A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own.

Author: Sarah P. Otto

Publisher: Princeton University Press

ISBN: 9781400840915

Category: Science

Page: 744

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Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Mathematical Modelling of Evolution

The De Gruyter Series in Mathematics and Life Sciences is devoted to the publication of monographs in the field.

Author: Igor M. Rouzine

Publisher: de Gruyter

ISBN: 3110607891

Category: Mathematics

Page: 181

View: 989

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This book focuses on the mathematical aspects of Darwinian evolution. It starts from the basic model of asexual stochastic evolution of a single isolated locus in the presence of mutation, including the results of different thought experiments. The

Mathematical Models of Social Evolution

Mathematical Models of Social Evolution equips behaviorists and evolutionary biologists with the mathematical knowledge to truly understand the models on which their research depends.

Author: Richard McElreath

Publisher: University of Chicago Press

ISBN: 9780226558288

Category: Social Science

Page: 432

View: 910

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Over the last several decades, mathematical models have become central to the study of social evolution, both in biology and the social sciences. But students in these disciplines often seriously lack the tools to understand them. A primer on behavioral modeling that includes both mathematics and evolutionary theory, Mathematical Models of Social Evolution aims to make the student and professional researcher in biology and the social sciences fully conversant in the language of the field. Teaching biological concepts from which models can be developed, Richard McElreath and Robert Boyd introduce readers to many of the typical mathematical tools that are used to analyze evolutionary models and end each chapter with a set of problems that draw upon these techniques. Mathematical Models of Social Evolution equips behaviorists and evolutionary biologists with the mathematical knowledge to truly understand the models on which their research depends. Ultimately, McElreath and Boyd’s goal is to impart the fundamental concepts that underlie modern biological understandings of the evolution of behavior so that readers will be able to more fully appreciate journal articles and scientific literature, and start building models of their own.

Ecological and Evolutionary Modelling

The aim of this book is to (i) introduce key concepts in ecology and evolution, (ii) explain classic and recent important mathematical models for investigating ecological and evolutionary dynamics, and (iii) provide real examples in ...

Author: Cang Hui

Publisher: Springer

ISBN: 9783319921501

Category: Science

Page: 86

View: 628

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Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify emerging ecological patterns and investigate their hidden mechanisms, we need to rely on the simplicity of mathematical language. Ecological patterns are emerging structures observed in populations, communities and ecosystems. Elucidating drivers behind ecological patterns can greatly improve our knowledge of how ecosystems assemble, function and respond to change and perturbation. Mathematical ecology has, thus, become an important interdisciplinary research field that can provide answers to complex global issues, such as climate change and biological invasions. The aim of this book is to (i) introduce key concepts in ecology and evolution, (ii) explain classic and recent important mathematical models for investigating ecological and evolutionary dynamics, and (iii) provide real examples in ecology/biology/environmental sciences that have used these models to address relevant issues. Readers are exposed to the key concepts, frameworks, and terminology in the studies of ecology and evolution, which will enable them to ask the correct and relevant research questions, and frame the questions using appropriate mathematical models.

Mathematical Modelling of Evolution

For this reason, works with up to four authors are preferred over edited volumes.

Author: Igor M. Rouzine

Publisher:

ISBN: 3110697319

Category:

Page: 260

View: 604

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This two-volume work focuses on the mathematical aspects of Darwinian evolution starting from the basic model of asexual stochastic evolution of a single isolated locus in the presence of mutation. Vol. 2 discusses fitness landscape, genealogy and various mathematical applications to virus evolution. Vol. 1: One-Locus and Multi-Locus Theory and Recombination.

An Introduction to Mathematical Models in Ecology and Evolution

This book is a first step to addressing these difficulties, providing a broad introduction to the key methods and underlying concepts of mathematical models in ecology and evolution.

Author: Mike Gillman

Publisher: John Wiley & Sons

ISBN: 9781444312072

Category: Science

Page: 168

View: 387

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Students often find it difficult to grasp fundamental ecologicaland evolutionary concepts because of their inherently mathematicalnature. Likewise, the application of ecological and evolutionarytheory often requires a high degree of mathematical competence. This book is a first step to addressing these difficulties,providing a broad introduction to the key methods and underlyingconcepts of mathematical models in ecology and evolution. The bookis intended to serve the needs of undergraduate and postgraduateecology and evolution students who need to access the mathematicaland statistical modelling literature essential to theirsubjects. The book assumes minimal mathematics and statistics knowledgewhilst covering a wide variety of methods, many of which are at thefore-front of ecological and evolutionary research. The book alsohighlights the applications of modelling to practical problems suchas sustainable harvesting and biological control. Key features: Written clearly and succinctly, requiring minimal in-depthknowledge of mathematics Introduces students to the use of computer models in bothfields of ecology and evolutionary biology Market - senior undergraduate students and beginningpostgraduates in ecology and evolutionary biology

Mathematical Modeling of Evolution

Tsimring, L.S., Levine, H., and Kessler, D., (1996). RNA virus evolution via a fitness-space model. Phys Rev Lett, 76, 4440–4443. Watterson, G.A., (1975). On the number of segregating sites in genetical models without recombination.

Author: Igor M. Rouzine

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110615456

Category: Mathematics

Page: 181

View: 798

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The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.

Mathematical Modeling of Complex Biological Systems

The book may be used for advanced graduate courses and seminars in biological systems modeling. This book describes the evolution of several socio-biological systems using mathematical kinetic theory.

Author: Abdelghani Bellouquid

Publisher: Springer Science & Business Media

ISBN: 9780817645038

Category: Science

Page: 188

View: 732

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This book describes the evolution of several socio-biological systems using mathematical kinetic theory. Specifically, it deals with modeling and simulations of biological systems whose dynamics follow the rules of mechanics as well as rules governed by their own ability to organize movement and biological functions. It proposes a new biological model focused on the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. Proposed models are related to the generalized Boltzmann equation. The book may be used for advanced graduate courses and seminars in biological systems modeling.

An Introduction to Mathematical Models in Ecology and Evolution

This book is a first step to addressing these difficulties, providing a broad introduction to the key methods and underlying concepts of mathematical models in ecology and evolution.

Author: Michael Gillman

Publisher: Wiley-Blackwell

ISBN: UOM:39015080861266

Category: Science

Page: 158

View: 489

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Students often find it difficult to grasp fundamental ecological and evolutionary concepts because of their inherently mathematical nature. Likewise, the application of ecological and evolutionary theory often requires a high degree of mathematical competence. This book is a first step to addressing these difficulties, providing a broad introduction to the key methods and underlying concepts of mathematical models in ecology and evolution. The book is intended to serve the needs of undergraduate and postgraduate ecology and evolution students who need to access the mathematical and statistical modelling literature essential to their subjects. The book assumes minimal mathematics and statistics knowledge whilst covering a wide variety of methods, many of which are at the fore-front of ecological and evolutionary research. The book also highlights the applications of modelling to practical problems such as sustainable harvesting and biological control. Key features: Written clearly and succinctly, requiring minimal in-depth knowledge of mathematics Introduces students to the use of computer models in both fields of ecology and evolutionary biology Market - senior undergraduate students and beginning postgraduates in ecology and evolutionary biology

Mathematical Methods for Cancer Evolution

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology.

Author: Takashi Suzuki

Publisher: Springer

ISBN: 9789811036712

Category: Mathematics

Page: 144

View: 166

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The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools.The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematical modeling is introduced, overviewing several biological insights, using partial differential equations. Transport and gradient are the main factors, and several models are introduced including the Keller‒Segel systems. The third chapter treats the method of averaging to model the movement of particles, based on mean field theories, employing deterministic and stochastic approaches. Then appropriate parameters for stochastic simulations are examined. The segment model is finally proposed as an application. In the fourth chapter, thermodynamic features of these models and how these structures are applied in mathematical analysis are examined, that is, negative chemotaxis, parabolic systems with non-local term accounting for chemical reactions, mass-conservative reaction-diffusion systems, and competitive systems of chemotaxis. The monograph concludes with the method of the weak scaling limit applied to the Smoluchowski‒Poisson equation.