Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat.

The iterated Prisoner's Dilemma has become the paradigm for the evolution of cooperation among egoists. Since Axelrod's classic computer tournaments and Nowak and Sigmund's extensive simulations of evolution, we know that natural selection can favor cooperative strategies in the Prisoner's Dilemma. According to recent developments of theory the last champion strategy of "win--stay, lose--shift" ("Pavlov") is the winner only if the players act simultaneously. In the more natural situation of players alternating the roles of donor and recipient a strategy of "Generous Tit-for-Tat" wins computer simulations of short-term memory strategies. We show here by experiments with humans that cooperation dominated in both the simultaneous and the alternating Prisoner's Dilemma. Subjects were consistent in their strategies: 30% adopted a Generous Tit-for-Tat-like strategy, whereas 70% used a Pavlovian strategy in both the alternating and the simultaneous game. As predicted for unconditional strategies, Pavlovian players appeared to be more successful in the simultaneous game whereas Generous Tit-for-Tat-like players achieved higher payoffs in the alternating game. However, the Pavlovian players were smarter than predicted: they suffered less from defectors and exploited cooperators more readily. Humans appear to cooperate either with a Generous Tit-for-Tat-like strategy or with a strategy that appreciates Pavlov's advantages but minimizes its handicaps.

Types of evolutionary stability and the problem of cooperation.

The evolutionary stability of cooperation is a problem of fundamental importance for the biological and social sciences. Different claims have been made about this issue: whereas Axelrod and Hamilton's [Axelrod, R. & Hamilton, W. (1981) Science 211, 1390-1398] widely recognized conclusion is that cooperative rules such as "tit for tat" are evolutionarily stable strategies in the iterated prisoner's dilemma (IPD), Boyd and Lorberbaum [Boyd, R. & Lorberbaum, J. (1987) Nature (London) 327, 58-59] have claimed that no pure strategy is evolutionarily stable in this game. Here we explain why these claims are not contradictory by showing in what sense strategies in the IPD can and cannot be stable and by creating a conceptual framework that yields the type of evolutionary stability attainable in the IPD and in repeated games in general. Having established the relevant concept of stability, we report theorems on some basic properties of strategies that are stable in this sense. We first show that the IPD has "too many" such strategies, so that being stable does not discriminate among behavioral rules. Stable strategies differ, however, on a property that is crucial for their evolutionary survival--the size of the invasion they can resist. This property can be interpreted as a strategy's evolutionary robustness. Conditionally cooperative strategies such as tit for tat are the most robust. Cooperative behavior supported by these strategies is the most robust evolutionary equilibrium: the easiest to attain, and the hardest to disrupt.

Working memory constrains human cooperation in the Prisoner’s Dilemma

Many problems in human society reflect the inability of selfish parties to cooperate. The “Iterated Prisoner’s Dilemma” has been used widely as a model for the evolution of cooperation in societies. Axelrod’s computer tournaments and the extensive simulations of evolution by Nowak and Sigmund and others have shown that natural selection can favor cooperative strategies in the Prisoner’s Dilemma. Rigorous empirical tests, however, lag behind the progress made by theorists. Clear predictions differ depending on the players’ capacity to remember previous rounds of the game. To test whether humans use the kind of cooperative strategies predicted, we asked students to play the iterated Prisoner’s Dilemma game either continuously or interrupted after each round by a secondary memory task (i.e., playing the game “Memory”) that constrained the students’ working-memory capacity. When playing without interruption, most students used “Pavlovian” strategies, as predicted, for greater memory capacity, and the rest used “generous tit-for-tat” strategies. The proportion of generous tit-for-tat strategies increased when games of Memory interfered with the subjects’ working memory, as predicted. Students who continued to use complex Pavlovian strategies were less successful in the Memory game, but more successful in the Prisoner’s Dilemma, which indicates a trade-off in memory capacity for the two tasks. Our results suggest that the set of strategies predicted by game theorists approximates human reality.

Solution to Darwin's dilemma: Discovery of the missing Precambrian record of life

In 1859, in On the Origin of Species, Darwin broached what he regarded to be the most vexing problem facing his theory of evolution—the lack of a rich fossil record predating the rise of shelly invertebrates that marks the beginning of the Cambrian Period of geologic time (≈550 million years ago), an “inexplicable” absence that could be “truly urged as a valid argument” against his all embracing synthesis. For more than 100 years, the “missing Precambrian history of life” stood out as one of the greatest unsolved mysteries in natural science. But in recent decades, understanding of life's history has changed markedly as the documented fossil record has been extended seven-fold to some 3,500 million years ago, an age more than three-quarters that of the planet itself. This long-sought solution to Darwin's dilemma was set in motion by a small vanguard of workers who blazed the trail in the 1950s and 1960s, just as their course was charted by a few pioneering pathfinders of the previous century, a history of bold pronouncements, dashed dreams, search, and final discovery.

Population dynamics, demographic stochasticity, and the evolution of cooperation

A basic evolutionary problem posed by the Iterated Prisoner’s Dilemma game is to understand when the paradigmatic cooperative strategy Tit-for-Tat can invade a population of pure defectors. Deterministically, this is impossible. We consider the role of demographic stochasticity by embedding the Iterated Prisoner’s Dilemma into a population dynamic framework. Tit-for-Tat can invade a population of defectors when their dynamics exhibit short episodes of high population densities with subsequent crashes and long low density periods with strong genetic drift. Such dynamics tend to have reddened power spectra and temporal distributions of population size that are asymmetric and skewed toward low densities. The results indicate that ecological dynamics are important for evolutionary shifts between adaptive peaks.

Unusual 1H NMR chemical shifts support (His) Cɛ1—H⋅⋅⋅O⩵C H-bond: Proposal for reaction-driven ring flip mechanism in serine protease catalysis

13C-selective NMR, combined with inhibitor perturbation experiments, shows that the Cɛ1—H proton of the catalytic histidine in resting α-lytic protease and subtilisin BPN′ resonates, when protonated, at 9.22 ppm and 9.18 ppm, respectively, which is outside the normal range for such protons and ≈0.6 to 0.8 ppm further downfield than previously reported. They also show that the previous α-lytic protease assignments [Markley, J. L., Neves, D. E., Westler, W. M., Ibanez, I. B., Porubcan, M. A. & Baillargeon, M. W. (1980) Front. Protein Chem. 10, 31–61] were to signals from inactive or denatured protein. Simulations of linewidth vs. pH demonstrate that the true signal is more difficult to detect than corresponding signals from inactive derivatives, owing to higher imidazole pKa values and larger chemical shift differences between protonated and neutral forms. A compilation and analysis of available NMR data indicates that the true Cɛ1—H signals from other serine proteases are similarly displaced downfield, with past assignments to more upfield signals probably in error. The downfield displacement of these proton resonances is shown to be consistent with an H-bond involving the histidine Cɛ1—H as donor, confirming the original hypothesis of Derewenda et al. [Derewenda, Z. S., Derewenda, U. & Kobos, P. M. (1994) J. Mol. Biol. 241, 83–93], which was based on an analysis of literature x-ray crystal structures of serine hydrolases. The invariability of this H-bond among enzymes containing Asp-His-Ser triads indicates functional importance. Here, we propose that it enables a reaction-driven imidazole ring flip mechanism, overcoming a major dilemma inherent in all previous mechanisms, namely how these enzymes catalyze both the formation and productive breakdown of tetrahedral intermediates.

Statistical prediction of single-stranded regions in RNA secondary structure and application to predicting effective antisense target sites and beyond

Single-stranded regions in RNA secondary structure are important for RNA–RNA and RNA–protein interactions. We present a probability profile approach for the prediction of these regions based on a statistical algorithm for sampling RNA secondary structures. For the prediction of phylogenetically-determined single-stranded regions in secondary structures of representative RNA sequences, the probability profile offers substantial improvement over the minimum free energy structure. In designing antisense oligonucleotides, a practical problem is how to select a secondary structure for the target mRNA from the optimal structure(s) and many suboptimal structures with similar free energies. By summarizing the information from a statistical sample of probable secondary structures in a single plot, the probability profile not only presents a solution to this dilemma, but also reveals ‘well-determined’ single-stranded regions through the assignment of probabilities as measures of confidence in predictions. In antisense application to the rabbit β-globin mRNA, a significant correlation between hybridization potential predicted by the probability profile and the degree of inhibition of in vitro translation suggests that the probability profile approach is valuable for the identification of effective antisense target sites. Coupling computational design with DNA–RNA array technique provides a rational, efficient framework for antisense oligonucleotide screening. This framework has the potential for high-throughput applications to functional genomics and drug target validation.

Alpha-helical, but not beta-sheet, propensity of proline is determined by peptide environment.

Proline is established as a potent breaker of both alpha-helical and beta-sheet structures in soluble (globular) proteins. Thus, the frequent occurrence of the Pro residue in the putative transmembrane helices of integral membrane proteins, particularly transport proteins, presents a structural dilemma. We propose that this phenomenon results from the fact that the structural propensity of a given amino acid may be altered to conform to changes imposed by molecular environment. To test this hypothesis on proline, we synthesized model peptides of generic sequence H2N-(Ser-LyS)2-Ala- Leu-Z-Ala-Leu-Z-Trp-Ala-Leu-Z-(Lys-Ser)3-OH (Z = Ala and/or Pro). Peptide conformations were analyzed by circular dichroism spectroscopy in aqueous buffer, SDS, lysophosphatidylglycerol micelles, and organic solvents (methanol, trifluoroethanol, and 2-propanol). The helical propensity of Pro was found to be greatly enhanced in the membrane-mimetic environments of both lipid micelles and organic solvents. Proline was found to stabilize the alpha-helical conformation relative to Ala at elevated temperatures in 2-propanol, an observation that argues against the doctrine that Pro is the most potent alpha-helix breaker as established in aqueous media. Parallel studies in deoxycholate micelles of the temperature-induced conformational transitions of the single-spanning membrane bacteriophage IKe major coat protein, in which the Pro-containing wild type was compared with Pro30 --> Ala mutant, Pro was found to protect the helix, but disrupt the beta-sheet structure as effectively as it does to model peptides in water. The intrinsic capacity of Pro to disrupt beta-sheets was further reflected in a survey of porins where Pro was found to be selectively excluded from the core of membrane-spanning beta-sheet barrels. The overall data provide a rationale for predicting and understanding the structural consequences when Pro occurs in the context of a membrane.