The Wright-Fisher model with temporally varying selection and population size

The Wright-Fisher model is considered in the case where the population size is random and the magnitude of the selective advantage of one of the alleles varies with time. The central question addressed is the possibility of ultimate genetic polymorphism. Partial results are obtained in the general case and complete results in the case where the population size and selective advantage are not density dependent. Bounds on the fixation probability are obtained when the selective advantage is constant.     

Sequence diversity under the multispecies coalescent with Yule process and constant population size

The study of sequence diversity under phylogenetic models is now classic. Theoretical studies of diversity under the Kingman coalescent appeared shortly after the introduction of the coalescent. In this paper we revisit this topic under the multispecies coalescent, an extension of the single population model to multiple populations. We derive exact formulas for the sequence dissimilarity of two sequences drawn at random under a basic multispecies setup. The multispecies model uses three parameters—the species tree birth rate under the pure birth process (Yule), the species effective population size and the mutation rate. We also discuss the effects of relaxing some of the model assumptions.     

A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit

The genealogical structure of neutral populations in which reproductive success is highly-skewed has been the subject of many recent studies. Here we derive a coalescent dual process for a related class of continuous-time Moran models with viability selection. In these models, individuals can give birth to multiple offspring whose survival depends on both the parental genotype and the brood size. This extends the dual process construction for a multi-type Moran model with genic selection described in Etheridge and Griffiths (2009). We show that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which we call the Λ-Fleming-Viot process with viability selection and we derive a coalescent dual for this process directly from the generator and as a limit from the Moran models. The dual is a branching-coalescing process similar to the Ancestral Selection Graph which follows the typed ancestry of genes backwards in time with real and virtual lineages. As an application, the transition functions of the non-neutral Moran and Λ-coalescent models are expressed as mixtures of the transition functions of the dual process.     

Effective population size of a population with stochastically varying size

For a Wright–Fisher model with mutation whose population size fluctuates stochastically from generation to generation, a heterozygosity effective population size is defined by means of the equilibrium average heterozygosity of the population. It is shown that this effective population size is equal to the harmonic mean of population size if and only if the stochastic changes of population size are uncorrelated. The effective population size is larger (resp. smaller) than the harmonic mean when the stochastic changes of population size are positively (resp. negatively) autocorrelated. These results and those obtained so far for other stochastic models with fluctuating population size suggest that the property that effective population sizes are always larger than the harmonic mean under the fluctuation of population size holds only for continuous time models such as diffusion and coalescent models, whereas effective population sizes can be equal to or smaller than the harmonic mean for discrete time models.     

Inference of population structure under a Dirichlet process model

Inferring population structure from genetic data sampled from some number of individuals is a formidable statistical problem. One widely used approach considers the number of populations to be fixed and calculates the posterior probability of assigning individuals to each population. More recently, the assignment of individuals to populations and the number of populations have both been considered random variables that follow a Dirichlet process prior. We examined the statistical behavior of assignment of individuals to populations under a Dirichlet process prior. First, we examined a best-case scenario, in which all of the assumptions of the Dirichlet process prior were satisfied, by generating data under a Dirichlet process prior. Second, we examined the performance of the method when the genetic data were generated under a population genetics model with symmetric migration between populations. We examined the accuracy of population assignment using a distance on partitions. The method can be quite accurate with a moderate number of loci. As expected, inferences on the number of populations are more accurate when theta = 4N(e)u is large and when the migration rate (4N(e)m) is low. We also examined the sensitivity of inferences of population structure to choice of the parameter of the Dirichlet process model. Although inferences could be sensitive to the choice of the prior on the number of populations, this sensitivity occurred when the number of loci sampled was small; inferences are more robust to the prior on the number of populations when the number of sampled loci is large. Finally, we discuss several methods for summarizing the results of a Bayesian Markov chain Monte Carlo (MCMC) analysis of population structure. We develop the notion of the mean population partition, which is the partition of individuals to populations that minimizes the squared partition distance to the partitions sampled by the MCMC algorithm.     

The coalescent process in models with selection, recombination and geographic subdivision

A population genetic model with a single locus at which balancing selection acts and many linked loci at which neutral mutations can occur is analysed using the coalescent approach. The model incorporates geographic subdivision with migration, as well as mutation, recombination, and genetic drift of neutral variation. It is found that geographic subdivision can affect genetic variation even with high rates of migration, providing that selection is strong enough to maintain different allele frequencies at the selected locus. Published sequence data from the alcohol dehydrogenase locus of Drosophila melanogaster are found to fit the proposed model slightly better than a similar model without subdivision.     

Analysis of a disease transmission model in a population with varying size

An S I R S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population.Partially supported by NSF Grant No. DMS-8703631. This work was done while this author was visiting the University of VictoriaResearch supported in part by NSERC A-8965     

Global dynamics of a SEIR model with varying total population size

A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied. The force of infection is of proportionate mixing type. A threshold sigma is identified which determines the outcome of the disease; if sigma < or = 1, the infected fraction of the population disappears so the disease dies out, while of sigma > 1, the infected fraction persists and a unique endemic equilibrium state is shown, under a mild restriction on the parameters, to be globally asymptotically stable in the interior of the feasible region. Two other threshold parameters sigma' and sigma are also identified; they determine the dynamics of the population sizes in the cases when the disease dies out and when it is endemic, respectively.     

Community size structure varies with predator–prey size relationships and temperature across Australian reefs

Climate change and fisheries exploitation are dramatically changing the abundances, species composition, and size spectra of fish communities. We explore whether variation in ‘abundance size spectra’, a widely studied ecosystem feature, is influenced by a parameter theorized to govern the shape of size‐structured ecosystems—the relationship between the sizes of predators and their prey (predator–prey mass ratios, or PPMRs). PPMR estimates are lacking for avast number of fish species, including at the scale of trophic guilds. Using measurements of 8128 prey items in gut contents of 97 reef fish species, we established predator–prey mass ratios (PPMRs) for four major trophic guilds (piscivores, invertivores, planktivores, and herbivores) using linear mixed effects models. To assess the theoretical predictions that higher community‐level PPMRs leads to shallower size spectrum slopes, we compared observations of both ecosystem metrics for ~15,000 coastal reef sites distributed around Australia. PPMRs of individual fishes were remarkably high (median ~71,000), with significant variation between different trophic guilds (~890 for piscivores; ~83,000 for planktivores), and ~8700 for whole communities. Community‐level PPMRs were positively related to size spectrum slopes, broadly consistent with theory, however, this pattern was also influenced by the latitudinal temperature gradient. Tropical reefs showed a stronger relationship between community‐level PPMRs and community size spectrum slopes than temperate reefs. The extent that these patterns apply outside Australia and consequences for community structure and dynamics are key areas for future investigation.     

Dynamics of a stochastic heroin epidemic model with bilinear incidence and varying population size

We investigate a stochastic heroin epidemic model with bilinear incidence and varying population size.Sufficient criteria for the extinction of the drug abusers and the existence of ergodic stationary distribution for the model are established by constructing suitable stochastic Lyapunov functions.By analyzing the sensitivity of the threshold of spread,we obtain that prevention is better than cure.Numerical simulations are carried out to confirm the analytical results.     

A coalescent model of background selection with recombination,demography and variation in selection coefficients

There is increasing evidence that background selection, the effects of the elimination of recurring deleterious mutations by natural selection on variability at linked sites, may be a major factor shaping genome-wide patterns of genetic diversity. To accurately quantify the importance of background selection, it is vital to have computationally efficient models that include essential biological features. To this end, a structured coalescent procedure is used to construct a model of background selection that takes into account the effects of recombination, recent changes in population size and variation in selection coefficients against deleterious mutations across sites. Furthermore, this model allows a flexible organization of selected and neutral sites in the region concerned, and has the ability to generate sequence variability at both selected and neutral sites, allowing the correlation between these two types of sites to be studied. The accuracy of the model is verified by checking against the results of forward simulations. These simulations also reveal several patterns of diversity that are in qualitative agreement with observations reported in recent studies of DNA sequence polymorphisms. These results suggest that the model should be useful for data analysis.     

Amino acid–base interactions: a three-dimensional analysis of protein–DNA interactions at an atomic level

To assess whether there are universal rules that govern amino acid–base recognition, we investigate hydrogen bonds, van der Waals contacts and water-mediated bonds in 129 protein–DNA complex structures. DNA–backbone interactions are the most numerous, providing stability rather than specificity. For base interactions, there are significant base–amino acid type correlations, which can be rationalised by considering the stereochemistry of protein side chains and the base edges exposed in the DNA structure. Nearly two-thirds of the direct read-out of DNA sequences involves complex networks of hydrogen bonds, which enhance specificity. Two-thirds of all protein–DNA interactions comprise van der Waals contacts, compared to about one-sixth each of hydrogen and water-mediated bonds. This highlights the central importance of these contacts for complex formation, which have previously been relegated to a secondary role. Although common, water-mediated bonds are usually non-specific, acting as space-fillers at the protein–DNA interface. In conclusion, the majority of amino acid–base interactions observed follow general principles that apply across all protein–DNA complexes, although there are individual exceptions. Therefore, we distinguish between interactions whose specificities are ‘universal’ and ‘context-dependent’. An interactive Web-based atlas of side chain–base contacts provides access to the collected data, including analyses and visualisation of the three-dimensional geometry of the interactions.     

UPA, a universal protein array system for quantitative detection of protein–protein, protein–DNA, protein–RNA and protein–ligand interactions

Protein–protein interactions have been widely used to study gene expression pathways and may be considered as a new approach to drug discovery. Here I report the development of a universal protein array (UPA) system that provides a sensitive, quantitative, multi-purpose, effective and easy technology to determine not only specific protein–protein interactions, but also specific interactions of proteins with DNA, RNA, ligands and other small chemicals. (i) Since purified proteins are used, the results can be easily interpreted. (ii) UPA can be used multiple times for different targets, making it economically affordable for most laboratories, hospitals and biotechnology companies. (iii) Unlike DNA chips or DNA microarrays, no additional instrumentation is required. (iv) Since the UPA uses active proteins (without denaturation and renaturation), it is more sensitive compared with most existing methods. (v) Because the UPA can analyze hundreds (even thousands on a protein microarray) of proteins in a single experiment, it is a very effective method to screen proteins as drug targets in cancer and other human diseases.     

Combining noninvasive genetics and a new mammalian sex‐linked marker provides new tools to investigate population size,structure and individual behaviour: An application to bats

Monitoring wild populations is crucial for their effective management. Noninvasive genetic methods provide robust data from individual free‐ranging animals, which can be used in capture–mark–recapture (CMR) models to estimate demographic parameters without capturing or disturbing them. However, sex‐ and status‐specific behaviour, which may lead to differences in detection probabilities, is rarely considered in monitoring. Here, we investigated population size, sex ratio, sex‐ and status‐related behaviour in 19 Rhinolophus hipposideros maternity colonies (Northern France) with a noninvasive genetic CMR approach (using faeces) combined with parentage assignments. The use of the DDX3X/Y‐Mam sexual marker designed in this study, which shows inter‐ and intrachromosomal length polymorphism across placental mammals, together with eight polymorphic microsatellite markers, produced high‐quality genetic data with limited genotyping errors and allowed us to reliably distinguish different categories of individuals (males, reproductive and nonreproductive females) and to estimate population sizes. We showed that visual counts represent well‐adult female numbers and that population composition in maternity colonies changes dynamically during the summer. Before parturition, colonies mainly harbour pregnant and nonpregnant females with a few visiting males, whereas after parturition, colonies are mainly composed of mothers and their offspring with a few visiting nonmothers and males. Our approach gives deeper insight into sex‐ and status‐specific behaviour, a prerequisite for understanding population dynamics and developing effective monitoring and management strategies. Provided sufficient samples can be obtained, this approach can be readily applied to a wide range of species.     

Simulation of a bacterial population structure in continuous cultivation by a dissociation process: An application to Rhodococcus rubropertinctus

An attempt is made to give a quantitative estimation of a possible contribution of the dissociation process in the formation of the heterogeneous population structure for the Rhodococcus rubropertinctus (Micobacterium lacticolum) in continuous cultivation. This estimation is realised with the help of a constructed mathematical model of the process. The model equations obtained describe particular biomass changes for R-, S- and M-dissociants and changes for substrate (glucose) concentration within the chemostate in continuous cultivation. Next, contributions to dissociant biomass changes were taken into account: (1) cell reproduction (each dissociant has its own specific growth rate depending on the substrate concentration), (2) cell outflow (in proportion to dissociant biomass) and (3) dissociation (dissociant genotype change during reproduction occurs for each dissociant with its own specific frequency). It is determined that if substrate growth constants are equal the rapidly growing dissociants (possessing maximal μ_max) outs the rest of them, and the greater the speed of the flow the less the time to reach a steady-state distribution of the dissociant biomasses. But, at the same time the slowly growing dissociant can become dominant in the population if it has a lower substrate growth constant.     

Reproductive responses to varying food supply in a population of Darwin's finches: Clutch size,growth rates and hatching synchrony

Summary I show how food shortage affects reproduction in a population of Darwin's Medium Ground Finches, Geospiza fortis. Despite the common occurrence of starvation and absence of nest predation, hatching is typically nighly synchronous and adaptive brood reductionappears to be absent. Variation in both growth rates and clutch size in association with the varying conditions is documented. This variation is interpreted as being a direct response to environmental conditions rather than adaptive phenotypic plasticity. I conclude that selection pressures to raise one or two chicks during times of food shortage, or to delay growth rates, are weak or absent.     

Sensing peptide–oligonucleotide interactions by a two-color fluorescence label: application to the HIV-1 nucleocapsid protein

We present a new methodology for site-specific sensing of peptide–oligonucleotide (ODN) interactions using a solvatochromic fluorescent label based on 3-hydroxychromone (3HC). This label was covalently attached to the N-terminus of a peptide corresponding to the zinc finger domain of the HIV-1 nucleocapsid protein (NC). On interaction with target ODNs, the labeled peptide shows strong changes in the ratio of its two emission bands, indicating an enhanced screening of the 3HC fluorophore from the bulk water by the ODN bases. Remarkably, this two-color response depends on the ODN sequence and correlates with the 3D structure of the corresponding complexes, suggesting that the 3HC label monitors the peptide–ODN interactions site-specifically. By measuring the two-color ratio, we were also able to determine the peptide–ODN-binding parameters and distinguish multiple binding sites in ODNs, which is rather difficult using other fluorescence methods. Moreover, this method was found to be more sensitive than the commonly used steady-state fluorescence anisotropy, especially in the case of small ODNs. The described methodology could become a new universal tool for investigating peptide–ODN interactions.