The Variance of Identity-by-Descent Sharing in the Wright–Fisher Model

Widespread sharing of long, identical-by-descent (IBD) genetic segments is a hallmark of populations that have experienced recent genetic drift. Detection of these IBD segments has recently become feasible, enabling a wide range of applications from phasing and imputation to demographic inference. Here, we study the distribution of IBD sharing in the Wright–Fisher model. Specifically, using coalescent theory, we calculate the variance of the total sharing between random pairs of individuals. We then investigate the cohort-averaged sharing: the average total sharing between one individual and the rest of the cohort. We find that for large cohorts, the cohort-averaged sharing is distributed approximately normally. Surprisingly, the variance of this distribution does not vanish even for large cohorts, implying the existence of “hypersharing” individuals. The presence of such individuals has consequences for the design of sequencing studies, since, if they are selected for whole-genome sequencing, a larger fraction of the cohort can be subsequently imputed. We calculate the expected gain in power of imputation by IBD and subsequently in power to detect an association, when individuals are either randomly selected or specifically chosen to be the hypersharing individuals. Using our framework, we also compute the variance of an estimator of the population size that is based on the mean IBD sharing and the variance in the sharing between inbred siblings. Finally, we study IBD sharing in an admixture pulse model and show that in the Ashkenazi Jewish population the admixture fraction is correlated with the cohort-averaged sharing.IN isolated populations, even purported unrelated individuals often share genetic material that is identical-by-descent (IBD). Traditionally, the term IBD sharing referred to coancestry at a single site (or autozygosity, in the case of a diploid individual) and was widely investigated as a measure of the degree of inbreeding in a population (Hartl and Clark 2006). Recent years have brought dramatic increases in the quantity and density of available genetic data and, together with new computational tools, these data have enabled the detection of IBD sharing of entire genomic segments (see, e.g., Purcell et al. 2007; Kong et al. 2008; Albrechtsen et al. 2009; Gusev et al. 2009; Browning and Browning 2011; Carr et al. 2011; Brown et al. 2012). The availability of IBD detection tools that are efficient enough to detect shared segments in large cohorts has resulted in numerous applications, from demographic inference (Davison et al. 2009; Palamara et al. 2012) and characterization of populations (Gusev et al. 2012a) to selection detection (Albrechtsen et al. 2010), relatedness detection and pedigree reconstruction (Huff et al. 2011; Kirkpatrick et al. 2011; Stevens et al. 2011; Henn et al. 2012), prioritization of individuals for sequencing (Gusev et al. 2012b), inference of HLA type (Setty et al. 2011), detection of haplotypes associated with a disease or a trait (Akula et al. 2011; Gusev et al. 2011; Browning and Thompson 2012), imputation (Uricchio et al. 2012), and phasing (Palin et al. 2011).Recently, some of us used coalescent theory to calculate several theoretical quantities of IBD sharing under a number of demographic histories. Then, shared segments were detected in real populations, and their demographic histories were inferred (Palamara et al. 2012). Here, we expand upon Palamara et al. (2012) to investigate additional aspects of the stochastic variation in IBD sharing. Specifically, we provide a precise calculation for the variance of the total sharing in the Wright–Fisher model, either between a random pair of individuals or between one individual and all others in the cohort.Understanding the variation in IBD sharing is an important theoretical characterization of the Wright–Fisher model, and additionally, it has several practical applications. For example, it can be used to calculate the variance of an estimator of the population size that is based on the sharing between random pairs. In a different domain, the variance in IBD sharing is needed to accurately assess strategies for sequencing study design, specifically, in prioritization of individuals to be sequenced. This is because imputation strategies use IBD sharing between sequenced individuals and genotyped, not-sequenced individuals to increase the number of effective sequences analyzed in the association study (Palin et al. 2011; Gusev et al. 2012b; Uricchio et al. 2012).In the remainder of this article, we first review the derivation of the mean fraction of the genome shared between two individuals (Palamara et al. 2012). We then calculate the variance of this quantity, using coalescent theory with recombination. We provide a number of approximations, one of which results in a surprisingly simple expression, which is then generalized to a variable population size and to the sharing of segments in a length range. We also numerically investigate the pairwise sharing distribution and provide an approximate fit. We then turn to the average total sharing between each individual and the entire cohort. We show that this quantity, which we term the cohort-averaged sharing, is approximately normally distributed, but is much wider than naively expected, implying the existence of hypersharing individuals. We consider several applications: the number of individuals needed to be sequenced to achieve a certain imputation power and the implications to disease mapping, inference of the population size based on the total sharing, and the variance of the sharing between siblings. We finally calculate the mean and the variance of the sharing in an admixture pulse model and show numerically that admixture results in a broader than expected cohort-averaged sharing. Therefore, large variance of the cohort-averaged sharing can indicate admixture. In the Ashkenazi Jewish population, we show that the cohort-averaged sharing is strongly anticorrelated with the fraction of European ancestry.     

Chk’n Out in Mitosis

No abstract available.     

On the Relation Between the Eigen Model and the Asexual Wright–Fisher Model

We show that the Eigen model and the asexual Wright–Fisher model can be obtained as two different limit cases of a single stochastic model. This result is used to enlighten the mathematical similarities and differences among these two models.     

Model of head–neck joint fast movements in the frontal plane

The objective of this work is to develop a model representing the physiological systems driving fast head movements in frontal plane. All the contributions occurring mechanically in the head movement are considered: damping, stiffness, physiological limit of range of motion, gravitational field, and muscular torques due to voluntary activation as well as to stretch reflex depending on fusal afferences. Model parameters are partly derived from the literature, when possible, whereas undetermined block parameters are determined by optimising the model output, fitting to real kinematics data acquired by a motion capture system in specific experimental set-ups. The optimisation for parameter identification is performed by genetic algorithms. Results show that the model represents very well fast head movements in the whole range of inclination in the frontal plane. Such a model could be proposed as a tool for transforming kinematics data on head movements in neural equivalent data, especially for assessing head control disease and properly planning the rehabilitation process. In addition, the use of genetic algorithms seems to fit well the problem of parameter identification, allowing for the use of a very simple experimental set-up and granting model robustness.     

Sister Chromatids Segregate at Mitosis Without Mother–Daughter Bias in Saccharomyces cerevisiae

There is evidence accumulating for nonrandom segregation of one or more chromosomes during mitosis in different cell types. We use cell synchrony and two methods to show that all chromatids of budding yeast segregate randomly and that there is no mother–daughter bias with respect to Watson and Crick-containing strands of DNA.     

The Neuroprotective Effect of the Thr–Ser–Lys–Tyr Peptide in a Goldfish Mauthner Cell Model in vivo

The effects of the Thr–Ser–Lys–Tyr peptide, which was shown to display neuroprotective activity in cell cultures in vitro, were studied in the model of paired Mauthner cells of goldfish. It was found that intracerebral injections provided the peptide to be applied into the zone of the right Mauthner cell under the fourth ventricle of the hindbrain lead to a dose-dependent decrease in the number of spontaneous turns of the goldfish to the left. It was shown that this effect is not eliminated under long-lasting optokinetic stimulation when the fish instinctively follow stimuli with a low spatial frequency that are moving in the nasal-to-temporal direction. We used the method of three-dimensional reconstruction by serial histological sections to study the dendrite morphology of the Mauthner cells in control and experimental goldfish. It was found that optokinetic stimulation of control goldfish evokes the dystrophy of the ventral dendrite of the right Mauthner cell, which is the target of this type of stimulation. Conversely, the peptide stabilize the size of the ventral dendrite of the right Mauthner cell under stimulation. These data could be interpreted as evidence of the neuroprotective effect of the Thr–Ser–Lys–Tyr peptide in vivo.     

The Quasispecies for the Wright–Fisher Model

We consider the classical Wright–Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies.     

A Model of the Broca–Sulzer Effect

Biophysics - The Broca–Sulzer phenomenon is one of the aspects of the problem of subjective deformation of the real world, the mystery of consciousness. The Broca–Sulzer effect is...     

Mitosis in plants: how far we have come at the molecular level?

The basic mechanism of mitosis is universally conserved in all eucaryotes, but specific solutions to achieve this process have been adapted by different organisms during evolution. Although cytological studies of plant cells have contributed to our understanding of chromatin dynamics during mitosis, many of the molecular mechanisms that control mitosis have been identified in yeast and animal cells. Nevertheless, recent advances have begun to fill the gaps in our understanding of how mitosis is regulated in plants, and raise intriguing questions to be answered in the future.     

Epitope Recognition in the Human–Pig Comparison Model on Fixed and Embedded Material

The conditions and the specificity by which an antibody binds to its target protein in routinely fixed and embedded tissues are unknown. Direct methods, such as staining in a knock-out animal or in vitro peptide scanning of the epitope, are costly and impractical. We aimed to elucidate antibody specificity and binding conditions using tissue staining and public genomic and immunological databases by comparing human and pig—the farmed mammal evolutionarily closest to humans besides apes. We used a database of 146 anti-human antibodies and found that antibodies tolerate partially conserved amino acid substitutions but not changes in target accessibility, as defined by epitope prediction algorithms. Some epitopes are sensitive to fixation and embedding in a species-specific fashion. We also find that half of the antibodies stain porcine tissue epitopes that have 60% to 100% similarity to human tissue at the amino acid sequence level. The reason why the remaining antibodies fail to stain the tissues remains elusive. Because of its similarity with the human, pig tissue offers a convenient tissue for quality control in immunohistochemistry, within and across laboratories, and an interesting model to investigate antibody specificity.     

A Model of the Hippocampal–cortical Memory System

Based on physiological evidence, we propose a theoretical model of the hippocampal–cortical memory system. The model consists of the following components: the sensory system, the hippocampus (short-term memory), and the association cortex (long-term memory). A series of key codes (local information) is supplied from the sensory system, while context (global information) is inputted from the hippocampus. The two inputs interact dynamically in the association cortex. The interactive neurons work as a detector of coincidence. The cortical network learns the memory information through the coincidence window and, finally, stores it in the form of attractors. This local–global information works as an addressor to designate the stored location of the memory in the association cortex and accelerates the process of storing and retrieving memory information.     

Investigation of Lysozyme–Antilysozyme Interactions in a Model Tetrahymena–EscherichiaCommunity

Lysozyme and antilysozyme activities present in a wide range of microorganisms determine the so-called lysozyme–antilysozyme system of hydrobionts, which greatly contribute to the formation of aquatic biocenoses. However, the mechanism of the functioning of this system in natural freshwater communities remains obscure. The experimental investigation of lysozyme–antilysozyme interactions in a model Tetrahymena–Escherichiacommunity showed that the antilysozyme activity of Escherichia colileads to incomplete phagocytosis, thus enhancing bacterial survival in a mixed culture with infusoria. The selection and reproduction of bacterial cells resistant to grazing by infusoria determine the character of host–parasite interactions and allow bacteria to survive. It was demonstrated that the antilysozyme activity of microorganisms, which is responsible for bacterial persistency in natural biocenoses, is involved in the maintenance of protozoa–bacteria communities in bodies of water.     

Legal Aspects of the Russian–Norwegian Model for Cross-Border Unitization in the Barents Sea and Arctic Ocean

This article examines the provisions in the 2010 Russian–Norwegian Treaty on Maritime Delimitation and Cooperation in the Barents Sea and the Arctic Ocean dealing with the management of transboundary hydrocarbon resources. How compatible is the unitization mechanism in the Treaty with Russian and Norwegian legislation? Will there be tension between Russian and Norwegian interpretations? How does Russian and Norwegian legislation support or challenge the concept of a “unit operator” in a cross-border unitization? What are the possible concerns and pitfalls related to mechanisms for consultations and procedures for dispute resolution?     

Characterizing the Freeze–Drying Behavior of Model Protein Formulations

The freeze–drying behavior of three model proteins, namely, lysozyme, BSA, and IgG, has been studied using a variety of techniques under two different primary drying conditions (shelf temperatures of −25°C and +25°C, respectively) in an amorphous formulation. Manometric temperature measurements were used to characterize product temperature (T _pr), sublimation rates, and product resistance (R _p) during primary drying. Biophysical techniques such as circular dichroism, fluorescence, and Fourier transform infrared spectroscopy were used to study protein conformation. Size exclusion chromatography was used to monitor the formation of high-molecular-weight species (HMWS) over time on storage, and cake morphology was studied using scanning electron microscopy. The differences in the freeze–drying behavior of the three proteins were more evident at higher protein concentrations, where the protein significantly influences the behavior of the formulation matrix. However, these differences were minimized in the aggressive mode and were insignificant at lower protein concentrations where excipients dominated the freeze–drying behavior. Differences in cake morphology were observed between the two drying conditions employed as well as between the three proteins studied. The stability and the protein structure, however, were equivalent for the protein cakes generated using the two different primary drying conditions.     

On the Delayed Ross–Macdonald Model for Malaria Transmission

The feedback dynamics from mosquito to human and back to mosquito involve considerable time delays due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a delayed Ross–Macdonald model. Then we calculate the basic reproduction number R ₀ and carry out some sensitivity analysis of R ₀ on the incubation periods, that is, to study the effect of time delays on the basic reproduction number. It is shown that the basic reproduction number is a decreasing function of both time delays. Thus, prolonging the incubation periods in either humans or mosquitos (via medicine or control measures) could reduce the prevalence of infection. S. Ruan’s research was partially supported by NIH grants P20RR020770-02 and R01GM083607-01, NSF grant DMS-0715772. D. Xiao’s research was supported by the National Natural Science Fund (NNSF) of China.     

Optimal Culling and Biocontrol in a Predator–Prey Model

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.     

Chaos and Peak-to-Peak Dynamics in a Plankton–Fish Model

A plankton–fish model, comprising phosphorus, algae, zooplankton, and young fish, with light intensity and water temperature varying periodically with the seasons, is analyzed in this paper. For realistic values of the parameters the model behaves chaotically, but its dynamics within the strange attractor can be described by a few one-dimensional maps that allow one to forecast the next yearly peak of plankton or fish from the last peaks. This property is an unambiguous mark of a special form of chaos. Unfortunately, the estimate of such peak-to-peak maps from field data is possible only if plankton or young fish biomass has been sampled accurately and frequently for a paramount number of years. In conclusion, the analysis shows that it might be that plankton dynamics are characterized by an interesting and peculiar form of chaos, but that inferences from recorded data on the existence of these forms of chaos are premature.