Fast Variables In Stochastic Population Dynamics
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| Author | : George William Albert Constable |
| Publisher | : Springer |
| Total Pages | : 172 |
| Release | : 2015-07-25 |
| Genre | : Science |
| ISBN | : 3319212184 |
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.
| Author | : George William Albert Constable |
| Publisher | : |
| Total Pages | : |
| Release | : 2015 |
| Genre | : |
| ISBN | : 9783319212197 |
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. .
| Author | : Pierre Magal |
| Publisher | : Springer |
| Total Pages | : 314 |
| Release | : 2008-04-12 |
| Genre | : Mathematics |
| ISBN | : 3540782737 |
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.
| Author | : Russell Lande |
| Publisher | : OUP Oxford |
| Total Pages | : 698 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780198525257 |
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.
| Author | : Peter O. Dunn |
| Publisher | : Oxford University Press |
| Total Pages | : 288 |
| Release | : 2019-07-16 |
| Genre | : Nature |
| ISBN | : 0192557580 |
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.
| Author | : T. Maruyama |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2013-03-13 |
| Genre | : Mathematics |
| ISBN | : 3642930654 |
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.
| Author | : Eric Renshaw |
| Publisher | : OUP Oxford |
| Total Pages | : 665 |
| Release | : 2015-03-19 |
| Genre | : Mathematics |
| ISBN | : 0191060399 |
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
| Author | : Roderick Melnik |
| Publisher | : Springer |
| Total Pages | : 437 |
| Release | : 2017-09-05 |
| Genre | : Mathematics |
| ISBN | : 1493969692 |
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.
| Author | : Robert F. Costantino |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2011-09-17 |
| Genre | : Science |
| ISBN | : 9781461278238 |
The study of populations is becoming increasingly focused on dynamics. We believe there are two reasons for this trend. The ftrst is the impactof nonlinear dynamics with its exciting ideas and colorful language: bifurcations, domains of attraction, chaos, fractals, strange attractors. Complexity, which is so very much a part of biology, now seems to be also a part of mathematics. A second trend is the accessibility of the new concepts. Thebarriers tocommunicationbetween theoristandexperimentalistseemless impenetrable. The active participationofthe experimentalist means that the theory will obtain substance. Our role is the application of the theory of dynamics to the analysis ofbiological populations. We began our work early in 1979 by writing an ordinary differential equation for the rateofchange in adult numbers which was based on an equilibrium model proposed adecadeearlier. Duringthenextfewmonths weftlledournotebookswithstraightforward deductions from the model and its associated biological implications. Slowly, some of the biological observations were explained and papers followed on a variety of topics: genetic and demographic stability, stationary probability distributions for population size,population growth asabirth-deathprocess, natural selectionanddensity-dependent population growth, genetic disequilibrium, and the stationary stochastic dynamics of adult numbers.
| Author | : Stuart K. Allison |
| Publisher | : Taylor & Francis |
| Total Pages | : 621 |
| Release | : 2017-05-18 |
| Genre | : Nature |
| ISBN | : 131741375X |
Ecological restoration is a rapidly evolving discipline that is engaged with developing both methodologies and strategies for repairing damaged and polluted ecosystems and environments. During the last decade the rapid pace of climate change coupled with continuing habitat destruction and the spread of non-native species to new habitats has forced restoration ecologists to re-evaluate their goals and the methods they use. This comprehensive handbook brings together an internationally respected group of established and rising experts in the field. The book begins with a description of current practices and the state of knowledge in particular areas of restoration, and then identifies new directions that will help the field achieve increasing levels of future success. Part I provides basic background about ecological and environmental restoration. Part II systematically reviews restoration in key ecosystem types located throughout the world. In Part III, management and policy issues are examined in detail, offering the first comprehensive treatment of policy relevance in the field, while Part IV looks to the future. Ultimately, good ecological restoration depends upon a combination of good science, policy, planning and outreach – all issues that are addressed in this unrivalled volume.
