The dynamics of neutral mutation

1978 ◽  
Vol 203 (1150) ◽  
pp. 91-91
Keyword(s):  
Stochastic Models ◽  
Diffusion Approximations ◽  
Neutral Systems ◽  
Effective Population ◽  
Gene Frequencies ◽  
Deterministic Models ◽  
New Approach ◽  
Large Populations ◽  
Quantitative Results ◽  
Infinite Alleles Model

A variety of mathematical models have been proposed, over the years since the pioneering work of Fisher and Wright, for the evolution of gene frequencies in large populations under the pressure of selection and mutation. It is broadly true to say that deterministic models are adequate, at least to a first approximation, when selective differences are large compared with the reciprocal of the effective population size. When selection is weaker than this, genetic drift is sufficiently obtrusive to make stochastic models essential. Such models are typically much more difficult to analyse than deterministic ones, and detailed studies have usually been confined to the very special situation of statistical equilibrium. But of course no biological system is really in equilibrium for very long, and moreover the relaxation of nearly neutral systems is usually slow; hence the need for dynamical stochastic models and for their analysis outside a state of equilibrium. The usual way of attacking this problem is by diffusion approximations, and the theory of such processes is surveyed. Questions of existence, uniqueness and adequacy of approximation are well understood, but much less is known about methods of deriving explicit quantitative results or qualitative insight. A new approach is suggested which is particularly useful for studying a locus at which many different alleles are possible. It leads, for example, to a dynamical picture (in terms of a diffusing Poisson process) for the neutral infinite-alleles model of Kimura & Crow.

scholarly journals The effect of population subdivision on two loci without selection

1974 ◽  
Vol 24 (2) ◽  
pp. 151-162 ◽  
Author(s):  
Marcus W. Feldman ◽  
Freddy Bugge Christiansen
Keyword(s):  
Rate Of Convergence ◽  
Recombination Frequency ◽  
Population Subdivision ◽  
Genetic Constitution ◽  
Gene Frequencies ◽  
Deterministic Models ◽  
Stepping Stone ◽  
Linkage Disequilibria ◽  
Large Populations ◽  
Finite Linear

SUMMARYThis paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 – c) and , where λ1 is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

scholarly journals Likelihoods and Simulation Methods for a Class of Nonneutral Population Genetics Models

Genetics ◽  
2001 ◽  
Vol 159 (2) ◽  
pp. 853-867 ◽  
Author(s):  
Peter Donnelly ◽  
Magnus Nordborg ◽  
Paul Joyce
Keyword(s):  
Population Genetics ◽  
Population Size ◽  
Mutant Allele ◽  
Mutation Rates ◽  
Simulation Methods ◽  
Large Populations ◽  
Selection Intensities ◽  
Infinite Alleles Model

Abstract Methods for simulating samples and sample statistics, under mutation-selection-drift equilibrium for a class of nonneutral population genetics models, and for evaluating the likelihood surface, in selection and mutation parameters, are developed and applied for observed data. The methods apply to large populations in settings in which selection is weak, in the sense that selection intensities, like mutation rates, are of the order of the inverse of the population size. General diploid selection is allowed, but the approach is currently restricted to models, such as the infinite alleles model and certain K-models, in which the type of a mutant allele does not depend on the type of its progenitor allele. The simulation methods have considerable advantages over available alternatives. No other methods currently seem practicable for approximating likelihood surfaces.

scholarly journals Methods for Estimating Gene Frequencies and Detecting Selection in Bacterial Populations

Genetics ◽  
2000 ◽  
Vol 155 (2) ◽  
pp. 499-508 ◽  
Author(s):  
Bruce Rannala ◽  
Wei-Gang Qiu ◽  
Daniel E Dykhuizen
Keyword(s):  
Ixodes Scapularis ◽  
Balancing Selection ◽  
Surface Protein ◽  
Allele Frequencies ◽  
Gene Frequencies ◽  
Bacterial Populations ◽  
Polymerase Chain ◽  
Host Infection ◽  
Infinite Alleles Model

Abstract Recent breakthroughs in molecular technology, most significantly the polymerase chain reaction (PCR) and in situ hybridization, have allowed the detection of genetic variation in bacterial communities without prior cultivation. These methods often produce data in the form of the presence or absence of alleles or genotypes, however, rather than counts of alleles. Using relative allele frequencies from presence-absence data as estimates of population allele frequencies tends to underestimate the frequencies of common alleles and overestimate those of rare ones, potentially biasing the results of a test of neutrality in favor of balancing selection. In this study, a maximum-likelihood estimator (MLE) of bacterial allele frequencies designed for use with presence-absence data is derived using an explicit stochastic model of the host infection (or bacterial sampling) process. The performance of the MLE is evaluated using computer simulation and a method is presented for evaluating the fit of estimated allele frequencies to the neutral infinite alleles model (IAM). The methods are applied to estimate allele frequencies at two outer surface protein loci (ospA and ospC) of the Lyme disease spirochete, Borrelia burgdorferi, infecting local populations of deer ticks (Ixodes scapularis) and to test the fit to a neutral IAM.

scholarly journals New Cancer Stochastic Models Involving Both Hereditary and Nonhereditary Cancer Cases: A New Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Wai-Yuan Tan ◽  
Hong Zhou
Keyword(s):  
Cancer Incidence ◽  
Stochastic Models ◽  
Biological Information ◽  
Cancer Genes ◽  
New Approach ◽  
Human Cancers ◽  
Seer Data ◽  
Sampling Procedures ◽  
And Control ◽  
Better Than

To incorporate biologically observed epidemics into multistage models of carcinogenesis, in this paper we have developed new stochastic models for human cancers. We have further incorporated genetic segregation of cancer genes into these models to derive generalized mixture models for cancer incidence. Based on these models we have developed a generalized Bayesian approach to estimate the parameters and to predict cancer incidence via Gibbs sampling procedures. We have applied these models to fit and analyze the SEER data of human eye cancers from NCI/NIH. Our results indicate that the models not only provide a logical avenue to incorporate biological information but also fit the data much better than other models. These models would not only provide more insights into human cancers but also would provide useful guidance for its prevention and control and for prediction of future cancer cases.

scholarly journals Estimating the distribution of time to extinction of infectious diseases in mean-field approaches

2020 ◽  
Author(s):  
Maryam Aliee ◽  
Kat S. Rock ◽  
Matt J. Keeling
Keyword(s):  
Infectious Diseases ◽  
Stochastic Models ◽  
Mean Field ◽  
Practical Method ◽  
Deterministic Models ◽  
Recovery Processes ◽  
Time To Extinction ◽  
And Control ◽  
Field Approaches ◽  
Birth Death

AbstractA key challenge for many infectious diseases is to predict the time to extinction under specific interventions. In general this question requires the use of stochastic models which recognise the inherent individual-based, chance-driven nature of the dynamics; yet stochastic models are inherently computationally expensive, especially when parameter uncertainty also needs to be incorporated. Deterministic models are often used for prediction as they are more tractable, however their inability to precisely reach zero infections makes forecasting extinction times problematic. Here, we study the extinction problem in deterministic models with the help of an effective “birth-death” description of infection and recovery processes. We present a practical method to estimate the distribution, and therefore robust means and prediction intervals, of extinction times by calculating their different moments within the birth-death framework. We show these predictions agree very well with the results of stochastic models by analysing the simplified SIS dynamics as well as studying an example of more complex and realistic dynamics accounting for the infection and control of African sleeping sickness (Trypanosoma brucei gambiense).

Scientific Management 2.0 – A Design Model for Experimental Research in Production Management

2014 ◽  
Vol 1018 ◽  
pp. 571-579
Author(s):  
Günther Schuh ◽  
Thomas Gartzen ◽  
Felix Basse
Keyword(s):  
Experimental Research ◽  
Theoretical Basis ◽  
Production Management ◽  
Production Systems ◽  
Scientific Management ◽  
Deterministic Models ◽  
New Approach ◽  
Technical Aspects ◽  
The Poor ◽  
And Performance

Reliable and accurate predictions on future states of production systems are the objective of production theories. In this paper, the authors determined shortcomings of current deterministic models and traced them back to the poor theoretical basis of scientific research in the area. The observations resulted in the development of the conceptScientific Management 2.0as an appropriate research methodology for production management. This new empirical approach takes into account three requirements to scientifically precise investigations: It expands existing theory by socio-technical aspects, uses embedded experiments as a profound basis for investigation and provides a design that warrants the methodical exactness required. RWTH Aachen’sDemonstration Factoryrepresents an adequate infrastructure to prove feasibility and performance of the new approach.

Optimization models for managing limited resources in logistics

2021 ◽  
Author(s):  
Aleksandr Mischenko ◽  
Anastasiya Ivanova
Keyword(s):  
Stochastic Models ◽  
Optimization Models ◽  
Limited Resources ◽  
Model Parameters ◽  
Systems Modeling ◽  
Deterministic Models ◽  
Logistics Systems ◽  
Industrial Enterprises ◽  
The Stability ◽  
Senior Students

In the proposed monograph, optimization models for managing limited resources in logical systems are considered. Such systems are primarily used by industrial enterprises, transport companies and trade organizations, including those that carry out wholesale activities. As a rule, the efficiency of these objects largely depends on how rational use of limited resources such as: consumer camera business, labor, vehicles, etc. In this paper, various approaches to managing such resources are considered both for deterministic models and for the situation when a number of model parameters are not specified exactly, that is, for stochastic models. In this case, it is proposed to evaluate the stability of models to the occurrence of various types of risk events, both by the structure of the solution and by the functionality. It is addressed to senior students, postgraduates and masters studying in the specialty "Management" and "Logistics", as well as specialists in the field of logistics systems modeling.

scholarly journals Translating environmental xenobiotic fate models across scales

1997 ◽  
Vol 1 (4) ◽  
pp. 895-904 ◽  
Author(s):  
O. Richter ◽  
B. Diekkrüger
Keyword(s):  
Stochastic Models ◽  
Process Models ◽  
Spatial Process ◽  
Soil Parameters ◽  
Deterministic Models ◽  
Deterministic Process ◽  
Statistical Variation ◽  
Scale Models ◽  
Classical Models ◽  
Environmental Xenobiotic

Abstract. The classical models developed for degradation and transport of xenobiotics have been derived with the assumption of homogeneous environments. Unfortunately, deterministic models function well in the laboratory under homogeneous conditions but such homogeneous conditions often do not prevail in the field. A possible solution is the incorporation of the statistical variation of soil parameters into deterministic process models. This demands the development of stochastic models of spatial variability. To this end, spatial soil parameter fields are conceived as the realisation of a random spatial process. Extrapolation of local fine scale models to large heterogeneous fields is achieved by coupling deterministic process models with random spatial field models.

scholarly journals Compton scattering tomography for agricultural measurements

2006 ◽  
Vol 26 (1) ◽  
pp. 151-160 ◽  
Author(s):  
Paulo E. Cruvinel ◽  
Fatai A. Balogun
Keyword(s):  
Compton Scattering ◽  
Linear Correlation ◽  
Imaging Technique ◽  
Reconstruction Algorithm ◽  
Transmission Tomography ◽  
Electronic Density ◽  
New Approach ◽  
Quantitative Results ◽  
Water Contents ◽  
Better Than

This paper presents a new approach in tomographic instrumentation for agriculture based on Compton scattering, which allows for the simultaneous measurements of density and moisture of soil samples. Compton tomography is a technique that can be used to obtain a spatial map of electronic density of samples. Quantitative results can be obtained by using a reconstruction algorithm that takes into account the absorption of incident and scattered radiation. Results show a coefficient of linear correlation better than 0.81, when comparison is made between soil density measurements based on this method and direct transmission tomography. For soil water contents, a coefficient of linear correlation better than 0.79 was found when compared with measurements obtained by time domain reflectrometry (TDR). In addition, a set of Compton scatter images are presented to illustrate the efficacy of this imaging technique, which makes possible improved spatial variability analysis of pre-established planes.

Likelihood ratios for the infinite alleles model

1994 ◽  
Vol 31 (03) ◽  
pp. 595-605 ◽  
Author(s):  
Paul Joyce
Keyword(s):  
Likelihood Ratio ◽  
Stationary Distribution ◽  
Random Sequence ◽  
Random Variable ◽  
Single Locus ◽  
Likelihood Ratios ◽  
Gene Frequencies ◽  
Random Samples ◽  
Infinite Alleles Model

The stationary distribution for the population frequencies under an infinite alleles model is described as a random sequence (x 1, x 2, · ··) such that Σxi = 1. Likelihood ratio theory is developed for random samples drawn from such populations. As a result of the theory, it is shown that any parameter distinguishing an infinite alleles model with selection from the neutral infinite alleles model cannot be consistently estimated based on gene frequencies at a single locus. Furthermore, the likelihood ratio (neutral versus selection) converges to a non-trivial random variable under both hypotheses. This shows that if one wishes to test a completely specified infinite alleles model with selection against neutrality, the test will not obtain power 1 in the limit.

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