations for integrating analyses from multiple populations, we identified quantitative trait loci (QTL) controlling flowering time in vernalized plants growing in 16 h days. We used the physical positions of markers to align the linkage maps of our populations with those of six existing populations. We identified seven QTL in genomic locations coinciding with those identified in previous studies and in addition a further eight QTL were identified. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. An erratum to this article can be found at     

Genetic basis of climatic adaptation in scots pine by bayesian quantitative trait locus analysis

We examined the genetic basis of large adaptive differences in timing of bud set and frost hardiness between natural populations of Scots pine. As a mapping population, we considered an "open-pollinated backcross" progeny by collecting seeds of a single F(1) tree (cross between trees from southern and northern Finland) growing in southern Finland. Due to the special features of the design (no marker information available on grandparents or the father), we applied a Bayesian quantitative trait locus (QTL) mapping method developed previously for outcrossed offspring. We found four potential QTL for timing of bud set and seven for frost hardiness. Bayesian analyses detected more QTL than ANOVA for frost hardiness, but the opposite was true for bud set. These QTL included alleles with rather large effects, and additionally smaller QTL were supported. The largest QTL for bud set date accounted for about a fourth of the mean difference between populations. Thus, natural selection during adaptation has resulted in selection of at least some alleles of rather large effect.     

The molecular basis of quantitative genetic variation in natural populations

DNA markers allow us to study quantitative trait loci (QTL) - the genes that control adaptation and quantitative variation. Experiments can map the genes responsible for quantitative variation and address the evolutionary and ecological significance of this variation. Recent studies suggest that major genes segregate within and among natural populations. It is now feasible to study the genes that cause morphological variation, life history trade-offs, heterosis and speciation. These methods can determine the role of epistasis and genotype-by-environment interaction in maintaining genetic variation. QTL mapping is an important tool used to address evolutionary and ecological questions of long-standing interest.     

Success and failure in replication of genotype–phenotype associations: How does replication help in understanding the genetic basis of phenotypic variation in outbred populations?

Recent developments in sequencing technologies have facilitated genomewide mapping of phenotypic variation in natural populations. Such mapping efforts face a number of challenges potentially leading to low reproducibility. However, reproducible research forms the basis of scientific progress. We here discuss the options for replication and the reasons for potential nonreproducibility. We then review the evidence for reproducible quantitative trait loci (QTL) with a focus on natural animal populations. Existing case studies of replication fall into three categories: (i) traits that have been mapped to major effect loci (including chromosomal inversion and supergenes) by independent research teams; (ii) QTL fine‐mapped in discovery populations; and (iii) attempts to replicate QTL across multiple populations. Major effect loci, in particular those associated with inversions, have been successfully replicated in several cases within and across populations. Beyond such major effect variants, replication has been more successful within than across populations, suggesting that QTL discovered in natural populations may often be population‐specific. This suggests that biological causes (differences in linkage patterns, allele frequencies or context‐dependencies of QTL) contribute to nonreproducibility. Evidence from other fields, notably animal breeding and QTL mapping in humans, suggests that a significant fraction of QTL is indeed reproducible in direction and magnitude at least within populations. However, there is also a large number of QTL that cannot be easily reproduced. We put forward that more studies should explicitly address the causes and context‐dependencies of QTL signals, in particular to disentangle linkage differences, allele frequency differences and gene‐by‐environment interactions as biological causes of nonreproducibility of QTL, especially between populations.     

Genetic diversity of Eurycoma longifolia inferred from single nucleotide polymorphisms

Eurycoma longifolia Jack. is a treelet that grows in the forests of Southeast Asia and is widely used throughout the region because of its reported medicinal properties. Widespread harvesting of wild-grown trees has led to rapid thinning of natural populations, causing a potential decrease in genetic diversity among E. longifolia. Suitable genetic markers would be very useful for propagation and breeding programs to support conservation of this species, although no such markers currently exist. To meet this need, we have applied a genome complexity reduction strategy to identify a series of single nucleotide polymorphisms (SNPs) within the genomes of several E. longifolia accessions. We have found that the occurrence of these SNPs reflects the geographic origins of individual plants and can distinguish different natural populations. This work demonstrates the rapid development of molecular genetic markers in species for which little or no genomic sequence information is available. The SNP markers that we have developed in this study will also be useful for identifying genetic fingerprints that correlate with other properties of E. longifolia, such as high regenerability or the appearance of bioactive metabolites.