Related papers: Punctuated evolution for the quasispecies model
We consider the optimal dynamics in the infinite population evolution models with general symmetric fitness landscape. The search of optimal evolution trajectories are complicated due to sharp transitions (like shock waves) in evolution…
Competitions can occur on an absolute scale, to be faster or more efficient, or they can occur on a relative scale, to "beat" one's competitor in a zero-sum game. Ecological models have focused on absolute competitions, in which optima…
Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates…
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…
The emerging field of high-throughput compartmentalized in vitro evolution is a promising new approach to protein engineering. In these experiments, libraries of mutant genotypes are randomly distributed and expressed in microscopic…
One of the key problems related to the Bak-Sneppen evolution model on the circle is to compute the limit distribution of the fitness at a fixed observation vertex in the stationary regime, as the size of the system tends to infinity.…
We study the evolution of sexual and asexual populations in general fitness landscapes. We find deep relations between the mathematics of biological evolution and the formalism of quantum mechanics. We give the general structure of the…
Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the…
We consider a biological population evolving under the joint action of selection, mutation and random genetic drift. The evolutionary dynamics are described by a one-dimensional Fokker-Planck equation whose eigenfunctions obey a confluent…
Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least…
As artificial intelligence systems (AIs) become increasingly produced by recursive self-improvement, a form of evolution may emerge, with the traits of AI systems shaped by the success of earlier AIs in designing and propagating their…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
We use finite-size scaling to investigate the critical behavior of the quasiespecies model of molecular evolution in the single-sharp-peak replication landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where Q is the…
We present some results of simulations of population growth and evolution, using the standard asexual Penna model, with individuals characterized by a string of bits representing a genome containing some possible mutations. After about…
We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model,…
The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts have been previously conjectured and…
Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…