x. functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in Eq (5).

<p></p><p></p><p></p><p><mi>x</mi><mo>.</mo></p><p></p><p></p> functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.e016" target="_blank">Eq (5)</a>.<p></p

Replicator dynamics analysis of representative S-MIGs on 2-dimensional simplex.

<p>The triangle represents the state space, Δ = {(<i>x</i>, <i>y</i>, <i>z</i>)*** : <i>x</i>, <i>y</i>, <i>z</i> ≥ 0, <i>x</i>+<i>y</i>+<i>z</i> = 1}, where <i>x</i>, <i>y</i>, and <i>z</i> are respectively the frequencies of the cooperative incentive-providers, cooperative incentive-non-providers, and non-cooperative incentive-non-providers. </p><p></p><p><mo stretchy="false">(</mo><mi>μ</mi><mo>,</mo><mi>δ</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo></p><p><mn>1</mn><mn>2</mn></p><mo stretchy="false">)</mo><p></p><p></p>. (A) PR+R, (B) PP, (C) PB+RB(Full), and (D) RB. The abbreviations are defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.t001" target="_blank">Table 1</a>. In (A), (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) is unstable, so cooperation is never achieved regardless of the values of (<i>μ</i>, <i>δ</i>). In (B), the whole line <i>z</i> = 0 consists of fixed points, and thus, neutral drift is possible. In (C) and (D), (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) is a locally asymptotically stable point depending on the values of (<i>μ</i>, <i>δ</i>), and thus, a cooperative regime can emerge. In (C), the unstable equilibrium in the internal part on <i>z</i> = 0, <i>K</i>_<i>z</i>, is a saddle, and that on <i>y</i> = 0, <i>K</i>_<i>y</i>, is a source. In (D), <i>K</i>_<i>z</i> is a source, while <i>K</i>_<i>y</i> is a saddle.<p></p

Presentation1.PDF

<p>Indirect reciprocity is one of the basic mechanisms to sustain mutual cooperation, by which beneficial acts are returned, not by the recipient, but by third parties. This mechanism relies on the ability of individuals to know the past actions of others, and to assess those actions. There are many different systems of assessing others, which can be interpreted as rudimentary social norms (i.e., views on what is “good” or “bad”). In this paper, impacts of different adaptive architectures, i.e., ways for individuals to adapt to environments, on indirect reciprocity are investigated. We examine two representative architectures: one based on replicator dynamics and the other on genetic algorithm. Different from the replicator dynamics, the genetic algorithm requires describing the mixture of all possible norms in the norm space under consideration. Therefore, we also propose an analytic method to study norm ecosystems in which all possible second order social norms potentially exist and compete. The analysis reveals that the different adaptive architectures show different paths to the evolution of cooperation. Especially we find that so called Stern-Judging, one of the best studied norms in the literature, exhibits distinct behaviors in both architectures. On one hand, in the replicator dynamics, Stern-Judging remains alive and gets a majority steadily when the population reaches a cooperative state. On the other hand, in the genetic algorithm, it gets a majority only temporarily and becomes extinct in the end.</p

Illustration of meta-incentive game (MIG).

<p>Four individuals are randomly drawn from the population and randomly assigned to one of four roles, recipient, donor, first-order player, and second-order player. In the first stage, the donor decides whether to help the recipient. In the second stage, the first-order player decides whether to provide an incentive for the donor; and in the last stage, the second-order player decides whether to provide an incentive to the first-order player.</p

Types of MIG.

<p>Types of MIG.</p

x. functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in Eq (5).

<p></p><p></p><p></p><p><mi>x</mi><mo>.</mo></p><p></p><p></p> functions on the lines <i>y</i> = 0 and <i>z</i> = 0 for each type of S-MIG. Here, <i>f</i>(<i>x</i>) and <i>g</i>(<i>x</i>) are defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.e016" target="_blank">Eq (5)</a>.<p></p

Illustration of replicator dynamics analyses for each type of S-MIG.

<p>This figure illustrates all 24 types of S-MIG. The abbreviations are defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.t001" target="_blank">Table 1</a>. Their vertical layering in the figure reflects the existence condition for the basin of attraction on the point (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0) related to (<i>μ</i>, <i>δ</i>) under which a cooperative regime emerges. The frames represent the form of local stability at point (<i>x</i>, <i>y</i>, <i>z</i>) = (1, 0, 0): the point is unstable for each type in the top frame which corresponds to (A) in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003" target="_blank">Fig 3</a>, is a non-isolated equilibrium for each type in the bottom right frame which corresponds to (B) in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003" target="_blank">Fig 3</a>, and is asymptotically stable for each type in the bottom left frame which corresponds to (C) and (D) in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.g003" target="_blank">Fig 3</a>.</p

Equations and solutions of <i>z</i>* in Eq (6) for each type.

<p>Equations and solutions of <i>z</i>* in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004232#pcbi.1004232.e060" target="_blank">Eq (6)</a> for each type.</p

Time course and SCS electrode, and the brain region punched out for protein assay.

<p>(A) Scheme showing overall experimental design. (B) Scheme showing experimental design for protein assay. (C) Photograph showing SCS electrode used in this study (diameter: 2 mm; wire length: 60 mm). (D) Scheme showing a rat during stimulation. (E) Brain tissue (diameter: 3 mm showing gray circle), corresponding to the striatum, was punched out from both the lesioned and the intact side.</p

Tyrosine hydroxylase (TH) immunostaining in the striatum and the ratio to the intact side.

<p>(A) TH immunostaining in the striatum. Severe loss of TH-positive fibers was seen in the lesioned striatum of control group. Preservation of TH-positive fibers was seen in the lesioned striatum of all SCS groups. Scale bar: 200 µm. (B) The all SCS groups showed significant preservation of TH-positive fibers in the lesioned striatum, compared to those in control group (*p<0.05, n = 10, respectively).</p