Download or read book Fast Variables in Stochastic Population Dynamics written by George William Albert Constable and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike. Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply. While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology. .

Download or read book Fast Variables in Stochastic Population Dynamics written by George William Albert Constable and published by Springer. This book was released on 2015-07-25 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike. Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply. While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.

Download or read book Fast Timescales in Stochastic Population Dynamics written by George William Albert Constable and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Population Processes written by Eric Renshaw and published by Oxford University Press. This book was released on 2015 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reference text presenting stochastic processes and a range of approximation and simulation techniques for extracting behavioural information in the context of stochastic population dynamics.

Download or read book Stochastic Differential Equations written by Michael J. Panik and published by John Wiley & Sons. This book was released on 2017-03-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: A beginner’s guide to stochastic growth modeling The chief advantage of stochastic growth models over deterministic models is that they combine both deterministic and stochastic elements of dynamic behaviors, such as weather, natural disasters, market fluctuations, and epidemics. This makes stochastic modeling a powerful tool in the hands of practitioners in fields for which population growth is a critical determinant of outcomes. However, the background requirements for studying SDEs can be daunting for those who lack the rigorous course of study received by math majors. Designed to be accessible to readers who have had only a few courses in calculus and statistics, this book offers a comprehensive review of the mathematical essentials needed to understand and apply stochastic growth models. In addition, the book describes deterministic and stochastic applications of population growth models including logistic, generalized logistic, Gompertz, negative exponential, and linear. Ideal for students and professionals in an array of fields including economics, population studies, environmental sciences, epidemiology, engineering, finance, and the biological sciences, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling: • Provides precise definitions of many important terms and concepts and provides many solved example problems • Highlights the interpretation of results and does not rely on a theorem-proof approach • Features comprehensive chapters addressing any background deficiencies readers may have and offers a comprehensive review for those who need a mathematics refresher • Emphasizes solution techniques for SDEs and their practical application to the development of stochastic population models An indispensable resource for students and practitioners with limited exposure to mathematics and statistics, Stochastic Differential Equations: An Introduction with Applications in Population Dynamics Modeling is an excellent fit for advanced undergraduates and beginning graduate students, as well as practitioners who need a gentle introduction to SDEs. Michael J. Panik, PhD, is Professor in the Department of Economics, Barney School of Business and Public Administration at the University of Hartford in Connecticut. He received his PhD in Economics from Boston College and is a member of the American Mathematical Society, The American Statistical Association, and The Econometric Society.

Download or read book Stochastic Models for Structured Populations written by Sylvie Meleard and published by Springer. This book was released on 2015-09-03 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book An Introduction to Continuous Time Stochastic Processes written by Vincenzo Capasso and published by Springer Science & Business Media. This book was released on 2012-07-27 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Download or read book Structured Population Models in Biology and Epidemiology written by Pierre Magal and published by Springer. This book was released on 2008-04-12 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this new century mankind faces ever more challenging environmental and publichealthproblems,suchaspollution,invasionbyexoticspecies,theem- gence of new diseases or the emergence of diseases into new regions (West Nile virus,SARS,Anthrax,etc.),andtheresurgenceofexistingdiseases(in?uenza, malaria, TB, HIV/AIDS, etc.). Mathematical models have been successfully used to study many biological, epidemiological and medical problems, and nonlinear and complex dynamics have been observed in all of those contexts. Mathematical studies have helped us not only to better understand these problems but also to ?nd solutions in some cases, such as the prediction and control of SARS outbreaks, understanding HIV infection, and the investi- tion of antibiotic-resistant infections in hospitals. Structuredpopulationmodelsdistinguishindividualsfromoneanother- cording to characteristics such as age, size, location, status, and movement, to determine the birth, growth and death rates, interaction with each other and with environment, infectivity, etc. The goal of structured population models is to understand how these characteristics a?ect the dynamics of these models and thus the outcomes and consequences of the biological and epidemiolo- cal processes. There is a very large and growing body of literature on these topics. This book deals with the recent and important advances in the study of structured population models in biology and epidemiology. There are six chapters in this book, written by leading researchers in these areas.

Download or read book Effects of Climate Change on Birds written by Peter O. Dunn and published by Oxford University Press. This book was released on 2019-07-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Climate change issues are attracting rapidly increasing interest from a wide range of biologists due to their unprecedented effects on global biodiversity, although there remains a lack of general knowledge as to the environmental consequences of such rapid change. Compared with any other class of animals, birds provide more long-term data and extensive time series, a more geographically and taxonomically diverse source of information, a richer source of data on a greater range of topics dealing with the effects of climate change, and a longer tradition of extensive research. The first edition of the book was widely cited and this new edition continues to provide an exhaustive and up-to-date synthesis of our rapidly expanding level of knowledge as it relates to birds, highlighting new methods and areas for future research.

Download or read book Equilibrium and Extinction in Stochastic Population Dynamics written by H. Roozen and published by . This book was released on 1986 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Population Theories written by D. Ludwig and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. 1 Continuous Time . •••. ••••••••••. •••••••••••••••••••. ••••••••. ••••.

Download or read book Stochastic Population Processes written by Eric Renshaw and published by OUP Oxford. This book was released on 2015-03-19 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: The vast majority of random processes in the real world have no memory - the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation

Download or read book Stochastic Problems in Population Genetics written by T. Maruyama and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are" notes based on courses in Theoretical Population Genetics given at the University of Texas at Houston during the winter quarter, 1974, and at the University of Wisconsin during the fall semester, 1976. These notes explore problems of population genetics and evolution involving stochastic processes. Biological models and various mathematical techniques are discussed. Special emphasis is given to the diffusion method and an attempt is made to emphasize the underlying unity of various problems based on the Kolmogorov backward equation. A particular effort was made to make the subject accessible to biology students who are not familiar with stochastic processes. The references are not exhaustive but were chosen to provide a starting point for the reader interested in pursuing the subject further. Acknowledgement I would like to use this opportunity to express my thanks to Drs. J. F. Crow, M. Nei and W. J. Schull for their hospitality during my stays at their universities. I am indebted to Dr. M. Kimura for his continuous encouragement. My thanks also go to the small but resolute groups of.students, visitors and colleagues whose enthusiasm was a great source of encouragement. I am especially obliged to Dr. Martin Curie-Cohen and Dr. Crow for reading a large part eX the manuscript and making many valuable comments. Special gratitude is expressed to Miss Sumiko Imamiya for her patience and endurance and for her efficient preparation of the manuscript.

Download or read book Stochastic Dynamics and Irreversibility written by Tânia Tomé and published by Springer. This book was released on 2014-11-26 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomena both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of physics and chemistry and for those interested in stochastic dynamics. It provides, by means of examples and problems, a comprehensive and detailed explanation of the theory and its applications.

Download or read book Equilibrium and Extinction in Stochastic Population Dynamics written by Henricus Nicolaas Maria Roozen and published by . This book was released on 1986 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recent Progress and Modern Challenges in Applied Mathematics Modeling and Computational Science written by Roderick Melnik and published by Springer. This book was released on 2017-09-05 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.

Download or read book Stochastic Population Dynamics in Ecology and Conservation written by Russell Lande and published by OUP Oxford. This book was released on 2003 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Demographic and environmental stochasticity -- 2. Extinction dynamics -- 3. Age structure -- 4. Spatial structure -- 5. Population viability analysis -- 6. Sustainable harvesting -- 7. Species diversity -- 8. Community dynamics.