A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto
Publisher: Princeton University Press
ISBN: 9781400840915
Release Date: 2011-09-19
Genre: Science

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
Publisher: Princeton University Press
ISBN: 9780691123448
Release Date: 2007-03-12
Genre: Mathematics

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: 9781139463652
Release Date: 2007-06-28
Genre: Medical

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: 9781316584057
Release Date: 2001-07-19
Genre: Nature

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.

Extended Heredity

Author: Russell Bonduriansky
Publisher: Princeton University Press
ISBN: 9781400890156
Release Date: 2018-04-17
Genre: Science

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.

Ecological Models and Data in R

Author: Benjamin M. Bolker
Publisher: Princeton University Press
ISBN: 9780691125220
Release Date: 2008-07-21
Genre: Computers

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.

The Princeton Guide to Ecology

Author: Simon A. Levin
Publisher: Princeton University Press
ISBN: 1400833027
Release Date: 2009-07-27
Genre: Nature

The Princeton Guide to Ecology is a concise, authoritative one-volume reference to the field's major subjects and key concepts. Edited by eminent ecologist Simon Levin, with contributions from an international team of leading ecologists, the book contains more than ninety clear, accurate, and up-to-date articles on the most important topics within seven major areas: autecology, population ecology, communities and ecosystems, landscapes and the biosphere, conservation biology, ecosystem services, and biosphere management. Complete with more than 200 illustrations (including sixteen pages in color), a glossary of key terms, a chronology of milestones in the field, suggestions for further reading on each topic, and an index, this is an essential volume for undergraduate and graduate students, research ecologists, scientists in related fields, policymakers, and anyone else with a serious interest in ecology. Explains key topics in one concise and authoritative volume Features more than ninety articles written by an international team of leading ecologists Contains more than 200 illustrations, including sixteen pages in color Includes glossary, chronology, suggestions for further reading, and index Covers autecology, population ecology, communities and ecosystems, landscapes and the biosphere, conservation biology, ecosystem services, and biosphere management

The Theoretical Biologist s Toolbox

Author: Marc Mangel
Publisher: Cambridge University Press
ISBN: 9781139455862
Release Date: 2006-07-27
Genre: Science

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.

Essential Mathematical Biology

Author: Nicholas F. Britton
Publisher: Springer Science & Business Media
ISBN: 9781447100492
Release Date: 2012-12-06
Genre: Mathematics

This self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.

How to be a Quantitative Ecologist

Author: Jason Matthiopoulos
Publisher: John Wiley & Sons
ISBN: 1119991722
Release Date: 2011-04-12
Genre: Mathematics

Ecological research is becoming increasingly quantitative, yet students often opt out of courses in mathematics and statistics, unwittingly limiting their ability to carry out research in the future. This textbook provides a practical introduction to quantitative ecology for students and practitioners who have realised that they need this opportunity. The text is addressed to readers who haven't used mathematics since school, who were perhaps more confused than enlightened by their undergraduate lectures in statistics and who have never used a computer for much more than word processing and data entry. From this starting point, it slowly but surely instils an understanding of mathematics, statistics and programming, sufficient for initiating research in ecology. The book’s practical value is enhanced by extensive use of biological examples and the computer language R for graphics, programming and data analysis. Key Features: Provides a complete introduction to mathematics statistics and computing for ecologists. Presents a wealth of ecological examples demonstrating the applied relevance of abstract mathematical concepts, showing how a little technique can go a long way in answering interesting ecological questions. Covers elementary topics, including the rules of algebra, logarithms, geometry, calculus, descriptive statistics, probability, hypothesis testing and linear regression. Explores more advanced topics including fractals, non-linear dynamical systems, likelihood and Bayesian estimation, generalised linear, mixed and additive models, and multivariate statistics. R boxes provide step-by-step recipes for implementing the graphical and numerical techniques outlined in each section. How to be a Quantitative Ecologist provides a comprehensive introduction to mathematics, statistics and computing and is the ideal textbook for late undergraduate and postgraduate courses in environmental biology. "With a book like this, there is no excuse for people to be afraid of maths, and to be ignorant of what it can do." —Professor Tim Benton, Faculty of Biological Sciences, University of Leeds, UK

The Comparative Approach in Evolutionary Anthropology and Biology

Author: Charles L. Nunn
Publisher: University of Chicago Press
ISBN: 9780226608983
Release Date: 2011-11-30
Genre: Science

Comparison is fundamental to evolutionary anthropology. When scientists study chimpanzee cognition, for example, they compare chimp performance on cognitive tasks to the performance of human children on the same tasks. And when new fossils are found, such as those of the tiny humans of Flores, scientists compare these remains to other fossils and contemporary humans. Comparison provides a way to draw general inferences about the evolution of traits and therefore has long been the cornerstone of efforts to understand biological and cultural diversity. Individual studies of fossilized remains, living species, or human populations are the essential units of analysis in a comparative study; bringing these elements into a broader comparative framework allows the puzzle pieces to fall into place, creating a means of testing adaptive hypotheses and generating new ones. With this book, Charles L. Nunn intends to ensure that evolutionary anthropologists and organismal biologists have the tools to realize the potential of comparative research. Nunn provides a wide-ranging investigation of the comparative foundations of evolutionary anthropology in past and present research, including studies of animal behavior, biodiversity, linguistic evolution, allometry, and cross-cultural variation. He also points the way to the future, exploring the new phylogeny-based comparative approaches and offering a how-to manual for scientists who wish to incorporate these new methods into their research.

Biocalculus Calculus for Life Sciences

Author: James Stewart
Publisher: Cengage Learning
ISBN: 9781133109631
Release Date: 2014-09-08
Genre: Mathematics

The chief goal in this textbook is to show students how calculus relates to biology, with a style that maintains rigor without being overly formal. The text motivates and illustrates the topics of calculus with examples drawn from many areas of biology, including genetics, biomechanics, medicine, pharmacology, physiology, ecology, epidemiology, and evolution, to name a few. Particular attention has been paid to ensuring that all applications of the mathematics are genuine, and references to the primary biological literature for many of these has been provided so that students and instructors can explore the applications in greater depth. Although the focus is on the interface between mathematics and the life sciences, the logical structure of the book is motivated by the mathematical material. Students will come away from a course based on this book with a sound knowledge of mathematics and an understanding of the importance of mathematical arguments. Equally important, they will also come away with a clear understanding of how these mathematical concepts and techniques are central in the life sciences. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Modeling Infectious Diseases in Humans and Animals

Author: Matt J. Keeling
Publisher: Princeton University Press
ISBN: 9781400841035
Release Date: 2011-09-19
Genre: Science

For epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recent developments as well as more traditional approaches. Matt Keeling and Pejman Rohani move from modeling with simple differential equations to more recent, complex models, where spatial structure, seasonal "forcing," or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory. In each of the eight chapters, they deal with a specific modeling approach or set of techniques designed to capture a particular biological factor. They illustrate the methodology used with examples from recent research literature on human and infectious disease modeling, showing how such techniques can be used in practice. Diseases considered include BSE, foot-and-mouth, HIV, measles, rubella, smallpox, and West Nile virus, among others. Particular attention is given throughout the book to the development of practical models, useful both as predictive tools and as a means to understand fundamental epidemiological processes. To emphasize this approach, the last chapter is dedicated to modeling and understanding the control of diseases through vaccination, quarantine, or culling. Comprehensive, practical introduction to infectious disease modeling Builds from simple to complex predictive models Models and methodology fully supported by examples drawn from research literature Practical models aid students' understanding of fundamental epidemiological processes For many of the models presented, the authors provide accompanying programs written in Java, C, Fortran, and MATLAB In-depth treatment of role of modeling in understanding disease control

Quantifying Life

Author: Dmitry A. Kondrashov
Publisher: University of Chicago Press
ISBN: 9780226371931
Release Date: 2016-08-04
Genre: Science

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.

Evolution Development the Predictable Genome

Author: David Lawrence Stern
Publisher: Roberts & Company
ISBN: STANFORD:36105215333076
Release Date: 2011
Genre: Science

For too long, efforts to synthesize evolution and development have failed to build a united view of the origins and evolution of biological diversity. In this groundbreaking book, David Stern sets out to draw evolutionary biology and developmental biology together by cutting through the differences that divide the disciplines and by revealing their deeper similarities. He draws upon the insights of generations of evolutionary biologists and scores of developmental biologists to build a solid foundation for future investigation of the genetic and developmental causes of diversity. Along the way, and in plain English, he explicates many of the guiding principles of evolution, population genetics, and developmental biology. Each chapter offers a clear review of fundamental principles, together with thoughtprovoking ideas that will be tested only with data emerging from current and future studies. With the basic principles established, he then offers a new way of thinking about development--backwards--to clarify precisely how the mechanisms of development influence evolution. In the same spirit, he takes a fresh look at evolution in populations, arguing that population history influences precisely how developmental mechanisms evolve. Both Stern's new perspective on development and his reassessment of the role of populations leads to the surprising conclusion that the evolution of genomes appears to be predictable. Stern argues that developmental biology and evolutionary biology are intertwined: it is impossible to understand one of them fully without understanding the other. This book provides a clear and wide-ranging introduction to evolution and development for the basic reader; graduate students will be introduced to the cutting-edge of research in evolutionary developmental biology; and experts in evolution or development will receive both an uncomplicated introduction to the other discipline and an abundance of new, provocative ideas.