Population Genetics Theory Research Articles

Using Gene Genealogies to Detect Rare Variants Associated with Complex Traits

Background and Objective: Standard population genetic theory says that deleterious genetic variants are likely rare and fairly recently introduced. However, can this expectation lead to more powerful tests of association between diseases and rare genetic variation? The gene genealogy describes the relationships between haplotypes sampled from the general population. Although ancestral tree-based methods, inspired by the gene genealogy concept, have been developed for finding associations with common genetic variants, here we ask whether gene genealogies can help in identifying genomic regions containing multiple rare causal variants. Methods: With data simulated under several demographic models and using known gene genealogies, we developed and compared several tree-based statistics to determine which, if any, could detect the type of clustering expected with rare causal variants and whether the genealogic tree provides additional information about disease associations. Results and Conclusions: We found that a novel statistic based on the scaled distance between the tips of a tree performed better than other tree-based statistics. When data were simulated with mild population growth, this statistic outperformed two standard non-tree-based methods, showing that an ancestral tree-based approach has potential for rare variant discovery.

Estimation of a genetically viable population for multigenerational interstellar voyaging: Review and data for project Hyperion

Designing interstellar starships for human migration to exoplanets requires establishing the starship population, which factors into many variables including closed-ecosystem design, architecture, mass and propulsion. I review the central issues of population genetics (effects of mutation, migration, selection and drift) for human populations on such voyages, specifically referencing a roughly 5-generation (c. 150-year) voyage currently in the realm of thought among Icarus Interstellar's Project Hyperion research group. I present several formulae as well as concrete numbers that can be used to help determine populations that could survive such journeys in good health. I find that previously proposed such populations, on the order of a few hundred individuals, are significantly too low to consider based on current understanding of vertebrate (including human) genetics and population dynamics. Population genetics theory, calculations and computer modeling determine that a properly screened and age- and sex-structured total founding population (Nc) of anywhere from roughly 14,000 to 44,000 people would be sufficient to survive such journeys in good health. A safe and well-considered Nc figure is 40,000, an Interstellar Migrant Population (IMP) composed of an Effective Population [Ne] of 23,400 reproductive males and females, the rest being pre- or post-reproductive individuals. This number would maintain good health over five generations despite (a) increased inbreeding resulting from a relatively small human population, (b) depressed genetic diversity due to the founder effect, (c) demographic change through time and (d) expectation of at least one severe population catastrophe over the 5-generation voyage.

A path integral formulation of the Wright–Fisher process with genic selection

The Wright–Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial differential equations framework. In this paper, I introduce a path integral formalism to study the Wright–Fisher process with selection and use that formalism to obtain a simple perturbation series to approximate the transition density. The perturbation series can be understood in terms of Feynman diagrams, which have a simple probabilistic interpretation in terms of selective events. The perturbation series proves to be an accurate approximation of the transition density for weak selection and is shown to be arbitrarily accurate for any selection coefficient.

Genome dynamics during experimental evolution

Evolutionary changes in organismal traits may occur either gradually or suddenly. However, until recently, there has been little direct information about how phenotypic changes are related to the rate and the nature of the underlying genotypic changes. Technological advances that facilitate whole-genome and whole-population sequencing, coupled with experiments that 'watch' evolution in action, have brought new precision to and insights into studies of mutation rates and genome evolution. In this Review, we discuss the evolutionary forces and ecological processes that govern genome dynamics in various laboratory systems in the context of relevant population genetic theory, and we relate these findings to evolution in natural populations.

Why Time Matters: Codon Evolution and the Temporal Dynamics of dN/dS

The ratio of divergence at nonsynonymous and synonymous sites, dN/dS, is a widely used measure in evolutionary genetic studies to investigate the extent to which selection modulates gene sequence evolution. Originally tailored to codon sequences of distantly related lineages, dN/dS represents the ratio of fixed nonsynonymous to synonymous differences. The impact of ancestral and lineage-specific polymorphisms on dN/dS, which we here show to be substantial for closely related lineages, is generally neglected in estimation techniques of dN/dS. To address this issue, we formulate a codon model that is firmly anchored in population genetic theory, derive analytical expressions for the dN/dS measure by Poisson random field approximation in a Markovian framework and validate the derivations by simulations. In good agreement, simulations and analytical derivations demonstrate that dN/dS is biased by polymorphisms at short time scales and that it can take substantial time for the expected value to settle at its time limit where only fixed differences are considered. We further show that in any attempt to estimate the dN/dS ratio from empirical data the effect of the intrinsic fluctuations of a ratio of stochastic variables, can even under neutrality yield extreme values of dN/dS at short time scales or in regions of low mutation rate. Taken together, our results have significant implications for the interpretation of dN/dS estimates, the McDonald–Kreitman test and other related statistics, in particular for closely related lineages.

Revisiting the diffusion approximation to estimate evolutionary rates of gene family diversification

Genetic diversity in multigene families is shaped by multiple processes, including gene conversion and point mutation. Because multi-gene families are involved in crucial traits of organisms, quantifying the rates of their genetic diversification is important. With increasing availability of genomic data, there is a growing need for quantitative approaches that integrate the molecular evolution of gene families with their higher-scale function. In this study, we integrate a stochastic simulation framework with population genetics theory, namely the diffusion approximation, to investigate the dynamics of genetic diversification in a gene family. Duplicated genes can diverge and encode new functions as a result of point mutation, and become more similar through gene conversion. To model the evolution of pairwise identity in a multigene family, we first consider all conversion and mutation events in a discrete manner, keeping track of their details and times of occurrence; second we consider only the infinitesimal effect of these processes on pairwise identity accounting for random sampling of genes and positions. The purely stochastic approach is closer to biological reality and is based on many explicit parameters, such as conversion tract length and family size, but is more challenging analytically. The population genetics approach is an approximation accounting implicitly for point mutation and gene conversion, only in terms of per-site average probabilities. Comparison of these two approaches across a range of parameter combinations reveals that they are not entirely equivalent, but that for certain relevant regimes they do match. As an application of this modelling framework, we consider the distribution of nucleotide identity among VSG genes of African trypanosomes, representing the most prominent example of a multi-gene family mediating parasite antigenic variation and within-host immune evasion.

Empirical Complexities in the Genetic Foundations of Lethal Mutagenesis

From population genetics theory, elevating the mutation rate of a large population should progressively reduce average fitness. If the fitness decline is large enough, the population will go extinct in a process known as lethal mutagenesis. Lethal mutagenesis has been endorsed in the virology literature as a promising approach to viral treatment, and several in vitro studies have forced viral extinction with high doses of mutagenic drugs. Yet only one empirical study has tested the genetic models underlying lethal mutagenesis, and the theory failed on even a qualitative level. Here we provide a new level of analysis of lethal mutagenesis by developing and evaluating models specifically tailored to empirical systems that may be used to test the theory. We first quantify a bias in the estimation of a critical parameter and consider whether that bias underlies the previously observed lack of concordance between theory and experiment. We then consider a seemingly ideal protocol that avoids this bias—mutagenesis of virions—but find that it is hampered by other problems. Finally, results that reveal difficulties in the mere interpretation of mutations assayed from double-strand genomes are derived. Our analyses expose unanticipated complexities in testing the theory. Nevertheless, the previous failure of the theory to predict experimental outcomes appears to reside in evolutionary mechanisms neglected by the theory (e.g., beneficial mutations) rather than from a mismatch between the empirical setup and model assumptions. This interpretation raises the specter that naive attempts at lethal mutagenesis may augment adaptation rather than retard it.

Lakes and ponds as model systems to study parallel evolution

Population genetic theory predicts that effective population size and gene flow can strongly influence the levels and patterns of genetic variability, and thereby also the likelihood, pace and direction of evolutionary transformations. Given that levels and patterns of genetic variability in lakes and ponds often differ from those observed in continuous marine environments, it follows that the dynamics of adaptation and evolution in freshwater habitats are also likely to differ from those in marine habitats. Here, I explore and discuss some ideas relating to the likelihood of parallel phenotypic evolution through similar (parallel) vs. different (convergent) genetic changes with particular focus on freshwater isolates. I will review and discuss the available genetic data with particular focus on freshwater fish populations, and outline possible avenues for future work in which ponds and small lakes could serve as useful model systems to study genetic parallelism and convergence, as well as molecular adaptation in general. Conservation issues related to genetics of isolated pond and lake populations are also addressed.

PROMISCUITY, SEXUAL SELECTION, AND GENETIC DIVERSITY: A REPLY TO SPURGIN

We recently reported a positive association between female promiscuity and genetic diversity across passerine birds, and launched the hypothesis that female promiscuity acts as a balancing selection, pressure maintaining genetic diversity in populations (Gohli et al.2013). Spurgin (2013) questions both our analyses and interpretations. While we agree that the hypothesis needs more comprehensive empirical testing, we find his specific points of criticism unjustified. In a more general perspective, we call for a more explicit recognition of female mating preferences as mechanisms of selection in population genetics theory.

On the Genetic Architecture of Cytoplasmic Incompatibility: Inference from Phenotypic Data

Numerous insects carry intracellular bacteria that manipulate the insects' reproduction and thus facilitate their own spread. Cytoplasmic incompatibility (CI) is a common form of such manipulation, where a (currently uncharacterized) bacterial modification of male sperm induces the early death of embryos unless the fertilized eggs carry the same bacteria, inherited from the mother. The death of uninfected embryos provides an indirect selective advantage to infected ones, thus enabling the spread of the bacteria. Here we use and expand recently developed algorithms to infer the genetic architecture underlying the complex incompatibility data from the mosquito Culex pipiens. We show that CI requires more genetic determinants than previously believed and that quantitative variation in gene products potentially contributes to the observed CI patterns. In line with population genetic theory of CI, our analysis suggests that toxin factors (those inducing embryo death) are present in fewer copies in the bacterial genomes than antitoxin factors (those ensuring that infected embryos survive). In combination with comparative genomics, our approach will provide helpful guidance to identify the genetic basis of CI and more generally of other toxin/antitoxin systems that can be conceptualized under the same framework.

Haplotype Kernel Association Test as a Powerful Method to Identify Chromosomal Regions Harboring Uncommon Causal Variants

For most complex diseases, the fraction of heritability that can be explained by the variants discovered from genome-wide association studies is minor. Although the so-called "rare variants" (minor allele frequency [MAF] < 1%) have attracted increasing attention, they are unlikely to account for much of the "missing heritability" because very few people may carry these rare variants. The genetic variants that are likely to fill in the "missing heritability" include uncommon causal variants (MAF < 5%), which are generally untyped in association studies using tagging single-nucleotide polymorphisms (SNPs) or commercial SNP arrays. Developing powerful statistical methods can help to identify chromosomal regions harboring uncommon causal variants, while bypassing the genome-wide or exome-wide next-generation sequencing. In this work, we propose a haplotype kernel association test (HKAT) that is equivalent to testing the variance component of random effects for distinct haplotypes. With an appropriate weighting scheme given to haplotypes, we can further enhance the ability of HKAT to detect uncommon causal variants. With scenarios simulated according to the population genetics theory, HKAT is shown to be a powerful method for detecting chromosomal regions harboring uncommon causal variants.

Natural and anthropogenic drivers of genetic structure and low genetic variation in the endangered freshwater cod, Maccullochella mariensis

Population genetic theory has identified several threats to small populations that have the potential to endanger species in the short and long term. Understanding these threats is particularly pertinent when management actions, such as stocking, have the potential to exacerbate them. In this study we explore existing genetic variation in the threatened Mary River Cod, Maccullochella mariensis, which has had a long stocking history in its endemic populations (Mary River and Tinana–Coondoo Creek) and has been translocated into other catchments in Southeast Queensland (SEQ). Using Bayesian clustering analysis, two genetically distinct sub-populations were detected (Mary and SEQ vs. Tinana–Coondoo), despite decades of stocking from one population (Tinana–Coondoo) into the other (Mary). Overall, genetic diversity (1–9 alleles per locus) and Ne (18–56) were low, but bigger in the Mary, relative to Tinana–Coondoo. Interestingly, evidence for historical unidirectional gene flow from Tinana–Coondoo into the Mary was detected, which was not as strongly reflected using contemporary estimators, suggesting stocking has not dramatically altered the existing genetic structure for this species. These results provide an opportunity for managers to strategically design stocking protocols and to improve the condition of this species in the wild.

Analysis of piRNA-Mediated Silencing of Active TEs in Drosophila melanogaster Suggests Limits on the Evolution of Host Genome Defense

The Piwi-interacting RNA (piRNA) pathway defends animal genomes against the harmful consequences of transposable element (TE) infection by imposing small-RNA-mediated silencing. Because silencing is targeted by TE-derived piRNAs, piRNA production is posited to be central to the evolution of genome defense. We harnessed genomic data sets from Drosophila melanogaster, including genome-wide measures of piRNA, mRNA, and genomic abundance, along with estimates of age structure and risk of ectopic recombination, to address fundamental questions about the functional and evolutionary relationships between TE families and their regulatory piRNAs. We demonstrate that mRNA transcript abundance, robustness of "ping-pong" amplification, and representation in piRNA clusters together explain the majority of variation in piRNA abundance between TE families, providing the first robust statistical support for the prevailing model of piRNA biogenesis. Intriguingly, we also discover that the most transpositionally active TE families, with the greatest capacity to induce harmful mutations or disrupt gametogenesis, are not necessarily the most abundant among piRNAs. Rather, the level of piRNA targeting is largely independent of recent transposition rate for active TE families, but is rapidly lost for inactive TEs. These observations are consistent with population genetic theory that suggests a limited selective advantage for host repression of transposition. Additionally, we find no evidence that piRNA targeting responds to selection against a second major cost of TE infection: ectopic recombination between TE insertions. Our observations confirm the pivotal role of piRNA-mediated silencing in defending the genome against selfish transposition, yet also suggest limits to the optimization of host genome defense.

Genetic Hitchhiking under Heterogeneous Spatial Selection Pressures

During adaptive evolutionary processes substantial heterogeneity in selective pressure might act across local habitats in sympatry. Examples are selection for drug resistance in malaria or herbicide resistance in weeds. In such setups standard population-genetic assumptions (homogeneous constant selection pressures, random mating etc.) are likely to be violated. To avoid misinferences on the strength and pattern of natural selection it is therefore necessary to adjust population-genetic theory to meet the specifics driving adaptive processes in particular organisms. We introduce a deterministic model in which selection acts heterogeneously on a population of haploid individuals across different patches over which the population randomly disperses every generation. A fixed proportion of individuals mates exclusively within patches, whereas the rest mates randomly across all patches. We study how the allele frequencies at neutral markers are affected by the spread of a beneficial mutation at a closely linked locus (genetic hitchhiking). We provide an analytical solution for the frequency change and the expected heterozygosity at the neutral locus after a single copy of a beneficial mutation became fixed. We furthermore provide approximations of these solutions which allow for more obvious interpretations. In addition, we validate the results by stochastic simulations. Our results show that the application of standard population-genetic theory is accurate as long as differences across selective environments are moderate. However, if selective differences are substantial, as for drug resistance in malaria, herbicide resistance in weeds, or insecticide resistance in agriculture, it is necessary to adapt available theory to the specifics of particular organisms.

Speciation in the asexual realm: Is the parthenogenetic weevil Naupactus cervinus a complex of species in statu nascendi?

Population genetic theory shows that asexual organisms may evolve into species, which behave as independent evolutionary units. As a result, they form genotypic clusters separated by deep gaps due to geographic isolation and/or divergent selection.Identification of several genetically divergent groups of weevils embodied in the nominal species Naupactus cervinus deserves further study, in order to test if these lineages are evolving independently. In the present paper we tested if the parthenogenetic weevil N. cervinus, native to South America and broadly distributed throughout the world, contains more than one evolutionary unit. For this purpose, we applied three different approaches, a multilocus phylogenetic analysis, the GMYC approach and the K/θ method. We accomplished these analyses through a survey of mitochondrial (COI and COII genes) and nuclear (ITS1 sequence) genetic variation and morphometric analysis in a sample which included individuals from different locations within the native geographic range of N. cervinus. In addition, we compared the divergence accumulated in this species with that in another weevil of the same tribe (Naupactini) showing identical reproductive mode to see if similar levels of morphological variation matches similar levels of genetic divergence.We report the presence of two independent evolutionary units living in sympatry in forest areas. The incongruence between mitochondrial and nuclear datasets analyzed herein reflects incomplete lineage sorting of the nuclear marker and different evolutionary rates between genomes.Ecological divergence driven by natural selection (sympatry) or secondary contact after geographic isolation (allopatry) might explain the deep gaps in mitochondrial phylogenies. Instead, Wolbachia infection was ruled out as a causal factor for such differentiation. We conclude that N. cervinus is probably a species complex with at least two well differentiated lineages that would represent a cluster of species in statu nascendi.

Genomic signatures of selection at linked sites: unifying the disparity among species

Population genetics theory supplies powerful predictions about how natural selection interacts with genetic linkage to sculpt the genomic landscape of nucleotide polymorphism. Both the spread of beneficial mutations and the removal of deleterious mutations act to depress polymorphism levels, especially in low-recombination regions. However, empiricists have documented extreme disparities among species. Here we characterize the dominant features that could drive differences in linked selection among species--including roles for selective sweeps being 'hard' or 'soft'--and the concealing effects of demography and confounding genomic variables. We advocate targeted studies of closely related species to unify our understanding of how selection and linkage interact to shape genome evolution.

Age-Dependent Transition from Cell-Level to Population-Level Control in Murine Intestinal Homeostasis Revealed by Coalescence Analysis

In multi-cellular organisms, tissue homeostasis is maintained by an exquisite balance between stem cell proliferation and differentiation. This equilibrium can be achieved either at the single cell level (a.k.a. cell asymmetry), where stem cells follow strict asymmetric divisions, or the population level (a.k.a. population asymmetry), where gains and losses in individual stem cell lineages are randomly distributed, but the net effect is homeostasis. In the mature mouse intestinal crypt, previous evidence has revealed a pattern of population asymmetry through predominantly symmetric divisions of stem cells. In this work, using population genetic theory together with previously published crypt single-cell data obtained at different mouse life stages, we reveal a strikingly dynamic pattern of stem cell homeostatic control. We find that single-cell asymmetric divisions are gradually replaced by stochastic population-level asymmetry as the mouse matures to adulthood. This lifelong process has important developmental and evolutionary implications in understanding how adult tissues maintain their homeostasis integrating the trade-off between intrinsic and extrinsic regulations.

Species detection and identification in sexual organisms using population genetic theory and DNA sequences.

Phylogenetic trees of DNA sequences of a group of specimens may include clades of two kinds: those produced by stochastic processes (random genetic drift) within a species, and clades that represent different species. The ratio of the mean pairwise sequence difference between a pair of clades (K) to the mean pairwise sequence difference within a clade (θ) can be used to determine whether the clades are samples from different species (K/θ≥4) or the same species (K/θ<4) with probability ≥0.95. Previously I applied this criterion to delimit species of asexual organisms. Here I use data from the literature to show how it can also be applied to delimit sexual species using four groups of sexual organisms as examples: ravens, spotted leopards, sea butterflies, and liverworts. Mitochondrial or chloroplast genes are used because these segregate earlier during speciation than most nuclear genes and hence detect earlier stages of speciation. In several cases the K/θ ratio was greater than 4, confirming the original authors' intuition that the clades were sufficiently different to be assigned to different species. But the K/θ ratio split each of two liverwort species into two evolutionary species, and showed that support for the distinction between the common and Chihuahuan raven species is weak. I also discuss some possible sources of error in using the K/θ ratio; the most significant one would be cases where males migrate between different populations but females do not, making the use of maternally inherited organelle genes problematic. The K/θ ratio must be used with some caution, like all other methods for species delimitation. Nevertheless, it is a simple theory-based quantitative method for using DNA sequences to make rigorous decisions about species delimitation in sexual as well as asexual eukaryotes.

Genómica de Poblaciones: Nada en Evolución va a tener sentido si no es a la luz de la Genómica, y nada en Genómica tendrá sentido si no es a la luz de la Evolución

The theory of population genetics originated over 80 years ago and allowed to explain, in terms of the evolutionary forces, the patterns of genetic variation within and between the populations that conform species. This research program generated the questions that have been empirically analyzed with the use of molecular markers for the last 50 years. A fundamental question within population genetics is if a reduced number of genes are representative of the evolutionary forces that affect the total genome of a species. This question has led to the development of molecular methods that allow the study of large sections of the genome in natural populations, giving rise to the field of population genomics. In recent years, techniques that are able to sequence DNA massively, usually called “Next generation sequencing” or “next-gen”, are helping us to obtain genome wide data in many species, without needing previous molecular information. Comparing the genomes of many individuals from different populations, now we have access to an archive of their evolutionary history that narrates the complex and dynamic balance in time between natural selection and other evolutionary forces, such as genetic drift and gene flow, which act mainly in neutral regions of the genomes. The amount of information that is being produced has required the development of new statistical and bioinformatics tools for their analyses. Diverse disciplines have profited from these new developments. In particular in evolutionary biology it is now possible to study in a more precise way the adaptive patterns of variation. The annotation of genomes and the mapping of traits are important and complicated, but recent technical developments are making these goals easier, and thus the future challenge will be in asking the right questions to make relevant inferences from the sea of information these new methods generate. The evolutionary and population genetics perspective will enrich genomics, in the same way that the genomic data will help us advance in the development of the program initiated by Theodosius Dobzhansky several decades ago.

The Number of Candidate Variants in Exome Sequencing for Mendelian Disease under No Genetic Heterogeneity

There has been recent success in identifying disease-causing variants in Mendelian disorders by exome sequencing followed by simple filtering techniques. Studies generally assume complete or high penetrance. However, there are likely many failed and unpublished studies due in part to incomplete penetrance or phenocopy. In this study, the expected number of candidate single-nucleotide variants (SNVs) in exome data for autosomal dominant or recessive Mendelian disorders was investigated under the assumption of “no genetic heterogeneity.” All variants were assumed to be under the “null model,” and sample allele frequencies were modeled using a standard population genetics theory. To investigate the properties of pedigree data, full-sibs were considered in addition to unrelated individuals. In both cases, particularly regarding full-sibs, the number of SNVs remained very high without controls. The high efficacy of controls was also confirmed. When controls were used with a relatively large total sample size (e.g., N = 20, 50), filtering incorporating of incomplete penetrance and phenocopy efficiently reduced the number of candidate SNVs. This suggests that filtering is useful when an assumption of no “genetic heterogeneity” is appropriate and could provide general guidelines for sample size determination.