Direct reciprocity on graphs

Direct reciprocity is a mechanism for the evolution of cooperation based on the idea of repeated encounters between the same two individuals. Here we examine direct reciprocity in structured populations, where individuals occupy the vertices of a graph. The edges denote who interacts with whom. The graph represents spatial structure or a social network. For birth-death or pairwise comparison updating, we find that evolutionary stability of direct reciprocity is more restrictive on a graph than in a well-mixed population, but the condition for reciprocators to be advantageous is less restrictive on a graph. For death-birth and imitation updating, in contrast, both conditions are easier to fulfill on a graph. Moreover, for all four update mechanisms, reciprocators can dominate defectors on a graph, which is never possible in a well-mixed population. We also study the effect of an error rate, which increases with the number of links per individual; interacting with more people simultaneously enhances the probability of making mistakes. We provide analytic derivations for all results.     

On intrapersonal reciprocity

The existence of conflicts between different sets of genes within the genome is now widely accepted. But where there is conflict, there are also benefits to be gained from cooperation between the contending parties to reduce conflict costs. The potential for reciprocal altruism [Trivers, 1971] within an individual organism has hitherto attracted little attention but raises the possibility of complex interactions within the self.     

The competition of assessment rules for indirect reciprocity

Indirect reciprocity is one of the basic mechanisms to sustain mutual cooperation. Beneficial acts are returned, not by the recipient, but by third parties. Indirect reciprocity is based on reputation and status: it pays to provide help because this makes one more likely to receive help in turn. The mechanism depends on knowing the past behavior of other players, and assessing that behavior. There are many different systems of assessing other individuals, which can be interpreted as rudimentary moral systems (i.e. views on what is ‘good’ or ‘bad’). In this paper, we describe the competition of some of the leading assessment rules called SUGDEN and KANDORI by analytic methods. We show that the sterner rule KANDORI has a slight advantage in the sense that KANDORI-players have more chance to earn higher payoff than SUGDEN-players in the presence of unconditional altruists. On the other hand, we see that the unconditional altruists are eliminated in the long run and that stable polymorphisms of KANDORI and SUGDEN can subsist, but that a moral consensus is realized even in those polymorphic states: all players’ images are the same in each observer's eyes.     

Generalized reciprocity in rats

The evolution of cooperation among nonrelatives has been explained by direct, indirect, and strong reciprocity. Animals should base the decision to help others on expected future help, which they may judge from past behavior of their partner. Although many examples of cooperative behavior exist in nature where reciprocity may be involved, experimental evidence for strategies predicted by direct reciprocity models remains controversial; and indirect and strong reciprocity have been found only in humans so far. Here we show experimentally that cooperative behavior of female rats is influenced by prior receipt of help, irrespective of the identity of the partner. Rats that were trained in an instrumental cooperative task (pulling a stick in order to produce food for a partner) pulled more often for an unknown partner after they were helped than if they had not received help before. This alternative mechanism, called generalized reciprocity, requires no specific knowledge about the partner and may promote the evolution of cooperation among unfamiliar nonrelatives.     

Nets with reciprocity bias

The random net is modified by the introduction of a finite probability that an arbitrarily selected axon is reciprocated. The resulting distribution of convergence orders is compared with the corresponding distribution for random nets (the Poisson distribution). It is shown that for small values of the bias the terms of the distribution near the modal term (within a range equal to the square root of the axon density) at first increase as the bias increases, while the remaining terms decrease. The modal term itself is shown to increase monotonically with the bias throughout the whole range of the bias. In some special cases, the general behavior of the terms is calculated for the whole range of the bias. Some implications are discussed related to the statistical properties of sociograms.     

Search for bioorganic compounds and organisms on Mars

A prototype of new instrument is under construction as a part of Russian Mars program to search for bioorganic compounds and microorganisms which might be frozen in rock under the places where the traces of water were found or near the poles of Mars. The proposed instrument consists of a quadrupole mass spectrometer (QMS) to detect chemical compounds and a fluorescent microscope system (FMS) to detect organisms and bioorganic compounds in bulk.     

Reactive strategies in indirect reciprocity

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean 'discriminatoriness' in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.     

Upstream reciprocity in heterogeneous networks

Many mechanisms for the emergence and maintenance of altruistic behavior in social dilemma situations have been proposed. Indirect reciprocity is one such mechanism, where other-regarding actions of a player are eventually rewarded by other players with whom the original player has not interacted. The upstream reciprocity (also called generalized indirect reciprocity) is a type of indirect reciprocity and represents the concept that those helped by somebody will help other unspecified players. In spite of the evidence for the enhancement of helping behavior by upstream reciprocity in rats and humans, theoretical support for this mechanism is not strong. In the present study, we numerically investigate upstream reciprocity in heterogeneous contact networks, in which the players generally have different number of neighbors. We show that heterogeneous networks considerably enhance cooperation in a game of upstream reciprocity. In heterogeneous networks, the most generous strategy, by which a player helps a neighbor on being helped and in addition initiates helping behavior, first occupies hubs in a network and then disseminates to other players. The scenario to achieve enhanced altruism resembles that seen in the case of the Prisoner's Dilemma game in heterogeneous networks.     

Evolution of indirect reciprocity in groups of various sizes and comparison with direct reciprocity

Recently many studies have investigated the evolution of indirect reciprocity through which cooperative action is returned by a third individual, e.g. individual A helped B and then receives help from C. Most studies on indirect reciprocity have presumed that only two individuals take part in a single interaction (group), e.g. A helps B and C helps A. In this paper, we investigate the evolution of indirect reciprocity when more than two individuals take part in a single group, and compare the result with direct reciprocity through which cooperative action is directly returned by the recipient. Our analyses show the following. In the population with discriminating cooperators and unconditional defectors, whether implementation error is included or not, (i) both strategies are evolutionarily stable and the evolution of indirect reciprocity becomes more difficult as group size increases, and (ii) the condition for the evolution of indirect reciprocity under standing reputation criterion where the third individuals distinguish between justified and unjustified defections is more relaxed than that under image scoring reputation criterion in which the third individuals do not distinguish with. Furthermore, in the population that also includes unconditional cooperators, (iii) in the presence of errors in implementation, the discriminating strategy is evolutionarily stable not only under standing but also under image scoring if group size is larger than two. Finally, (iv) in the absence of errors in implementation, the condition for the evolution of direct reciprocity is equivalent to that for the evolution of indirect reciprocity under standing, and, in the presence of errors, the condition for the evolution of direct reciprocity is very close to that for the evolution of indirect reciprocity under image scoring.     

Strong reciprocity and human sociality

Human groups maintain a high level of sociality despite a low level of relatedness among group members. This paper reviews the evidence for an empirically identifiable form of prosocial behavior in humans, which we call "strong reciprocity", that may in part explain human sociality. A strong reciprocator is predisposed to cooperate with others and punish non-cooperators, even when this behavior cannot be justified in terms of extended kinship or reciprocal altruism. We present a simple model, stylized but plausible, of the evolutionary emergence of strong reciprocity.     

Indirect reciprocity among imperfect individuals

Reciprocal cooperation occurs when the overall benefits of receiving help exceed the costs of donating help (Q. Rev. Biol. 46 (197) 35). That is, individuals in good condition--for whom the pertinent costs are relatively small; donate help in order to secure reciprocity in their hour of need--when the benefits of receiving a donation are large. Consequently, reciprocity occurs among individuals who occasionally need help. In particular, such individuals will be unable to help others, no matter how deserving, when in need of help themselves--involuntary defection. This paper deals with the effects of involuntary defection in the context of a specific model of indirect reciprocity (i.e. reciprocal altruism that is directed toward all the cooperative members of the community) due to Nowak and Sigmund (J. Theor. Biol.194 (1998b) 561: Sections 2-4). In that model, the authors formulate the decision rules for conditional cooperation in the context of indirect reciprocity, and demonstrate that these decision rules can account for a long-term persistence of cooperation. Here we show that addition of involuntary defection to the decision rules formulated by Nowak and Sigmund results in indirect reciprocity that is evolutionary stable under appropriate conditions. Moreover, for a wide range of parameter values, evolutionary stability of cooperation requires a mixture of conditional- and unconditional-altruist behaviors. To recollect, unconditional altruist strategy can be viewed as conditional altruist strategy sans the ability to decide when the help-soliciting individual should be refused help. That is, given involuntary defection, stability of cooperation requires an occasional forgiveness, if only by default, of a failure to donate help. Thus, we see that evolutionary stable indirect reciprocity does not require perfection in either the ability to assess the merits of the help-soliciting individuals, or the ability to donate help when it is merited. On the contrary, we are forced to conclude that reciprocity, at least in the current case, is stable only among imperfect individuals.     

Marmoset monkeys evaluate third-party reciprocity

Many non-human primates have been observed to reciprocate and to understand reciprocity in one-to-one social exchanges. A recent study demonstrated that capuchin monkeys are sensitive to both third-party reciprocity and violation of reciprocity; however, whether this sensitivity is a function of general intelligence, evidenced by their larger brain size relative to other primates, remains unclear. We hypothesized that highly pro-social primates, even with a relatively smaller brain, would be sensitive to others'' reciprocity. Here, we show that common marmosets discriminated between human actors who reciprocated in social exchanges with others and those who did not. Monkeys accepted rewards less frequently from non-reciprocators than they did from reciprocators when the non-reciprocators had retained all food items, but they accepted rewards from both actors equally when they had observed reciprocal exchange between the actors. These results suggest that mechanisms to detect unfair reciprocity in third-party social exchanges do not require domain-general higher cognitive ability based on proportionally larger brains, but rather emerge from the cooperative and pro-social tendencies of species, and thereby suggest this ability evolved in multiple primate lineages.     

Indirect reciprocity under incomplete observation

Indirect reciprocity, in which individuals help others with a good reputation but not those with a bad reputation, is a mechanism for cooperation in social dilemma situations when individuals do not repeatedly interact with the same partners. In a relatively large society where indirect reciprocity is relevant, individuals may not know each other's reputation even indirectly. Previous studies investigated the situations where individuals playing the game have to determine the action possibly without knowing others' reputations. Nevertheless, the possibility that observers of the game, who generate the reputation of the interacting players, assign reputations without complete information about them has been neglected. Because an individual acts as an interacting player and as an observer on different occasions if indirect reciprocity is endogenously sustained in a society, the incompleteness of information may affect either role. We examine the game of indirect reciprocity when the reputations of players are not necessarily known to observers and to interacting players. We find that the trustful discriminator, which cooperates with good and unknown players and defects against bad players, realizes cooperative societies under seven social norms. Among the seven social norms, three of the four suspicious norms under which cooperation (defection) to unknown players leads to a good (bad) reputation enable cooperation down to a relatively small observation probability. In contrast, the three trustful norms under which both cooperation and defection to unknown players lead to a good reputation are relatively efficient.     

Invertebrates as model organisms for research on aging biology

Invertebrate model systems, such as nematodes and fruit flies, have provided valuable information about the genetics and cellular biology involved in aging. However, limitations of these simple, genetically tractable organisms suggest the need for other model systems, some of them invertebrate, to facilitate further advances in the understanding of mechanisms of aging and longevity in mammals, including humans. This paper introduces 10 review articles about the use of invertebrate model systems for the study of aging by authors who participated in an ‘NIA-NIH symposium on aging in invertebrate model systems’ at the 2013 International Congress for Invertebrate Reproduction and Development. In contrast to the highly derived characteristics of nematodes and fruit flies as members of the superphylum Ecdysozoa, cnidarians, such as Hydra, are more ‘basal’ organisms that have a greater number of genetic orthologs in common with humans. Moreover, some other new model systems, such as the urochordate Botryllus schlosseri, the tunicate Ciona, and the sea urchins (Echinodermata) are members of the Deuterostomia, the same superphylum that includes all vertebrates, and thus have mechanisms that are likely to be more closely related to those occurring in humans. Additional characteristics of these new model systems, such as the recent development of new molecular and genetic tools and a more similar pattern to humans of regeneration and stem cell function suggest that these new model systems may have unique advantages for the study of mechanisms of aging and longevity.     

Constraints on models for the flagellar rotary motor

Most bacteria that swim are propelled by flagellar filaments, each driven at its base by a rotary motor embedded in the cell wall and cytoplasmic membrane. A motor is about 45 nm in diameter and made up of about 20 different kinds of parts. It is assembled from the inside out. It is powered by a proton (or in some species, a sodium-ion) flux. It steps at least 400 times per revolution. At low speeds and high torques, about 1000 protons are required per revolution, speed is proportional to protonmotive force, and torque varies little with temperature or hydrogen isotope. At high speeds and low torques, torque increases with temperature and is sensitive to hydrogen isotope. At room temperature, torque varies remarkably little with speed from about -100 Hz (the present limit of measurement) to about 200 Hz, and then it declines rapidly reaching zero at about 300 Hz. These are facts that motor models should explain. None of the existing models for the flagellar rotary motor completely do so.     

The evolution of generalized reciprocity on social interaction networks

Generalized reciprocity (help anyone, if helped by someone) is a minimal strategy capable of supporting cooperation between unrelated individuals. Its simplicity makes it an attractive model to explain the evolution of reciprocal altruism in animals that lack the information or cognitive skills needed for other types of reciprocity. Yet, generalized reciprocity is anonymous and thus defenseless against exploitation by defectors. Recognizing that animals hardly ever interact randomly, we investigate whether social network structure can mitigate this vulnerability. Our results show that heterogeneous interaction patterns strongly support the evolution of generalized reciprocity. The future probability of being rewarded for an altruistic act is inversely proportional to the average connectivity of the social network when cooperators are rare. Accordingly, sparse networks are conducive to the invasion of reciprocal altruism. Moreover, the evolutionary stability of cooperation is enhanced by a modular network structure. Communities of reciprocal altruists are protected against exploitation, because modularity increases the mean access time, that is, the average number of steps that it takes for a random walk on the network to reach a defector. Sparseness and community structure are characteristic properties of vertebrate social interaction patterns, as illustrated by network data from natural populations ranging from fish to primates.