scholarly journals Simulating the Emergence of Mutations and Their Subsequent Evolution in an Age-Structured Stochastic Self-Regulating Process with Two Sexes

2013 ◽  
Vol 2013 ◽  
pp. 1-23 ◽  
Author(s):  
Charles J. Mode ◽  
Candace K. Sleeman ◽  
Towfique Raj
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Branching Process ◽  
Initial Population ◽  
Expected Number ◽  
Parametric Function ◽  
Simulation Experiments ◽  
Multitype Branching Process ◽  
Male Sexual Partner ◽  
Age Structured

The stochastic process under consideration is intended to be not only part of the working paradigm of evolutionary and population genetics but also that of applied probability and stochastic processes with an emphasis on computer intensive methods. In particular, the process is an age-structured self-regulating multitype branching process with a genetic component consisting of an autosomal locus with two alleles for females and males. It is within this simple context that mutation will be quantified in terms of probabilities that a given allele mutates to the other per meiosis. But, unlike many models that are currently being used in mathematical population genetics, in which natural selection is often characterized in terms of parameters called fitness by genotype or phenotype, in this paper the parameterization of submodules of the model provides a framework for characterizing natural selection in terms of some of its components. One of these modules consists of reproductive success that is quantified in terms of the total expected number of offspring a female contributes to the population throughout her fertile years. Another component consists of survival probabilities that characterize an individual’s ability to compete for limited environmental resources. A third module consists of a parametric function that expresses the probabilities of survival in a birth cohort of individuals by age for both females and males. A forth module of the model as an acceptance matrix of conditional probabilities such female may show a preference for the genotype or phenotype as her male sexual partner. It is assumed that any force of natural selection acts at the level of the three genotypes under consideration for each sex. By assigning values of the parameters in each of the modules under consideration, it is possible to conduct Monte Carlo simulation experiments designed to study the effects of each component of selection separately or in any combination on a population evolving from a given initial population over some specified period of time.

scholarly journals An Algorithmic Approach to Modelling the Co-Evolution of Parasites and Their Hosts

2020 ◽  
Vol 9 (2) ◽  
pp. 13
Author(s):  
Charles J. Mode
Keyword(s):  
Host Plants ◽  
Branching Process ◽  
Branching Processes ◽  
Focus Of Attention ◽  
Point Of View ◽  
Simulation Experiments ◽  
Multitype Branching Process ◽  
Algorithmic Approach ◽  
Multitype Branching Processes ◽  
Growing Crop

This paper is a reformulation of the paper, Mode 1958 Evolution 12:158 - 165, which was written in terms of a deterministic paradigm, using di erential equations In this paper, however, the working paradigm will be stochastic, and from the mathematical point of view, it will be a stochastic process that may be viewed as a branching process within a branching process. In particular, it will be assumed that the population of host plants will evolve as a multitype branching process, and the pathogen, which grows on the leaves of the host in every generation of the host, will also be assumed to evolve as a multitype branching processes during each generation of the host. The contents of this paper, were motivated by problems in Agriculture in which Plant Pathologists and Plant Breeders work together to control the damage inflicted by a pathogen on a growing crop of a cultivar such as flax, wheat. and many other cultivars. The focus of attention in this paper is the development of algorithms that will guide the development of software to run Monte Carol simulation experiments taking into account mutations in the host and pathogen. The writing of software to implement the algorithms developed in this paper would require a major e ort, and is, therefore, beyond the scope of this paper

scholarly journals Demographic Dynamics in Multitype Populations with Migrations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 246
Author(s):  
Manuel Molina-Fernández ◽  
Manuel Mota-Medina
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics ◽  
Branching Process ◽  
Probability Model ◽  
Biological Systems ◽  
Research Work ◽  
General Setting ◽  
Process Theory ◽  
Multitype Branching Process ◽  
Demographic Dynamics

This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies.

Branching processes and functional differential equations determining steady-size distributions in cell populations

1995 ◽  
Vol 32 (01) ◽  
pp. 1-10
Author(s):  
Ziad Taib
Keyword(s):  
Differential Equation ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Differential Equations ◽  
Cell Populations ◽  
Size Distributions ◽  
Multitype Branching Process ◽  
Functional Differential ◽  
Intuitive Interpretation ◽  
Infinite Sum

The functional differential equation y′(x) = ay(λx) + by(x) arises in many different situations. The purpose of this note is to show how it arises in some multitype branching process cell population models. We also show how its solution can be given an intuitive interpretation as the probability density function of an infinite sum of independent but not identically distributed random variables.

A genealogical approach to variable-population-size models in population genetics

1986 ◽  
Vol 23 (02) ◽  
pp. 283-296 ◽  
Author(s):  
Peter Donnelly
Keyword(s):  
Population Genetics ◽  
Branching Process ◽  
Sufficient Conditions ◽  
Process Models ◽  
Moran Model ◽  
Fisher Model ◽  
Variable Population ◽  
Exchangeable Model ◽  
Necessary And Sufficient ◽  
Variable Population Size

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

scholarly journals Intragenomic variation in mutation biases causes underestimation of selection on synonymous codon usage

2021 ◽  
Author(s):  
Alexander L Cope ◽  
Premal Shah
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Codon Usage ◽  
Codon Bias ◽  
Synonymous Codon ◽  
Synonymous Codon Usage ◽  
Mutation Bias ◽  
Biased Gene Conversion ◽  
Intragenomic Variation ◽  
The Impact

Patterns of non-uniform usage of synonymous codons (codon bias) varies across genes in an organism and across species from all domains of life. The bias in codon usage is due to a combination of both non-adaptive (e.g. mutation biases) and adaptive (e.g. natural selection for translation efficiency/accuracy) evolutionary forces. Most population genetics models quantify the effects of mutation bias and selection on shaping codon usage patterns assuming a uniform mutation bias across the genome. However, mutation biases can vary both along and across chromosomes due to processes such as biased gene conversion, potentially obfuscating signals of translational selection. Moreover, estimates of variation in genomic mutation biases are often lacking for non-model organisms. Here, we combine an unsupervised learning method with a population genetics model of synonymous codon bias evolution to assess the impact of intragenomic variation in mutation bias on the strength and direction of natural selection on synonymous codon usage across 49 Saccharomycotina budding yeasts. We find that in the absence of a priori information, unsupervised learning approaches can be used to identify regions evolving under different mutation biases. We find that the impact of intragenomic variation in mutation bias varies widely, even among closely-related species. We show that the overall strength and direction of selection on codon usage can be underestimated by failing to account for intragenomic variation in mutation biases. Interestingly, genes falling into clusters identified by machine learning are also often physically clustered across chromosomes, consistent with processes such as biased gene conversion. Our results indicate the need for more nuanced models of sequence evolution that systematically incorporate the effects of variable mutation biases on codon frequencies.

scholarly journals Galton–Watson and branching process representations of the normalized Perron–Frobenius eigenvector

2019 ◽  
Vol 23 ◽  
pp. 797-802
Author(s):  
Raphaël Cerf ◽  
Joseba Dalmau
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Branching Process ◽  
Invariant Probability Measure ◽  
Classical Formula ◽  
Multitype Branching Process ◽  
Primitive Matrix ◽  
Watson Process

Let A be a primitive matrix and let λ be its Perron–Frobenius eigenvalue. We give formulas expressing the associated normalized Perron–Frobenius eigenvector as a simple functional of a multitype Galton–Watson process whose mean matrix is A, as well as of a multitype branching process with mean matrix e(A−I)t. These formulas are generalizations of the classical formula for the invariant probability measure of a Markov chain.

Applications of Supercomputers in Population Genetics

2015 ◽  
pp. 176-200
Author(s):  
Gerard G. Dumancas
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Genetic Drift ◽  
Critical Role ◽  
Allele Frequency Distribution ◽  
Modern Approach ◽  
Mathematical Discipline ◽  
Modern Evolutionary Synthesis ◽  
Changes Over Time ◽  
Over Time

Population genetics is the study of the frequency and interaction of alleles and genes in population and how this allele frequency distribution changes over time as a result of evolutionary processes such as natural selection, genetic drift, and mutation. This field has become essential in the foundation of modern evolutionary synthesis. Traditionally regarded as a highly mathematical discipline, its modern approach comprises more than the theoretical, lab, and fieldwork. Supercomputers play a critical role in the success of this field and are discussed in this chapter.

Evolution: Medicine’s most basic science

2020 ◽  
pp. 39-42
Author(s):  
Randolph M. Nesse ◽  
Richard Dawkins
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Basic Science ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
The Body ◽  
Clinical Implications ◽  
Trade Offs ◽  
The Cost

The role of evolutionary biology as a basic science for medicine is expanding rapidly. Some evolutionary methods are already widely applied in medicine, such as population genetics and methods for analysing phylogenetic trees. Newer applications come from seeking evolutionary as well as proximate explanations for disease. Traditional medical research is restricted to proximate studies of the body’s mechanism, but separate evolutionary explanations are needed for why natural selection has left many aspects of the body vulnerable to disease. There are six main possibilities: mismatch, infection, constraints, trade-offs, reproduction at the cost of health, and adaptive defences. Like other basic sciences, evolutionary biology has limited direct clinical implications, but it provides essential research methods, encourages asking new questions that foster a deeper understanding of disease, and provides a framework that organizes the facts of medicine.

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