Three-person game facilitates indirect reciprocity under image scoring

Reputation building plays an important role in the evolution of reciprocal altruism when the same individuals do not interact repeatedly because, by referring to reputation, a reciprocator can know which partners are cooperative and can reciprocate with a cooperator. This reciprocity based on reputation is called indirect reciprocity. Previous studies of indirect reciprocity have focused only on two-person games in which only two individuals participate in a single interaction, and have claimed that indirectly reciprocal cooperation cannot be established under image scoring reputation criterion where the reputation of an individual who has cooperated (defected) becomes good (bad). In this study, we specifically examine three-person games, and reveal that indirectly reciprocal cooperation can be formed and maintained stably, even under image scoring, by a nucleus shield mechanism. In the nucleus shield, reciprocators are a shield that keeps out unconditional defectors, whereas unconditional cooperators are the backbone of cooperation that retains a good reputation among the population.     

The evolution of n-player cooperation-threshold games and ESS bifurcations

An evolutionary game of individuals cooperating to obtain a collective benefit is here modelled as an n-player Prisoner's Dilemma game. With reference to biological situations, such as group foraging, we introduce a threshold condition in the number of cooperators required to obtain the collective benefit. In the simplest version, a three-player game, complex behaviour appears as the replicator dynamics exhibits a catastrophic event separating a parameter region allowing for coexistence of cooperators and defectors and a region of pure defection. Cooperation emerges through an ESS bifurcation, and cooperators only thrive beyond a critical point in cost-benefit space. Moreover, a repelling fixed point of the dynamics acts as a barrier to the introduction of cooperation in defecting populations. The results illustrate the qualitative difference between two-player games and multiple player games and thus the limitations to the generality of conclusions from two-player games. We present a procedure to find the evolutionarily stable strategies in any n-player game with cost and benefit depending on the number of cooperators. This was previously done by Motro [1991. Co-operation and defection: playing the field and the ESS. J. Theor. Biol. 151, 145-154] in the special cases of convex and concave benefit functions and constant cost.     

The role of low avidity T cells in the protection against type 1 diabetes: a modeling investigation

Cytotoxic T lymphocytes (CTLs) play a dominant role in the pathogenesis of autoimmune diabetes, commonly denoted Type 1 Diabetes (T1D). These CTLs (notably CD8⁺ T cells) recognize and kill insulin-secreting pancreatic β cells, reducing their number by ∼90%. The resulting reduction of insulin secretion causes the defective regulation of glucose metabolism, leading to the characteristic symptoms of diabetes. Recognition of β cells as targets by CTLs depends on the interactions between MHC-peptide complexes on the surface of β cells and receptors (TCRs) on T cells. Those CTLs with high affinity TCRs (also called high avidity T cells) cause most of the harm, while those with low affinity TCRs (also called low avidity T cells) play a more mysterious role. Recent experimental evidence suggests that low avidity T cells accumulate as memory T cells during the disease and may be protective in NOD mice (a strain prone to developing T1D), delaying disease progression. It has been hypothesized that such low avidity T cells afford disease protection either by crowding the islets of Langerhans, where β cells reside, or by killing antigen presenting cells (APCs).In this paper, we explore the hypothesized mechanisms for this protective effect in the context of a series of models for (1) the interactions of low and high avidity T cells, (2) the effect of APCs and (3) the feedback from β cell killing to autoantigen-induced T cell proliferation. We analyze properties of these models, noting consistency of predictions with observed behaviour. We then use the models to examine the influence of various treatment strategies on the progression of the disease. The model reveals that progressive accumulation of memory low avidity autoreactive T cells during disease progression makes treatments aimed at expanding these protective T cell types more effective close to, or at the onset of clinical disease. It also provides evidence for the hypothesis that low avidity T cells kill APCs (rather than the alternate hypothesis that they crowd the islets).     

Population differentiation and migration: coalescence times in a two-sex island model for autosomal and X-linked loci

Evolutionists have debated whether population-genetic parameters, such as effective population size and migration rate, differ between males and females. In humans, most analyses of this problem have focused on the Y chromosome and the mitochondrial genome, while the X chromosome has largely been omitted from the discussion. Past studies have compared F_ST values for the Y chromosome and mitochondrion under a model with migration rates that differ between the sexes but with equal male and female population sizes. In this study we investigate rates of coalescence for X-linked and autosomal lineages in an island model with different population sizes and migration rates for males and females, obtaining the mean time to coalescence for pairs of lineages from the same deme and for pairs of lineages from different demes. We apply our results to microsatellite data from the Human Genome Diversity Panel, and we examine the male and female migration rates implied by observed F_ST values.     

Genetic diversity of microsatellite loci in hierarchically structured populations

Microsatellite loci are widely used for investigating patterns of genetic variation within and among populations. Those patterns are in turn determined by population sizes, migration rates, and mutation rates. We provide exact expressions for the first two moments of the allele frequency distribution in a stochastic model appropriate for studying microsatellite evolution with migration, mutation, and drift under the assumption that the range of allele sizes is bounded. Using these results, we study the behavior of several measures related to Wright’s F_ST, including Slatkin’s R_ST. Our analytical approximations for F_ST and R_ST show that familiar relationships between N_em and F_ST or R_ST hold when the migration and mutation rates are small. Using the exact expressions for F_ST and R_ST, our numerical results show that, when the migration and mutation rates are large, these relationships no longer hold. Our numerical results also show that the diversity measures most closely related to F_ST depend on mutation rates, mutational models (stepwise versus two-phase), migration rates, and population sizes. Surprisingly, R_ST is relatively insensitive to the mutation rates and mutational models. The differing behaviors of R_ST and F_ST suggest that properties of the among-population distribution of allele frequencies may allow the roles of mutation and migration in producing patterns of diversity to be distinguished, a topic of continuing investigation.     

Evolutionary stability of first-order-information indirect reciprocity in sizable groups

Indirect reciprocity is considered as a key mechanism for explaining the evolution of cooperation in situations where the same individuals interact only a few times. Under indirect reciprocity, an individual who helps others gets returns indirectly from others who know her good reputation. Recently, many studies have discussed the effect of reputation criteria based only on the former actions of the others (first-order information) and of those based also on the former reputation of opponents of the others (second-order information) on the evolution of indirect reciprocity. In this study, we investigate the evolutionary stability of the indirectly reciprocal strategy (discriminating strategy: DIS), which cooperates only with opponents who have good reputations, in -person games where more than two individuals take part in a single group (interaction). We show that in n-person games, DIS is an evolutionarily stable strategy (ESS) even under the image-scoring reputation criterion, which is based only on first-order information and where cooperations (defections) are judged to be good (bad). This result is in contrast to that of 2-person games where DIS is not an ESS under reputation criteria based only on first-order information.     

Replicator dynamics of reward & reputation in public goods games

Public goods games have become the mathematical metaphor for game theoretical investigations of cooperative behavior in groups of interacting individuals. Cooperation is a conundrum because cooperators make a sacrifice to benefit others at some cost to themselves. Exploiters or defectors reap the benefits and forgo costs. Despite the fact that groups of cooperators outperform groups of defectors, Darwinian selection or utilitarian principles based on rational choice should favor defectors. In order to overcome this social dilemma, much effort has been expended for investigations pertaining to punishment and sanctioning measures against defectors. Interestingly, the complementary approach to create positive incentives and to reward cooperation has received considerably less attention—despite being heavily advocated in education and social sciences for increasing productivity or preventing conflicts. Here we show that rewards can indeed stimulate cooperation in interaction groups of arbitrary size but, in contrast to punishment, fail to stabilize it. In both cases, however, reputation is essential. The combination of reward and reputation result in complex dynamics dominated by unpredictable oscillations.     

Self-organization at the origin of life

The concept of an (M,R) system with organizational invariance allows one to understand how a system may be able to maintain itself indefinitely if it is coupled to an external source of energy and materials. However, although this constitutes an important step towards understanding the difference between a living and a non-living system, it is not clear that an (M,R) system with organizational invariance is sufficient to define a living system. To take a further step towards defining what it means to be alive it is necessary to add to a simple (M,R) system some property that represents its identity, and which can be maintained and modified in subsequent generations.     

Evolution of cooperation in patchy habitat under patch decay and isolation

The spatial version of Prisoners Dilemma (PD) is studied, which incorporates habitat decay through change in the mortality parameter and habitat isolation through change in the colonization coefficient. We found four kinds of evolutionary results, which are affected profoundly by the elements of the payoff matrix and the ratio of the colonization coefficient to the mortality parameter: population extinction, a pure cooperator population, coexistence of cooperators and defectors, and a pure defector population. First, the parameter region of cooperation (pure cooperator and coexistence region) shrinks with an increase in the cooperative cost, and that of defection extends. The increase in cooperative reward makes the cooperative region extend and the defector region become small. Second, the cooperative reward can compensate for the extinction risk due to habitat destruction and allow a population to survive even if the colonization coefficient is smaller than the mortality parameter. Third, although habitat destruction (including decay and isolation) increase the extinction risk of a population, moderate external power can push the evolution of cooperation ahead of population extinction, and even make a completely cooperative world come into being. Finally, for certain values of elements of the payoff matrix, the population suffering habitat destruction can maintain a stable population size by regulating the frequencies of cooperators and defectors. This implies that the multi-behavior strategy within a population may be a mechanism to defend against the influences of a changing environment.     

Transmission dynamics of Toxoplasma gondii along an urban-rural gradient

Recently, several authors have proposed that the availability of intermediate hosts (IHs) for definitive hosts (DHs) may contribute to determining the dynamics and evolutionary ecology of parasites with facultative complex life cycles. The protozoa Toxoplasma gondii may be transmitted to DHs either via predation of infected IHs through a complex life cycle (CLC) or directly from a contaminated environment through a simple life cycle (SLC). This parasite is also present in contrasting host density environments. We tested the hypothesis that the relative contributions of the CLC and SLC along an urban-rural gradient depend on the IH supply. We built and analysed a deterministic model of the T. gondii transmission cycle. The SLC relative contribution is important only in urban-type environments, i.e., with low predation rate on IHs. In contrast, the parasite is predominantly transmitted through a CLC in suburban and rural environments. The association of the two cycles enables the parasite to spread in situations of low IH availability and low DH population size for which each cycle alone is insufficient.     

Spatial invasion of cooperation

The evolutionary puzzle of cooperation describes situations where cooperators provide a fitness benefit to other individuals at some cost to themselves. Under Darwinian selection, the evolution of cooperation is a conundrum, whereas non-cooperation (or defection) is not. In the absence of supporting mechanisms, cooperators perform poorly and decrease in abundance. Evolutionary game theory provides a powerful mathematical framework to address the problem of cooperation using the prisoner's dilemma. One well-studied possibility to maintain cooperation is to consider structured populations, where each individual interacts only with a limited subset of the population. This enables cooperators to form clusters such that they are more likely to interact with other cooperators instead of being exploited by defectors. Here we present a detailed analysis of how a few cooperators invade and expand in a world of defectors. If the invasion succeeds, the expansion process takes place in two stages: first, cooperators and defectors quickly establish a local equilibrium and then they uniformly expand in space. The second stage provides good estimates for the global equilibrium frequencies of cooperators and defectors. Under hospitable conditions, cooperators typically form a single, ever growing cluster interspersed with specks of defectors, whereas under more hostile conditions, cooperators form isolated, compact clusters that minimize exploitation by defectors. We provide the first quantitative assessment of the way cooperators arrange in space during invasion and find that the macroscopic properties and the emerging spatial patterns reveal information about the characteristics of the underlying microscopic interactions.     

Invasion and expansion of cooperators in lattice populations: Prisoner's dilemma vs. snowdrift games

The evolution of cooperation is an enduring conundrum in biology and the social sciences. Two social dilemmas, the prisoner's dilemma and the snowdrift game have emerged as the most promising mathematical metaphors to study cooperation. Spatial structure with limited local interactions has long been identified as a potent promoter of cooperation in the prisoner's dilemma but in the spatial snowdrift game, space may actually enhance or inhibit cooperation. Here we investigate and link the microscopic interaction between individuals to the characteristics of the emerging macroscopic patterns generated by the spatial invasion process of cooperators in a world of defectors. In our simulations, individuals are located on a square lattice with Moore neighborhood and update their strategies by probabilistically imitating the strategies of better performing neighbors. Under sufficiently benign conditions, cooperators can survive in both games. After rapid local equilibration, cooperators expand quadratically until global saturation is reached. Under favorable conditions, cooperators expand as a large contiguous cluster in both games with minor differences concerning the shape of embedded defectors. Under less favorable conditions, however, distinct differences arise. In the prisoner's dilemma, cooperators break up into isolated, compact clusters. The compact clustering reduces exploitation and leads to positive assortment, such that cooperators interact more frequently with other cooperators than with defectors. In contrast, in the snowdrift game, cooperators form small, dendritic clusters, which results in negative assortment and cooperators interact more frequently with defectors than with other cooperators. In order to characterize and quantify the emerging spatial patterns, we introduce a measure for the cluster shape and demonstrate that the macroscopic patterns can be used to determine the characteristics of the underlying microscopic interactions.     

Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma

Explaining the evolution of cooperation among non-relatives is one of the major challenges for evolutionary biology. In this study, we experimentally examined human cooperation in the iterated Snowdrift game (ISD), which has received little attention so far, and compared it with human cooperation in the iterated Prisoner's Dilemma (IPD), which has become the paradigm for the evolution of cooperation. We show that iteration in the ISD leads to consistently higher levels of cooperation than in the IPD. We further demonstrate that the most successful strategies known for the IPD (generous Tit-for-Tat and Pavlov) were also successfully used in the ISD. Interestingly, we found that female players cooperated significantly more often than male players in the IPD but not in the ISD. Moreover, female players in the IPD applied Tit-for-Tat-like or Pavlovian strategies significantly more often than male players, thereby achieving significantly higher pay-offs than male players did. These data demonstrate that the willingness to cooperate does not only depend on the type of the social dilemma, but also on the class of individuals involved. Altogether, our study shows that the ISD can potentially explain high levels of cooperation among non-relatives in humans. In addition, the ISD seems to reflect the social dilemma more realistically than the IPD because individuals obtain immediate direct benefits from the cooperative acts they perform and costs of cooperation are shared between cooperators.     

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y₆ receptors activated by the ubiquitous signaling nucleotide uridine 5’-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5’-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.     

E versus Z geometry in β-d-arabino-hexopyranosidulose oximes

Koenigs-Knorr-type glycosidations of peracylated 2Z-benzoyloxyimino-glycopyranosyl bromides invariably proceed with retention of the Z-geometry. Accordingly, the many β-d-hexosidulose oximes in literature which were prepared in this way and for which the oxime geometry has not been addressed explicitly, are the Z-oximes throughout. By contrast, oximation of β-d-hexopyranosid-2-uloses leads to mixtures of E and Z oximes readily separable and structurally verifiable by ¹H and ¹³C NMR. Configurational assignments rested on comparative evaluation of NMR data of E and Z isomers, and, most notably on an X-ray structural analysis of the pivaloylated isopropyl 2E-benzoyloxyimino-2-deoxy-β-d-arabino-hexopyranoside revealing the unusual ¹S₅?^1,4B conformation for the pyranoid ring.     

Uncovering operational interactions in genetic networks using asynchronous Boolean dynamics

Biological networks of large dimensions, with their diagram of interactions, are often well represented by a Boolean model with a family of logical rules. The state space of a Boolean model is finite, and its asynchronous dynamics are fully described by a transition graph in the state space. In this context, a model reduction method will be developed for identifying the active or operational interactions responsible for a given dynamic behaviour. The first step in this procedure is the decomposition of the asynchronous transition graph into its strongly connected components, to obtain a “reduced” and hierarchically organized graph of transitions. The second step consists of the identification of a partial graph of interactions and a sub-family of logical rules that remain operational in a given region of the state space. This model reduction method and its usefulness are illustrated by an application to a model of programmed cell death. The method identifies two mechanisms used by the cell to respond to death-receptor stimulation and decide between the survival and apoptotic pathways.     

Melanoblast proliferation dynamics during mouse embryonic development. Modeling and validation

In this paper, we are looking for mathematical modeling of mouse embryonic melanoblast proliferation dynamics, taking into account, the expression level of β‐catenin. This protein plays an important role into the whole signal pathway process. Different assumptions on some unobservable features lead to different candidate models. From real data measured, from biological experiments and from a priori biological knowledge, it was able to validate or invalidate some of the candidate models. Data assimilation and parameter identification allowed us to derive a mathematical model that is in very good agreement with biological data. As a result, the produced model can give tracks for biologists into their biological investigations and experimental evidence. Another interest is the use of this model for robust hidden parameter identification like double times or number of founder melanoblasts.     

On the dynamic persistence of cooperation: how lower individual fitness induces higher survivability

We study a model in which cooperation and defection coexist in a dynamical steady state. In our model, subpopulations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoner's dilemma (PD) game, determine their fitnesses. The chosen PD payoff allows cooperators, but not defectors, to maintain a homogeneous population. Individuals mutate between types and migrate to neighboring sites with low probabilities. We consider both density-dependent and density-independent versions of the model. The persistence of cooperation in this model can be explained in terms of the life cycle of a population at a site. This life cycle starts when one cooperator establishes a population. Then defectors invade and eventually take over, resulting finally in the death of the population. During this life cycle, single cooperators migrate to empty neighboring sites to found new cooperator populations. The system can reach a steady state where cooperation prevails if the global "birth" rate of populations is equal to their global "death" rate. The dynamic persistence of cooperation ranges over a large section of the model's parameter space. We compare these dynamics to those from other models for the persistence of altruism and to predator-prey models.