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Evolutionary Dynamics: Exploring the Equations of Life
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 A. 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.
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.
355 pages, Kindle Edition
First published September 29, 2006
33 people are currently reading
636 people want to read
About the author
M.A. Nowak
4 books42 followers
Martin A. Nowak
is Professor of Biology and Mathematics and Director of the Program for Evolutionary Dynamics at Harvard University.
(His writings are indexed under the name M.A. Nowak.)
(His writings are indexed under the name M.A. Nowak.)
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Displaying 1 - 11 of 11 reviews
July 25, 2012
This book develops the mathematical equations for modeling a variety of fascinating topics in evolution. If you are comfortable with equations, and have some background in linear algebra, then you are well-equipped for the formalism in this book.
What is best about this book, is how Martin Nowak develops the models starting from simple sets of equations. As the subject matter is developed, the models gain sophistication as additional parameters and feedback mechanisms are introduced. I especially like the game theory models, that are pretty much all based on the so-called "Prisoner's Dilemma". I also like the evolution of spatial structures through fractals.
I thought that I would enjoy the penultimate chapter, on language evolution. But then it suddenly hit me; none of the models are quantitatively compared against observations or data. The chapter on evolution of the HIV virus mentions that the model explains the long incubation period of AIDS. But, aside from such qualitative explanations, I was really disillusioned by the lack of model-data comparisons. The book also lacks good discussions about how the mathematical models can be interpreted and applied; they all contain parameters that seem to be totally arbitrary, and it is not at all clear what ranges are reasonable. The book would be much improved by additional interpretation of the models in terms of biology.
What is best about this book, is how Martin Nowak develops the models starting from simple sets of equations. As the subject matter is developed, the models gain sophistication as additional parameters and feedback mechanisms are introduced. I especially like the game theory models, that are pretty much all based on the so-called "Prisoner's Dilemma". I also like the evolution of spatial structures through fractals.
I thought that I would enjoy the penultimate chapter, on language evolution. But then it suddenly hit me; none of the models are quantitatively compared against observations or data. The chapter on evolution of the HIV virus mentions that the model explains the long incubation period of AIDS. But, aside from such qualitative explanations, I was really disillusioned by the lack of model-data comparisons. The book also lacks good discussions about how the mathematical models can be interpreted and applied; they all contain parameters that seem to be totally arbitrary, and it is not at all clear what ranges are reasonable. The book would be much improved by additional interpretation of the models in terms of biology.
March 4, 2017
An interesting introduction to evolution and the equations that govern it.
The book gets started with an introduction to the concept of evolution and how replication, mutation, and selection, affect it. Every simple mechanism that is in action in nature, is modeled using differential equations. In other words, the author explains mathematical biology in the first few chapters. As soon as the author introduces game theory and applies it to the modelings, you have to follow the rest of the book with a big WoW on your face. The mathematical methods and formulations are really simple, but these simple basics, result in emergent properties. The combination of the necessary elements of evolution (replication, mutation, and selection), game theory, and differential equations, decode many of the biological and social traits that are easily observed in our daily life.
Martin A. Nowak is the master who teams up these elements and implements them in deciphering the equations of life.
If you are interested in the topics of the book do not miss the page to the Program for Evolutionary Dynamics at Harvard University: http://ped.fas.harvard.edu
The book gets started with an introduction to the concept of evolution and how replication, mutation, and selection, affect it. Every simple mechanism that is in action in nature, is modeled using differential equations. In other words, the author explains mathematical biology in the first few chapters. As soon as the author introduces game theory and applies it to the modelings, you have to follow the rest of the book with a big WoW on your face. The mathematical methods and formulations are really simple, but these simple basics, result in emergent properties. The combination of the necessary elements of evolution (replication, mutation, and selection), game theory, and differential equations, decode many of the biological and social traits that are easily observed in our daily life.
Martin A. Nowak is the master who teams up these elements and implements them in deciphering the equations of life.
If you are interested in the topics of the book do not miss the page to the Program for Evolutionary Dynamics at Harvard University: http://ped.fas.harvard.edu
June 28, 2023
Reread - liked it more than first time. Maybe not the simplest introduction to how to use mathematics in evolutionary sciences but very good.
State of the art - read also Supercooperators by Nowak.
State of the art - read also Supercooperators by Nowak.
February 3, 2020
First of all, a frivolous comment: this is a heavy book. No, not the ideas in it. The book itself. No, it's not especially big; less than 400 pages all told. But, for some reason, it's really heavy. For some reason this was satisfying, in a manner similar to how a pen is more satisfying to hold if it's heavy.
Anyway, on to the actual contents.
The starting point is the (in?)famous Prisoner's Dilemma. Most of you have already of heard of it, but just in case: imagine two criminals, in prison and charged with a crime. They are both offered a deal for reduced sentence if they rat on their partner. If they both refuse, then they will likely get a light sentence for a lesser crime, because the prosecutor really needs the testimony of one against the other to go for the more serious charge. So "rationally", they should both refuse.
Here's the thing. Looked at from each individual's point of view, it is only better to refuse if you can count on the other prisoner to refuse as well. This mimics a lot of other situations in life, where we would all be better off if we could all trust each other, but if you're trustworthy when the others aren't, you are the one who loses out.
Nowak studies this kind of mechanism, from the point of view of populations. If you have a whole society of people playing this game, and over time the losers tend eventually to imitate the winners (with a little bit of random mutation), then eventually you will get a society of people who always defect. So far, no surprises.
However, keep things going, and you will eventually see that society of non-stop backstabbers taken over by "tit-for-tat", a strategy where you do whatever the other side did to you last time. This is because, when they are paired with each other, two "tit-for-tat" players do better than two "backstabbers".
But that isn't stable either. Once everyone is doing "tit-for-tat", random genetic drift allows for "always cooperate". This does just as well, since it doesn't allow the occasional random mistake to create a "tit-for-tat" style backstabbing. Ah, how pleasant. Forgiveness and mercy are eventually the winning evolutionary strategy.
Except that once this becomes dominant, it is a perfect playing ground for "backstabber"...and the cycle starts all over again. There is no stable state. Ponder the theological and moral implications of this at your own risk.
This is the kind of uncomfortable, but ruthlessly well thought out analysis that Nowak delights in showing us. He is part of a relatively new field, which uses evolution as a principle of analysis far outside of its original Darwinian context. How does morality evolve? How do diseases evolve? How does cancer evolve? For an idea that's over 150 years old, evolution has a lot of new light to shed on a large range of fields. Nowak uses a modicum of math, and a plethora of diagrams and images, to explain all of this in a way that is easy to understand.
Deciding what you think about it after you understand it, may take longer...
Anyway, on to the actual contents.
The starting point is the (in?)famous Prisoner's Dilemma. Most of you have already of heard of it, but just in case: imagine two criminals, in prison and charged with a crime. They are both offered a deal for reduced sentence if they rat on their partner. If they both refuse, then they will likely get a light sentence for a lesser crime, because the prosecutor really needs the testimony of one against the other to go for the more serious charge. So "rationally", they should both refuse.
Here's the thing. Looked at from each individual's point of view, it is only better to refuse if you can count on the other prisoner to refuse as well. This mimics a lot of other situations in life, where we would all be better off if we could all trust each other, but if you're trustworthy when the others aren't, you are the one who loses out.
Nowak studies this kind of mechanism, from the point of view of populations. If you have a whole society of people playing this game, and over time the losers tend eventually to imitate the winners (with a little bit of random mutation), then eventually you will get a society of people who always defect. So far, no surprises.
However, keep things going, and you will eventually see that society of non-stop backstabbers taken over by "tit-for-tat", a strategy where you do whatever the other side did to you last time. This is because, when they are paired with each other, two "tit-for-tat" players do better than two "backstabbers".
But that isn't stable either. Once everyone is doing "tit-for-tat", random genetic drift allows for "always cooperate". This does just as well, since it doesn't allow the occasional random mistake to create a "tit-for-tat" style backstabbing. Ah, how pleasant. Forgiveness and mercy are eventually the winning evolutionary strategy.
Except that once this becomes dominant, it is a perfect playing ground for "backstabber"...and the cycle starts all over again. There is no stable state. Ponder the theological and moral implications of this at your own risk.
This is the kind of uncomfortable, but ruthlessly well thought out analysis that Nowak delights in showing us. He is part of a relatively new field, which uses evolution as a principle of analysis far outside of its original Darwinian context. How does morality evolve? How do diseases evolve? How does cancer evolve? For an idea that's over 150 years old, evolution has a lot of new light to shed on a large range of fields. Nowak uses a modicum of math, and a plethora of diagrams and images, to explain all of this in a way that is easy to understand.
Deciding what you think about it after you understand it, may take longer...
October 28, 2018
This book is one of the importance source for my thesis. It is very practical and interesting book about evolution, game theory and biology
April 25, 2024
The author expresses complex topics in a very easy and eloquent way. One of the best textbooks I have ever read.
August 20, 2008
This incredible book manages to clearly approach evolution from a mathematical perspective. This text succeeds in both presenting topics so that one who is not familiar with advanced maths can understand and benefit from it, yet still includes the equations and fundamental mathematical relations that will entice and empower one with a mathematical background. Everything is so clearly explained that it is a real pleasure to read. I would love to take his course. The first half of the book develops the mathematical ideas of game theory and deterministic and stochastic approaches to modeling biological systems. After the foundations are firmly set, Nowak applies them to cutting edge research, such as the evolution of cancer, viruses, HIV, and language. Really an incredible text. How do you even publish a 350 page, full color illustrated, hardbound book for under 25 dollars? No matter how you would approach the science of evolution, from a mathematic or biological perspective, this book is a must read for anyone who is fascinated by the connexions between the phenomenal complexity of life and the beautiful simplicity of the mathematics that can lead to new insights in this vital field.
February 23, 2014
Incredible book. Read it for a game theory course. Very math-heavy, but with basic algebra skills you can work it out. For a non-mathematician, it will take time to go through each chapter (at least it did for me!). Don't let it frighten you; if you are at all interested in evolution, you can pick through the chapters and glean plenty. It's really fun to work these things out on the subway or in a cafe as a lot of the math is like a puzzle. This author has written some of the seminal works in game theory/population dynamics. Worth it, have no fear!
Bonus: makes you look cool and super-smart to keep on your bookshelf ^_^
Bonus: makes you look cool and super-smart to keep on your bookshelf ^_^
July 26, 2014
This was an interesting book. It covers a range of topics with a range of applications. It is easy to read and most of the chapters are written such that they could stand alone, or at least be read out of order. I wish he would make a second edition to fix typos and mistakes (both in the text and figures) as well as bring everything into conformity.
Want to read
July 11, 2010Nothing makes me more excited than when a physicist writes a book on biology. Except when a mathematician does so.
December 16, 2014
Important content, but somewhat too dumbed down.
Displaying 1 - 11 of 11 reviews