Single-crossover dynamics: finite versus infinite populations

Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the {\em expected} type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.Comment: 21 pages, 4 figure

Fast flowing populations are not well mixed

In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of individuals mixed by flows. We propose an analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.Comment: 19 pages, 8 figure

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Impact of FTO genotypes on BMI and weight in polycystic ovary syndrome : a systematic review and meta-analysis

Aims/hypothesis FTO gene single nucleotide polymorphisms (SNPs) have been shown to be associated with obesity-related traits and type 2 diabetes. Several small studies have suggested a greater than expected effect of the FTO rs9939609 SNP on weight in polycystic ovary syndrome (PCOS). We therefore aimed to examine the impact of FTO genotype on BMI and weight in PCOS. Methods A systematic search of medical databases (PubMed, EMBASE and Cochrane CENTRAL) was conducted up to the end of April 2011. Seven studies describing eight distinct PCOS cohorts were retrieved; seven were genotyped for SNP rs9939609 and one for SNP rs1421085. The per allele effect on BMI and body weight increase was calculated and subjected to meta-analysis. Results A total of 2,548 women with PCOS were included in the study; 762 were TT homozygotes, 1,253 had an AT/CT genotype, and 533 were AA/CC homozygotes. Each additional copy of the effect allele (A/C) increased the BMI by a mean of 0.19 z score units (95% CI 0.13, 0.24; p = 2.26 × 10−11) and body weight by a mean of 0.20 z score units (95% CI 0.14, 0.26; p = 1.02 × 10−10). This translated into an approximately 3.3 kg/m2 increase in BMI and an approximately 9.6 kg gain in body weight between TT and AA/CC homozygotes. The association between FTO genotypes and BMI was stronger in the cohorts with PCOS than in the general female populations from large genome-wide association studies. Deviation from an additive genetic model was observed in heavier populations. Conclusions/interpretation The effect of FTO SNPs on obesity-related traits in PCOS seems to be more than two times greater than the effect found in large population-based studies. This suggests an interaction between FTO and the metabolic context or polygenic background of PCOS

The power to detect artificial selection acting on single loci in recently domesticated species

<p>Abstract</p> <p>Background</p> <p>An increasing number of aquaculture species are subjected to artificial selection in systematic breeding programs. Rapid improvements of important commercial traits are reported, but little is known about the effects of the strong directional selection applied, on gene level variation. Large numbers of genetic markers are becoming available, making it feasible to detect and estimate these effects. Here a simulation tool was developed in order to explore the power by which single genetic loci subjected to uni-directional selection in parallel breeding populations may be detected.</p> <p>Findings</p> <p>Two simulation models were pursued: 1) screening for loci displaying higher genetic differentiation than expected (high-F_SToutliers), from neutral evolution between a pool of domesticated populations and a pool of wild populations; 2) screening for loci displaying lower genetic differentiation (low-F_SToutliers) between domesticated strains than expected from neutral evolution. The premise for both approaches was that the isolated domesticated strains are subjected to the same breeding goals. The power to detect outlier loci was calculated under the following parameter values: number of populations, effective population size per population, number of generations since onset of selection, initial F_ST, and the selection coefficient acting on the locus. Among the parameters investigated, selection coefficient, the number of generation since onset of selection, and number of populations, had the largest impact on power. The power to detect loci subjected to directional in breeding programmes was high when applying the between farmed and wild population approach, and low for the between farmed populations approach.</p> <p>Conclusions</p> <p>A simulation tool was developed for estimating the power to detect artificial selection acting directly on single loci. The simulation tool should be applicable to most species subject to domestication, as long as a reasonable high accuracy in input parameters such as effective population size, number of generations since the initiation of selection, and initial differentiation (F_ST) can be obtained. Identification of genetic loci under artificial selection would be highly valuable, since such loci could be used to monitor maintenance of genetic variation in the breeding populations and monitoring possible genetic changes in wild populations from genetic interaction between escapees and their wild counterpart.</p

Occupancy Modeling, Maximum Contig Size Probabilities and Designing Metagenomics Experiments

Mathematical aspects of coverage and gaps in genome assembly have received substantial attention by bioinformaticians. Typical problems under consideration suppose that reads can be experimentally obtained from a single genome and that the number of reads will be set to cover a large percentage of that genome at a desired depth. In metagenomics experiments genomes from multiple species are simultaneously analyzed and obtaining large numbers of reads per genome is unlikely. We propose the probability of obtaining at least one contig of a desired minimum size from each novel genome in the pool without restriction based on depth of coverage as a metric for metagenomic experimental design. We derive an approximation to the distribution of maximum contig size for single genome assemblies using relatively few reads. This approximation is verified in simulation studies and applied to a number of different metagenomic experimental design problems, ranging in difficulty from detecting a single novel genome in a pool of known species to detecting each of a random number of novel genomes collectively sized and with abundances corresponding to given distributions in a single pool

Generic modes of consensus formation in stochastic language dynamics

We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are distinguished by the way agents handle variability in the language (i.e., multiple forms for the same meaning). The class of models includes as special cases two previously-studied models of language dynamics, the Naming Game, in which agents tend to standardise on variants they have encountered most frequently, and the Utterance Selection Model, in which agents tend to preserve variability by uniform sampling of a pool of utterances. We reduce the full complexities of the dynamics to a single-coordinate stochastic model which allows the probability and time taken for speakers to reach consensus on a single variant to be calculated for large communities. This analysis suggests that in the broad class of models considered, consensus is formed in one of three generic ways, according to whether agents tend to eliminate, accentuate or sample neutrally the variability in the language. These different regimes are observed in simulations of the full dynamics, and for which the simplified model in some cases makes good quantitative predictions. We use these results, along with comparisons with related models, to conjecture the likely behaviour of more general models, and further make use of empirical data to argue that in reality, biases away from neutral sampling behaviour are likely to be small.Comment: 36 pages; 22 eps figures; embarrassing sign error in v2 corrected; to appear J Stat Mec

Commitment versus persuasion in the three-party constrained voter model

In the framework of the three-party constrained voter model, where voters of two radical parties (A and B) interact with "centrists" (C and Cz), we study the competition between a persuasive majority and a committed minority. In this model, A's and B's are incompatible voters that can convince centrists or be swayed by them. Here, radical voters are more persuasive than centrists, whose sub-population consists of susceptible agents C and a fraction zeta of centrist zealots Cz. Whereas C's may adopt the opinions A and B with respective rates 1+delta_A and 1+delta_B (with delta_A>=delta_B>0), Cz's are committed individuals that always remain centrists. Furthermore, A and B voters can become (susceptible) centrists C with a rate 1. The resulting competition between commitment and persuasion is studied in the mean field limit and for a finite population on a complete graph. At mean field level, there is a continuous transition from a coexistence phase when zeta= Delta_c. In a finite population of size N, demographic fluctuations lead to centrism consensus and the dynamics is characterized by the mean consensus time tau. Because of the competition between commitment and persuasion, here consensus is reached much slower (zeta=Delta_c) than in the absence of zealots (when tau\simN). In fact, when zeta<Delta_c and there is an initial minority of centrists, the mean consensus time asymptotically grows as tau\simN^{-1/2} e^{N gamma}, where gamma is determined. The dynamics is thus characterized by a metastable state where the most persuasive voters and centrists coexist when delta_A>delta_B, whereas all species coexist when delta_A=delta_B. When zeta>=Delta_c and the initial density of centrists is low, one finds tau\simln N (when N>>1). Our analytical findings are corroborated by stochastic simulations.Comment: 25 pages, 6 figures. Final version for the Journal of Statistical Physics (special issue on the "applications of statistical mechanics to social phenomena"

Compare the differences of synonymous codon usage between the two species within cardiovirus

<p>Abstract</p> <p>Background</p> <p>Cardioviruses are positive-strand RNA viruses in the Picornaviridae family that can cause enteric infection in rodents and also been detected at lower frequencies in other mammals such as pigs and human beings. The Cardiovirus genus consists two distinct species: Encephalomyocarditis virus (EMCV) and Theilovirus (ThV). There are a lot differences between the two species. In this study, the differences of codon usage in EMCV and ThV were compared.</p> <p>Results</p> <p>The mean ENC values of EMCV and ThV are 54.86 and 51.08 respectively, higher than 40.And there are correlations between (C+G)₁₂% and (C+G)₃% for both EMCV and ThV (r = -0.736;r = 0.986, P < 0.01, repectively). For ThV the (C+G)₁₂%, (C+G)₃%, axis <it>f</it>'₁and axis <it>f</it>'₂had a significant correlations respectively but not for EMCV. According to the RSCU values, the EMCV species seemed to prefer U, G and C ending codon, while the ThV spice seemed to like using U and A ending codon. However, in both genus AGA for Arg, AUU for Ile, UCU for Ser, and GGA for Gly were chosen preferentially. Correspondence analysis detected one major trend in the first axis (<it>f</it>'₁) which accounted for 22.89% of the total variation, and another major trend in the second axis (<it>f</it>'₂) which accounted for 17.64% of the total variation. And the plots of the same serotype seemed at the same region at the coordinate.</p> <p>Conclusion</p> <p>The overall extents of codon usage bias in both EMCV and ThV are low. The mutational pressure is the main factor that determines the codon usage bias, but the (C+G) content plays a more important role in codon usage bias for ThV than for EMCV. The synonymous codon usage pattern in both EMCV and ThV genes is gene function and geography specific, but not host specific. Maybe the serotype is one factor effected the codon bias for ThV, and location has no significant effect on the variations of synonymous codon usage in these virus genes.</p