A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

A Biologist s Guide to Mathematical Modeling in Ecology and Evolution
Author: Sarah P. Otto,Troy Day
Publsiher: Princeton University Press
Total Pages: 744
Release: 2011-09-19
Genre: Science
ISBN: 9781400840915

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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

A Biologist s Guide to Mathematical Modeling in Ecology and Evolution

A Biologist s Guide to Mathematical Modeling in Ecology and Evolution
Author: Sarah P. Otto,Troy Day
Publsiher: Princeton University Press
Total Pages: 746
Release: 2007-03-12
Genre: Mathematics
ISBN: 9780691123448

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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

The Theory of Evolution

The Theory of Evolution
Author: Samuel M. Scheiner,David P. Mindell
Publsiher: University of Chicago Press
Total Pages: 464
Release: 2020-04-03
Genre: Science
ISBN: 9780226671338

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Darwin’s nineteenth-century writings laid the foundations for modern studies of evolution, and theoretical developments in the mid-twentieth century fostered the Modern Synthesis. Since that time, a great deal of new biological knowledge has been generated, including details of the genetic code, lateral gene transfer, and developmental constraints. Our improved understanding of these and many other phenomena have been working their way into evolutionary theory, changing it and improving its correspondence with evolution in nature. And while the study of evolution is thriving both as a basic science to understand the world and in its applications in agriculture, medicine, and public health, the broad scope of evolution—operating across genes, whole organisms, clades, and ecosystems—presents a significant challenge for researchers seeking to integrate abundant new data and content into a general theory of evolution. This book gives us that framework and synthesis for the twenty-first century. The Theory of Evolution presents a series of chapters by experts seeking this integration by addressing the current state of affairs across numerous fields within evolutionary biology, ranging from biogeography to multilevel selection, speciation, and macroevolutionary theory. By presenting current syntheses of evolution’s theoretical foundations and their growth in light of new datasets and analyses, this collection will enhance future research and understanding.

The Theoretical Biologist s Toolbox

The Theoretical Biologist s Toolbox
Author: Marc Mangel
Publsiher: Cambridge University Press
Total Pages: 135
Release: 2006-07-27
Genre: Science
ISBN: 9781139455862

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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.

Population Biology

Population Biology
Author: Alan Hastings
Publsiher: Springer Science & Business Media
Total Pages: 220
Release: 2013-03-14
Genre: Science
ISBN: 9781475727319

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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.

Elements of Mathematical Ecology

Elements of Mathematical Ecology
Author: Mark Kot
Publsiher: Cambridge University Press
Total Pages: 135
Release: 2001-07-19
Genre: Nature
ISBN: 9781316584057

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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 Biology II

Mathematical Biology II
Author: James D. Murray
Publsiher: Springer Science & Business Media
Total Pages: 834
Release: 2011-02-15
Genre: Mathematics
ISBN: 9780387952284

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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

Game Theoretical Models in Biology

Game Theoretical Models in Biology
Author: Mark Broom,Jan Rychtar
Publsiher: CRC Press
Total Pages: 522
Release: 2013-03-27
Genre: Mathematics
ISBN: 9781439853214

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Covering the major topics of evolutionary game theory, Game-Theoretical Models in Biology presents both abstract and practical mathematical models of real biological situations. It discusses the static aspects of game theory in a mathematically rigorous way that is appealing to mathematicians. In addition, the authors explore many applications of game theory to biology, making the text useful to biologists as well. The book describes a wide range of topics in evolutionary games, including matrix games, replicator dynamics, the hawk-dove game, and the prisoner’s dilemma. It covers the evolutionarily stable strategy, a key concept in biological games, and offers in-depth details of the mathematical models. Most chapters illustrate how to use MATLAB® to solve various games. Important biological phenomena, such as the sex ratio of so many species being close to a half, the evolution of cooperative behavior, and the existence of adornments (for example, the peacock’s tail), have been explained using ideas underpinned by game theoretical modeling. Suitable for readers studying and working at the interface of mathematics and the life sciences, this book shows how evolutionary game theory is used in the modeling of these diverse biological phenomena.