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Mathematical Models of Social Evolution: A Guide for the Perplexed
Over the last several decades, mathematical models have become central to the study of social evolution, both in biology and the social sciences. But students in these disciplines often seriously lack the tools to understand them. A primer on behavioral modeling that includes both mathematics and evolutionary theory, Mathematical Models of Social Evolution aims to make the student and professional researcher in biology and the social sciences fully conversant in the language of the field.
Teaching biological concepts from which models can be developed, Richard McElreath and Robert Boyd introduce readers to many of the typical mathematical tools that are used to analyze evolutionary models and end each chapter with a set of problems that draw upon these techniques. Mathematical Models of Social Evolution equips behaviorists and evolutionary biologists with the mathematical knowledge to truly understand the models on which their research depends. Ultimately, McElreath and Boyd’s goal is to impart the fundamental concepts that underlie modern biological understandings of the evolution of behavior so that readers will be able to more fully appreciate journal articles and scientific literature, and start building models of their own.
Teaching biological concepts from which models can be developed, Richard McElreath and Robert Boyd introduce readers to many of the typical mathematical tools that are used to analyze evolutionary models and end each chapter with a set of problems that draw upon these techniques. Mathematical Models of Social Evolution equips behaviorists and evolutionary biologists with the mathematical knowledge to truly understand the models on which their research depends. Ultimately, McElreath and Boyd’s goal is to impart the fundamental concepts that underlie modern biological understandings of the evolution of behavior so that readers will be able to more fully appreciate journal articles and scientific literature, and start building models of their own.
425 pages, Paperback
First published March 15, 2007
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August 22, 2018
Cooperation as a Maximizing Strategy
The heart of the authors' approach is to use equations and analytically solve them using abstract costs and benefits to evaluate the effectiveness of different social strategies using the Prisoner's Dilemmagame as a basic model. The alternate approach, using simulation (they argue) is both slow and costly in terms of computing time, and fails to yield the same insights into the model. However Roger Penrose's dictum that the number of readers drops in half with every equation applies - if you can't handle looking at algebra you won't follow the arguments. Nonetheless it's a very instructive book and it builds on some earlier research by Robert Axelrod in The Evolution of Cooperation which, if I would highly recommend reading first as IMHO it lays the groundwork for much of what is published afterwards in this field.
In a society where everyone cooperates with everyone else, a strategy of always co-operating works fine. Call this strategy ALLC. However such a society is vulnerable to invasion by an alternate strategy, always take advantage, call this ALLD, 'D' meaning defector (exploitive non-co-operator). Pure altruism looses to ALLD all the time.
Now consider an alternate strategy called Tit For Tat (TFT). You're nice to me, I'll be nice to you. You don't act nice, I'll retaliate next time. However if you act nice I'll go back to cooperating. TFT gets along well with ALLC. In fact, for all intents and purposes they look alike. TFT can survive an invasion by ALLD (Always "defect") as long as there aren't too many ALLDs around - if they can choose the TFTs just cooperate with each other. The interesting result is that a society composed of a mix of TFT and ALLC can also survive an invasion of ALLD. The presence of TFT in most cases would incur a sufficient penalty on an invading ALLD to make the ALLD approach less attractive. Axelrod's version assumes that the ALLDs would die out from lack of cooperation, or would learn after enough interactions to change their strategy.
However TFT is not the final word. This is still chapter 2. TFT is not stable if the two sides start off on different feet - two TFTs will just alternate and nobody every wins. However TFT2 - A tit for two tats which allows for mistakes is shown to be more stable. And there is no significant difference in net benefit between TFT2 and TFT3, 4 and 5 etc, assuming an extended set of interactions. Note I'm giving a non-mathematical translation here. The authors examine other strategies as well and analytically consider the effect of mixing them and estimating how well each strategy does.
Chapter 5 adds in the effect of memory and the cost of signalling behaviour.
Next one adds a memory of the past n interactions and decides whether or not the individual (or group) that you are interacting with has made a mistake or is acting malevolently, in which case signalling cooperation might be a good or bad idea.
Successive chapters layer these ideas further. In Chapter 6 the idea of random selection of intersection is refined and the reasonable notion that we tend to interact with those who benefit us most; but also keeping in mind the idea that we don't always have a choice in our neighbours or colleagues by introducing a factor representing physical dispersion. And Chapters 7 and 8 take a look at the factor of sexual selection and it's long term inter generational effects.
A robust society has to be willing to co-operate. Following one strategy though is a bad idea because any single strategy can be gamed by a knowledgeable participant, except possibly ALLD, which is pretty negative to start with. On the other hand a mix of strategies including a history of past interactions may in the long run prove to be robust.
The book is set up be used in a university course on evolutionary biology, but it would also apply to game theory or political science. They problem, as I see it, is that few exceptions, political advisers and sociologist often don't understand this kind of analysis. Most political theorists rely solely on anecdote and rhetoric. An exception - Networks of Nations: The Evolution, Structure, and Impact of International Networks, 1816-2001, which I read in 2011, uses a different set of propositions, but is also analytic in nature.
Highly interesting but somewhat abstract, I would say that this modelling technique has a role in arguments about pure theory and the range of possible reactions, but in practice can only serve as an approximation. The best use would be to predict, as with weather systems, that given equilibria are inherently stable or unstable.
With the caveats expressed above, recommended.
The heart of the authors' approach is to use equations and analytically solve them using abstract costs and benefits to evaluate the effectiveness of different social strategies using the Prisoner's Dilemmagame as a basic model. The alternate approach, using simulation (they argue) is both slow and costly in terms of computing time, and fails to yield the same insights into the model. However Roger Penrose's dictum that the number of readers drops in half with every equation applies - if you can't handle looking at algebra you won't follow the arguments. Nonetheless it's a very instructive book and it builds on some earlier research by Robert Axelrod in The Evolution of Cooperation which, if I would highly recommend reading first as IMHO it lays the groundwork for much of what is published afterwards in this field.
In a society where everyone cooperates with everyone else, a strategy of always co-operating works fine. Call this strategy ALLC. However such a society is vulnerable to invasion by an alternate strategy, always take advantage, call this ALLD, 'D' meaning defector (exploitive non-co-operator). Pure altruism looses to ALLD all the time.
Now consider an alternate strategy called Tit For Tat (TFT). You're nice to me, I'll be nice to you. You don't act nice, I'll retaliate next time. However if you act nice I'll go back to cooperating. TFT gets along well with ALLC. In fact, for all intents and purposes they look alike. TFT can survive an invasion by ALLD (Always "defect") as long as there aren't too many ALLDs around - if they can choose the TFTs just cooperate with each other. The interesting result is that a society composed of a mix of TFT and ALLC can also survive an invasion of ALLD. The presence of TFT in most cases would incur a sufficient penalty on an invading ALLD to make the ALLD approach less attractive. Axelrod's version assumes that the ALLDs would die out from lack of cooperation, or would learn after enough interactions to change their strategy.
However TFT is not the final word. This is still chapter 2. TFT is not stable if the two sides start off on different feet - two TFTs will just alternate and nobody every wins. However TFT2 - A tit for two tats which allows for mistakes is shown to be more stable. And there is no significant difference in net benefit between TFT2 and TFT3, 4 and 5 etc, assuming an extended set of interactions. Note I'm giving a non-mathematical translation here. The authors examine other strategies as well and analytically consider the effect of mixing them and estimating how well each strategy does.
Chapter 5 adds in the effect of memory and the cost of signalling behaviour.
Next one adds a memory of the past n interactions and decides whether or not the individual (or group) that you are interacting with has made a mistake or is acting malevolently, in which case signalling cooperation might be a good or bad idea.
Successive chapters layer these ideas further. In Chapter 6 the idea of random selection of intersection is refined and the reasonable notion that we tend to interact with those who benefit us most; but also keeping in mind the idea that we don't always have a choice in our neighbours or colleagues by introducing a factor representing physical dispersion. And Chapters 7 and 8 take a look at the factor of sexual selection and it's long term inter generational effects.
A robust society has to be willing to co-operate. Following one strategy though is a bad idea because any single strategy can be gamed by a knowledgeable participant, except possibly ALLD, which is pretty negative to start with. On the other hand a mix of strategies including a history of past interactions may in the long run prove to be robust.
The book is set up be used in a university course on evolutionary biology, but it would also apply to game theory or political science. They problem, as I see it, is that few exceptions, political advisers and sociologist often don't understand this kind of analysis. Most political theorists rely solely on anecdote and rhetoric. An exception - Networks of Nations: The Evolution, Structure, and Impact of International Networks, 1816-2001, which I read in 2011, uses a different set of propositions, but is also analytic in nature.
Highly interesting but somewhat abstract, I would say that this modelling technique has a role in arguments about pure theory and the range of possible reactions, but in practice can only serve as an approximation. The best use would be to predict, as with weather systems, that given equilibria are inherently stable or unstable.
With the caveats expressed above, recommended.
February 19, 2022
I learned so much reading this book as a biologist and only took a few weeks! Already recommended it to many of my peers. Worked through it on paper, might have occasionally skipped some exercises but liked to work through the main examples as I read along, replicating what they found to help me understand the content. Started making my own models as well.
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