A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto,Troy Day

Publisher: Princeton University Press

ISBN: 1400840910

Category: Science

Page: 744

View: 6986

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

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto,Troy Day

Publisher: Princeton University Press

ISBN: 0691123446

Category: Mathematics

Page: 732

View: 1414

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

Modelling for Field Biologists and Other Interesting People

Author: Hanna Kokko

Publisher: Cambridge University Press

ISBN: 1139463659

Category: Medical

Page: N.A

View: 8511

Students of evolutionary and behavioural ecology are often unfamiliar with mathematical techniques, though much of biology relies on mathematics. Evolutionary ideas are often complex, meaning that the logic of hypotheses proposed should not only be tested empirically but also mathematically. There are numerous different modelling tools used by ecologists, ranging from population genetic 'bookkeeping', to game theory and individual-based computer simulations. Due to the many different modelling options available, it is often difficult to know where to start. Hanna Kokko has designed this 2007 book to help with these decisions. Each method described is illustrated with one or two biologically interesting examples that have been chosen to help overcome fears of many biologists when faced with mathematical work, whilst also providing the programming code (Matlab) for each problem. Aimed primarily at students of evolutionary and behavioural ecology, this book will be of interest to any biologist interested in mathematical modelling.

Elements of Mathematical Ecology

Author: Mark Kot

Publisher: Cambridge University Press

ISBN: 1316584054

Category: Nature

Page: N.A

View: 9243

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

Mathematical Ecology of Populations and Ecosystems

Author: John Pastor

Publisher: John Wiley & Sons

ISBN: 1444358456

Category: Science

Page: 344

View: 7962

Population ecologists study how births and deaths affect the dynamics of populations and communities, while ecosystem ecologists study how species control the flux of energy and materials through food webs and ecosystems. Although all these processes occur simultaneously in nature, the mathematical frameworks bridging the two disciplines have developed independently. Consequently, this independent development of theory has impeded the cross-fertilization of population and ecosystem ecology. Using recent developments from dynamical systems theory, this advanced undergraduate/graduate level textbook shows how to bridge the two disciplines seamlessly. The book shows how bifurcations between the solutions of models can help understand regime shifts in natural populations and ecosystems once thresholds in rates of births, deaths, consumption, competition, nutrient inputs, and decay are crossed. Mathematical Ecology is essential reading for students of ecology who have had a first course in calculus and linear algebra or students in mathematics wishing to learn how dynamical systems theory can be applied to ecological problems.

Extended Heredity

A New Understanding of Inheritance and Evolution

Author: Russell Bonduriansky,Troy Day

Publisher: Princeton University Press

ISBN: 1400890152

Category: Science

Page: 280

View: 1619

How genes are not the only basis of heredity—and what this means for evolution, human life, and disease For much of the twentieth century it was assumed that genes alone mediate the transmission of biological information across generations and provide the raw material for natural selection. In Extended Heredity, leading evolutionary biologists Russell Bonduriansky and Troy Day challenge this premise. Drawing on the latest research, they demonstrate that what happens during our lifetimes--and even our grandparents' and great-grandparents' lifetimes—can influence the features of our descendants. On the basis of these discoveries, Bonduriansky and Day develop an extended concept of heredity that upends ideas about how traits can and cannot be transmitted across generations. By examining the history of the gene-centered view in modern biology and reassessing fundamental tenets of evolutionary theory, Bonduriansky and Day show that nongenetic inheritance—involving epigenetic, environmental, behavioral, and cultural factors—could play an important role in evolution. The discovery of nongenetic inheritance therefore has major implications for key questions in evolutionary biology, as well as human health. Extended Heredity reappraises long-held ideas and opens the door to a new understanding of inheritance and evolution.

The Theoretical Biologist's Toolbox

Quantitative Methods for Ecology and Evolutionary Biology

Author: Marc Mangel

Publisher: Cambridge University Press

ISBN: 1139455869

Category: Science

Page: N.A

View: 9627

Mathematical modelling is widely used in ecology and evolutionary biology and it is a topic that many biologists find difficult to grasp. In this new textbook Marc Mangel provides a no-nonsense introduction to the skills needed to understand the principles of theoretical and mathematical biology. Fundamental theories and applications are introduced using numerous examples from current biological research, complete with illustrations to highlight key points. Exercises are also included throughout the text to show how theory can be applied and to test knowledge gained so far. Suitable for advanced undergraduate courses in theoretical and mathematical biology, this book forms an essential resource for anyone wanting to gain an understanding of theoretical ecology and evolution.

Theoretical Ecology

Principles and Applications

Author: Robert May

Publisher: Oxford University Press on Demand

ISBN: 0199209995

Category: Computers

Page: 257

View: 4034

Robert May's seminal book has played a central role in the development of ecological science. Originally published in 1976, this influential text has overseen the transition of ecology from an observational and descriptive subject to one with a solid conceptual core. Indeed, it is a testament to its influence that a great deal of the novel material presented in the earlier editions has now been incorporated into standard undergraduate textbooks. It is now a quarter of a century since the publication of the second edition, and a thorough revision is timely. Theoretical Ecology provides a succinct, up-to-date overview of the field set in the context of applications, thereby bridging the traditional division of theory and practice. It describes the recent advances in our understanding of how interacting populations of plants and animals change over time and space, in response to natural or human-created disturbance. In an integrated way, initial chapters give an account of the basic principles governing the structure, function, and temporal and spatial dynamics of populations and communities of plants and animals. Later chapters outline applications of these ideas to practical issues including fisheries, infectious diseases, tomorrow's food supplies, climate change, and conservation biology. Throughout the book, emphasis is placed on questions which as yet remain unanswered. The editors have invited the top scientists in the field to collaborate with the next generation of theoretical ecologists. The result is an accessible, advanced textbook suitable for senior undergraduate and graduate level students as well as researchers in the fields of ecology, mathematical biology, environment and resources management. It will also be of interest to the general reader seeking a better understanding of a range of global environmental problems.

Ecological Models and Data in R

Author: Benjamin M. Bolker

Publisher: Princeton University Press

ISBN: 0691125228

Category: Computers

Page: 396

View: 4234

Introduction and background; Exploratory data analysis and graphics; Deterministic functions for ecological modeling; Probability and stochastic distributions for ecological modeling; Stochatsic simulation and power analysis; Likelihood and all that; Optimization and all that; Likelihood examples; Standar statistics revisited; Modeling variance; Dynamic models.

Dynamic Models in Biology

Author: Stephen P. Ellner,John Guckenheimer

Publisher: Princeton University Press

ISBN: 1400840961

Category: Science

Page: 352

View: 6585

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.

Mathematical Biology II

Spatial Models and Biomedical Applications

Author: James D. Murray

Publisher: Springer Science & Business Media

ISBN: 0387952284

Category: Mathematics

Page: 814

View: 558

This richly illustrated third edition provides a thorough training in practical mathematical biology and shows how exciting mathematical challenges can arise from a genuinely interdisciplinary involvement with the biosciences. It has been extensively updated and extended to cover much of the growth of mathematical biology. From the reviews: ""This book, a classical text in mathematical biology, cleverly combines mathematical tools with subject area sciences."--SHORT BOOK REVIEWS

Applied Mathematical Ecology

Author: Simon A. Levin,Thomas G. Hallam,Louis J. Gross

Publisher: Springer Science & Business Media

ISBN: 3642613179

Category: Mathematics

Page: 491

View: 491

The Second Autumn Course on Mathematical Ecology was held at the Intern ational Centre for Theoretical Physics in Trieste, Italy in November and December of 1986. During the four year period that had elapsed since the First Autumn Course on Mathematical Ecology, sufficient progress had been made in applied mathemat ical ecology to merit tilting the balance maintained between theoretical aspects and applications in the 1982 Course toward applications. The course format, while similar to that of the first Autumn Course on Mathematical Ecology, consequently focused upon applications of mathematical ecology. Current areas of application are almost as diverse as the spectrum covered by ecology. The topiys of this book reflect this diversity and were chosen because of perceived interest and utility to developing countries. Topical lectures began with foundational material mostly derived from Math ematical Ecology: An Introduction (a compilation of the lectures of the 1982 course published by Springer-Verlag in this series, Volume 17) and, when possible, progressed to the frontiers of research. In addition to the course lectures, workshops were arranged for small groups to supplement and enhance the learning experience. Other perspectives were provided through presentations by course participants and speakers at the associated Research Conference. Many of the research papers are in a companion volume, Mathematical Ecology: Proceedings Trieste 1986, published by World Scientific Press in 1988. This book is structured primarily by application area. Part II provides an introduction to mathematical and statistical applications in resource management.

Modelling Complex Ecological Dynamics

An Introduction into Ecological Modelling for Students, Teachers & Scientists

Author: Fred Jopp,Hauke Reuter,Broder Breckling

Publisher: Springer Science & Business Media

ISBN: 9783642050299

Category: Science

Page: 397

View: 8547

Model development is of vital importance for understanding and management of ecological processes. Identifying the complex relationships between ecological patterns and processes is a crucial task. Ecological modelling—both qualitatively and quantitatively—plays a vital role in analysing ecological phenomena and for ecological theory. This textbook provides a unique overview of modelling approaches. Representing the state-of-the-art in modern ecology, it shows how to construct and work with various different model types. It introduces the background of each approach and its application in ecology. Differential equations, matrix approaches, individual-based models and many other relevant modelling techniques are explained and demonstrated with their use. The authors provide links to software tools and course materials. With chapters written by leading specialists, “Modelling Complex Ecological Dynamics” is an essential contribution to expand the qualification of students, teachers and scientists alike.

Population Biology

Concepts and Models

Author: Alan Hastings

Publisher: Springer Science & Business Media

ISBN: 1475727313

Category: Science

Page: 220

View: 6645

Population biology has been investigated quantitatively for many decades, resulting in a rich body of scientific literature. Ecologists often avoid this literature, put off by its apparently formidable mathematics. This textbook provides an introduction to the biology and ecology of populations by emphasizing the roles of simple mathematical models in explaining the growth and behavior of populations. The author only assumes acquaintance with elementary calculus, and provides tutorial explanations where needed to develop mathematical concepts. Examples, problems, extensive marginal notes and numerous graphs enhance the book's value to students in classes ranging from population biology and population ecology to mathematical biology and mathematical ecology. The book will also be useful as a supplement to introductory courses in ecology.

Numerical Ecology

Author: Pierre Legendre,Louis Legendre

Publisher: Elsevier

ISBN: 0444538682

Category: SCIENCE

Page: 990

View: 4962

The book describes and discusses the numerical methods which are successfully being used for analysing ecological data, using a clear and comprehensive approach. These methods are derived from the fields of mathematical physics, parametric and nonparametric statistics, information theory, numerical taxonomy, archaeology, psychometry, sociometry, econometry and others. Compared to the first edition of Numerical Ecology, this second edition includes three new chapters, dealing with the analysis of semiquantitative data, canonical analysis and spatial analysis. New sections have been added to almost all other chapters. There are sections listing available computer programs and packages at the end of several chapters. As in the previous English and French editions, there are numerous examples from the ecological literature, and the choice of methods is facilitated by several synoptic tables.

Individual-based Modeling and Ecology

Author: Volker Grimm,Steven F. Railsback

Publisher: Princeton University Press

ISBN: 1400850622

Category: Science

Page: 448

View: 385

Individual-based models are an exciting and widely used new tool for ecology. These computational models allow scientists to explore the mechanisms through which population and ecosystem ecology arises from how individuals interact with each other and their environment. This book provides the first in-depth treatment of individual-based modeling and its use to develop theoretical understanding of how ecological systems work, an approach the authors call "individual-based ecology." Grimm and Railsback start with a general primer on modeling: how to design models that are as simple as possible while still allowing specific problems to be solved, and how to move efficiently through a cycle of pattern-oriented model design, implementation, and analysis. Next, they address the problems of theory and conceptual framework for individual-based ecology: What is "theory"? That is, how do we develop reusable models of how system dynamics arise from characteristics of individuals? What conceptual framework do we use when the classical differential equation framework no longer applies? An extensive review illustrates the ecological problems that have been addressed with individual-based models. The authors then identify how the mechanics of building and using individual-based models differ from those of traditional science, and provide guidance on formulating, programming, and analyzing models. This book will be helpful to ecologists interested in modeling, and to other scientists interested in agent-based modeling.

Quantitative Ecology and Evolutionary Biology

Integrating Models with Data

Author: Otso Ovaskainen,Henrik Johan De Knegt,Maria Del Mar Delgado

Publisher: Oxford University Press

ISBN: 0198714866

Category:

Page: 304

View: 9830

This novel, interdisciplinary text achieves an integration of empirical data and theory with the aid of mathematical models and statistical methods. The emphasis throughout is on spatial ecology and evolution, especially on the interplay between environmental heterogeneity and biological processes. The book provides a coherent theme by interlinking the modelling approaches used for different subfields of spatial ecology: movement ecology, population ecology, community ecology, and genetics and evolutionary ecology (each being represented by a separate chapter). Each chapter starts by describing the concept of each modelling approach in its biological context, goes on to present the relevant mathematical models and statistical methods, and ends with a discussion of the benefits and limitations of each approach. The concepts and techniques discussed throughout the book are illustrated throughout with the help of empirical examples. This is an advanced text suitable for any biologist interested in the integration of empirical data and theory in spatial ecology/evolution through the use of quantitative/statistical methods and mathematical models. The book will also be of relevance and use as a textbook for graduate-level courses in spatial ecology, ecological modelling, theoretical ecology, and statistical ecology.

Mathematical Models in Biology

An Introduction

Author: Elizabeth S. Allman,John A. Rhodes

Publisher: Cambridge University Press

ISBN: 9780521525862

Category: Mathematics

Page: 370

View: 901

Linear and non-linear models of populations, molecular evolution, phylogenetic tree construction, genetics, and infectious diseases are presented with minimal prerequisites.

Quantifying Life

A Symbiosis of Computation, Mathematics, and Biology

Author: Dmitry A. Kondrashov

Publisher: University of Chicago Press

ISBN: 022637193X

Category: Science

Page: 304

View: 3073

Since the time of Isaac Newton, physicists have used mathematics to describe the behavior of matter of all sizes, from subatomic particles to galaxies. In the past three decades, as advances in molecular biology have produced an avalanche of data, computational and mathematical techniques have also become necessary tools in the arsenal of biologists. But while quantitative approaches are now providing fundamental insights into biological systems, the college curriculum for biologists has not caught up, and most biology majors are never exposed to the computational and probabilistic mathematical approaches that dominate in biological research. With Quantifying Life, Dmitry A. Kondrashov offers an accessible introduction to the breadth of mathematical modeling used in biology today. Assuming only a foundation in high school mathematics, Quantifying Life takes an innovative computational approach to developing mathematical skills and intuition. Through lessons illustrated with copious examples, mathematical and programming exercises, literature discussion questions, and computational projects of various degrees of difficulty, students build and analyze models based on current research papers and learn to implement them in the R programming language. This interplay of mathematical ideas, systematically developed programming skills, and a broad selection of biological research topics makes Quantifying Life an invaluable guide for seasoned life scientists and the next generation of biologists alike.

Ecological Statistics

Contemporary theory and application

Author: Gordon A. Fox,Simoneta Negrete-Yankelevich,Vinicio J. Sosa

Publisher: OUP Oxford

ISBN: 0191652881

Category: Science

Page: 400

View: 5996

The application and interpretation of statistics are central to ecological study and practice. Ecologists are now asking more sophisticated questions than in the past. These new questions, together with the continued growth of computing power and the availability of new software, have created a new generation of statistical techniques. These have resulted in major recent developments in both our understanding and practice of ecological statistics. This novel book synthesizes a number of these changes, addressing key approaches and issues that tend to be overlooked in other books such as missing/censored data, correlation structure of data, heterogeneous data, and complex causal relationships. These issues characterize a large proportion of ecological data, but most ecologists' training in traditional statistics simply does not provide them with adequate preparation to handle the associated challenges. Uniquely, Ecological Statistics highlights the underlying links among many statistical approaches that attempt to tackle these issues. In particular, it gives readers an introduction to approaches to inference, likelihoods, generalized linear (mixed) models, spatially or phylogenetically-structured data, and data synthesis, with a strong emphasis on conceptual understanding and subsequent application to data analysis. Written by a team of practicing ecologists, mathematical explanations have been kept to the minimum necessary. This user-friendly textbook will be suitable for graduate students, researchers, and practitioners in the fields of ecology, evolution, environmental studies, and computational biology who are interested in updating their statistical tool kits. A companion web site provides example data sets and commented code in the R language.