The diversity of a distributed genome in bacterial populations

The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to generation. We use the random genealogy given by a Kingman coalescent in order to superimpose events of gene gain and loss along ancestral lines. Gene gains occur at a constant rate along ancestral lines. We assume that gained genes have never been present in the population before. Gene losses occur at a rate proportional to the number of genes present along the ancestral line. In this infinitely many genes model we derive moments for several statistics within a sample: the average number of genes per individual, the average number of genes differing between individuals, the number of incongruent pairs of genes, the total number of different genes in the sample and the gene frequency spectrum. We demonstrate that the model gives a reasonable fit with gene frequency data from marine cyanobacteria.Comment: Published in at http://dx.doi.org/10.1214/09-AAP657 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Singular solutions of the diffusion equation of population genetics

The forward diffusion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene fixation, with the "weight" associated with the spikes corresponding to the probability of loss or fixation. The forward diffusion equation is thus solved for all gene frequencies, namely the absorbing frequencies of 0 and 1 along with the continuous range of gene frequencies on the interval (0; 1) that excludes the frequencies 0 and 1. Previously, the probabilities if the absorbing frequencies 0 and 1 were found by appeal to the backward diffusion equation, while those in the continuous range (0; 1) were found from the forward diffusion equation. Our uni fied approach does not require two separate equations for a complete dynamical treatment of all gene frequencies within a diffusion approximation framework. For cases involving mutation, migration and selection, it is shown that a property of the deterministic part of gene frequency dynamics determines when fixation and loss can occur. It is also shown how solution of the forward equation, at long times, leads to the standard result for the fixation probability

A neutral theory of genome evolution and the frequency distribution of genes

<p>Abstract</p> <p>Background</p> <p>The gene composition of bacteria of the same species can differ significantly between isolates. Variability in gene composition can be summarized in terms of gene frequency distributions, in which individual genes are ranked according to the frequency of genomes in which they appear. Empirical gene frequency distributions possess a U-shape, such that there are many rare genes, some genes of intermediate occurrence, and many common genes. It would seem that U-shaped gene frequency distributions can be used to infer the essentiality and/or importance of a gene to a species. Here, we ask: can U-shaped gene frequency distributions, instead, arise generically via neutral processes of genome evolution?</p> <p>Results</p> <p>We introduce a neutral model of genome evolution which combines birth-death processes at the organismal level with gene uptake and loss at the genomic level. This model predicts that gene frequency distributions possess a characteristic U-shape even in the absence of selective forces driving genome and population structure. We compare the model predictions to empirical gene frequency distributions from 6 multiply sequenced species of bacterial pathogens. We fit the model with constant population size to data, matching U-shape distributions albeit without matching all quantitative features of the distribution. We find stronger model fits in the case where we consider exponentially growing populations. We also show that two alternative models which contain a "rigid" and "flexible" core component of genomes provide strong fits to gene frequency distributions.</p> <p>Conclusions</p> <p>The analysis of neutral models of genome evolution suggests that U-shaped gene frequency distributions provide less information than previously suggested regarding gene essentiality. We discuss the need for additional theory and genomic level information to disentangle the roles of evolutionary mechanisms operating within and amongst individuals in driving the dynamics of gene distributions.</p

Human gene copy number spectra analysis in congenital heart malformations

The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 groups and verified in accordance with the European Paediatric Cardiac Code, were compared with two control groups, a disease-free cohort (n = 2,026) and a population with coronary artery disease (n = 880). Gains (≥200 kb) and losses (≥100 kb) were determined over 100 CHD risk genes and compared using a Barnard exact test. Six subphenotypes showed significant enrichment (P ≤ 0.05), including aortic stenosis (valvar), atrioventricular canal (partial), atrioventricular septal defect with tetralogy of Fallot, subaortic stenosis, tetralogy of Fallot, and truncus arteriosus. Furthermore, CNV gene frequency spectra were enriched (P ≤ 0.05) for losses at: FKBP6, ELN, GTF2IRD1, GATA4, CRKL, TBX1, ATRX, GPC3, BCOR, ZIC3, FLNA and MID1; and gains at: PRKAB2, FMO5, CHD1L, BCL9, ACP6, GJA5, HRAS, GATA6 and RUNX1. Of CHD subjects, 14% had causal chromosomal abnormalities, and 4.3% had likely causal (significantly enriched), large, rare CNVs. CNV frequency spectra combined with precision phenotyping may lead to increased molecular understanding of etiologic pathways

Population Genetics: Estimation of Distributions through Systems of Non-Linear Differential Equations

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic than those treated previously, called the Gauss Galerkin method

Spatial gene frequency waves under genotype dependent dispersal

Dispersal is a crucial factor in natural evolution, since it determines the habitat experienced by any population and defines the spatial scale of interactions between individuals. There is compelling evidence for systematic differences in dispersal characteristics within the same population, i.e., genotype-dependent dispersal. The consequences of genotype-dependent dispersal on other evolutionary phenomena, however, are poorly understood. In this article we investigate the effect of genotype-dependent dispersal on spatial gene frequency patterns, using a generalization of the classical diffusion model of selection and dispersal. Dispersal is characterized by the variance of dispersal (diffusion coefficient) and the mean displacement (directional advection term). We demonstrate that genotype-dependent dispersal may change the qualitative behavior of Fisher waves, which change from being “pulled” to being “pushed” wave fronts as the discrepancy in dispersal between genotypes increases. The speed of any wave is partitioned into components due to selection, genotype-dependent variance of dispersal, and genotype-dependent mean displacement. We apply our findings to wave fronts maintained by selection against heterozygotes. Furthermore, we identify a benefit of increased variance of dispersal, quantify its effect on the speed of the wave, and discuss the implications for the evolution of dispersal strategies

Keragaman Protein Plasma Darah pada Kambing Kejobong dan Kambing Peranakan Ettawa

The objective of this study was to evaluate the genotype variations of Kejobong and Ettawa Grade (EG) goats based on the blood plasm protein using gel polyacrilamide electrophoresis (PAGE). Twenty four of blood samples taken from Kejobong goat in Purbalingga regency and twenty four of blood samples taken from Ettawa Grade (EG) goat in Purworejo regency were used as materials. Data were analyzed to calculate gene frequency, individual heterozygosity and average heterozygosity. The independent t-test was performed to analyzed the significance of gene frequency, total genotype and average heterozygosity from six locus of blood plasm protein between Kejobong and Ettawa Grade (EG) goats. Result showed that locus of pre albumin (P-alb), albumin (Alb), ceruloplasmin (Cp), transferrin (Tf), post transferrin (P-tf) and amylase-I (Amy-I) on Kejobong and Ettawa Grade (EG) goats were polymorphic. The total genotype, gene frequency and average heterozygosity of six locus blood plasm protein between Kejobong and Ettawa Grade (EG) goats were not different. Average heterozygosity of Kejobong and Ettawa Grade (EG) goats was 0.423 and 0.435, respectively