Book Description
At a time of unprecedented expansion in the life sciences, evolution is the one theory that transcends all of biology. Any observation of a living system must ultimately be interpreted in the context of its evolution. Evolutionary change is the consequence of mutation and natural selection, which are two concepts that can be described by mathematical equations.Evolutionary Dynamics is concerned with these equations of life. In this book, Martin Nowak draws on the languages of biology and mathematics to outline the mathematical principles according to which life evolves. His work introduces readers to the powerful yet simple laws that govern the evolution of living systems, no matter how complicated they might seem.
Evolution has become a mathematical theory, Nowak suggests, and any idea of an evolutionary process or mechanism should be studied in the context of the mathematical equations of evolutionary dynamics. His book presents a range of analytical tools that can be used to this end: fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators, the Prisoner's Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids, evolutionary kaleidoscopes, fractals, and spatial chaos. Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system--and everything that arises as a consequence of living systems--in terms of evolutionary dynamics.
Customer Reviews:
An engrossing read - highly recommended.......2007-09-05
This is a wonderful book by a master of the field. Prof. Nowak, who teaches at Harvard, has managed a minor miracle: writing a book on mathematical biology that is mathematically rigorous and extremely readable at the same time.
The book is divided into two broad sections. The first nine chapters explore various abstract models of evolution. Simple models of evolution do not demonstrate cooperation between individuals, while examples of it abound in the real world. This fact quite rightly fascinates the author and informs his presentation. The last four chapters of the book use some of the modeling techniques developed in previous chapters to study real-world systems, such as HIV infection and cancer.
This book is highly recommended for anyone interested in the mathematical aspects of biology. More broadly, it will be of interest to anyone who's interested in mathematical models of complex systems.
Excellent and Approachable Survey.......2007-05-23
This book is an accessible introduction to the mathematics of evolution and results in the field of evolutionary dynamics with a heavy emphasis on applications including the immune system, virulence, AIDS, and even the evolution of language. Many of the ideas are from fairly recent papers and results in mathematical biology, particularly the sections regarding the evolution of universal grammar and in the emerging field of evolutionary graph theory, which adds population structure to the mathematical analysis. (This is a now necessary generalization of evolutionary game theory, which assumes uniform population structure.) As noted above, this is the first book to present many of these ideas outside of scientific and mathematical journals.
Although the mathematical content is significant, Nowak diligently explains the implications of the mathematics in the text of the book, widening the potential audience of the book dramatically. Simply put, this book is filled with delicious evolutionary content, backed up with mathematical rigor for the interested reader, but you need not have a degree in mathematics in order to understand much of the material.
Highly recommended for those truly interested in evolution.
The Marriage of Mathematics and Evolution.......2007-01-10
Excellent book for the mathematically and evolutionarily minded. However, not for general reading unless you are doing graduate work in either mathematics or evolutionary biology. Just excellent survey.
A dazzling book.......2006-11-22
This is, quite simply, a dazzling book. Nowak manages to take very deep mathematical ideas that are on the cutting edge of science and make them fun and pretty rigorous at the same time. The review in Nature said "It should be on the shelf of anyone who has, or thinks they might have, an interest in theoretical biology" and I completely agree. The section on HIV, explaining mathematically why there is a long delay between infection and the disease, and how this proposal in 1990 correctly predicted several biolgical facts which were subseqently discovered (but not mentioning execpt in the notes, that this was his work) is truly exceptional. We are moving beyond the "Just So stories" phase of evolution (such as wooly rhetoric about "Selfish Genes") to real, mathematically rigorous, science.
wonderful life.......2006-10-13
This is a remarkable book, absolutely original, containing a lot of material which has never before appeared in book form. It is written in a very accessible style, and leads almost effortlessly from first principles to state-of-the-art research.
The book takes an eagle's view on evolution, covering an vast range of topics from molecules to man. It emphasises analytical methods and presents a large canvas of superbly elegant mathematical models.
The author has chosen a very personal, highly idiosyncratic sample of subjects of amazing diversity, basically because he feels excited about them: and this excitement shows through, and makes the book very engaging, a positively bracing experience. On all of the topics, the author has contributed substantially, and the feel to get it `straight from the horse's mouth' is one of the great assets of the book. I believe that it will be a splendid hit with students, and regret that I did not have anything like that when I was young.
The style of the book is lucid and vigorous, with short, clear sentences, occasionally in staccato style. The mathematics is reduced to the bare minimum. It is incredible how much mileage the author can get out of it. The illustrations play an important role, and are well devised.
The chapters are short, and they address an amazing array of topics, ranging from molecular evolution to evolutionary games, from HIV to cancer, and from cooperation to language. In spite of their different subjects, they are homogenous: first comes a breezy introduction to the biological (or chemical, or linguistic) facts, then a simple model, then an analysis, without heavy machinery, usually leading up to some remarkable results which could not be obtained without mathematics, then a summary in a few short statements and finally an extensive list of references, including both the classics and the very newest results in the field. The fact that in each case, a few pages suffice to start from scratch and lead to the cutting edge of present-day research is quite remarkable.
The book will certainly have a big impact, and raise a lot of follow-up work. There is hardly a better recipe for young PhDs than to pick one of the chapters and start doing their own research. But in addition, `the whole is more than the sum of its parts'. I usually hate this slogan but here it holds in a spectacular way. By simply putting together the different applications of simple models in so spectacularly diverse fields, Nowak's book promotes a radical `hands-on'-approach to evolution which, I am sure, will have seminal repercussions.
Book Description
Occupancy Estimation and Modeling is the first book to examine the latest methods in analyzing presence/absence data surveys. Using four classes of models (single-species, single-season; single-species, multiple season; multiple-species, single-season; and multiple-species, multiple-season), the authors discuss the practical sampling situation, present a likelihood-based model enabling direct estimation of the occupancy-related parameters while allowing for imperfect detectability, and make recommendations for designing studies using these models.
* Provides authoritative insights into the latest in estimation modeling
* Discusses multiple models which lay the groundwork for future study designs
* Addresses critical issues of imperfect detectibility and its effects on estimation
* Explores the role of probability in estimating in detail
Customer Reviews:
Great book for understanding site occupancy modeling.......2006-03-10
I think this is a pretty good book. It is the only reference on this relatively new type of patch occupancy modeling. It is mainly focused on the models of MacKenzie et al. and the Royle and Nichols model. This is a great place to start if you know nothing about this method or a good reference for advanced users.
This book does not fill the need of an introductory "how-to" book. If you want to know how to set up models and run them in program PRESENCE or MARK you will need to wait. Such a book does not exist. This is not a cookbook, but a compilation of the theory and an explanantion of the methodology behind occupancy estimation.
Book Description
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.
Customer Reviews:
An excellent recent overview of modeling.......2007-06-14
This is an excellent book for students or faculty interested in learning more about the current state of the art in modeling of biological systems. The authors make a great effort to keep the mathematical sophistication at a level that students (or faculty) who primarily have a biological background will still be able to follow in some detail. They are also able to suggest some of the exciting current areas of research and new areas for the future. All in all, well worth reading if you are interested in the topic of modeling of biological systems.
Book Description
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.
Customer Reviews:
Thorough.......2007-09-10
I haven't finished the book, but so far it's been very thorough on the subject and has given me lots of ideas for how to proceed on the project I'm working on. Would definitely recommend it.
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Dynamic Modeling in Behavioral Ecology
Marc Mangel , and
Colin Whitcomb Clark
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Dynamic State Variable Models in Ecology: Methods and Applications (Oxford Series in Ecology and Evolution)
ASIN: 0691085064 |
Book Description
This book describes a powerful and flexible technique for modeling of behavior, based on evolutionary principles.
Book Description
Ocean Biogeochemical Dynamics provides a broad theoretical framework upon which graduate students and upper-level undergraduates can formulate an understanding of the processes that control the mean concentration and distribution of biologically utilized elements and compounds in the ocean. Though it is written as a textbook, it will also be of interest to more advanced scientists as a wide-ranging synthesis of our present understanding of ocean biogeochemical processes.
The first two chapters of the book provide an introductory overview of biogeochemical and physical oceanography. The next four chapters concentrate on processes at the air-sea interface, the production of organic matter in the upper ocean, the remineralization of organic matter in the water column, and the processing of organic matter in the sediments. The focus of these chapters is on analyzing the cycles of organic carbon, oxygen, and nutrients.
The next three chapters round out the authors' coverage of ocean biogeochemical cycles with discussions of silica, dissolved inorganic carbon and alkalinity, and CaCO
3. The final chapter discusses applications of ocean biogeochemistry to our understanding of the role of the ocean carbon cycle in interannual to decadal variability, paleoclimatology, and the anthropogenic carbon budget. The problem sets included at the end of each chapter encourage students to ask critical questions in this exciting new field. While much of the approach is mathematical, the math is at a level that should be accessible to students with a year or two of college level mathematics and/or physics.
Customer Reviews:
great textbook for oceanography students.......2007-03-10
This book will introduce you to the basics and important concepts of biogeochemical oceanography. It's a good reference book and I think it will be helpful for graduate students to prepare for their qualification exams.
Book Description
Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.
Customer Reviews:
The Best There Is On Evolutionary Dynamics.......2000-07-14
When I was writing the chapter on evolutionary dynamics for my book Game Theory Evolving (Princeton, 2000), I looked at all the books available and found nothing. Then Hofbauer and Sigmund's new book (a totally revised version of their earlier Theory of Evolution and Dynamical Systems) came out, and I knew I had a masterpiece in hand.
The book does not assume the reader knows basic differential equation theory--it presents all the theory necessary. Indeed, it is a wonderful way to learn differential equation theory, since one immediately is faced with meaningful problems to solve. It does assume the reader is familiar with multivariate calculus. The book should be accessible to biologists and game theorists with a minimum understanding of each other's disciplines.
There are four parts. First, HS deal with Lotka-Volterra equations of the type prevalent in predator-prey models, which they extend to ecological models and several populations. Like the rest of the book, there are lots of problems and the presentation is elegant and succinct.
The second part deals with game theory dynamics and replicator equations, including sections on evolutionary games and asymmetric games. This too is extremely nicely presented, and the links to the Lotka-Volterra models are made clear.
Part three is on dynamical systems especially of relevance to biochemistry--catalytic hypercycles--as well as higher dimensional phase space dynamics of ecological models.
Part four deal with population genetic models using a differential equation approach. This section is also excellent, though for serious readers it should be complemented by Karlin and Taylor's Second Course in Stochastic Processes (which is much more mathematically demanding).
The physical production of the book is also first rate--a pleasure to read and use.
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Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges (Contemporary Mathematics)
Manufacturer: American Mathematical Society
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ASIN: 0821837753
Release Date: 2006-11-01 |
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This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Modeling the Dynamics of Human Diseases: Emerging Paradigms and Challenges, held in Snowbird, Utah, July 17-21, 2005. The goal of the conference was to bring together leading and upcoming researchers to discuss the latest advances and challenges associated with the modeling of the dynamics of emerging and re-emerging diseases, and to explore various control strategies. The articles included in this book are devoted to some of the significant recent advances, trends, and challenges associated with the mathematical modeling and analysis of the dynamics and control of some diseases of public health importance. In addition to illustrating many of the diverse prevailing epidemiological challenges, together with the diversity of mathematical approaches needed to address them, this book provides insights on a number of topical modeling issues such as the modeling and control of mosquito-borne diseases, respiratory diseases, animal diseases (such as foot-and-mouth disease), cancer and tumor growth modeling, influenza, HIV, HPV, rotavirus, etc. This book also touches upon other important topics such as the use of modeling in homeland security and some review and new results on various modeling paradigms including network, stochastic and deterministic formulations together with the use of optimal control and related methods for evaluating control strategies.
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- The Theory of Chemostat:Dynamics of Microbial Competition
- The Theory of Chemostat:Dynamics of Microbial Competition
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The Theory of the Chemostat: Dynamics of Microbial Competition (Cambridge Studies in Mathematical Biology)
Hal L. Smith , and
Paul Waltman
Manufacturer: Cambridge University Press
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ASIN: 0521470277 |
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The chemostat is a basic piece of laboratory apparatus, yet it has begun to occupy an increasingly central role in ecological studies. The ecological environment created by a chemostat is one of the few completely controlled experimental systems for testing microbial growth and competition. As a tool in biotechnology, the chemostat plays an important role in bioprocessing. This book presents the theory of the chemostat as a model for larger ecological problems such as food chains, competition along a gradient, competition in the presence of an inhibitor, and the effects of time varying inputs. Mathematical models that take account of size structure, variable yields, and diffusion are also considered. The basic phenomena are modeled and analyzed using the dynamical systems approach. New directions for research and open problems are discussed. Six appendices provide an elementary description of the necessary mathematical tools.
Customer Reviews:
The Theory of Chemostat:Dynamics of Microbial Competition.......1999-12-31
"The best mathematical book I've ever read, Hal is truly the best".
The Theory of Chemostat:Dynamics of Microbial Competition.......1999-12-31
"The best mathmatical book I've ever read, Hal is truly the best".
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- A little bit disappointing
- Mathematical Darwinism
- Life is a game
- A Mathematical Approach to Evolution
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Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics
Thomas L. Vincent , and
Joel S. Brown
Manufacturer: Cambridge University Press
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Evolutionary Game Theory
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Evolution and the Theory of Games
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Designing Economic Mechanisms
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Evolutionary Theory
ASIN: 0521841704 |
Book Description
All of life is a game and evolution by natural selection is no exception. The evolutionary game theory developed in this book provides the tools necessary for understanding many of nature’s mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher’s Fundamental Theorem of Natural Selection, and the nature of life’s evolutionary game.
Download Description
All of life is a game and evolution by natural selection is no exception. The evolutionary game theory developed in this book provides the tools necessary for understanding many of nature's mysteries, including co-evolution, speciation, extinction and the major biological questions regarding fit of form and function, diversity, procession, and the distribution and abundance of life. Mathematics for the evolutionary game are developed based on Darwin's postulates leading to the concept of a fitness generating function (G-function). G-function is a tool that simplifies notation and plays an important role developing Darwinian dynamics that drive natural selection. Natural selection may result in special outcomes such as the evolutionarily stable strategy (ESS). An ESS maximum principle is formulated and its graphical representation as an adaptive landscape illuminates concepts such as adaptation, Fisher's Fundamental Theorem of Natural Selection, and the nature of life's evolutionary game.
Customer Reviews:
A little bit disappointing.......2006-04-19
I am not a biologist, but an engineer interested in evolution and mathematics.
The mathematics of the book is very easy, the only (very) confusing issue are the indices.
The G-function is introduced a bit ad-hoc, but as a definition, this might not matter much. It is very clear, that by allowing the strategy to vary, one can get optimal (at least stationary) values. The strategy dynamics are introduced in a rather confusing way, without much of an explanation.
For the rest, it seems, that 80% of the book are numerical examples, which seem to prove mostly, that with nonlinear differential equations, the behaviour of (e.g.) stationary points can vary quite a bit, if the coefficients in those equations are changed.
Maybe a professional biologist gets a lot out of this book, but for the interested layman it offers little (except upteen numerical examples, see above)
Mathematical Darwinism.......2005-11-17
First, full disclosure: I am a colleague and friend of the authors, Thomas L. Vincent and Joel S. Brown, and I reviewed the entire book during its writing.
Game theory is a fairly recent development in mathematics, having been introduced in the 1940's. Evolutionary Game Theory is more recent yet - Maynard Smith and Price put it on the map with their publication in Nature in 1973 on the Logic of Animal Conflict. Maynard Smith then more fully elaborated the application of matrix games to evolution with his 1982 volume, Evolution and the Theory of Games. Vincent and Brown trace their contribution to the pioneering developments of Maynard Smith, but in this volume, they go much further. As I reviewed the eleven chapters as they were first written, I felt the privilege of observing, first hand, the construction of a great edifice. In this edifice, the dynamics of ecology is dovetailed with the dynamics of heritable strategies. The tool that accomplishes this is the fitness generating function, known as the G-function. Particularly brilliant is the invention of the virtual strategy, a scalar or vector "place holder" in the G-function. The great virtue of the virtual strategy is that it represents any focal individual taking on any strategy within the entire strategy set of the species. The fitness generating function then determines the fitness for that virtual strategy within the biotic and abiotic environment defined by the set of arguments (e.g., resident strategies, their population sizes, abundance of resources, etc.) defining the G-function. With G-function in hand, Evolutionary Game Theorists now have a mathematical Darwinism - a formal mathematical expression of Darwin's three postulates: a) like begets like; b) organisms struggle for existence; c) heritable traits help determine the outcome of the struggle. With the G-function, we can predict both the dynamics of heritable strategies and the adaptive outcome of natural selection.
Vincent and Brown begin, in Chapter 1, with an historical and philosophical overview of Evolutionary Game Theory and its relationship to the more traditional approach of Evolutionary Genetics. They then proceed to lay the mathematical foundations (Chapters 2 - 7), constructing the theory of Evolutionary Games and the G-function. These chapters each contain useful examples, teaching the student of evolutionary games how to apply the G-function. Noteworthy is that most all of the examples in these chapters represent continuous, as opposed to matrix games. In matrix games, which constitute the bulk of early development of Evolutionary Game Theory, and with which most readers are probably most familiar, strategies are discrete rather than continuous. However, the continuous games elaborated by Vincent and Brown (and now, many others) are of far more useful application in Evolutionary Ecology. Key contributions here are the precise mathematical definition of Maynard Smith's seminal Evolutionarily Stable Strategy (ESS) in Chapter 6, and the formulation of the ESS Maximum Principle in Chapter 7. This principle establishes the well-recognized properties of the ESS of invasion resistance and convergent stability, but also the fit of form and function - the ESS strategy is an adaptation - it maximizes individual fitness given the circumstances.
Chapter 8, which treats species concepts, speciation, and extinction, is particularly enlightening. Here the G-function shines! Under traditional approaches, a huge chasm, conceptual and methodological, separates microevolution and macroevolution. Vincent and Brown, armed with the G-function, unify the two: Microevolution is repeatable and reversible evolutionary dynamics within a G-function. Macroevolution is the production of novel G-functions. They demonstrate the versatility of the G-function approach to Evolutionary Game Theory in their discussion of three contexts for extinction (which is as integral to evolution as is speciation). Vincent and Brown introduce many key concepts in Chapter 8. Perhaps most important is their strategy species concept, which relies on their definition of the species archetype. They provide a particularly cogent definition of a species that is ecologically keystone (its presence promotes the persistence, in ecological time, of other species in the community), but they also point out that a species can by evolutionarily keystone - when its presence increases the numbers of species at an ESS. Using these developments, Vincent and Brown investigate mechanisms of speciation, including sympatric speciation, allopatric speciation, adaptive radiations, coevolution, Wright's shifting balance theory, and incumbent replacement. They conclude with a tour de force: a concise and brilliant discussion of the Procession of Life. As they aptly demonstrate, with the G-function approach to the Game of Life, theories such as Punctuated Equilibrium, oft cited as a contradiction of Darwinian Evolution, instead result naturally from Darwin's three postulates!
Chapter 9 is perhaps the least exciting chapter, but it serves the utilitarian purpose of melding the matrix approach to Evolutionary Game Theory with the G-function approach. This is, indeed, required reading for those who think matrix games are the only game in town.
Chapters 10 and 11 are well worth the wait and development. In these chapters, Vincent and Brown apply the G-function to an impressive diversity of problems arising in the beautiful metaphor of Hutchinson, the Ecological Theater and Evolutionary Play. Though the diversity of topics covered in these two chapters is impressive, as Vincent and Brown state, it represents only a subset of the problems that can be investigated with G-functions. Chapter 10 addresses "basic" issues of Evolutionary Ecology - a who's who of fundamental subjects. These include: Habitat selection and the ideal free distribution; Consumer-resource games, with examples on plant competition and root-shoot ratio; Carcinogenesis (a must read for all interested in Darwinian Medicine); Flowering time for annual plants; Root competition; and Foraging games.
Chapter 11 turns to the G-function as a fundamental tool for Applied Evolutionary Ecology. Here Vincent and Brown examine: Evolutionary responses to harvesting; Resource management and conservation; and Chemotherapy-driven evolution. They contrast management based on ecological enlightenment with that based on evolutionary enlightenment (prescriptions based on each emphasis are not always identical!). They point out the resemblance of control of a cancer with chemotherapy with control of a population through hunting. The analysis is striking, with the main message that if all cancer cells are not destroyed by a chemotherapy session, the survivors will evolve as the first step of what they call chemotherapy-driven evolution. If ever Evolutionary Ecologists were looking for a raison d'être, here they have it!
Life is a game.......2005-08-29
Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics by Thomas L. Vincent and Joel S. Brown is a book that not only belongs among the classics of evolutionary theory, but should have pride of place on the shelf right after Darwin's Origin of Species and Maynard Smith's Evolution and the Theory of Games.
This book makes a novel, interesting and readable contribution to the proper understanding of Darwinian processes in evolution. Based on more than twenty years of collaboration between the authors, the book is a comprehensive review of Darwinian theory newly cast in an over-arching mathematical framework. Unlike Stephen Jay Gould's recent overview of evolutionary theory (The Structure of Evolutionary Theory, 2002, 1433 pages), Vincent & Brown's book is concise (382 pages), uncluttered, and supported by an elegant skeleton of mathematical theory.
Don't let the math dissuade you however. If you have read Origin of Species and have a familiarity with classic evolutionary games, you won't have trouble understanding this book. Text and numerous examples provide a clear conceptual explanation of equations throughout.
The book's premise is that life is a game and its players have strategies. Understood as such, the authors present fitness-generating functions (G-functions) that encompass strategy, population, and Darwinian dynamics to model evolutionary outcomes. The first chapter introduces this philosophy; the next six chapters develop the theory, presenting classic population models (Ch. 2) and evolutionary games (Ch. 3), then forging new theory through deriving G-functions (Ch. 4), modeling Darwinian dynamics (Ch. 5), finding the evolutionary stable strategies (ESS, Ch. 6) and developing their general ESS maximum principle (Ch. 7).
The authors are able to side-step population-genetics models (and notably, are able to explain WHY this is possible), and build a general model of Darwinian evolution. An immediate insight of their general model is the concept of flexible landscapes, which re-envisions the notion that natural selection cannot cross valleys on evolutionary landscapes, one of the fundamental criticisms of Darwinian theory since the New Synthesis. Exploration of Vincent & Brown's model illustrates that flexible landscapes can shift under evolving populations so that "valleys" are spanned by continuously uphill routes, re-forming behind evolving populations after they have passed. Further, Vincent & Brown derive the general conditions where flexible landscapes will or will not occur (frequency-dependent vs. -independent evolution respectively).
Armed with their general theory, Vincent & Brown are not content to stop after illuminating the valley conundrum, however, and go on in subsequent chapters to apply their theory to classic problems in evolution (Ch. 8; sympatric and allopatric speciation, co-evolution, the difference between micro- and macro-evolution) and ecology (Ch. 9 & 10; sex ratios, cooperation, ideal free distribution, consumer-resource competition), and even medicine (Ch. 10; the ontogenesis of cancer, chemotherapy) and ecosystem management (Ch. 11, evolutionary stable and ecologically enlightened resource management).
In short, Vincent and Brown have written a marvelous book; and from the day it was published, any evolutionary scholar who has not read it has been behind in the field, and has some catching up to do. It should also be read by ecologists, behaviorists, medical researchers and resource managers interested in evolutionary aspects of their work.
A Mathematical Approach to Evolution.......2005-08-03
Charles Darwin published his primary thesis 'The Origin of Species' in 1859. It was a masterpiece of logical deduction based on the observations he had made while serving as a naturalist aboard the H.M.S. Beagle on a scientific expedition around the world. His views were both orthodox for the day and flawed.
Only seven years later Mendel published the results of his research on genetics. Over time these sciences were merged together into what is now called the 'Modern Synthesis.' Genetics explains the why and the how of species begetting species, and how changes in the species are made when a change is made in the genes.
In 1944, with the advances in mathematics, von Neumann and Morgenstern published 'Theory of Games and Economic Behavior.' Over time the modern synthesis of the genertic approach to evolution has been fit into game theory to help understand how the randomness of genetic evolution can be predicted using game theory.
This book gives a rigorous introduction to the mathematics of game theory as applied to Natural Selection. The book presents the tools necessary for understanding many of Nature's mysteries.
Books:
- Evolutionary Pathways in Nature: A Phylogenetic Approach
- Fields Virology 2 volume set
- Fisher-Price: Historical, Rarity, and Value Guide, 1931-Present (Fisher-Price: a Historical, Rarity & Value Guide)
- Fishes: A Field and Laboratory Manual on Their Structure, Identification and Natural History
- Fundamentals of Molecular Virology
- Ghosts of Spain: Travels Through Spain and Its Secret Past
- Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century
- Graph Drawing: Algorithms for the Visualization of Graphs
- Handbook of Food Analytical Chemistry, Water, Proteins, Enzymes, Lipids, and Carbohydrates
- Handheld Usability
Books Index
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