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

Otto, Sarah P.; Day, Troy

Hardcover

ISBN 10: 0691123446 ISBN 13: 9780691123448

Verlag: Princeton University Press, 2007

Inhaltsangabe

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

Über diesen Titel

Über die Autorin bzw. den Autor

Sarah P. Otto is Professor of Zoology at the University of British Columbia. Troy Day is Associate Professor of Mathematics and Biology at Queen's University

Von der hinteren Coverseite

"A wonderfully pedagogical introduction to mathematical modeling in population biology: an ideal first course for biologists."--Simon A. Levin, Princeton University

"This book is an amazing teaching resource for developing a comprehensive understanding of the methods and importance of biological modeling. But more than that, this book should be read by every student of evolutionary biology and ecology so that they can come to a deeper appreciation of the fundamental ideas and models that underlie these fields."--Patrick C. Phillips, University of Oregon

"There is an increasing use of mathematics throughout the biological sciences, yet the training of most biologists still woefully lacks crucial mathematical tools. Sally Otto and Troy Day are themselves two masters at the deft use of theoretical models to crystallize conceptual insights about ecological and evolutionary problems, and in this wonderful book they make accessible to a broad audience the essential mathematical tool kit biologists need, both to read the literature and to craft and analyze models themselves."--Robert D. Holt, University of Florida

"I am often asked by biologists to recommend a book on mathematical modeling, but I must tell them that there is no single good book that will guide them through the difficult first stages of learning to make models. Otto and Day's book fills the gap. The quality is high throughout, the scholarship is sound, the book is comprehensive. The authors are both first-rate scientists. I think this will be a classic."--Steven A. Frank, author ofImmunology and Evolution of Infectious Disease

"This book provides a general introduction to mathematical modeling--in particular, to population modeling--in the biological sciences. This past year I taught a 400-level course in mathematical modeling of biological systems, and I had to do so without a textbook because no adequate text existed. Otto and Day's book would have met my needs beautifully. This book is an important addition to the field."--Carl Bergstrom, University of Washington

"This book has the ambitious and worthy goal of teaching biologists enough about modeling and about mathematical methods to be both intelligent consumers of models and competent creators of their own models. Its concentration on the process of building rather than analyzing models is its strongest point."--Frederick R. Adler, author ofModeling the Dynamics of Life: Calculus and Probability for Life Scientists

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

Biologist's Guide to Mathematical Modeling in Ecology and Evolution

By Sarah P. Otto Troy Day

Princeton University Press

Copyright © 2007 Princeton University Press
All right reserved.
ISBN: 978-0-691-12344-8

Chapter One

Mathematical Modeling in Biology

1.1 Introduction

Mathematics permeates biology. Unfortunately, this is far from obvious to most students of biology. While many biology courses cover results and insights from mathematical models, they rarely describe how these results were obtained. Typically, it is only when biologists start reading research articles that they come to appreciate just how common mathematical modeling is in biology. For many students, this realization comes long after they have chosen the majority of their courses, making it difficult to build the mathematical background needed to appreciate and feel comfortable with the mathematics that they encounter. This book is a guide to help any student develop this appreciation and comfort. To motivate learning more mathematics, we devote this first chapter to emphasizing just how common mathematical models are in biology and to highlighting some of the important ways in which mathematics has shaped our understanding of biology.

Let's begin with some numbers. According to BIOSIS, 886,101 articles published in biological journals contain the keyword "math" (including math, mathematical, mathematics, etc.) as of April 2006. Some of these articles are in specialized journals in mathematical biology, such as the Bulletin of Mathematical Biology, the Journal of Mathematical Biology, Mathematical Biosciences, and Theoretical Population Biology. Many others, however, are published in the most prestigious journals in science, including Nature and Science. Such a coarse survey, however, misses a large fraction of articles describing theoretical models without using "math" as a keyword.

We performed a more in-depth survey of all of the articles published in one year within some popular ecology and evolution journals (Table 1.1). Given that virtually every statistical analysis is based on an underlying mathematical model, nearly all articles relied on mathematics to some extent. With a stricter definition that excludes papers whose only use of mathematics is through statistical analyses, 35% of Evolution and Ecology articles and nearly 60% of American Naturalist articles reported predictions or results obtained using mathematical models. The extent of mathematical analysis varied greatly, but mathematical equations appeared in almost all of these articles. Furthermore, many of the articles used computer simulations to describe changes that occur over time in the populations under study. Such simulations can be incredibly helpful, allowing the reader to "see" what the equations predict and allowing authors to obtain results from even the most complicated models.

An important motivation for learning mathematical biology is that mathematical equations typically "say" more than the surrounding text. Given the space constraints of many journals, authors often leave out intermediate steps or fail to state every assumption that they have made. Being able to read and interpret mathematical equations is therefore extremely important, both to verify the conclusions of an author and to evaluate the limitations of unstated assumptions.

To describe all of the biological insights that have come from mathematical models would be an impossible task. Therefore, we focus the rest of this chapter on the insights obtained from mathematical models in one tiny, but critically important, area of biology: the ecology and epidemiology of the human immunodeficiency virus (HIV). As we shall see, mathematical models have allowed biologists to understand otherwise hidden aspects of HIV, they have produced testable predictions about how HIV replicates and spreads, and they have generated forecasts that improve the efficacy of prevention and health care programs.

1.2 HIV

On June 5, 1981, the Morbidity and Mortality Weekly Report of the Centers for Disease Control reported the deaths of five males in Los Angeles, all of whom had died from pneumocystis, a form of pneumonia that rarely causes death in individuals with healthy immune systems. Since this first report, acquired immunodeficiency syndrome (AIDS), as the disease has come to be known, has reached epidemic proportions, having caused more than 20 million deaths worldwide (Joint United Nations Programme on HIV/AIDS 2004b). AIDS results from the deterioration of the immune system, which then fails to ward off various cancers (e.g., Karposi's sarcoma) and infectious agents (e.g., the protozoa that cause pneumocystis, the viruses that cause retinitis, and the bacteria that cause tuberculosis). The collapse of the immune system is caused by infection with the human immunodeficiency virus (Figure 1.1). HIV is transmitted from infected to susceptible individuals by the exchange of bodily fluids, primarily through sexual intercourse without condoms, sharing of unsterilized needles, or transfusion with infected blood supplies (although routine testing for HIV in donated blood has reduced the risk of infection through blood transfusion from 1 in 2500 to 1 in 250,000 [Revelle 1995]).

Once inside the body, HIV particles infect white blood cells by attaching to the CD4 protein embedded in the cell membranes of helper T cells, macrophages, and dendritic cells. The genome of the virus, which is made up of RNA, then enters these cells and is reverse transcribed into DNA, which is subsequently incorporated into the genome of the host. (The fact that normal transcription from DNA to RNA is reversed is why HIV is called a retrovirus.) The virus may then remain latent within the genome of the host cell or become activated, in which case it is transcribed to produce both the proteins necessary to replicate and daughter RNA particles (Figure 1.2). When actively replicating, HIV can produce hundreds of daughter viruses per day per host cell (Dimitrov et al. 1993), often killing the host cell in the process. These virus particles (or virions) then go on to infect other CD4-bearing cells, repeating the process. Eventually, without treatment, the population of CD4+ helper T cells declines dramatically from about 1000 cells per cubic millimeter of blood to about 200 cells, signaling the onset of AIDS (Figure 1.3).

Normally, CD4+ helper T cells function in the cellular immune response by binding to fragments of viruses and other foreign proteins presented on the surface of other immune cells. This binding activates the helper T cells to release chemicals (cytokines), which stimulate both killer T cells to attack the infected cells and B cells to manufacture antibodies against the foreign particles. What makes HIV particularly harmful to the immune system is that the virus preferentially attacks activated helper T cells; by destroying such cells, HIV can eliminate the very cells that recognize and fight other infections.

Early on in the epidemic, the median period between infection with HIV-1 (the strain most common in North America) and the onset of AIDS was about ten years (Bacchetti and Moss 1989). The median survival time following the onset of an AIDS-associated condition (e.g., Karposi's sarcoma or pneumocystis) was just under one year (Bacchetti et al. 1988). Survival statistics have improved dramatically with the development of effective antiretroviral therapies, such as protease inhibitors, which first became available in 1995, and with...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2007
• Sprache: Englisch
• ISBN 10: 0691123446
• ISBN 13: 9780691123448
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 732
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar