scholarly journals Overdominant Alleles in a Population of Variable Size

Genetics ◽  
1999 ◽  
Vol 152 (2) ◽  
pp. 775-781 ◽  
Author(s):  
Montgomery Slatkin ◽  
Christina A Muirhead
Keyword(s):  
Markov Chain ◽  
Approximate Method ◽  
Population Size ◽  
Transition Matrix ◽  
Markov Chain Model ◽  
Population Bottleneck ◽  
The Other ◽  
Chain Model ◽  
Variable Size ◽  
Constant Size

Abstract An approximate method is developed to predict the number of strongly overdominant alleles in a population of which the size varies with time. The approximation relies on the strong-selection weak-mutation (SSWM) method introduced by J. H. Gillespie and leads to a Markov chain model that describes the number of common alleles in the population. The parameters of the transition matrix of the Markov chain depend in a simple way on the population size. For a population of constant size, the Markov chain leads to results that are nearly the same as those of N. Takahata. The Markov chain allows the prediction of the numbers of common alleles during and after a population bottleneck and the numbers of alleles surviving from before a bottleneck. This method is also adapted to modeling the case in which there are two classes of alleles, with one class causing a reduction in fitness relative to the other class. Very slight selection against one class can strongly affect the relative frequencies of the two classes and the relative ages of alleles in each class.

A MARKOV CHAIN MODEL OF PREDATOR-MODEL-MIMIC INTERACTIONS

2005 ◽  
Vol 13 (03) ◽  
pp. 273-286 ◽  
Author(s):  
A. TSOULARIS ◽  
J. WALLACE
Keyword(s):  
Population Dynamics ◽  
Markov Chain ◽  
Mathematical Models ◽  
Population Size ◽  
Markov Chain Model ◽  
Prey Population ◽  
Chain Model ◽  
Complex Situation ◽  
Benefit Function ◽  
Predator Model

The population dynamics for predator and prey environments have been studied extensively, and several major mathematical models have been introduced to quantify this. The situation becomes more complex, however, when the prey incorporates preservation strategies for survival. One of the most interesting approaches here is the use of mimicry of prey which are unacceptable to the predator, to avoid being consumed. Here we develop a Markov chain model of interactions between a predator and a prey population comprising unpalatable models, general mimics and specific mimics. This incorporates a simple stochastic procedure for the predator, enabling modifiable behavior to be modeled. We calculate equilibrium consumption probabilities and introduce a fitness measure for each type of prey. Finally, by taking into account the population size of each type of prey, we extend the previously reported notion of a predator benefit function for this more complex situation and provide various mathematical forms of optimal benefit for the predator under selected scenarios of biological importance.

scholarly journals Numerical Study of Turbid Slab Optical Properties Reconstruction from Multiple Scattering Signals Using Time-Based Markov Chain Model

2021 ◽  
Vol 11 (2) ◽  
pp. 588
Author(s):  
Hujie Pan ◽  
Qinglin Xu ◽  
Xuesong Li ◽  
Shangning Wang ◽  
Min Xu
Keyword(s):  
Optical Properties ◽  
Markov Chain ◽  
Multiple Scattering ◽  
Transition Matrix ◽  
Numerical Study ◽  
Markov Chain Model ◽  
Chain Model ◽  
Layer By Layer ◽  
Reconstruction Process ◽  
Computational Costs

The reconstruction of optical properties for opaque mediums is highly desired for medical, atmosphere and aerosol applications. However, the modeling and reconstruction process is highly related with multiple scattering phenomena, which elevates both the complexity and computational costs for such efforts. This work introduces a time-based Markov chain method, which uses a sparse transition matrix to represent the likelihood for a photon to transit in the turbid media. The accuracy of the time-based Markov chain model was verified against the forwarding calculations of the scattering-based Markov chain model and Monte Carlo simulations. Then, reconstruction was performed with backscattered photon angular distributions. Based on the characteristics of the sparse transition matrix, the optical properties (droplet diameters) could be obtained layer by layer with transmitted photon distributions at different time durations. It is shown that the time-based Markov chain model can reconstruct the optical properties of a turbid slab with satisfactory accuracy and lower computational costs.

scholarly journals A MARKOV CHAIN MODEL FOR ISLAMIC MICRO-FINANCING

2019 ◽  
Vol 5 (4) ◽  
pp. 763-784
Author(s):  
Djaffar Lessy ◽  
Fouad Khoudjeti ◽  
Marc Diener ◽  
Francine Diener
Keyword(s):  
Markov Chain ◽  
Asymmetric Information ◽  
Moral Hazard ◽  
Adverse Selection ◽  
Markov Chain Model ◽  
The Other ◽  
Chain Model ◽  
Business Sector ◽  
Islamic Banks ◽  
Strategic Default

            This paper introduces a Markov chain model for Islamic micro-financing, especially mudarabah  and murababah contract. Mudarabah and murabahah  are two Islamic micro-financing contracts that have enormous potential in creating a balance between the monetary and sharia sector because these two products are moving to manage the business sector which undoubtedly adds value to the economic movement directly.  On the other hand, these two contracts have the potential to cause problems in their implementation. The most common problem of the two contracts is asymmetric information, which consists of adverse selection and moral hazard. We propose the Markov chain model as a solution for the Islamic banks to reduce the risk because of adverse selection and moral hazard in mudarabah  and murabahah  contract. In our model, we also propose a mechanism to avoid strategic default in mudarabah contract. We observed two different probabilities of an applicant to become a beneficiary to find the solution to the problems. The results of this study, the bank can decrease the probability of an applicant to become a beneficiary to reduce the adverse selection and moral hazard in mudarabah  and murabahah contract.

An Efficient Markov Chain Model for the Simulation of Heterogeneous Soil Structure

2004 ◽  
Vol 68 (2) ◽  
pp. 346 ◽  
Author(s):  
Keijan Wu ◽  
Naoise Nunan ◽  
John W. Crawford ◽  
Iain M. Young ◽  
Karl Ritz
Keyword(s):  
Markov Chain ◽  
Soil Structure ◽  
Markov Chain Model ◽  
Chain Model ◽  
Heterogeneous Soil

Data Mining Technique Applied To DNA Sequencing

2015 ◽  
Vol 2 (7) ◽  
pp. 18
Author(s):  
R. Jamuna
Keyword(s):  
Data Mining ◽  
Dna Methylation ◽  
Markov Chain ◽  
Human Genome ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Effective Means ◽  
Cpg Islands ◽  
Chain Model ◽  
The Given

CpG islands (CGIs) play a vital role in genome analysis as genomic markers.  Identification of the CpG pair has contributed not only to the prediction of promoters but also to the understanding of the epigenetic causes of cancer. In the human genome [1] wherever the dinucleotides CG occurs the C nucleotide (cytosine) undergoes chemical modifications. There is a relatively high probability of this modification that mutates C into a T. For biologically important reasons the mutation modification process is suppressed in short stretches of the genome, such as ‘start’ regions. In these regions [2] predominant CpG dinucleotides are found than elsewhere. Such regions are called CpG islands. DNA methylation is an effective means by which gene expression is silenced. In normal cells, DNA methylation functions to prevent the expression of imprinted and inactive X chromosome genes. In cancerous cells, DNA methylation inactivates tumor-suppressor genes, as well as DNA repair genes, can disrupt cell-cycle regulation. The most current methods for identifying CGIs suffered from various limitations and involved a lot of human interventions. This paper gives an easy searching technique with data mining of Markov Chain in genes. Markov chain model has been applied to study the probability of occurrence of C-G pair in the given   gene sequence. Maximum Likelihood estimators for the transition probabilities for each model and analgously for the  model has been developed and log odds ratio that is calculated estimates the presence or absence of CpG is lands in the given gene which brings in many  facts for the cancer detection in human genome.

Evaluating basketball player’s rotation line-ups performance via statistical markov chain modelling

2021 ◽  
pp. 174795412110090
Author(s):  
Pavlos Kolias ◽  
Nikolaos Stavropoulos ◽  
Alexandra Papadopoulou ◽  
Theodoros Kostakidis
Keyword(s):  
Markov Chain ◽  
Markov Chain Model ◽  
Specific Rotation ◽  
Multiple Regression Model ◽  
Chain Model ◽  
Know How ◽  
Basketball Game ◽  
Long Run ◽  
Rotation Line ◽  
Rating Category

Coaches in basketball often need to know how specific rotation line-ups perform in either offense or defense and choose the most efficient formation, according to their specific needs. In this research, a sample of 1131 ball possession phases of Greek Basket League was utilized, in order to estimate the offensive and defensive performance of each formation. Offensive and defensive ratings for each formation were calculated as a function of points scored or received, respectively, over possessions, where possessions were estimated using a multiple regression model. Furthermore, a Markov chain model was implemented to estimate the probabilities of the associated formation’s performance in the long run. The model could allow us to distinguish between overperforming and underperforming formations and revealed the probabilities over the evolution of the game, for each formation to be in a specific rating category. The results indicated that the most dominant formation, in terms of offense, is Point Guard-Point Guard-Small Forward-Power Forward-Center, while defensively schema Point Guard-Shooting Guard-Small Forward-Center-Center had the highest rating. Such results provide information, which could operate as a supplementary tool for the coach’s decisions, related to which rotation line-up patterns are mostly suitable during a basketball game.

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