Mutation Rate Evolution in Replicator Dynamics

The stabilization of equilibria in evolutionary game dynamics through mutation: mutation limits in evolutionary games

The multi-population replicator dynamics is a dynamic approach to coevolving populations and multi-player games and is related to Cross learning. In general, not every equilibrium is a Nash equilibrium of the underlying game, and the convergence is not guaranteed. In particular, no interior equilibrium can be asymptotically stable in the multi-population replicator dynamics, e.g. resulting in cyclic orbits around a single interior Nash equilibrium. We introduce a new notion of equilibria of replicator dynamics, called mutation limits, based on a naturally arising, simple form of mutation, which is invariant under the specific choice of mutation parameters. We prove the existence of mutation limits for a large class of games, and consider a particularly interesting subclass called attracting mutation limits. Attracting mutation limits are approximated in every (mutation-)perturbed replicator dynamics, hence they offer an approximate dynamic solution to the underlying game even if the original dynamic is not convergent. Thus, mutation stabilizes the system in certain cases and makes attracting mutation limits near attainable. Hence, attracting mutation limits are relevant as a dynamic solution concept of games. We observe that they have some similarity to Q-learning in multi-agent reinforcement learning. Attracting mutation limits do not exist in all games, however, raising the question of their characterization.

Attenuation of Live-Attenuated Yellow Fever 17D Vaccine Virus Is Localized to a High-Fidelity Replication Complex

Live-attenuated viral vaccines are highly safe and efficacious but represent complex and often multigenic attenuation mechanisms. Most of these vaccines have been generated empirically by serial passaging of a wild-type (WT) virus in cell culture. One of the safest and most effective live-attenuated vaccines is yellow fever (YF) virus strain 17D, which has been used for over 80 years to control YF disease. The availability of the WT parental strain of 17D, Asibi virus, and large quantities of clinical data showing the effectiveness of the 17D vaccine make this WT parent/vaccine pair an excellent model for investigating RNA virus attenuation. Here, we investigate a mechanism of 17D attenuation and show that the vaccine virus is resistant to the antiviral compound ribavirin. The findings suggest that attenuation is in part due to a low probability of reversion or mutation of the vaccine virus genome to WT, thus maintaining a stable genotype despite external pressures.

The molecular basis of attenuation for live-attenuated vaccines is poorly understood. The yellow fever (YF) 17D vaccine virus was derived from the wild-type, parental strain Asibi virus by serial passage in chicken tissue and has proven to be a very safe and efficacious vaccine. We have previously shown that wild-type Asibi is a typical RNA virus with high genetic diversity, while the 17D vaccine virus has very little genetic diversity. To investigate this further, we treated Asibi and 17D viruses with ribavirin, a GTP analog with strong antiviral activity that increases levels of mutations in the viral genome. As expected, ribavirin treatment introduced mutations into the Asibi virus genome at a very high frequency and decreased viral infectivity while, in contrast, the 17D vaccine virus was resistant to ribavirin, as treatment with the antiviral introduced very few mutations into the genome, and viral infectivity was not lost. The results were confirmed for another YF wild-type parental and vaccine pair, a wild-type French viscerotropic virus and French neurotropic vaccine. Using recombinant Asibi and 17D viruses, ribavirin sensitivity was located to viral nonstructural genes. Thus, two live-attenuated YF vaccine viruses are genetically stable even under intense mutagenic pressure, suggesting that attenuation of live-attenuated YF vaccines is due, at least in part, to fidelity of the replication complex resulting in high genetic stability.

Conditional rehabilitation of cooperation under strategic uncertainty

In order to address the topic of the tragedy of the commons, more specifically that of tropical forest ecosystems explored as common-pool resources endowed with public-good features and exposed to deforestation risks, we consider game-theoretic population dynamics contingent on various differential equations. We propose an evolutionary model handed down to the Price theorem of selection. In a set of model-players evolving in strategic uncertainty and subject to certain mutation toward cooperation, the Price equation evens out unstructured and structured population replicator dynamics. According to the model outputs, avoiding the tragedy of the commons can be achieved on condition that half of the population temporarily exhibits a cooperative behavior. Furthermore, cooperative model-players ought to be rewarded at a level equivalent to the joint selection of cooperators and competitors issued from the unifying Price identity.

Landscape and flux for quantifying global stability and dynamics of game theory

Game theory has been widely applied to many research areas including economics, biology and social sciences. However, it is still challenging to quantify the global stability and global dynamics of the game theory. We developed a landscape and flux framework to quantify the global stability and global dynamics of the game theory. As an example, we investigated a model of three-strategy game: a special replicator mutator game termed as the repeated Prison Dilemma model. In this model, one stable state, two stable states and limit cycle can emerge under different parameters. The repeated Prisoner's Dilemma system has Hopf bifurcation from one stable state to limit cycle state, and then to another one stable state or two stable states, and vice versa. We quantified the global stability of the repeated Prisoner's Dilemma system and identified optimal kinetic paths between the basins of attractor. The optimal paths are irreversible due to the non-zero flux. We also quantified the interplay between Peace and War.

Biodiversity in the cyclic competition system of three species according to the emergence of mutant species

Understanding mechanisms which promote or hinder existing ecosystems are important issues in ecological sciences. In addition to fundamental interactions such as competition and migration among native species, existing ecosystems can be easily disturbed by external factors, and the emergence of new species may be an example in such cases. The new species which does not exist in a current ecosystem can be regarded as either alien species entered from outside or mutant species born by mutation in existing normal species. Recently, as existing ecosystems are getting influenced by various physical/chemical external factors, mutation due to anthropogenic and environmental factors can occur more frequently and is thus attracting much attention for the maintenance of ecosystems. In this paper, we consider emergences of mutant species among self-competing three species in the cyclic dominance. By defining mutation as the birth of mutant species, we investigate how mutant species can affect biodiversity in the existing ecosystem. Through microscopic and macroscopic approaches, we have found that the society of existing normal species can be disturbed by mutant species either the society is maintained accompanying with the coexistence of all species or jeopardized by occupying of mutant species. Due to the birth of mutant species, the existing society may be more complex by constituting two different groups of normal and mutant species, and our results can be contributed to analyze complex ecosystems of many species. We hope our findings may propose a new insight on mutation in cyclic competition systems of many species.

Unified reduction principle for the evolution of mutation, migration, and recombination

Modifier-gene models for the evolution of genetic information transmission between generations of organisms exhibit the reduction principle: Selection favors reduction in the rate of variation production in populations near equilibrium under a balance of constant viability selection and variation production. Whereas this outcome has been proven for a variety of genetic models, it has not been proven in general for multiallelic genetic models of mutation, migration, and recombination modification with arbitrary linkage between the modifier and major genes under viability selection. We show that the reduction principle holds for all of these cases by developing a unifying mathematical framework that characterizes all of these evolutionary models.