Generalized population models and the nature of genetic drift

The Wright–Fisher model of allele dynamics forms the basis for most theoretical and applied research in population genetics. Our understanding of genetic drift, and its role in suppressing the deterministic forces of Darwinian selection has relied on the specific form of sampling inherent to the Wright–Fisher model and its diffusion limit. Here we introduce and analyze a broad class of forward-time population models that share the same mean and variance as the Wright–Fisher model, but may otherwise differ. The proposed class unifies and further generalizes a number of population-genetic processes of recent interest, including the Λ and Cannings processes. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We characterize in detail the behavior of standard population-genetic quantities across this family of generalized models. Some quantities, such as heterozygosity, remain unchanged; but others, such as neutral absorption times and fixation probabilities under selection, deviate by orders of magnitude from the Wright–Fisher model. We show that generalized population models can produce startling phenomena that differ qualitatively from classical behavior — such as assured fixation of a new mutant despite the presence of genetic drift. We derive the forward-time continuum limits of the generalized processes, analogous to Kimura’s diffusion limit of the Wright–Fisher process, and we discuss their relationships to the Kingman and non-Kingman coalescents. Finally, we demonstrate that some non-diffusive, generalized models are more likely, in certain respects, than the Wright–Fisher model itself, given empirical data from Drosophila populations.     

Mathematical models in genetics

In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.     

Antibiotic and insecticide resistance modeling--is it time to start talking?

Mathematical models have played an important part in understanding both antibiotic and insecticide resistance. However, there has been little, if any, interdisciplinary work between these two areas of active research. One primary reason for this is that bacterial population genetics differ substantially from the population genetics of diploid organisms. This article examines these differences and their effect on resistance. It explores what efforts have gone into modeling resistance mathematically in both arenas, and offers suggestions on how the two groups could work together to gain a more comprehensive understanding of the resistance phenomenon     

Quantitative similarity-based association tests using population samples

Although genetic association studies using unrelated individuals may be subject to bias caused by population stratification, alternative methods that are robust to population stratification, such as family-based association designs, may be less powerful. Furthermore, it is often more feasible and less expensive to collect unrelated individuals. Recently, several statistical methods have been proposed for case-control association tests in a structured population; these methods may be robust to population stratification. In the present study, we propose a quantitative similarity-based association test (QSAT) to identify association between a candidate marker and a quantitative trait of interest, through use of unrelated individuals. For the QSAT, we first determine whether two individuals are from the same subpopulation or from different subpopulations, using genotype data at a set of independent markers. We then perform an association test between the candidate marker and the quantitative trait, through incorporation of such information. Simulation results based on either coalescent models or empirical population genetics data show that the QSAT has a correct type I error rate in the presence of population stratification and that the power of the QSAT is higher than that of family-based association designs.     

Population genetics of fungal diseases of plants

Although parasitism is one of the most common lifestyles among eukaryotes, population genetics on parasites lag for behind those on free-living organisms. Yet, the advent of molecular markers offers great tools for studying important processes, such as dispersal, mating systems, adaptation to host and speciation. Here we highlight some studies that used molecular markers to address questions about the population genetics of fungal (including oomycetes) plant pathogens. We conclude that population genetics approaches have provided tremendous insights into the biology of a few fungal parasites and warrant more wide use in phytopathology. However, theoretical advances are badly needed to best apply the existing methods. Fungi are of prime interest not only because they are major parasites of plants and animals, but they also constitute tractable and highly useful models for understanding evolutionary processes. We hope that the emerging field of fungal evolution will attract more evolutionary biologists in the near future.     

A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity.     

A practical approach to parameter estimation applied to model predicting heart rate regulation

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The “best” subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.     

Quantitative approximation of the discrete Moran process by a Wright–Fisher diffusion

Journal of Mathematical Biology - The Moran discrete process and the Wright–Fisher model are the most popular models in population genetics. The Wright–Fisher diffusion is commonly used...     

Practical use of modified maximum likelihoods for stratified data

Stratified data arise in several settings, such as longitudinal studies or multicenter clinical trials. Between-strata heterogeneity is usually addressed by random effects models, but an alternative approach is given by fixed effects models, which treat the incidental nuisance parameters as fixed unknown quantities. This approach presents several advantages, like computational simplicity and robustness to confounding by strata. However, maximum likelihood estimates of the parameter of interest are typically affected by incidental parameter bias. A remedy to this is given by the elimination of stratum-specific parameters by exact or approximate conditioning. The latter solution is afforded by the modified profile likelihood, which is the method applied in this paper. The aim is to demonstrate how the theory of modified profile likelihoods provides convenient solutions to various inferential problems in this setting. Specific procedures are available for different kinds of response variables, and they are useful both for inferential purposes and as a diagnostic method for validating random effects models. Some examples with real data illustrate these points.     

Purifying Selection,Drift, and Reversible Mutation with Arbitrarily High Mutation Rates

Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations, and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample statistics and discuss their implications for studies of natural genetic and epigenetic variation. In particular, we find that (1) many more intermediate-frequency variants are expected than under standard models, even with moderately strong purifying selection, and (2) rates of evolution under purifying selection may be close to, or even exceed, neutral rates. These findings are related to empirical studies of sequence and epigenetic variation.     

Mathematical approach to modeling of the treatment of suppurative processes

Consideration of an inflammation focus as an "open system" provided analogy between microbiological processes in inflamed wounds and in systems of continuous cultivation of microorganisms. Mathematical modeling of such systems is widely used. Some of the methods for the mathematical modeling were applied to chemoprophylaxis and chemotherapy of postoperative wounds. In modeling continuous cultivation of microorganisms it is usually necessary to determine optimal conditions for the maximum yield of their biomass. In modeling of wound treatment the aim was to determine the process parameters providing the minimum biomass. The described simple models showed that there could be certain optimal flow rate of the washing fluid in the aspiration-washing procedure for wound treatment at which the drug was not completely washed out while the growth rate of the microbial population was minimal. Such mathematical models were shown valuable in optimizing the use of bactericidal and bacteriostatic antibiotics.     

Calculation of Disease Dynamics in a Population of Households

Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-susceptible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks.     

Analysis of continuous covariables in epidemiological studies: Dose‐response modelling and confounder adjustment

The analysis of continuous covariables with regression models commonly used in epidemiology are reviewed and compared. While some methods have been in use for decades, other more recent methods are not yet common or have not yet been formally described. It is shown that recently developed methods such as fractional polynomials and others are very useful to obtain dose‐response curves or for confounder adjustment. Different methods have their specific merits making it difficult to give general recommendations. The application of some of the methods is demonstrated with real data examples from epidemiological studies. Some suggestions for practical strategies in analysing continuous covariables are given.     

oSCR: a spatial capture–recapture R package for inference about spatial ecological processes

Spatial capture–recapture (SCR) methods have become widely applied in ecology. The immediate adoption of SCR is due to the fact that it resolves some major criticisms of traditional capture–recapture methods related to heterogeneity in detectabililty, and the emergence of new technologies (e.g. camera traps, non‐invasive genetics) that have vastly improved our ability to collection spatially explicit observation data on individuals. However, the utility of SCR methods reaches far beyond simply convenience and data availability. SCR presents a formal statistical framework that can be used to test explicit hypotheses about core elements of population and landscape ecology, and has profound implications for how we study animal populations. In this software note, we describe the technical basis and analytical workflow of oSCR, an R package for analyzing spatial encounter history data using a multi‐session sex‐structured likelihood. The impetus for developing oSCR was to create an accessible and transparent analysis tool that allows users to conveniently and intuitively formulate statistical models that map directly to fundamental processes of interest in spatial population ecology (e.g. space use, resource selection, density and connectivity). We have placed an emphasis on creating a transparent and accessible code base that is coupled with a logical workflow that we hope stimulates active participation in further technical developments.     

Statistics for Microsatellite Variation Based on Coalescence

The stepwise mutation model, which was at one time chiefly of interest in studying the evolution of protein charge-states, has recently undergone a resurgence of interest with the new popularity of microsatellites as phylogenetic markers. In this paper we describe a method which makes it possible to transfer many population genetics results from the standard infinite sites model to the stepwise mutation model. We study in detail the properties of pairwise differences in microsatellite repeat number between randomly chosen alleles. We show that the problem of finding the expected squared distance between two individuals and finding the variance of the squared distance can be reduced for a wide range of population models to finding the mean and mean square coalescence times. In many cases the distributions of coalescence times have already been studied for infinite site problems. In this study we show how to calculate these quantities for several population models. We also calculate the variance in mean squared pairwise distance (an estimator of mutation rate × population size) for samples of arbitrary size and show that this variance does not approach zero as the sample size increases. We can also use our method to study alleles at linked microsatellite loci. We suggest a metric which quantifies the level of association between loci—effectively a measure of linkage disequilibrium. It is shown that there can be linkage disequilibrium between partially linked loci at mutation–drift equilibrium.     

Dual processes and an invariance result for exchangeable models in population genetics

By means of a representation as interactive particle systems, dual processes are constructed for a large class of exchangeable models in population genetics. It is shown that as the population size becomes large these dual processes tend in distribution to a particularly tractable limiting dual process. Properties of the models are analyzed using the duality relationship and approximate expressions are obtained for various quantities. Diffusion approximations follow easily from the invariance result.     

On the quantitative genetics of mixture characters

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure. Quantitative genetics issues of continuous characters having a finite mixture of Gaussian components as statistical distribution are explored in this article. The partition of variance in a mixture, the covariance between relatives under the supposition of an additive genetic model, and the offspring-parent regression are derived. Formulas for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic and phenotypic correlations between mixture and Gaussian traits and between two mixture traits are presented. It is found that, if there is heterogeneity in a population at the genetic or environmental level, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Some peculiarities of mixture characters are: heritability depends on the mean values of the component distributions, the offspring-parent regression is nonlinear, and genetic or phenotypic correlations cannot be interpreted devoid of the mixture proportions and of the parameters of the distributions mixed.     

海洋生化生态遗传学的研究——海洋生态学研究的新分支

生化生态遗传学是生态学、遗传学、分子生物学和生物化学等多学科的融合体。由于有现代生物学技术的渗入,使传统的生态遗传学研究发生了重大变革。尽管这支新学科起步较迟,但近年来发展却非常迅速,研究内容相当     

Model-based inference of biochemical parameters and dynamic properties of microbial signal transduction networks

Because of the inherent uncertainty about quantitative aspects of signalling networks it is of substantial interest to use computational methods that allow inferring non-measurable quantities such as rate constants, from measurable quantities such as changes in protein abundances. We argue that true biochemical parameters like rate constants can generally not be inferred using models due to their non-identifiability. Recent advances, however, facilitate the analysis of parameter identifiability of a given model and automated discrimination of candidate models, both being important techniques to still extract quantitative biological information from experimental data.