about me
art
biz
Chess
corrections
economics
EconoSchool
Finance
friends
fun
game theory
games
geo
mathstat
misc
NatScience
... more
Profil
Logout
Subscribe Weblog

 

In a series of laboratory experiments, evolutionary biologist Paul Turner at Yale University (nice website) has now discovered cheaters among viruses. Turner applied game theory to the experimental evolution of a virus that preys on bacteria, the phi-6 bacteriophage. According to him, the study is the first to demonstrate the evolution of irrational, selfish behavior in a biological system.

In a featured article in the September-October 2005 issue of Amercian Scientist ($, 9 pages) he writes: The temptation to cheat appears to be a universal fact of life. In the struggle to survive and reproduce that drives evolution, selfish individuals may be favored over cooperators because they are more energy efficient. By definition, cheaters expend relatively little energy in a task because they specialize in taking advantage of others—“suckers”—whose efforts they co-opt to their own advantage. In certain animal species some males exert tremendous energy maintaining and defending territories to attract females. Meanwhile, the population may contain subordinate “sneaker” males that are uninterested in territory but linger at the boundaries and specialize in surreptitious copulations. This strategy is very successful for maintaining a subpopulation of sneakers, but it’s unlikely that the population will evolve to contain only cheaters because territorial males are most attractive to female mates. In general, cheaters are highly successful when they are rare because they frequently encounter suckers. The benefits of cheating wane as more individuals in the population opt to cheat. In the parlance of evolutionary biology, the success of cheaters should be governed by frequency-dependent selection. That is, some cost should be associated with a cheating strategy so that selfish individuals are at an advantage when they are rare, but disadvantaged when they are common.<> Our experiments suggest that yes, perhaps at this moment, there may be cheaters among the viruses vying for survival within and near your own cells. But in the long run, such crimes don’t always pay.

Here is how he estimated the payoffs:
payoffmatrix_turner"Experiments between cheating and cooperating viruses allow scientists to estimate the fitness payoffs for each of the strategies in a 2×2 matrix (right). In the prisoner’s dilemma, when two cooperators interact the reward is defined as R = 1. When a cheater meets a cooperator, the temptation to cheat, T, must exceed the reward for cooperating by some value, say s2, so that T = 1 + s2. So the fitness of the cheater relative to the cooperator is T/R, when the cheaters are rare. The value of s2 can be determined from experimental data. My colleagues and I set the equation, T/R = (1 + s2)/1, equal to the left y-intercept of the regression line for the data (see graph below).
turner01
The y-intercept represents the case where a cheater is very rare [...] and therefore guaranteed of interacting with cooperators. So an individual cheater receives the maximum benefit: T/R = (1 + s2)/1 = 1.99, and s2 = 0.99. When two cheaters meet, there is a loss of fitness, and the punishment for cheating is defined as P = 1 – c. A cooperator also loses fitness when interacting with a cheater and receives the “sucker’s payoff,” S = 1 – s1. Here we set P/S = (1 – c)/( 1 – s1) equal to the right y-intercept of the regression line, which represents the case when there is the greatest frequency of cheaters. Because our results found that the right y-intercept was a number greater than one, P had to be a value greater than S. However, the ratio cannot be solved because of two unknown variables, c and s1. We needed to devise an additional experiment to directly estimate P or S. We did this by measuring the growth rates of the cheaters and cooperators when co-infecting cells on their own. turner02This experiment mimics the situation when the cheater viruses take over the virus population. We found that the growth rate of the cheaters was 83 percent of the cooperators’ growth rate. So P = 1 – c = 0.83. We substitute the value c = 0.17 in the equation for P/S. It was then trivial to estimate the parameter s1, so we could fill in the payoff matrix. Because the cheater ultimately replaces the cooperator, while lowering the fitness of the population (see graph below, right), the results are consistent with the prisoner’s dilemma."


My take: It's entirely clear to me that in this setting cheaters can successfully displace cooperators, while simultaneously lowering the average fitness of the population. But are individual cheaters really acting irrationally? Plagued by a couple of other questions, I decided to forward the article to guest blogger Michael Sigmund who knows a heck of a lot more about game theory than I do. Here is his reply:

First, in the chapter "Cheaters Sometimes Prosper", the author sets up a game theory model and introduces the well-known prisoner's dilemma. Non-cooperative game theory has a clear solution for this game: Both players defect (if the payoff matrix has certain properties). So the strategy-pair (defection, defection) is caused by rationality of the players and not by the fact that defection offers the only possibility of obtaining the best pay-off. Behaving "collectively irrational" is an unusual phrase and could mean that the outcome of the prisoner's dilemma is not pareto-efficient. However, pareto-efficiency is an axiom commonly imposed on solution concepts of cooperative game theory which is something totally different. Moreover, I think that in order to model the evolution of the populations of the different virus types, we need concepts of evolutionary game theory. In particular we should use the concept of evolutionary stable strategies (ESS). Although this concept is correctly introduced on page 431 it isn't mentioned that it is a refinement of the Nash equilibrium which is the usual concept to solve the static one shot prisoner's dilemma.

Second, in the chapter "Game-Theory Solutions", he misses the key elements of an evolutionary game theoretic model. First of all, the author should have pointed out why we can model the evolution of a certain system by a game theoretic model. Especially the question of existence of an ESS is not mentioned. Without going into details, this describes the relation between stationary points (stationäre Punkte) and systems of differential equations.

Third, the concept to solve such games (ESS) is not mentioned explicitly in this chapter. In short an ESS gives the equilibrium frequency distribution of the virus types under a certain fitness matrix.

Finally the argument "our study was the first to demonstrate the evolution of irrational, selfish behavior in a biological system" is simply wrong. Viruses don't play strategies, hence they cannot show selfish behavior. The frequency distribution of the virus types is caused by the initial probability of the different types and by the payoffs (fitness matrix in general) if two viruses, possibly of different types are randomly matched.

Name

Url

Remember my settings?

Title:

Text:


JCaptcha - you have to read this picture in order to proceed
Change Picture