Mutation, Sexual Reproduction and Survival in Dynamic Environments

@inproceedings{Mehta2017MutationSR,
  title={Mutation, Sexual Reproduction and Survival in Dynamic Environments},
  author={Ruta Mehta and Ioannis Panageas and Georgios Piliouras and Prasad Tetali and Vijay V. Vazirani},
  booktitle={ITCS},
  year={2017}
}
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative Weight Update (MWU) Algorithm in coordination games played among genes [CLPV14]. Using this machinery, we study the role of mutation in changing environments in the presence of sexual reproduction. Following [WVA05], we model changing environments via a Markov… 

Figures and Tables from this paper

Learning Dynamics and the Co-Evolution of Competing Sexual Species
TLDR
A stylized model of co-evolution between any two purely competing species, both sexually reproducing, to establish a novel class of conservative dynamical systems that makes a simple and robust behavioral prediction.
Cycles in Zero-Sum Differential Games and Biological Diversity
TLDR
It is shown that first order methods (e.g., gradient descent/ascent) do cycle even in online settings in which the loss function changes with time, i.e., no species goes extinct and diversity is maintained.
Modeling Population Dynamics in Changing Environments
Discrete replicator dynamics view evolution as a coordination game played among genes. While previous models of discrete replicator dynamics do not consider environments that respond to the mixed
Opinion Dynamics in Networks: Convergence, Stability and Lack of Explosion
TLDR
A model on opinion formation is introduced and it is shown that starting uniformly at random over all population vectors on the simplex, the dynamics converges point-wise with probability one to an independent set and settles an open problem of Kempe et.
A Coupling Approach to Analyzing Games with Dynamic Environments
—The theory of learning in games has exten- sively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic
Average Case Performance of Replicator Dynamics in Potential Games via Computing Regions of Attraction
TLDR
This average case analysis is shown to offer novel insights in classic game theoretic challenges, including quantifying the risk dominance in stag-hunt games and allowing for more nuanced performance analysis in networked coordination and congestion games with large gaps between price of stability and price of anarchy.
Rock-Paper-Scissors, Differential Games and Biological Diversity
TLDR
A model in which a collection of species derive their fitnesses via a rock-paper-scissors-type game is cast and it is shown that for a certain setting of parameters, this dynamics cycles and no species goes extinct and diversity is maintained.
A Unified Perspective of Evolutionary Game Dynamics Using Generalized Growth Transforms
TLDR
By introducing a population dependent time-constant in the generalized growth transform model, the proposed framework can be used to explain a vast repertoire of evolutionary dynamics, including some novel forms of game dynamics with non-linear payoffs.
Cooperate or Not Cooperate in Predictable but Periodically Varying Situations? Cooperation in Fast Oscillating Environment
TLDR
The two‐population prisoner's dilemma game with periodically oscillating payoffs is discussed, such that the time‐average of these oscillations over the period of environmental variations vanishes.
Growth transform dynamical system model Type I Type II Replication Quasispecies evolution Replicator-Mutator Logit BNN
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth
...
...

References

SHOWING 1-10 OF 69 REFERENCES
Multiplicative updates in coordination games and the theory of evolution
TLDR
The standard equations of population genetics for Evolution, in the presence of recombination (sex), are studied, focusing on the important special case of weak selection, in which all fitness values are assumed to be close to one another.
Natural Selection as an Inhibitor of Genetic Diversity: Multiplicative Weights Updates Algorithm and a Conjecture of Haploid Genetics [Working Paper Abstract]
TLDR
It is established that, under specific assumptions, mathematical models of biological evolution can be reduced to studying discrete replicator dynamics, a close variant of MWUA, in coordination games, and it is shown that haploid evolution imply the extinction of genetic diversity in the long term limit.
Evolutionary Dynamics in Finite Populations Mix Rapidly
TLDR
This paper proves that the mixing time of a broad class of evolutionary dynamics in finite, unstructured populations is roughly logarithmic in the size of the state space, and makes a novel connection between Markov chains arising in evolutionary dynamics and dynamical systems on the probability simplex.
Algorithms, games, and evolution
TLDR
In the regime of weak selection, the standard equations of population genetics describing natural selection in the presence of sex become identical to those of a repeated game between genes played according to multiplicative weight updates (MWUA), an algorithm known in computer science to be surprisingly powerful and versatile.
The Computational Complexity of Genetic Diversity
TLDR
The key contribution is to establish complexity theoretic hardness results implying that even in the textbook case of single locus (gene) diploid models, predicting whether diversity survives or not given its fitness landscape is algorithmically intractable.
Evolutionary Games and Population Dynamics
TLDR
In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.
The Speed of Evolution
TLDR
The main result of this paper is an analytical bound on the mixing time of a Wright-Fisher model for two genotypes when there is no restriction on the mutation rate or the fitness.
Mathematical structures in population genetics
In the theory of population genetics, fundamental results on its dynamical processes and equilibrium laws have emerged during the last few decades. This monograph systematically reviews these
A Finite Population Model of Molecular Evolution: Theory and Computation
TLDR
A population genetics-based model aimed at understanding the evolution of haploid organisms that reproduce asexually with finite population sizes is considered and it is shown that, at any time during the evolution, the distribution of genomes predicted by this model converges to that predicted by the quasispecies model.
...
...