Multi-locus penetrance variance analysis method for association study in complex diseases

Common heritable diseases often result from the action of several different genes, each of which contributes to the total observed variability in the disease trait. Traditional single-locus association approaches rely heavily on the marginal effects of single-locus and tend to ignore the multigenic nature of complex diseases. The increasing request for localizing genes underlying traits in multi-gene diseases has led to the development of some statistical methods. In this study, we develop a multi-locus analysis method - multi-locus penetrance variance analysis (MPVA), and conduct systematical simulation studies to evaluate its performance. Our results show that compared with other multi-locus methods, MPVA has some advantage in detecting complicated interactions under different epistatic models, and its performance is stable and robust.     

Effect of balancing selection on spatial genetic structure within populations: theoretical investigations on the self-incompatibility locus and empirical studies in Arabidopsis halleri

The effect of selection on patterns of genetic structure within and between populations may be studied by contrasting observed patterns at the genes targeted by selection with those of unlinked neutral marker loci. Local directional selection on target genes will produce stronger population genetic structure than at neutral loci, whereas the reverse is expected for balancing selection. However, theoretical predictions on the intensity of this signal under precise models of balancing selection are still lacking. Using negative frequency-dependent selection acting on self-incompatibility systems in plants as a model of balancing selection, we investigated the effect of such selection on patterns of spatial genetic structure within a continuous population. Using numerical simulations, we tested the effect of the type of self-incompatibility system, the number of alleles at the self-incompatibility locus and the dominance interactions among them, the extent of gene dispersal, and the immigration rate on spatial genetic structure at the selected locus and at unlinked neutral loci. We confirm that frequency-dependent selection is expected to reduce the extent of spatial genetic structure as compared to neutral loci, particularly in situations with low number of alleles at the self-incompatibility locus, high frequency of codominant interactions among alleles, restricted gene dispersal and restricted immigration from outside populations. Hence the signature of selection on spatial genetic structure is expected to vary across species and populations, and we show that empirical data from the literature as well as data reported here on three natural populations of the herb Arabidopsis halleri confirm these theoretical results.     

Microevolutionary selection dynamics acting on immune genes of the green‐veined white butterfly,Pieris napi

Insects rely on their innate immune system to successfully mediate complex interactions with their microbiota, as well as the microbes present in the environment. Previous work has shown that components of the canonical immune gene repertoire evolve rapidly and have evolutionary characteristics originating from interactions with fast‐evolving microorganisms. Although these interactions are likely to vary among populations, there is a poor understanding of the microevolutionary dynamics of immune genes, especially in non‐Dipteran insects. Here, we use the full set of canonical insect immune genes to investigate microevolutionary dynamics acting on these genes between and among populations by comparing three allopatric populations of the green‐veined white butterfly, Pieris napi (Linné; Lepidoptera, Pieridae). Immune genes showed increased genetic diversity compared to genes from the rest of the genome and various functional categories exhibited different types of signatures of selection, at different evolutionary scales, presenting a complex pattern of selection dynamics. Signatures of balancing selection were identified in 10 genes, and 17 genes appear to be under positive selection. Genes involved with the cellular arm of the immune response as well as the Toll pathway appear to be enriched among our outlier loci, regardless of functional category. This suggests that the targets of selection might focus upon an entire pathway, rather than functional subsets across pathways. Our microevolutionary results are similar to previously observed macroevolutionary patterns from diverse taxa, suggesting that either the immune system is robust to dramatic differences in life history and microbial communities, or that diverse microbes exert similar selection pressures.     

Genome-wide polymorphisms show unexpected targets of natural selection

Natural selection can act on all the expressed genes of an individual, leaving signatures of genetic differentiation or diversity at many loci across the genome. New power to assay these genome-wide effects of selection comes from associating multi-locus patterns of polymorphism with gene expression and function. Here, we performed one of the first genome-wide surveys in a marine species, comparing purple sea urchins, Strongylocentrotus purpuratus, from two distant locations along the species' wide latitudinal range. We examined 9112 polymorphic loci from upstream non-coding and coding regions of genes for signatures of selection with respect to gene function and tissue- and ontogenetic gene expression. We found that genetic differentiation (F(ST)) varied significantly across functional gene classes. The strongest enrichment occurred in the upstream regions of E3 ligase genes, enzymes known to regulate protein abundance during development and environmental stress. We found enrichment for high heterozygosity in genes directly involved in immune response, particularly NALP genes, which mediate pro-inflammatory signals during bacterial infection. We also found higher heterozygosity in immune genes in the southern population, where disease incidence and pathogen diversity are greater. Similar to the major histocompatibility complex in mammals, balancing selection may enhance genetic diversity in the innate immune system genes of this invertebrate. Overall, our results show that how genome-wide polymorphism data coupled with growing databases on gene function and expression can combine to detect otherwise hidden signals of selection in natural populations.     

Backward genotype-trait association (BGTA)-based dissection of complex traits in case-control designs

BACKGROUND: The studies of complex traits project new challenges to current methods that evaluate association between genotypes and a specific trait. Consideration of possible interactions among loci leads to overwhelming dimensions that cannot be handled using current statistical methods. METHODS: In this article, we evaluate a multi-marker screening algorithm--the backward genotype-trait association (BGTA) algorithm for case-control designs, which uses unphased multi-locus genotypes. BGTA carries out a global investigation on a candidate marker set and automatically screens out markers carrying diminutive amounts of information regarding the trait in question. To address the 'too many possible genotypes, too few informative chromosomes' dilemma of a genomic-scale study that consists of hundreds to thousands of markers, we further investigate a BGTA-based marker selection procedure, in which the screening algorithm is repeated on a large number of random marker subsets. Results of these screenings are then aggregated into counts that the markers are retained by the BGTA algorithm. Markers with exceptional high counts of returns are selected for further analysis. RESULTS AND CONCLUSION: Evaluated using simulations under several disease models, the proposed methods prove to be more powerful in dealing with epistatic traits. We also demonstrate the proposed methods through an application to a study on the inflammatory bowel disease.     

The strength of the selection barrier between populations

Genetic differences among populations exposed to selection form barriers against genetic exchange by mortality among hybrids. The strength of such a selection barrier, with which one (recipient) population reacts against immigration from another (donor) population, may be measured as the cumulative mean fitness of hybrids and their descendants relative to the fitness of the recipient population. Previous work analysed a case of weak selection with pairwise epistatic interactions by assuming small genetic distance between two populations in contact. The present study allows large genetic difference between the donor and recipient populations and considers weak multilocus selection with arbitrary epistatic interactions between two or more linked loci. An approximate analytical expression for the barrier strength is obtained as an expansion in which the strength of selection plays the role of a small parameter. It is shown that allele frequencies and gametic linkage disequilibria contribute in different ways to the strength of the selection barrier.     

Dynamic Epistasis under Varying Environmental Perturbations

Epistasis describes the phenomenon that mutations at different loci do not have independent effects with regard to certain phenotypes. Understanding the global epistatic landscape is vital for many genetic and evolutionary theories. Current knowledge for epistatic dynamics under multiple conditions is limited by the technological difficulties in experimentally screening epistatic relations among genes. We explored this issue by applying flux balance analysis to simulate epistatic landscapes under various environmental perturbations. Specifically, we looked at gene-gene epistatic interactions, where the mutations were assumed to occur in different genes. We predicted that epistasis tends to become more positive from glucose-abundant to nutrient-limiting conditions, indicating that selection might be less effective in removing deleterious mutations in the latter. We also observed a stable core of epistatic interactions in all tested conditions, as well as many epistatic interactions unique to each condition. Interestingly, genes in the stable epistatic interaction network are directly linked to most other genes whereas genes with condition-specific epistasis form a scale-free network. Furthermore, genes with stable epistasis tend to have similar evolutionary rates, whereas this co-evolving relationship does not hold for genes with condition-specific epistasis. Our findings provide a novel genome-wide picture about epistatic dynamics under environmental perturbations.     

Epistasis and the mutation load: a measurement-theoretical approach

An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.     

Effect of varying epistasis on the evolution of recombination

Whether recombination decelerates or accelerates a population's response to selection depends, at least in part, on how fitness-determining loci interact. Realistically, all genomes likely contain fitness interactions both with positive and with negative epistasis. Therefore, it is crucial to determine the conditions under which the potential beneficial effects of recombination with negative epistasis prevail over the detrimental effects of recombination with positive epistasis. Here, we examine the simultaneous effects of diverse epistatic interactions with different strengths and signs in a simplified model system with independent pairs of interacting loci and selection acting only on the haploid phase. We find that the average form of epistasis does not predict the average amount of linkage disequilibrium generated or the impact on a recombination modifier when compared to results using the entire distribution of epistatic effects and associated single-mutant effects. Moreover, we show that epistatic interactions of a given strength can produce very different effects, having the greatest impact when selection is weak. In summary, we observe that the evolution of recombination at mutation-selection balance might be driven by a small number of interactions with weak selection rather than by the average epistasis of all interactions. We illustrate this effect with an analysis of published data of Saccharomyces cerevisiae. Thus to draw conclusions on the evolution of recombination from experimental data, it is necessary to consider the distribution of epistatic interactions together with the associated selection coefficients.     

A new theory of MHC evolution: beyond selection on the immune genes

The major histocompatibility complex (MHC) is a dense region of immune genes with high levels of polymorphism, which are arranged in haplotype blocks. Traditional models of balancing selection (i.e. overdominance and negative frequency dependence) were developed to study the population genetics of single genes. However, the MHC is a multigene family surrounded by linked (non-neutral) polymorphisms, and not all of its features are well explained by these models. For example, (i) the high levels of polymorphism in small populations, (ii) the unexpectedly large genetic differentiation between populations, (iii) the shape of the allelic genealogy associated with trans-species evolution, and (iv) the close associations between particular MHC (human leucocyte antigen, HLA) haplotypes and the approximately 100 pathologies in humans. Here, I propose a new model of MHC evolution named Associative Balancing Complex evolution that can explain these phenomena. The model proposes that recessive deleterious mutations accumulate as a 'sheltered load' nearby MHC genes. These mutations can accumulate because (i) they are rarely expressed as homozygotes given the high MHC gene diversity and (ii) purifying selection is inefficient with low recombination rates (cf. Muller's ratchet). Once fixed, these mutations add to balancing selection and further reinforce linkage through epistatic selection against recombinants.     

A Model-Based Approach for Identifying Signatures of Ancient Balancing Selection in Genetic Data

While much effort has focused on detecting positive and negative directional selection in the human genome, relatively little work has been devoted to balancing selection. This lack of attention is likely due to the paucity of sophisticated methods for identifying sites under balancing selection. Here we develop two composite likelihood ratio tests for detecting balancing selection. Using simulations, we show that these methods outperform competing methods under a variety of assumptions and demographic models. We apply the new methods to whole-genome human data, and find a number of previously-identified loci with strong evidence of balancing selection, including several HLA genes. Additionally, we find evidence for many novel candidates, the strongest of which is FANK1, an imprinted gene that suppresses apoptosis, is expressed during meiosis in males, and displays marginal signs of segregation distortion. We hypothesize that balancing selection acts on this locus to stabilize the segregation distortion and negative fitness effects of the distorter allele. Thus, our methods are able to reproduce many previously-hypothesized signals of balancing selection, as well as discover novel interesting candidates.     

Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and G x E interactions

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.     

An evolution-based high-fidelity method of epistasis measurement: Theory and application to influenza

Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data.     

A semi-symmetric two-locus model

The two-locus symmetric viability model characterized by its invariance with respect to the exchange of alleles at each locus, is a well-studied model of classical two-locus theory. The symmetric model introduced by Lewontin and Kojima is among the few multi-locus models with epistatic interactions between loci for which a polymorphism with linkage equilibrium can be stable and this happens when recombination is sufficiently large. We show that an analogous property holds true for a different model, in which symmetry need exist at only one locus. The properties of this new semi-symmetric model are compared with those of the classical symmetric model. For tight linkage, two classes of polymorphisms are possible, depending on the magnitude of additive epistasis. The recombination rate above which linkage equilibrium becomes stable is derived analytically. As in the symmetric model, intervals of recombination in which no polymorphism is stable are possible, and stable polymorphisms can coexist with stable fixations.     

The role of pleiotropy vs signaller-receiver gene epistasis in life history trade-offs: dissecting the genomic architecture of organismal design in social systems

Traditional life history theory ignores trade-offs due to social interactions, yet social systems expand the set of possible trade-offs affecting a species evolution--by introducing asymmetric interactions between the sexes, age classes and invasion of alternative strategies. We outline principles for understanding gene epistasis due to signaller-receiver dynamics, gene interactions between individuals, and impacts on life history trade-offs. Signaller-receiver epistases create trade-offs among multiple correlated traits that affect fitness, and generate multiple fitness optima conditional on frequency of alternative strategies. In such cases, fitness epistasis generated by selection can maintain linkage disequilibrium, even among physically unlinked loci. In reviewing genetic methods for studying life history trade-offs, we conclude that current artificial selection or gene manipulation experiments focus on pleiotropy. Multi-trait selection experiments, multi-gene engineering methods or multiple endocrine manipulations can test for epistasis and circumvent these limitations. In nature, gene mapping in field pedigrees is required to study social gene epistases and associated trade-offs. Moreover, analyses of correlational selection and frequency-dependent selection are necessary to study epistatic social system trade-offs, which can be achieved with group-structured versions of Price's (1970) equation.     

Signatures of demographic history and natural selection in the human major histocompatibility complex Loci

Many lines of evidence show that several HLA loci have experienced balancing selection. However, distinguishing among demographic and selective explanations for patterns of variation observed with HLA genes remains a challenge. In this study we address this issue using data from a diverse set of human populations at six classical HLA loci and, employing a comparative genomics approach, contrast results for HLA loci to those for non-HLA markers. Using a variety of analytic methods, we confirm and extend evidence for selection acting on several HLA loci. We find that allele frequency distributions for four of the six HLA loci deviate from neutral expectations and show that this is unlikely to be explained solely by demographic factors. Other features of HLA variation are explained in part by demographic history, including decreased heterozygosity and increased LD for populations at greater distances from Africa and a similar apportionment of genetic variation for HLA loci compared to putatively neutral non-HLA loci. On the basis of contrasts among different HLA loci and between HLA and non-HLA loci, we conclude that HLA loci bear detectable signatures of both natural selection and demographic history.     

Contrasting patterns of selection acting on MHC class I and class II DRB genes in the Alpine marmot (Marmota marmota)

The major histocompatibility complex (MHC) genes code for proteins that play a critical role in the immune system response. The MHC genes are among the most polymorphic genes in vertebrates, presumably due to balancing selection. The two MHC classes appear to differ in the rate of evolution, but the reasons for this variation are not well understood. Here, we investigate the level of polymorphism and the evolution of sequences that code for the peptide-binding regions of MHC class I and class II DRB genes in the Alpine marmot (Marmota marmota). We found evidence for four expressed MHC class I loci and two expressed MHC class II loci. MHC genes in marmots were characterized by low polymorphism, as one to eight alleles per putative locus were detected in 38 individuals from three French Alps populations. The generally limited degree of polymorphism, which was more pronounced in class I genes, is likely due to bottleneck the populations undergone. Additionally, gene duplication within each class might have compensated for the loss of polymorphism at particular loci. The two gene classes showed different patterns of evolution. The most polymorphic of the putative loci, Mama-DRB1, showed clear evidence of historical positive selection for amino acid replacements. However, no signal of positive selection was evident in the MHC class I genes. These contrasting patterns of sequence evolution may reflect differences in selection pressures acting on class I and class II genes.     

Toll‐like receptor variation in the bottlenecked population of the Seychelles warbler: computer simulations see the ‘ghost of selection past’ and quantify the ‘drift debt’

Balancing selection can maintain immunogenetic variation within host populations, but detecting its signal in a postbottlenecked population is challenging due to the potentially overriding effects of drift. Toll‐like receptor genes (TLRs) play a fundamental role in vertebrate immune defence and are predicted to be under balancing selection. We previously characterized variation at TLR loci in the Seychelles warbler (Acrocephalus sechellensis), an endemic passerine that has undergone a historical bottleneck. Five of seven TLR loci were polymorphic, which is in sharp contrast to the low genomewide variation observed. However, standard population genetic statistical methods failed to detect a contemporary signature of selection at any TLR locus. We examined whether the observed TLR polymorphism could be explained by neutral evolution, simulating the population's demography in the software DIYABC. This showed that the posterior distributions of mutation rates had to be unrealistically high to explain the observed genetic variation. We then conducted simulations with an agent‐based model using typical values for the mutation rate, which indicated that weak balancing selection has acted on the three TLR genes. The model was able to detect evidence of past selection elevating TLR polymorphism in the prebottleneck populations, but was unable to discern any effects of balancing selection in the contemporary population. Our results show drift is the overriding evolutionary force that has shaped TLR variation in the contemporary Seychelles warbler population, and the observed TLR polymorphisms might be merely the ‘ghost of selection past’. Forecast models predict immunogenetic variation in this species will continue to be eroded in the absence of contemporary balancing selection. Such ‘drift debt’ occurs when a gene pool has not yet reached its new equilibrium level of polymorphism, and this loss could be an important threat to many recently bottlenecked populations.     

The Effects of Lethal Selection on the EST-6 to PGM Region of Chromosome 3 in DROSOPHILA MELANOGASTER

A powerful means of studying the effects of selection on chromosome segments in Drosophila melanogaster has been described by Clegg et. al. (1976, 1978). This method utilizes a recessive lethal, dominant visible allele whose selection dynamics can be accurately modelled to predict the fates of nonlethal alleles at linked loci. Results of these experiments indicate that strong epistatic interactions among loci occur that effect fitnesses associated with gametic types in the basal region of chromosome 3. We have used similar methods in studying a different segment of chromosome 3, that spanned by Est-6 (3-36.8) and Pgm (3-43.4), with the aim of determining whether the results of Clegg and his colleagues could be reproduced when a different region was studied. Our experiment showed that selection did operate on a region of the chromosome marked by Pgm, but that no evidence of selection at loci marked by Est-6 was apparent. Weak evidence for epistatic interactions among loci within the marked region was also found. Three possible explanations for the discrepancies between our experiments and those of Clegg et al. are suggested. First, the geographically homogeneous origin of our populations may preclude selectively significant changes as a result of recombination. Second, the results seen by Clegg et al. may have been unique to the regions they studied, which included the basal heterochromatin of the chromosomes. Finally, the three loci employed may not adequately mark the unit of selection, so that actual departures from predictions of selective neutrality may not have been apparent.