author={Michael Doebeli and Iaroslav Ispolatov},
The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long‐term evolutionary chaos is rarely considered. The concept of “survival of the fittest” is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This… 
Chaos and the (un)predictability of evolution in a changing environment
Investigation of how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment shows that strong environmental forcing can improve the predictability of evolution.
A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape
A predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape is described, showing that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection.
Diversity and Coevolutionary Dynamics in High-Dimensional Phenotype Spaces*
The coevolutionary dynamics tend to be fast and nonstationary for an intermediate number of coexisting lineages but tend to stabilize as the evolving communities reach a saturation level of diversity and the amount of diversity at the saturation level increases rapidly (exponentially) with the dimension of phenotype space.
Inevitability of Red Queen evolution driven by organismic complexity and simple feedback via environmental modification
The simplest approximation of evolution, an almost-always clonal population evolving by small effect mutations under deterministic “adaptive” dynamics, is studied and organismic complexities, caricatured by a large number of constraints on the molecular-level phenotype, are shown to be sufficient to cause such Red Queen dynamics.
Evolutionary dynamics from deterministic microscopic ecological processes.
This work develops a theory for a class of deterministic individual-based models describing individual births and deaths, which captures the essential features of standard stochastic individual- based models and becomes identical to the latter under maximal competition.
Individual-based models for adaptive diversification in high-dimensional phenotype spaces.
Competition-driven evolution of organismal complexity
It is argued that non-uniform evolutionary increases in phenotypic complexity can be caused by a threshold-like response to growing ecological pressures resulting from evolutionary diversification at a given level of complexity.
Duality Of Stochasticity And Natural Selection: A Cybernetic Evolution Theory
Variation is pervasive at every level of biological organization and is created by a multitude of processes: mutagenesis, epimutagenisation, recombination, transposon mobility, repeat instability, gene expression noise, cellular network dynamics, physiology, phenotypic plasticity, behavior, and life history strategy.
Evolution through the stochastic dyadic Cantor Set: the uniqueness of mankind in the Universe
  • D. Mahecha
  • Physics
    International Journal of Astrobiology
  • 2015
Abstract The search for intelligent life or any type of life involves processes with nonlinear chaotic behaviours throughout the Universe. Through the sensitive dependence condition, chaotic dynamics
Deciphering chaos in evolutionary games.
This work constructs a game-theoretic solution that is realized as the chaotic outcomes in the selection monotone game dynamic that is optimized over the generations of the evolutionary process.


Intermittency and transient chaos from simple frequency-dependent selection
This analysis of a simple deterministic model for frequency-dependent selection shows that complex dynamic behaviour is possible under a broad range of parameter values, and exhibits not only cycles and chaos but also, for a more restricted set of parameters, transient chaos and intermittency.
Coevolution of slow–fast populations: evolutionary sliding, evolutionary pseudo-equilibria and complex Red Queen dynamics
The eco-evolutionary dynamics of the system show a number of other distinctive features, including evolutionary extinction and two forms of Red Queen dynamics, including intermittent bouts of cyclic oscillations of the two populations.
Chaos and the evolution of cooperation.
  • M. Nowak, K. Sigmund
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 1993
Here it is shown that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular oscillations in the frequencies of the strategies and the overall level of cooperation.
Chaos from Linear Frequency-Dependent Selection
The simplest diploid form of frequency-dependent selection can generate periodic and chaotic trajectories for the allele frequency, which follows the period-doubling route to chaos, as seen with logistic growth models, but includes additional phenomena such as the simultaneous stability of cycling and chaos.
The dynamical theory of coevolution: a derivation from stochastic ecological processes
It is shown that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space and a quantitative description of this stochastic process in terms of a master equation is derived.
Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications
The first comprehensive book on Adaptive Dynamics (AD), a quantitative modeling approach that explicitly links evolutionary changes to demographic ones, shows how the so-called AD canonical equation can answer questions of paramount interest in biology, engineering, and the social sciences, especially economics.
Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree
A haploid version of Levene's ‘soft selection’ model is developed as a specific example to demonstrate evolutionary dynamics and branching in monomorphic and polymorphic populations.
Long-Term Dynamics of Adaptation in Asexual Populations
It is demonstrated that even after 50,000 generations over 20 years, gains in fitness show no evidence of leveling off, and mean fitness appears to increase without bound, consistent with a power law.
Evolutionary Cycling in Predator – Prey Interactions : Population Dynamics and the Red Queen
It is shown that evolutionary cycling is a likely outcome of the coevolution of phenotypes in a community comprising a population of predators and of prey, and argues for an extension to a dynamical framework for describing asymptotic states of evolution.
Chaotic dynamics of allele frequencies in condition-dependent mating systems.