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Author: Sarah P. Otto Publisher: Princeton University Press ISBN: 1400840910 Category : Science Languages : en Pages : 745
Book Description
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
Author: Sarah P. Otto Publisher: Princeton University Press ISBN: 1400840910 Category : Science Languages : en Pages : 745
Book Description
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
Author: C. Jeffries Publisher: Springer Science & Business Media ISBN: 1461245508 Category : Mathematics Languages : en Pages : 202
Book Description
Mathematical ecology is the application of mathematics to describe and understand ecosystems. There are two main approaches. One is to describe natural communities and induce statistical patterns or relationships which should generally occur. However, this book is devoted entirely to introducing the student to the second approach: to study deterministic mathematical models and, on the basis of mathematical results on the models, to look for the same patterns or relationships in nature. This book is a compromise between three competing desiderata. It seeks to: maximize the generality of the models; constrain the models to "behave" realistically, that is, to exhibit stability and other features; and minimize the difficulty of presentations of the models. The ultimate goal of the book is to introduce the reader to the general mathematical tools used in building realistic ecosystem models. Just such a model is presented in Chapter Nine. The book should also serve as a stepping-stone both to advanced mathematical works like Stability of Biological Communities by Yu. M. Svirezhev and D. O. Logofet (Mir, Moscow, 1983) and to advanced modeling texts like Freshwater Ecosystems by M. Straskraba and A. H. Gnauch (Elsevier, Amsterdam, 1985).
Author: Mike Gillman Publisher: John Wiley & Sons ISBN: 1444312073 Category : Science Languages : en Pages : 168
Book Description
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
Author: Thomas G. Hallam Publisher: Springer Science & Business Media ISBN: 3642698883 Category : Mathematics Languages : en Pages : 455
Book Description
There isprobably no more appropriate location to hold a course on mathematical ecology than Italy, the countryofVito Volterra, a founding father ofthe subject. The Trieste 1982Autumn Course on Mathematical Ecology consisted of four weeksofvery concentrated scholasticism and aestheticism. The first weeks were devoted to fundamentals and principles ofmathematicalecology. A nucleusofthe material from the lectures presented during this period constitutes this book. The final week and a half of the Course was apportioned to the Trieste Research Conference on Mathematical Ecology whose proceedings have been published as Volume 54, Lecture Notes in Biomathematics, Springer-Verlag. The objectivesofthe first portionofthe course wereambitious and, probably, unattainable. Basic principles of the areas of physiological, population, com munitY, and ecosystem ecology that have solid ecological and mathematical foundations were to be presented. Classical terminology was to be introduced, important fundamental topics were to be developed, some past and some current problems of interest were to be presented, and directions for possible research were to be provided. Due to time constraints, the coverage could not be encyclopedic;many areas covered already have merited treatises of book length. Consequently, preliminary foundation material was covered in some detail, but subject overviewsand area syntheseswerepresented when research frontiers were being discussed. These lecture notes reflect this course philosophy.
Author: Mike Gillman Publisher: John Wiley & Sons ISBN: 1405194898 Category : Science Languages : en Pages : 165
Book Description
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
Author: Leah Edelstein-Keshet Publisher: SIAM ISBN: 9780898719147 Category : Mathematics Languages : en Pages : 629
Book Description
Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.
Author: Edward Beltrami Publisher: Academic Press ISBN: 0124046932 Category : Social Science Languages : en Pages : 281
Book Description
Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book
Author: Richard McElreath Publisher: University of Chicago Press ISBN: 0226558282 Category : Social Science Languages : en Pages : 429
Book Description
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.
Author: Yasuhiro Takeuchi Publisher: Springer Science & Business Media ISBN: 3540344284 Category : Mathematics Languages : en Pages : 189
Book Description
This volume discusses the rich and interesting properties of dynamical systems that appear in ecology and environmental sciences. It provides a fascinating survey of the theory of dynamical systems in ecology and environmental science. Each chapter introduces students and scholars to the state-of-the-art in an exciting area, presents new results, and inspires future contributions to mathematical modeling in ecology and environmental sciences.
Author: Fred Brauer Publisher: Springer Science & Business Media ISBN: 1475735162 Category : Science Languages : en Pages : 432
Book Description
The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.
Author: Sarah P. Otto
Author: Sarah P. Otto
Author: C. Jeffries
Author: Mike Gillman
Author: Thomas G. Hallam
Author: Mike Gillman
Author: Leah Edelstein-Keshet
Author: Edward Beltrami
Author: Richard McElreath
Author: Yasuhiro Takeuchi
Author: Fred Brauer