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Modelling Biological Populations in Space and Time

1993-08-26 Mathematics
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Release : 1993-08-26
Genre : Mathematics
Kind : eBook
Book Rating : 550/5 ( reviews)

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Book Synopsis Modelling Biological Populations in Space and Time by : Eric Renshaw

Download or read book Modelling Biological Populations in Space and Time written by Eric Renshaw. This book was released on 1993-08-26. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.

Modelling Population Dynamics

2014-07-16 Medical
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Release : 2014-07-16
Genre : Medical
Kind : eBook
Book Rating : 770/5 ( reviews)

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Book Synopsis Modelling Population Dynamics by : K. B. Newman

Download or read book Modelling Population Dynamics written by K. B. Newman. This book was released on 2014-07-16. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models). The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.

Spatial Dynamics and Pattern Formation in Biological Populations

2021-02-24 Mathematics
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Release : 2021-02-24
Genre : Mathematics
Kind : eBook
Book Rating : 35X/5 ( reviews)

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Book Synopsis Spatial Dynamics and Pattern Formation in Biological Populations by : Ranjit Kumar Upadhyay

Download or read book Spatial Dynamics and Pattern Formation in Biological Populations written by Ranjit Kumar Upadhyay. This book was released on 2021-02-24. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

Introduction to Population Modeling

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 220/5 ( reviews)

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Book Synopsis Introduction to Population Modeling by : J.C. Frauenthal

Download or read book Introduction to Population Modeling written by J.C. Frauenthal. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The text of this monograph represents the author's lecture notes from a course taught in the Department of Applied Mathematics and Statistics at the State University of New York at Stony Brook in the Spring of 1977. On account of its origin as lecture notes, some sections of the text are telegraphic in style while other portions are overly detailed. This stylistic foible has not been modified as it does not appear to detract seriously from the readability and it does help to indicate which topics were stressed. The audience for the course at Stony Brook was composed almost entirely of fourth year undergraduates majoring in the mathematical sciences. All of these students had studied at least four semesters of calculus and one of probability; few had any prior experience with either differential equations or ecology. It seems prudent to point out that the author's background is in engineering and applied mathematics and not in the biological sciences. It is hoped that this is not painfully obvious. -vii- The focus of the monograph is on the formulation and solution of mathematical models; it makes no pretense of being a text in ecology. The idea of a population is employed mainly as a pedagogic tool, providing unity and intuitive appeal to the varied mathematical ideas introduced. If the biological setting is stripped away, what remains can be interpreted as topics on the qualitative behavior of differential and difference equations.

Population Dynamics in Ecological Space and Time

1996-08 Nature
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Release : 1996-08
Genre : Nature
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Population Dynamics in Ecological Space and Time by : Olin E. Rhodes

Download or read book Population Dynamics in Ecological Space and Time written by Olin E. Rhodes. This book was released on 1996-08. Available in PDF, EPUB and Kindle. Book excerpt: As profound threats to ecosystems increase worldwide, ecologists must move beyond studying single communities at a single point in time. All of the dynamic, interconnected spatial and temporal processes that determine the distribution and abundance of species must be understood in order to develop new conservation and management strategies. This volume is the first to integrate mathematical and biological approaches to these crucial topics. The editors include not only a wide variety of theoretical approaches, but also a broad range of experimental and field studies, with chapters written by renowned experts in community ecology, ecological modeling, population genetics, and conservation biology. In addition to providing new insights into well-known topics such as migration, the authors also introduce some less familiar subjects, including bacterial population genetics and ecotoxicology. For anyone interested in the study, management, and conservation of populations, this book will prove to be a valuable resource.

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