Inference on the strength of balancing selection for epistatically interacting loci

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci. In this paper, we address this problem by presenting statistical methods that can account for epistatic interactions in making inference about balancing selection. A theoretical result due to Fearnhead (2006) is used to build a multi-locus Wright-Fisher model of balancing selection, allowing for epistatic interactions among loci. Antagonistic and synergistic types of interactions are examined. The joint posterior distribution of the selection and mutation parameters is sampled by Markov chain Monte Carlo methods, and the plausibility of models is assessed via Bayes factors. As a component of the inference process, an algorithm to generate multi-locus allele frequencies under balancing selection models with epistasis is also presented. Recent evidence on interactions among a set of human immune system genes is introduced as a motivating biological system for the epistatic model, and data on these genes are used to demonstrate the methods.     

Reasons for failure of genetic classifications of South Amerind populations

Previous attempts to classify South American Indian tribes according to genetic characteristics have failed to yield a hierarchical system of relationships. This can be explained by the facts that (1) tribal populations did not evolve through sequential fissions but through frequent fusions of groups with diverse histories and (2) allele frequencies have been held at nearly common values by intertribal migration or balancing selection. A valid model must allow for fusion and mixed populations as well as for fission; factor analysis or newer methods of fuzzy mathematics permit this. The effects of migration and balancing can be made more manageable by partitioning them according to the limited time periods recorded by haplotypes. An initial attempt using factor analysis and HLA haplotype data on 19 rain forest tribes revealed two overlapping clusters that are largely but not neatly separated by the lower Amazon River. Several tribes, especially in the west, were excluded from these clusters.     

Detecting balancing selection in genomes: limits and prospects

In spite of the long‐term interest in the process of balancing selection, its frequency in genomes and evolutionary significance remain unclear due to challenges related to its detection. Current statistical approaches based on patterns of variation observed in molecular data suffer from low power and a high incidence of false positives. This raises the question whether balancing selection is rare or is simply difficult to detect. We discuss genetic signatures produced by this mode of selection and review the current approaches used for their identification in genomes. Advantages and disadvantages of the available methods are presented, and areas where improvement is possible are identified. Increased specificity and reduced rate of false positives may be achieved by using a demographic model, applying combinations of tests, appropriate sampling scheme and taking into account intralocus variation in selection pressures. We emphasize novel solutions, recently developed model‐based approaches and good practices that should be implemented in future studies looking for signals of balancing selection. We also draw attention of the readers to the results of recent theoretical studies, which suggest that balancing selection may be ubiquitous but transient, leaving few signatures detectable by existing methods. Testing this new theory may require the development of novel high‐throughput methods extending beyond genomic scans.     

Identifying adaptive genetic divergence among populations from genome scans

The identification of signatures of natural selection in genomic surveys has become an area of intense research, stimulated by the increasing ease with which genetic markers can be typed. Loci identified as subject to selection may be functionally important, and hence (weak) candidates for involvement in disease causation. They can also be useful in determining the adaptive differentiation of populations, and exploring hypotheses about speciation. Adaptive differentiation has traditionally been identified from differences in allele frequencies among different populations, summarised by an estimate of FST. Low outliers relative to an appropriate neutral population-genetics model indicate loci subject to balancing selection, whereas high outliers suggest adaptive (directional) selection. However, the problem of identifying statistically significant departures from neutrality is complicated by confounding effects on the distribution of FST estimates, and current methods have not yet been tested in large-scale simulation experiments. Here, we simulate data from a structured population at many unlinked, diallelic loci that are predominantly neutral but with some loci subject to adaptive or balancing selection. We develop a hierarchical-Bayesian method, implemented via Markov chain Monte Carlo (MCMC), and assess its performance in distinguishing the loci simulated under selection from the neutral loci. We also compare this performance with that of a frequentist method, based on moment-based estimates of FST. We find that both methods can identify loci subject to adaptive selection when the selection coefficient is at least five times the migration rate. Neither method could reliably distinguish loci under balancing selection in our simulations, even when the selection coefficient is twenty times the migration rate.     

Calculability analysis in underdetermined metabolic networks illustrated by a model of the central metabolism in purple nonsulfur bacteria

Metabolite balancing has turned out to be a powerful computational tool in metabolic engineering. However, the linear equation systems occurring in this analysis are often underdetermined. If it is difficult or impossible to find the missing constraints, it is nevertheless feasible in some cases to determine the values of a subset of the unknown rates. Here, a procedure for finding out which reaction rates can be uniquely calculated in underdetermined metabolic networks and computing these rates is given. The method is based on the null space to the stoichiometry matrix corresponding to the reactions with unknown rates. It is shown that this method is considerably easier to handle than an algorithm given previously (Van der Heijden et al., 1994a). Furthermore, a useful elementary representation of the null space is presented which is closely related with the elementary flux modes. This unique representation is central to a more general approach to observability/calculability analysis. In particular, it allows one to find, in an easy way, those sets of measurable rates that enable a calculation of a certain unknown rate. Besides, rates which are never calculable by metabolite balancing may be easily detected by this method. The applicability of these methods is illustrated by a model of the central metabolism in purple nonsulfur bacteria. The photoheterotrophic growth of these representatives of anoxygenic photosynthetic bacteria is stoichiometrically analyzed. Interesting metabolic constraints caused by the necessary balancing of NADPH can be detected in a highly underdetermined system. This is, to our knowledge, the first application of stoichiometric analysis to the metabolic network in this bacteria group using metabolite balancing techniques. A new software tool, the FluxAnalyzer, is introduced. It allows quantitative and structural analysis of metabolic networks in a graphical user interface.     

A Model-Based Approach for Identifying Signatures of Ancient Balancing Selection in Genetic Data

While much effort has focused on detecting positive and negative directional selection in the human genome, relatively little work has been devoted to balancing selection. This lack of attention is likely due to the paucity of sophisticated methods for identifying sites under balancing selection. Here we develop two composite likelihood ratio tests for detecting balancing selection. Using simulations, we show that these methods outperform competing methods under a variety of assumptions and demographic models. We apply the new methods to whole-genome human data, and find a number of previously-identified loci with strong evidence of balancing selection, including several HLA genes. Additionally, we find evidence for many novel candidates, the strongest of which is FANK1, an imprinted gene that suppresses apoptosis, is expressed during meiosis in males, and displays marginal signs of segregation distortion. We hypothesize that balancing selection acts on this locus to stabilize the segregation distortion and negative fitness effects of the distorter allele. Thus, our methods are able to reproduce many previously-hypothesized signals of balancing selection, as well as discover novel interesting candidates.     

On the predictability of protein database search complexity and its relevance to optimization of distributed searches

We discuss several aspects related to load balancing of database search jobs in a distributed computing environment, such as Linux cluster. Load balancing is a technique for making the most of multiple computational resources, which is particularly relevant in environments in which the usage of such resources is very high. The particular case of the Sequest program is considered here, but the general methodology should apply to any similar database search program. We show how the runtimes for Sequest searches of tandem mass spectral data can be predicted from profiles of previous representative searches, and how this information can be used for better load balancing of novel data. A well-known heuristic load balancing method is shown to be applicable to this problem, and its performance is analyzed for a variety of search parameters.     

Toll‐like receptor variation in the bottlenecked population of the Seychelles warbler: computer simulations see the ‘ghost of selection past’ and quantify the ‘drift debt’

Balancing selection can maintain immunogenetic variation within host populations, but detecting its signal in a postbottlenecked population is challenging due to the potentially overriding effects of drift. Toll‐like receptor genes (TLRs) play a fundamental role in vertebrate immune defence and are predicted to be under balancing selection. We previously characterized variation at TLR loci in the Seychelles warbler (Acrocephalus sechellensis), an endemic passerine that has undergone a historical bottleneck. Five of seven TLR loci were polymorphic, which is in sharp contrast to the low genomewide variation observed. However, standard population genetic statistical methods failed to detect a contemporary signature of selection at any TLR locus. We examined whether the observed TLR polymorphism could be explained by neutral evolution, simulating the population's demography in the software DIYABC. This showed that the posterior distributions of mutation rates had to be unrealistically high to explain the observed genetic variation. We then conducted simulations with an agent‐based model using typical values for the mutation rate, which indicated that weak balancing selection has acted on the three TLR genes. The model was able to detect evidence of past selection elevating TLR polymorphism in the prebottleneck populations, but was unable to discern any effects of balancing selection in the contemporary population. Our results show drift is the overriding evolutionary force that has shaped TLR variation in the contemporary Seychelles warbler population, and the observed TLR polymorphisms might be merely the ‘ghost of selection past’. Forecast models predict immunogenetic variation in this species will continue to be eroded in the absence of contemporary balancing selection. Such ‘drift debt’ occurs when a gene pool has not yet reached its new equilibrium level of polymorphism, and this loss could be an important threat to many recently bottlenecked populations.     

Impact of the method of exposure in total hip arthroplasty on balancing ability in response to sudden unidirectional perturbation in the first six months of the postoperative period

Introduction and objectiveTotal hip arthroplasty affects 3–5% of the elderly population. Therefore, the effectiveness of surgery and the ensuing rehabilitation is of great significance. This study investigated balancing ability in response to sudden unidirectional perturbation changes during the first 6 months of the postoperative period with respect to different methods of joint exposure during the operation (antero-lateral, direct-lateral and posterior to preserve the joint capsule). Our hypothesis is that the results may provide a tool to improve the rehabilitation procedures.Materials and methodsThe dynamic balancing ability of 25 patients with direct-lateral exposure, 22 with antero-lateral exposure and 25 with posterior exposure during a total hip arthroplasty was examined using ultrasound-based provocation tests prior to and at 6 weeks, 12 weeks and 6 months after total hip arthroplasty. The control group was represented by 45 healthy subjects of identical age. The dynamic balancing ability after unidirectional perturbation was characterised by Lehr’s damping ratio calculated from the results of tests performed with the patient standing on both limbs, standing on the affected limb and standing on the non-affected limb.ResultsIn the case of direct-lateral and antero-lateral exposure, Lehr’s damping ratio significantly decreased compared to the preoperative values at 6 weeks postoperatively, but it increased steadily afterwards. Lehr’s damping ratio while standing on the affected limb was significantly lower – even at 6 months postoperatively – than that of the control group. In the case of posterior exposure, Lehr’s damping ratio continuously increased in the postoperative period and corresponded to that of the control group at 6 months after total hip arthroplasty.Discussion and conclusionFor patients operated on using direct-lateral and antero-lateral exposure methods, the dynamic balancing ability continuously improved in the first 6 months of the postoperative period, but the dynamic balancing ability of the affected limb differed from that of the control group. In the case of posterior exposure to preserve the joint capsule the dynamic balancing ability evaluated a more rapidly compared to the other two exposure methods. There was no significant difference in the balancing ability of the control group at 6 months after total hip arthroplasty with posterior exposure. The increasing range of joint motion, muscle development, and the development of the dynamic balancing ability should be taken into account when compiling rehabilitation protocols. Differences related to the method of exposure should be considered when developing the dynamic balancing ability and abandoning therapeutic aids.     

Genetic architecture and balancing selection: the life and death of differentiated variants

Balancing selection describes any form of natural selection, which results in the persistence of multiple variants of a trait at intermediate frequencies within populations. By offering up a snapshot of multiple co‐occurring functional variants and their interactions, systems under balancing selection can reveal the evolutionary mechanisms favouring the emergence and persistence of adaptive variation in natural populations. We here focus on the mechanisms by which several functional variants for a given trait can arise, a process typically requiring multiple epistatic mutations. We highlight how balancing selection can favour specific features in the genetic architecture and review the evolutionary and molecular mechanisms shaping this architecture. First, balancing selection affects the number of loci underlying differentiated traits and their respective effects. Control by one or few loci favours the persistence of differentiated functional variants by limiting intergenic recombination, or its impact, and may sometimes lead to the evolution of supergenes. Chromosomal rearrangements, particularly inversions, preventing adaptive combinations from being dissociated are increasingly being noted as features of such systems. Similarly, due to the frequency of heterozygotes maintained by balancing selection, dominance may be a key property of adaptive variants. High heterozygosity and limited recombination also influence associated genetic load, as linked recessive deleterious mutations may be sheltered. The capture of deleterious elements in a locus under balancing selection may reinforce polymorphism by further promoting heterozygotes. Finally, according to recent genomewide scans, balanced polymorphism might be more pervasive than generally thought. We stress the need for both functional and ecological studies to characterize the evolutionary mechanisms operating in these systems.     

Balancing selection and its effects on sequences in nearby genome regions

Our understanding of balancing selection is currently becoming greatly clarified by new sequence data being gathered from genes in which polymorphisms are known to be maintained by selection. The data can be interpreted in conjunction with results from population genetics models that include recombination between selected sites and nearby neutral marker variants. This understanding is making possible tests for balancing selection using molecular evolutionary approaches. Such tests do not necessarily require knowledge of the functional types of the different alleles at a locus, but such information, as well as information about the geographic distribution of alleles and markers near the genes, can potentially help towards understanding what form of balancing selection is acting, and how long alleles have been maintained.     

13C tracer experiments and metabolite balancing for metabolic flux analysis: comparing two approaches

Conventional metabolic flux analysis uses the information gained from determination of measurable fluxes and a steady-state assumption for intracellular metabolites to calculate the metabolic fluxes in a given metabolic network. The determination of intracellular fluxes depends heavily on the correctness of the assumed stoichiometry including the presence of all reactions with a noticeable impact on the model metabolite balances. Determination of fluxes in complex metabolic networks often requires the inclusion of NADH and NADPH balances, which are subject to controversial debate. Transhydrogenation reactions that transfer reduction equivalents from NADH to NADPH or vice versa can usually not be included in the stoichiometric model, because they result in singularities in the stoichiometric matrix. However, it is the NADPH balance that, to a large extent, determines the calculated flux through the pentose phosphate pathway. Hence, wrong assumptions on the presence or activity of transhydrogenation reactions will result in wrong estimations of the intracellular flux distribution. Using 13C tracer experiments and NMR analysis, flux analysis can be performed on the basis of only well established stoichiometric equations and measurements of the labeling state of intracellular metabolites. Neither NADH/NADPH balancing nor assumptions on energy yields need to be included to determine the intracellular fluxes. Because metabolite balancing methods and the use of 13C labeling measurements are two different approaches to the determination of intracellular fluxes, both methods can be used to verify each other or to discuss the origin and significance of deviations in the results. Flux analysis based entirely on metabolite balancing and flux analysis, including labeling information, have been performed independently for a wild-type strain of Aspergillus oryzae producing alpha-amylase. Two different nitrogen sources, NH4+ and NO3-, have been used to investigate the influence of the NADPH requirements on the intracellular flux distribution. The two different approaches to the calculation of fluxes are compared and deviations in the results are discussed. Copyright 1998 John Wiley & Sons, Inc.     

The biomechanics of standing and balancing in paralyzed people

Prolonged immobilization results in several physiological problems. It has been demonstrated that standing exercises can ameliorate many of these problems. Standing exercises can be performed efficiently with the help of functional electrical stimulation (FES). A novel robotic mechanism which aids the unsupported standing of paraplegics, providing balancing exercise has been developed. The balancing strategy is based on voluntary activity of the paraplegic's upper body and artificially controlled stiffness in the ankles.     

Analysis of biochemical phase shift oscillators by a harmonic balancing technique

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.     

Speciation as a sieve for ancestral polymorphism

Because they are considered rare, balanced polymorphisms are often discounted as crucial constituents of genome‐wide variation in sequence diversity. Despite its perceived rarity, however, long‐term balancing selection can elevate genetic diversity and significantly affect observed divergence between species. Here, we discuss how ancestral balanced polymorphisms can be “sieved” by the speciation process, which sorts them unequally across descendant lineages. After speciation, ancestral balancing selection is revealed by genomic regions of high divergence between species. This signature, which resembles that of other evolutionary processes, can potentially confound genomic studies of population divergence and inferences of “islands of speciation.”     

Imbalance and balancing: Development of ecological flow networks

In this paper we address balancing process of ecological flow networks. In existing approaches, macroscopic objectives to which systems organize are assumed. Flow balance provides only constraints for the optimization. Since flow balance and objectives are separated from each other, it is impossible to address how the appearance of objectives is related to flow balance. Therefore, we take an alternative approach, in which we directly describe a dynamics of balancing process. We propose a simple mathematical formula for local balancing dynamics and show that it can generate a self-organizing property, which could be seen as a primitive objective.     

Design and analysis of a replicated server architecture for supporting IP–host mobility

Mobility support in IP networks requires servers to forward packets to mobile hosts and to maintain information pertaining to a mobile host's location in the network. In the mobile Internet Protocol (mobile-IP), location and packet forwarding functions are provided by servers referred to as home agents. These home agents may become the bottleneck when there are a large number of mobile hosts in the network. In this paper, we consider the design and analysis of a replicated server architecture in which multiple home agents are used to provide mobility support. In order to minimize the delay across the home agents, one of the key aspects is the design of load balancing schemes in which a home agent may transfer the control of a mobile host to another home agent in the same network. The methods for triggering the transfer and the policy for selecting the next home agent define various load balancing schemes which have different performance characteristics. In this paper, we design a protocol that forms the building block for implementing such load balancing schemes, and we then study the performance characteristics of three selection schemes, namely, random, round-robin, and join the shortest queue (JSQ), and three transfers policies, namely, timer-, counter- and threshold-based. The key results of this study are as follows: (1) The results show that both random and round-robin selection policies can yield modest load balancing gains, and that these gains increase when the traffic is more bursty (burstiness is defined as the ratio of the peak arrival rate to the mean arrival rate) as well as when there are more home agents. (2) The threshold-based transfer policy performs better than timer-based and counter-based policies, since in threshold-based policies transfers are made only when the queue is overloaded, unlike counter- and timer-based policies in which transfers can be made from an unloaded home agent to an overloaded home agent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Propensity score modeling strategies for the causal analysis of observational data

Propensity score methods are used to estimate a treatment effect with observational data. This paper considers the formation of propensity score subclasses by investigating different methods for determining subclass boundaries and the number of subclasses used. We compare several methods: balancing a summary of the observed information matrix and equal-frequency subclasses. Subclasses that balance the inverse variance of the treatment effect reduce the mean squared error of the estimates and maximize the number of usable subclasses.     

A concept of welfare based on reward evaluating mechanisms in the brain: anticipatory behaviour as an indicator for the state of reward systems

In this review we attempt to link the efficiency by which animals behave (economy of animal behaviour) to a neuronal substrate and subjective states to arrive at a definition of animal welfare which broadens the scope of its study. Welfare is defined as the balance between positive (reward, satisfaction) and negative (stress) experiences or affective states. The state of this balance may range from positive (good welfare) to negative (poor welfare). These affective states are momentary or transient states which occur against the background of and are integrated with the state of this balancing system. As will be argued the efficiency in behaviour requires that, for instance, satisfaction is like a moving target: reward provides the necessary feedback to guide behaviour; it is a not steady-state which can be maintained for long. This balancing system is reflected in the brain by the concerted action of opioid and mesolimbic dopaminergic systems. The state of this system reflects the coping capacity of the animal and is determined by previous events. In other words, this integrative approach of behavioural biology and neurobiology aims at understanding how the coping capacity of animals may be affected and measured. We argue that this balancing system underlies the economy of behaviour. Furthermore we argue that among other techniques anticipation in Pavlovian conditioning is an easy and useful tool to assess the state of this balancing system: for estimating the state of an animal in terms of welfare we focus on the conditions when an animal is facing a challenge.