Biomedical subjects

Hisashi Ohtsuki

Publications and source records attributed to Hisashi Ohtsuki.

8 recordsLinked to original sources

PubMed2006

Evolutionary games on cycles.

Traditional evolutionary game theory explores frequency-dependent selection in well-mixed populations without spatial or stochastic effects. But recently there has been much interest in studying the evolutionary game dynamics in spatial settings, on lattices and other graphs. Here, we present an analytic approach for the stochastic evolutionary game dynamics on the simplest possible graph, the cycle. For three different update rules, called 'birth-death' (BD), 'death-birth' (DB) and 'imitation' (IM), we derive exact conditions for natural selection to favour one strategy over another. As specific examples, we consider a coordination game and Prisoner's Dilemma. In the latter case, selection can favour cooperators over defectors for DB and IM updating. We also study the case where the replacement graph of evolutionary updating remains a cycle, but the interaction graph for playing the game is a complete graph. In this setting, all three update rules lead to identical conditions in the limit of weak selection, where we find the '1/3-law' of well-mixed populations.

Biological Evolution↗

PubMed2006

Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation.

Reputation formation is a key to understanding indirect reciprocity. In particular, the way to assign reputation to each individual, namely a norm that describes who is good and who is bad, greatly affects the possibility of sustained cooperation in the population. Previously, we have exhaustively studied reputation dynamics that are able to maintain a high level of cooperation at the ESS. However, this analysis examined the stability of monomorphic population and did not investigate polymorphic population where several strategies coexist. Here, we study the evolutionary dynamics of multiple behavioral strategies by replicator dynamics. We exhaustively study all 16 possible norms under which the reputation of a player in the next round is determined by the action of the self and the reputation of the opponent. For each norm, we explore evolutionary dynamics of three strategies: unconditional cooperators, unconditional defectors, and conditional cooperators. We find that only three norms, simple-standing, Kandori, and shunning, can make conditional cooperation evolutionarily stable, hence, realize sustained cooperation. The other 13 norms, including scoring, ultimately lead to the invasion by defectors. Also, we study the model in which private reputation errors exist to a small extent. In this case, we find the stable coexistence of unconditional and conditional cooperators under the three norms.

Biological Evolution↗

PubMed2006

The replicator equation on graphs.

We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called 'birth-death', 'death-birth' and 'imitation'. A fourth update rule, 'pairwise comparison', is shown to be equivalent to birth-death updating in our model. We use pair approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner's Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game.

Animals↗

PubMed2006

A simple rule for the evolution of cooperation on graphs and social networks.

A fundamental aspect of all biological systems is cooperation. Cooperative interactions are required for many levels of biological organization ranging from single cells to groups of animals. Human society is based to a large extent on mechanisms that promote cooperation. It is well known that in unstructured populations, natural selection favours defectors over cooperators. There is much current interest, however, in studying evolutionary games in structured populations and on graphs. These efforts recognize the fact that who-meets-whom is not random, but determined by spatial relationships or social networks. Here we describe a surprisingly simple rule that is a good approximation for all graphs that we have analysed, including cycles, spatial lattices, random regular graphs, random graphs and scale-free networks: natural selection favours cooperation, if the benefit of the altruistic act, b, divided by the cost, c, exceeds the average number of neighbours, k, which means b/c > k. In this case, cooperation can evolve as a consequence of 'social viscosity' even in the absence of reputation effects or strategic complexity.

Altruism↗

PubMed2005

The leading eight: social norms that can maintain cooperation by indirect reciprocity.

The theory of indirect reciprocation explains the evolution of cooperation among unrelated individuals, engaging in one-shot interaction. Using reputation, a player acquires information on who are worth cooperating and who are not. In a previous paper, we formalized the reputation dynamics, a rule to assign a binary reputation (good or bad) to each player when his action, his current reputation, and the opponent's reputation are given. We then examined all the possible reputation dynamics, and found that there exist only eight reputation dynamics named "leading eight" that can maintain the ESS with a high level of cooperation, even if errors are included in executing intended cooperation and in reporting the observation to the public. In this paper, we study the nature of these successful social norms. First, we characterize the role of each pivot of the reputation dynamics common to all of the leading eight. We conclude that keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving. Second, we prove the two basic properties of the leading eight, which give a quantitative evaluation of the ESS condition and the level of cooperation maintained at the ESS.

Biological Evolution↗

PubMed2004

How should we define goodness?--reputation dynamics in indirect reciprocity.

Theory of indirect reciprocity is important in explaining cooperation between humans. Since a partner of a social interaction often changes, an individual should assess his partner by using social information such as reputation and make decisions whether to help him or not. To those who have 'good' social reputation does a player give aid as reciprocation, whereas he has to refuse to help those who have 'bad' reputation. Otherwise benefits of altruism is easily exploited by them. Little has been known, however, about the definition of 'goodness' in reputation. What kind of actions are and should be regarded as good and what kind of actions bad? And what sort of goodness enables sustaining exchange of altruism? We herein challenge this question with an evolutionary perspective. We generalize social reputation as 'Honor-score' (H-score) and examine the conditions under which individuals in a group stably maintain cooperative relationships based on indirect reciprocity. We examine the condition for evolutionarily stable strategies (ESSs) over 4096 possible cases exhaustively. Mathematical analysis reveals that only eight cases called 'leading eight' are crucial to the evolution of indirect reciprocity. Each in the leading eight shares two common characteristics: (i) cooperation with good persons is regarded as good while defection against them is regarded as bad, and (ii) defection against bad persons should be regarded as a good behavior because it works as sanction. Our results give one solution to the definition of goodness from an evolutionary viewpoint. In addition, we believe that the formalism of reputation dynamics gives general insights into the way social information is generated, handled, and transmitted in animal societies.

Altruism↗

PubMed2004

The role of pigment cells in the brain of ascidian larva.

The functions of melanin in the pigment cells, the ocellus and the otolith, of ascidian larvae were studied by their swimming behavior and cell morphology with and without 1-phenyl-2-thiourea (PTU), an inhibitor of vertebrate tyrosinase. Melanin formation in both the otolith and the ocellus of PTU-treated larvae at 12 hours of development was completely inhibited. These larvae were unable to swim because of abnormal tail development, but expression of rhodopsin in the outer segments of the photoreceptor was normal. In the PTU-treated larvae at 15 hours of development, melanin formation in the ocellus was inhibited, but that in the otolith seemed to be normal. The photic behavior of these larvae was normal, as was rhodopsin expression in the outer segments. However, the treated larvae lost upward swimming behavior. Synchrotron radiation X-ray fluorescence images showed that metallic elements of K, Ca, and Zn in the statocyte of larva were greatly decreased by PTU treatment, which may result in lowering the specific gravity of the pigment mass. SEM observations showed that the statocyte of Ciona intestinalis was supported by three parts, a foot-piece of the statocyte itself and two fibrous spring-like structures produced from protuberances. All three structures were synaptotagmin-positive. Movement of the statocyte would be detected by these three structures and thus would be responsible for the gravitational orientation.

Animals↗

PubMed2004

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.

Altruism↗