Related papers: Simple model of self-organized biological evolutio…
Self-organization is the autonomous assembly of a network of interacting components into a stable, organized pattern. This article shows that the process of self-assembly can be encoded in terms of evolutionary entropy, a statistical…
Exploiting the mathematical curiosity of intransitive dice, we present a simple theoretical model for co-evolution that captures scales ranging from the genome of the individual to the system-wide emergence of species diversity. We study a…
Biological evolution in a sequence space with random fitnesses is studied within Eigen's quasispecies model. A strong selection limit is employed, in which the population resides at a single sequence at all times. Evolutionary trajectories…
With a view to connecting random mutation on the molecular level to punctuated equilibrium behavior on the phenotype level, we propose a new model for biological evolution, which incorporates random mutation and natural selection. In this…
Interaction strength is introduced in a model of evolution in d-dimension space. It is realized by imposing a constraint concerning 2d differences of fitnesses between that of any extremal site and those of its 2d nearest neighbours at each…
We have investigated the essential ingredients allowing a system to show Self Organized Criticality (SOC) in its collective behavior. Using the Bak-Sneppen model of biological evolution as our paradigm, we show that the random microscopic…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
We introduce a model of biological evolution where species evolve in response to biotic interactions and a fluctuating environmental stress. The species may either become extinct or mutate to acquire a new fitness value when the effective…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age,…
The idea that there are any large-scale trends in the evolution of biological organisms is highly controversial. It is commonly believed, for example, that there is a large-scale trend in evolution towards increasing complexity, but…
The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of…
A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of…
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev.…
It is increasingly evident that there is more to biological evolution than natural selection; moreover, the concept of evolution is not limited to biology. We propose an integrative framework for characterizing how entities evolve, in which…
Recently, Lenski et al \cite{Elena,Lenski,Travisano} have carried out several experiments on bacterial evolution. Their findings support the theory of punctuated equilibrium in biological evolution. They have further quantified the relative…
The idea of this review is to connect the different models of evolution to those of biological ageing through Darwin's theory. We start with the Eigen model of quasispecies for microevolution, then introduce the Bak-Sneppen model for…
What determines biodiversity in nature is a prominent issue in ecology, especially in biotic resource systems that are typically devoid of cross-feeding. Here, we show that by incorporating pairwise encounters among consumer individuals…