Related papers: Non-Archimedean Replicator Dynamics and Eigen's Pa…
We analyze the geometry of the species- and genotype-size distribution in evolving and adapting populations of single-stranded self-replicating genomes: here programs in the Avida world. We find that a scale-free distribution (power law)…
Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
The problem of the directionality of genome evolution is studied from the information-theoretic view. We propose that the function-coding information quantity of a genome always grows in the course of evolution through sequence duplication,…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
p-Adic mathematical physics emerged as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale. One of its main achievements is a successful formulation and development of p-adic and…
We study quasi-species and closely related evolutionary dynamics like the replicator-mutator equation in high dimensions. In particular, we show that under certain conditions the fitness of almost all quasi-species becomes independent of…
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…
We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A…
A central problem in comparative genomics consists in computing a (dis-)similarity measure between two genomes, e.g. in order to construct a phylogeny. All the existing measures are defined on genomes without duplicates. However, we know…
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…
The time evolution of O(N) symmetric lambda Phi^4 scalar field theory is studied in the large N limit. In this limit the <Phi> mean field and two-point correlation function <Phi Phi> evolve together as a self-consistent closed Hamiltonian…
A renormalizable non-abelian vector meson dominance model coupled to pions is constructed which exhibits a ${\rm SO}\left(4,3\right)$ vacuum symmetry. Tree-level predictions for $p$-$p$ scattering lengths and slopes at leading order are in…
The self-alignment concentrations, $c(x)$, as functions of the length, $x$, of the identically matching maximal segments in the genomes of a variety of species, typically present power-law tails extending to the largest scales, i.e., $c(x)…
We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior…
We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
We study macroevolutionary dynamics by extending microevolutionary competition models to long time scales. It has been shown that for a general class of competition models, gradual evolutionary change in continuous phenotypes (evolutionary…
The adiabatic theorem is an important concept in quantum mechanics, it tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In…
Consider a population that is expanding in two-dimensional space. Suppose we collect data from a sample of individuals taken at random either from the entire population, or from near the outer boundary of the population. A quantity of…