Understanding recessive disease risk in multi-ethnic populations with different degrees of consanguinity

Population medical genetics aims at translating clinically relevant findings from recent studies of large cohorts into healthcare for individuals. Genetic counseling concerning reproductive risks and options is still mainly based on family history, and consanguinity is viewed to increase the risk for recessive diseases regardless of the demographics. However, in an increasingly multi-ethnic society with diverse approaches to partner selection, healthcare professionals should also sharpen their intuition for the influence of different mating schemes in non-equilibrium dynamics. We, therefore, revisited the so-called out-of-Africa model and studied in forward simulations with discrete and not overlapping generations the effect of inbreeding on the average number of recessive lethals in the genome. We were able to reproduce in both frameworks the drop in the incidence of recessive disorders, which is a transient phenomenon during and after the growth phase of a population, and therefore showed their equivalence. With the simulation frameworks, we also provide the means to study and visualize the effect of different kin sizes and mating schemes on these parameters for educational purposes.

Eco-evolutionary maintenance of diversity in fluctuating environments

Growing evidence suggests that temporally fluctuating environments are important in maintaining variation both within and between species. To date, however, studies of genetic variation within a population have been largely conducted by evolutionary biologists (particularly population geneticists), while population and community ecologists have concentrated more on diversity at the species level. Despite considerable conceptual overlap, the commonalities and differences of these two alternative paradigms have yet to come under close scrutiny. Here, we review theoretical and empirical studies in population genetics and community ecology focusing on the 'temporal storage effect' and synthesise theories of diversity maintenance across different levels of biological organisation. Drawing on Chesson's coexistence theory, we explain how temporally fluctuating environments promote the maintenance of genetic variation and species diversity. We propose a further synthesis of the two disciplines by comparing models employing traditional frequency-dependent dynamics and those adopting density-dependent dynamics. We then address how temporal fluctuations promote genetic and species diversity simultaneously via rapid evolution and eco-evolutionary dynamics. Comparing and synthesising ecological and evolutionary approaches will accelerate our understanding of diversity maintenance in nature.

How Well Can We Infer Selection Benefits and Mutation Rates from Allele Frequencies?

Experimentalists observe allele frequency distributions and try to infer mutation rates and selection coefficients. How easy is this? We calculate limits to their ability in the context of the Wright-Fisher model by first finding the maximal amount of information that can be acquired using allele frequencies about the mutation rate and selection coefficient- at least 2 bits per allele- and then by finding how the organisms would have shaped their mutation rates and selection coefficients so as to maximize the information transfer.

Diffusion approximations in population genetics and the rate of Muller's ratchet

The Wright-Fisher binomial model of allele frequency change is often approximated by a scaling limit in which selection, mutation and drift all decrease at the same 1/N rate. This construction restricts the applicability of the resulting 'Wright-Fisher diffusion equation' to the weak selection, weak mutation regime of evolution. We argue that diffusion approximations of the Wright-Fisher model can be used more generally, for instance in cases where genetic drift is much weaker than selection. One important example of this regime is Muller's ratchet phenomenon, whereby deleterious mutations slowly but irreversibly accumulate through rare stochastic fluctuations. Using a modified diffusion equation we derive improved analytical estimates for the mean click time of the ratchet.

Extinction threshold and large population limit of a plant metapopulation model with recurrent extinction events and a seed bank component

We introduce a new model for plant metapopulations with a seed bank component, living in a fragmented environment in which local extinction events are frequent. This model is an intermediate between population dynamics models with a seed bank component, based on the classical Wright-Fisher model, and Stochastic Patch Occupancy Models (SPOMs) used in metapopulation ecology. Its main feature is the use of "ghost" individuals, which can reproduce but with a very strong selective disadvantage against "real" individuals, to artificially ensure a constant population size. We show the existence of an extinction threshold above which persistence of the subpopulation of "real" individuals is not possible, and investigate how the seed bank characteristics affect this extinction threshold. We also show the convergence of the model to a SPOM under an appropriate scaling, bridging the gap between individual-based models and occupancy models.

Evaluating the contributions of purifying selection and progeny-skew in dictating within-host Mycobacterium tuberculosis evolution

The within-host evolutionary dynamics of tuberculosis (TB) remain unclear, and underlying biological characteristics render standard population genetic approaches based upon the Wright-Fisher model largely inappropriate. In addition, the compact genome combined with an absence of recombination is expected to result in strong purifying selection effects. Thus, it is imperative to establish a biologically relevant evolutionary framework incorporating these factors in order to enable an accurate study of this important human pathogen. Further, such a model is critical for inferring fundamental evolutionary parameters related to patient treatment, including mutation rates and the severity of infection bottlenecks. We here implement such a model and infer the underlying evolutionary parameters governing within-patient evolutionary dynamics. Results demonstrate that the progeny skew associated with the clonal nature of TB severely reduces genetic diversity and that the neglect of this parameter in previous studies has led to significant mis-inference of mutation rates. As such, our results suggest an underlying de novo mutation rate that is considerably faster than previously inferred, and a progeny distribution differing significantly from Wright-Fisher assumptions. This inference represents a more appropriate evolutionary null model, against which the periodic effects of positive selection, associated with drug-resistance for example, may be better assessed.

Bayesian inference of selection in the Wright-Fisher diffusion model

The increasing availability of population-level allele frequency data across one or more related populations necessitates the development of methods that can efficiently estimate population genetics parameters, such as the strength of selection acting on the population(s), from such data. Existing methods for this problem in the setting of the Wright-Fisher diffusion model are primarily likelihood-based, and rely on numerical approximation for likelihood computation and on bootstrapping for assessment of variability in the resulting estimates, requiring extensive computation. Recent work has provided a method for obtaining exact samples from general Wright-Fisher diffusion processes, enabling the development of methods for Bayesian estimation in this setting. We develop and implement a Bayesian method for estimating the strength of selection based on the Wright-Fisher diffusion for data sampled at a single time point. The method utilizes the latest algorithms for exact sampling to devise a Markov chain Monte Carlo procedure to draw samples from the joint posterior distribution of the selection coefficient and the allele frequencies. We demonstrate that when assumptions about the initial allele frequencies are accurate the method performs well for both simulated data and for an empirical data set on hypoxia in flies, where we find evidence for strong positive selection in a region of chromosome 2L previously identified. We discuss possible extensions of our method to the more general settings commonly encountered in practice, highlighting the advantages of Bayesian approaches to inference in this setting.

Effects of the Ordering of Natural Selection and Population Regulation Mechanisms on Wright-Fisher Models

We explore the effect of different mechanisms of natural selection on the evolution of populations for one- and two-locus systems. We compare the effect of viability and fecundity selection in the context of the Wright-Fisher model with selection under the assumption of multiplicative fitness. We show that these two modes of natural selection correspond to different orderings of the processes of population regulation and natural selection in the Wright-Fisher model. We find that under the Wright-Fisher model these two different orderings can affect the distribution of trajectories of haplotype frequencies evolving with genetic recombination. However, the difference in the distribution of trajectories is only appreciable when the population is in significant linkage disequilibrium. We find that as linkage disequilibrium decays the trajectories for the two different models rapidly become indistinguishable. We discuss the significance of these findings in terms of biological examples of viability and fecundity selection, and speculate that the effect may be significant when factors such as gene migration maintain a degree of linkage disequilibrium.

Detecting and Quantifying Changing Selection Intensities from Time-Sampled Polymorphism Data

During his well-known debate with Fisher regarding the phenotypic dataset of Panaxia dominula, Wright suggested fluctuating selection as a potential explanation for the observed change in allele frequencies. This model has since been invoked in a number of analyses, with the focus of discussion centering mainly on random or oscillatory fluctuations of selection intensities. Here, we present a novel method to consider nonrandom changes in selection intensities using Wright-Fisher approximate Bayesian (ABC)-based approaches, in order to detect and evaluate a change in selection strength from time-sampled data. This novel method jointly estimates the position of a change point as well as the strength of both corresponding selection coefficients (and dominance for diploid cases) from the allele trajectory. The simulation studies of this method reveal the combinations of parameter ranges and input values that optimize performance, thus indicating optimal experimental design strategies. We apply this approach to both the historical dataset of P. dominula in order to shed light on this historical debate, as well as to whole-genome time-serial data from influenza virus in order to identify sites with changing selection intensities in response to drug treatment.

Bayesian inference of selection in a heterogeneous environment from genetic time-series data

Evolutionary geneticists have sought to characterize the causes and molecular targets of selection in natural populations for many years. Although this research programme has been somewhat successful, most statistical methods employed were designed to detect consistent, weak to moderate selection. In contrast, phenotypic studies in nature show that selection varies in time and that individual bouts of selection can be strong. Measurements of the genomic consequences of such fluctuating selection could help test and refine hypotheses concerning the causes of ecological specialization and the maintenance of genetic variation in populations. Herein, I proposed a Bayesian nonhomogeneous hidden Markov model to estimate effective population sizes and quantify variable selection in heterogeneous environments from genetic time-series data. The model is described and then evaluated using a series of simulated data, including cases where selection occurs on a trait with a simple or polygenic molecular basis. The proposed method accurately distinguished neutral loci from non-neutral loci under strong selection, but not from those under weak selection. Selection coefficients were accurately estimated when selection was constant or when the fitness values of genotypes varied linearly with the environment, but these estimates were less accurate when fitness was polygenic or the relationship between the environment and the fitness of genotypes was nonlinear. Past studies of temporal evolutionary dynamics in laboratory populations have been remarkably successful. The proposed method makes similar analyses of genetic time-series data from natural populations more feasible and thereby could help answer fundamental questions about the causes and consequences of evolution in the wild.

The evolution of moment generating functions for the Wright-Fisher model of population genetics

We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.

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.