Evolutionary Models In Structured Populations
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Evolutionary Models In Structured Populations
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Author : C. Hadjichrysanthou
language : en
Publisher:
Release Date : 2012
Evolutionary Models In Structured Populations written by C. Hadjichrysanthou and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Evolutionary dynamics have been traditionally studied in infinitely large homogeneous populations where each individual is equally likely to interact with every other individual. However, real populations are finite and characterised by complex interactions among individuals. In this work, the influence of the population structure on the outcome of the evolutionary process is explored. Through an analytic approach, this study first examines the stochastic evolutionary game dynamics following the update rules of the invasion process, an adaptation of the Moran process, on finite populations represented by three simple graphs; the complete graph, the circle and the star graph. The exact formulae for the fixation probability and the speed of the evolutionary process under different conditions are derived, and the effect of the population structure on each of these quantities is studied. The research then considers to what extent the change of the strategy update rules of the evolutionary dynamics can affect the evolutionary process in structured populations compared to the process in homogeneous well-mixed populations. As an example, the evolutionary game dynamics on the extreme heterogeneous structure of the star graph is studied analytically under different update rules. It is shown that in contrast to homogeneous populations, the choice of the update rules might be crucial for the evolution of a non-homogeneous population. Although an analytic investigation of the process is possible when the contact structure of the population has a simple form, this is usually infeasible on complex structures and the use of various assumptions and approximations is necessary. This work introduces an effective method for the approximation of the evolutionary process in populations with a complex structure. Another component of this research work involves the use of game theory for the modelling of a very common phenomenon in the natural world. The models developed examine the evolution of kleptoparasitic populations, foraging populations in which animals can steal the prey from other animals for their survival. A basic game-theoretical model of kleptoparasitism in an infinite homogeneous well-mixed population is extended to structured populations represented by different graphs. The features of the population structure that might favour the appearance of kleptoparasitic behaviour among animals are addressed. In addition, a game-theoretical model is proposed for the investigation of the ecological conditions that encourage foraging animals to share their prey, a very common behaviour occurring in a wide range of animal species.
Data Driven Modelling Of Structured Populations
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Author : Stephen P. Ellner
language : en
Publisher: Springer
Release Date : 2016-05-13
Data Driven Modelling Of Structured Populations written by Stephen P. Ellner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Mathematics categories.
This book is a “How To” guide for modeling population dynamics using Integral Projection Models (IPM) starting from observational data. It is written by a leading research team in this area and includes code in the R language (in the text and online) to carry out all computations. The intended audience are ecologists, evolutionary biologists, and mathematical biologists interested in developing data-driven models for animal and plant populations. IPMs may seem hard as they involve integrals. The aim of this book is to demystify IPMs, so they become the model of choice for populations structured by size or other continuously varying traits. The book uses real examples of increasing complexity to show how the life-cycle of the study organism naturally leads to the appropriate statistical analysis, which leads directly to the IPM itself. A wide range of model types and analyses are presented, including model construction, computational methods, and the underlying theory, with the more technical material in Boxes and Appendices. Self-contained R code which replicates all of the figures and calculations within the text is available to readers on GitHub. Stephen P. Ellner is Horace White Professor of Ecology and Evolutionary Biology at Cornell University, USA; Dylan Z. Childs is Lecturer and NERC Postdoctoral Fellow in the Department of Animal and Plant Sciences at The University of Sheffield, UK; Mark Rees is Professor in the Department of Animal and Plant Sciences at The University of Sheffield, UK.
Evolution In Age Structured Populations
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Author : Brian Charlesworth
language : en
Publisher: Cambridge University Press
Release Date : 1994-06-30
Evolution In Age Structured Populations written by Brian Charlesworth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-30 with Mathematics categories.
The populations of many species of animals and plants are age-structured, i.e. the individuals present at any one time were born over a range of different times, and their fertility and survival depend on age. The properties of such populations are important for interpreting experiments and observations on the genetics of populations for animal and plant breeding, and for understanding the evolution of features of life-histories such as senescence and time of reproduction. In this new edition Brian Charlesworth provides a comprehensive review of the basic mathematical theory of the demography and genetics of age-structured populations. The mathematical level of the book is such that it will be accessible to anyone with a knowledge of basic calculus and linear algebra.
Some Models For Evolution In Geographically Structured Populations With Selection And Selective Migration
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Author : Minoru Ueda
language : en
Publisher:
Release Date : 1985
Some Models For Evolution In Geographically Structured Populations With Selection And Selective Migration written by Minoru Ueda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Biometry categories.
Stochastic Models For Structured Populations
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Author : Sylvie Meleard
language : en
Publisher: Springer
Release Date : 2015-09-03
Stochastic Models For Structured Populations written by Sylvie Meleard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Mathematics categories.
In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.
Game Theoretical Models In Biology
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Author : Mark Broom
language : en
Publisher: CRC Press
Release Date : 2022-08-03
Game Theoretical Models In Biology written by Mark Broom and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-03 with Mathematics categories.
Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology, Second Edition presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well. The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use Python to solve various games. Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behaviour, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modelling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modelling of these diverse biological phenomena. In this thoroughly revised new edition, the authors have added three new chapters on the evolution of structured populations, biological signalling games, and a topical new chapter on evolutionary models of cancer. There are also new sections on games with time constraints that convert simple games to potentially complex nonlinear ones; new models on extortion strategies for the Iterated Prisoner’s Dilemma and on social dilemmas; and on evolutionary models of vaccination, a timely section given the current Covid pandemic. Features Presents a wide range of biological applications of game theory. Suitable for researchers and professionals in mathematical biology and the life sciences, and as a text for postgraduate courses in mathematical biology. Provides numerous examples, exercises, and Python code.
Size Structured Populations
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Author : Bo Ebenman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Size Structured Populations written by Bo Ebenman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
At last both ecology and evolution are covered in this study on the dynamics of size-structured populations. How does natural selection shape growth patterns and life cycles of individuals, and hence the size-structure of populations? This book will stimulate biologists to look into some important and interesting biological problems from a new angle of approach, concerning: - life history evolution, - intraspecific competition and niche theory, - structure and dynamics of ecological communities.
Genetic Structure And Selection In Subdivided Populations Mpb 40
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Author : François Rousset
language : en
Publisher: Princeton University Press
Release Date : 2013-02-15
Genetic Structure And Selection In Subdivided Populations Mpb 40 written by François Rousset and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-15 with Science categories.
Various approaches have been developed to evaluate the consequences of spatial structure on evolution in subdivided populations. This book is both a review and new synthesis of several of these approaches, based on the theory of spatial genetic structure. François Rousset examines Sewall Wright's methods of analysis based on F-statistics, effective size, and diffusion approximation; coalescent arguments; William Hamilton's inclusive fitness theory; and approaches rooted in game theory and adaptive dynamics. Setting these in a framework that reveals their common features, he demonstrates how efficient tools developed within one approach can be applied to the others. Rousset not only revisits classical models but also presents new analyses of more recent topics, such as effective size in metapopulations. The book, most of which does not require fluency in advanced mathematics, includes a self-contained exposition of less easily accessible results. It is intended for advanced graduate students and researchers in evolutionary ecology and population genetics, and will also interest applied mathematicians working in probability theory as well as statisticians.
Discrete Mathematical Models In Population Biology
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Author : Saber N. Elaydi
language : en
Publisher: Springer
Release Date : 2024-10-26
Discrete Mathematical Models In Population Biology written by Saber N. Elaydi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-26 with Mathematics categories.
This text lays the foundation for understanding the beauty and power of discrete-time models. It covers rich mathematical modeling landscapes, each offering deep insights into the dynamics of biological systems. A harmonious balance is achieved between theoretical principles, mathematical rigor, and practical applications. Illustrative examples, numerical simulations, and empirical case studies are provided to enhance mastery of the subject and facilitate the translation of discrete-time mathematical biology into real-world challenges. Mainly geared to upper undergraduates, the text may also be used in graduate courses focusing on discrete-time modeling. Chapters 1–4 constitute the core of the text. Instructors will find the dependence chart quite useful when designing their particular course. This invaluable resource begins with an exploration of single-species models where frameworks for discrete-time modeling are established. Competition models and Predator-prey interactions are examined next followed by evolutionary models, structured population models, and models of infectious diseases. The consequences of periodic variations, seasonal changes, and cyclic environmental factors on population dynamics and ecological interactions are investigated within the realm of periodically forced biological models. This indispensable resource is structured to support educational settings: A first course in biomathematics, introducing students to the fundamental mathematical techniques essential for biological research. A modeling course with a concentration on developing and analyzing mathematical models that encapsulate biological phenomena. An advanced mathematical biology course that offers an in-depth exploration of complex models and sophisticated mathematical frameworks designed to tackle advanced problems in biology. With its clear exposition and methodical approach, this text educates and inspires students and professionals to apply mathematical biology to real-world situations. While minimal knowledge of calculus is required, the reader should have a solid mathematical background in linear algebra.
Mathematical Models Of Ecology And Evolution
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Author : Lai Zhang
language : en
Publisher:
Release Date : 2011
Mathematical Models Of Ecology And Evolution written by Lai Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.