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PubMed1997

The genealogy of samples in models with selection.

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman's well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman's coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models. DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.

Genealogy and Heraldry↗
PubMed2006

Model-free model elimination: a new step in the model-free dynamic analysis of NMR relaxation data.

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R1, R2, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a chi2 function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, tau(e), tau(f), or tau(s), or the global correlation time parameter, local tau(m), heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised chi2 value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.

Magnetic Resonance Spectroscopy↗
PubMed1975

A conceptual overview of selected consultation models.

Because of their current popularity and utility 4 consultation models have been selected for analysis: consultee centered, group process, social action, and ecological (exemplified by Gerald Caplan, Ronald Lippitt, Saul Alinsky, and James Kelly, respectively). The process of consultation as outlined by these models is described along the following dimensions: definitions of consultation, self-perceptions of the consultant, target populations, motivation of the client system, entry, goals, diagnosis, techniques, termination, and evaluation. The discussion focuses on criteria for selecting an appropriate consultation model.

Goals↗
PubMed2005

Evolution of virulence: interdependence, constraints, and selection using nested models.

Natural selection acts on virus populations at two distinct but interrelated levels: within individual hosts and between them. Studies of the evolution of virulence typically focus on selection acting at the epidemiological or between-host level and demonstrate the importance of trade-offs between disease transmission and virulence rates. Within-host studies reach similar conclusions regarding trade-offs between transmission and virulence at the level of individual cells. Studies which examine selection at both scales assume that between- and within-host selection are necessarily in conflict. We explicitly examine these ideas and assumptions using a model of within-host viral dynamics nested within a model of between-host disease dynamics. Our approach allows us to evaluate the direction of selection at the within- and between-host levels and identify situations leading to conflict and accord between the two levels of selection.

Host-Parasite Interactions↗
PubMed2007

Using variable rate models to identify genes under selection in sequence pairs: their validity and limitations for EST sequences.

Using likelihood-based variable selection models, we determined if positive selection was acting on 523 EST sequence pairs from two lineages of sunflower and lettuce. Variable rate models are generally not used for comparisons of sequence pairs due to the limited information and the inaccuracy of estimates of specific substitution rates. However, previous studies have shown that the likelihood ratio test (LRT) is reliable for detecting positive selection, even with low numbers of sequences. These analyses identified 56 genes that show a signature of selection, of which 75% were not identified by simpler models that average selection across codons. Subsequent mapping studies in sunflower show four of five of the positively selected genes identified by these methods mapped to domestication QTLs. We discuss the validity and limitations of using variable rate models for comparisons of sequence pairs, as well as the limitations of using ESTs for identification of positively selected genes.

Base Pairing↗
PubMed1996

Impact of model-form selection on the accuracy of rate estimation.

A key assumption underlying the use of model-based estimates in epidemiology is that the structural-model form is an adequate mathematical description of the dependence of disease occurrence on exposures and covariates (that is, the model form is correctly specified). If this assumption is violated, model-based point estimators and variance estimators may be biased, standard confidence intervals may be invalid, and inferences derived from these estimators may be incorrect. In practice, the true structural-model form is usually unknown, and investigators frequently use their data to help select a model form. We conducted a simulation study to examine the impact of model-form selection on the accuracy of rate estimation in cohort-study situations resembling those found in environmental and occupational epidemiology. For the situations we examined, the increase in variance produced by using model-form selection was often more than offset by the corresponding reduction in bias, sometimes resulting in a dramatic increase in accuracy. Model-form selection was observed to be most beneficial relative to no selection when effects were stronger, the sample size was larger, and the candidate model forms included the true model form or allowed the model to more closely approximate the true model form. It was least beneficial when effects were weak and the sample size was small, even if the candidate model forms included the true model form.

Cohort Studies↗
PubMed1990

Some consideration on diversifying selection.

The diversifying selection due to genotype-environment interaction can increase the genetic variation in natural populations. It is known, however, that the conditions for stable genetic polymorphism or marginal overdominance are quite restricted in this selection model. In this paper a simple model of diversifying selection was examined, and the following results were obtained: (1) Even when the conditions for marginal overdominance are not satisfied, if the diversifying selection is operating, the frequency of mutants can be higher than that in the case of simple mutation-selection balance. (2) This selection model causes a large amount of genetic load (environment load), even when the conditions for marginal overdominance are not satisfied, namely even when the equilibrium frequency of mutant is very low. From these results it can be concluded that the number of loci on which this type of diversifying selection is operating is very small, if any.

Animals↗
PubMed2006

An automated process for building reliable and optimal in vitro/in vivo correlation models based on Monte Carlo simulations.

Many mathematical models have been proposed for establishing an in vitro/in vivo correlation (IVIVC). The traditional IVIVC model building process consists of 5 steps: deconvolution, model fitting, convolution, prediction error evaluation, and cross-validation. This is a time-consuming process and typically a few models at most are tested for any given data set. The objectives of this work were to (1) propose a statistical tool to screen models for further development of an IVIVC, (2) evaluate the performance of each model under different circumstances, and (3) investigate the effectiveness of common statistical model selection criteria for choosing IVIVC models. A computer program was developed to explore which model(s) would be most likely to work well with a random variation from the original formulation. The process used Monte Carlo simulation techniques to build IVIVC models. Data-based model selection criteria (Akaike Information Criteria [AIC], R2) and the probability of passing the Food and Drug Administration "prediction error" requirement was calculated. To illustrate this approach, several real data sets representing a broad range of release profiles are used to illustrate the process and to demonstrate the advantages of this automated process over the traditional approach. The Hixson-Crowell and Weibull models were often preferred over the linear. When evaluating whether a Level A IVIVC model was possible, the model selection criteria AIC generally selected the best model. We believe that the approach we proposed may be a rapid tool to determine which IVIVC model (if any) is the most applicable.

Automation↗
PubMed2003

Observability in strategic models of viability selection.

Strategic models of frequency-dependent viability selection, in terms of mathematical systems theory, are considered as a dynamic observation system. Using a general sufficient condition for observability of nonlinear systems with invariant manifold, it is studied whether, observing certain phenotypic characteristics of the population, the development of its genetic state can be recovered, at least near equilibrium.

Biological Evolution↗
PubMed2005

A model order selection criterion with applications to cardio-respiratory-renal systems.

We introduce a model order selection criterion called signal prediction error (SPE) for the identification of a linear regression model, which can be an adequate representation of a resting physiologic system. SPE is an estimate of the prediction error variance due only to model estimation error and not unobserved noise, which distinguishes it from the widely used final prediction error (FPE). We then present a theoretical analysis of SPE, which predicts that its ability to select correctly the model order is more dependent on the signal-to-noise ratio (SNR) and less dependent on the number of data samples available for analysis. We next propose a heuristic procedure based on SPE (called SPE(D)) to improve its robustness to SNR levels. We then demonstrate, through simulated physiologic data at high SNR levels, that SPE will be equivalent to consistent model order selection criteria for long data records but will become superior to FPE and other model order selection criteria as the size of the data record decreases. The simulated data results also show that SPE(D) is indeed a significant improvement over SPE in terms of robustness to SNR. Finally, we demonstrate the applicability of SPE and SPE(D) to actual cardio-respiratory-renal data.

Algorithms↗
PubMed2003

Selective acylation of 2 methoxynaphthalene by large pore zeolites: catalyst selection through molecular modeling.

The selective acylation of 2-methoxynaphthalene (2-MON) is commercially very important to produce selectively 2-acyl-6-methoxynaphthalene (2,6-AMON), which is a precursor to Naproxen, an anti-inflammatory drug. Most of the laboratory investigations conducted with different solid acids show that the undesirable products are formed in large quantities. Thus, various molecular modeling techniques were used to investigate selectivity towards desired 2,6-AMON isomer over undesired 1,2-AMON, in four large-pore zeolites, namely, mordenite (MOR), zeolite L (LTL), zeolite beta (BEA) and ITQ-7 (ISV). The qualitative results were obtained by using simple molecular graphics (MG) and structural fitting approach. The quantitative results were obtained by incorporating the interaction of atoms of the molecules and those of the zeolite frameworks. From diffusion energy profile calculations the diffusion energy barriers for self-diffusion of 2-MON and the acylated isomers were obtained. From these energy barrier values the selectivity offered by zeolites towards desired product was determined and it was found to be in the order of ISV>BEA>MOR>LTL. Hybrid Quantum Mechanics-Molecular Mechanics (QM/MM) approach was used to study the effect of Brønsted acidity on the activity and selectivity offered by zeolites. The interaction of the reactant and product species with the acidic protons at T3 and T9 sites in BEA, having different acidities was studied by this method. The QM energy values indicate that acidity affected the catalytic activity but not the regioselectivity towards the desired 2,6-AMON isomer.

Journal Article↗
PubMed2005

Equilibrium, observability and controllability in selection-mutation models.

In this paper we shortly discuss the problem of the equilibrium in the well-known Fisher type selection-mutation model, also providing a formula for particular three-allele models. The considered continuous-time dynamics is a known extension of the classical model of natural selection given by Fisher. We also extend the existing investigation of the observability of Fisher's model to the case when another evolutionary factor, mutation is also present. Moreover, we prove a result of technical character, which makes it possible to apply the methodology of nonlinear systems with invariant manifold, to models of artificial selection. For an illustration, a class of three-allele systems is presented in which the controllability into equilibrium is guaranteed without any condition on the biological parameters.

Algorithms↗
PubMed2006

A novel genetic model of selective COX-2 inhibition: comparison with COX-2 null mice.

Prostaglandin H Synthase (PGHS) is a bi-functional enzyme with a cyclooxygenase (COX) activity and a functionally linked peroxidase (POX) activity that exists in two isoforms (COX-1, COX-2). Non-steroidal anti-inflammatory drugs (NSAIDs), including the selective COX-2 inhibitors, block COX activity while leaving POX activity unscathed. Recently, some selective COX-2 inhibitors were withdrawn from the market due to elevated cardiovascular risk in placebo-controlled trials. Mice deficient for PGHS2 were developed in 1995 and through numerous subsequent studies have revealed significant roles in renal development, ductus arteriosus patency/closure, skin carcinogenesis and cardiovascular function. In this short review, we compare a novel genetic COX-2 selective inhibition mouse model with the originally described COX-2 null mice in these different physiological functions.

Amino Acid Substitution↗
PubMed1999

The FeatureGate model of visual selection.

The model presented here is an attempt to explain the results from a number of different studies in visual attention, including parallel feature searches and serial conjunction searches. Variations in such slope with variations in feature contrast and individual subject differences, attentional gradients triggered by cueing, feature-driven spatial selection, split attention, inhibition of distractor locations, and flanking inhibition. The model is implemented in a neural network consisting of a hierarchy of spatial maps. Attentional gates control the flow of information from each level of the hierarchy to the next. The gates are jointly controlled by a Bottom-Up System favoring locations with unique features and a Top-Down System favoring locations with features designated as target features. Because the gating of each location depends on the features presented there, the model is called FeatureGate.

Attention↗
PubMed2005

SSR181507, a dopamine D(2) receptor antagonist and 5-HT(1A) receptor agonist, alleviates disturbances of novelty discrimination in a social context in rats, a putative model of selective attention deficit.

RATIONALE: Selective attention deficit, characterised by the inability to differentiate relevant from irrelevant information, is considered to underlie many cognitive deficits of schizophrenia, and appears to be only marginally responsive to treatment with current antipsychotics. OBJECTIVES: We compared the activity of the putative atypical antipsychotic SSR181507 (a dopamine D(2) receptor antagonist and 5HT(1A) receptor agonist) with reference compounds, on disturbances of novelty discrimination in a social context in rats, a behavioural paradigm that putatively models selective attention deficit. METHODS: A first (familiar) juvenile rat was presented to an adult rat for a period (P1) of 30 min. A second (novel) juvenile was then introduced at the end of P1 for a period (P2) of 5 min. The ability of the adult rat to discriminate between the two juveniles, presented at the same time, was evaluated by measuring the ratio of the time spent in interaction with the novel vs the familiar juvenile during P2. RESULTS: Adult rats spent more time exploring the novel than the familiar juvenile. This novelty discrimination capacity was disrupted by: (1) parametric modification of the procedure (reduction of time spent in contact with the familiar juvenile during P1); (2) acute injection of psychotomimetics that are known to induce schizophrenia-like symptoms in humans, such as phencyclidine (PCP; 3 mg/kg, i.p.) and d-amphetamine (1 mg/kg, i.p.) and (3) neonatal treatment with PCP (three injections of 10 mg/kg, s.c.), a model based on the neurodevelopmental hypothesis of schizophrenia. The potential atypical antipsychotic SSR181507 (0.03-3 mg/kg, i.p.) and the atypical antipsychotics clozapine (0.1-1 mg/kg, i.p.) and amisulpride (1-3 mg/kg, i.p.) attenuated deficits in novelty discrimination produced by parametric manipulation and by acute or neonatal treatment with PCP. The typical antipsychotic haloperidol (up to 0.3 mg/kg, i.p.) attenuated only deficits in novelty discrimination produced by parametric modification. CONCLUSION: Collectively, these results suggest that SSR181507 can alleviate disturbances of novelty discrimination in a social context in rats, and that this paradigm may represent a suitable animal model of selective attention deficits observed in schizophrenia.

Age Factors↗
PubMed2005

Cue-guided search: a computational model of selective attention.

Selective visual attention in a natural environment can be seen as the interaction between the external visual stimulus and task specific knowledge of the required behavior. This interaction between the bottom-up stimulus and the top-down, task-related knowledge is crucial for what is selected in the space and time within the scene. In this paper, we propose a computational model for selective attention for a visual search task. We go beyond simple saliency-based attention models to model selective attention guided by top-down visual cues, which are dynamically integrated with the bottom-up information. In this way, selection of a location is accomplished by interaction between bottom-up and top-down information. First, the general structure of our model is briefly introduced and followed by a description of the top-down processing of task-relevant cues. This is then followed by a description of the processing of the external images to give three feature maps that are combined to give an overall bottom-up map. Second, the development of the formalism for our novel interactive spiking neural network (ISNN) is given, with the interactive activation rule that calculates the integration map. The learning rule for both bottom-up and top-down weight parameters are given, together with some further analysis of the properties of the resulting ISNN. Third, the model is applied to a face detection task to search for the location of a specific face that is cued. The results show that the trajectories of attention are dramatically changed by interaction of information and variations of cues, giving an appropriate, task-relevant search pattern. Finally, we discuss ways in which these results can be seen as compatible with existing psychological evidence.

Algorithms↗
PubMed1997

Models of selective mating and the initiation of the Fisherian process.

The effects of various rules of selective mating on the initial stages of Fisherian sexual selection are investigated. A comparison of three models of selective mating, fixed relative preference, best of N males and absolute preference is provided, with a special emphasis on their mathematical properties. Using a two-locus haploid model of sexual selection in a polygamous population, I show that the absolute preference rule of selective mating may lower the threshold frequency of the preference trait, required for the initiation of the Fisherian process, as low as zero. This was not observed in the previous analyses with fixed relative preference or best of N male rules. It is then argued that absolute preference may cause the initiations of the Fisherian process more easily without introducing additional assumptions such as pleiotropy or random genetic drift. Some problems associated with the mating rule are also discussed.

Animals↗
PubMed2003

Scaling of mutational effects in models for pleiotropy.

Mutation-selection models provide a framework to relate the parameters of microevolution to properties of populations. Like all models, these must be subject to test and refinement in light of experiments. The standard mutation-selection model assumes that the effects of a pleiotropic mutation on different characters are uncorrelated. As a consequence of this assumption, mutations of small overall effect are suppressed. For strong enough pleiotropy, the result is a nonvanishing fraction of a population with the "perfect" phenotype. However, experiments on microorganisms and experiments on protein structure and function contradict the assumptions of the standard model, and Kimura's observations of heterogeneity within populations contradict its conclusions. Guided by these observations, we present an alternative model for pleiotropic mutations. The new model allows mutations of small overall effect and thus eliminates the finite fraction of the population with the perfect phenotype.

Genetics, Population↗