Related papers: Uniform growth rate
By measuring or calculating coalescence times for several models of coalescence or evolution, with and without selection, we show that the ratios of these coalescence times become universal in the large size limit and we identify a few…
The emergence of a predominant phenotype within a cell population is often triggered by a rare accumulation of DNA mutations in a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to…
A general model for the ontogenetic growth of living organisms has been recently proposed. Here we investigate the extension of this model to the growth of solid malignant tumors. A variety of in vitro and in vivo data are analyzed and…
Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…
We study the macroscopic evolution of the growing cluster in the exactly solvable corner growth model with independent exponentially distributed waiting times. The rates of the exponentials are given by an addivitely separable function of…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…
Is evolution always gradual or can it make leaps? We examine a mathematical model of an evolutionary process on a fitness landscape and obtain analytic solutions for the probability of multi-mutation leaps, that is, several mutations…
We present a survey of results related to the Milnor's problem on group growth. We discuss the cases of polynomial growth, exponential but not uniformly exponential growth, but the main part of the article is devoted to the intermediate…
In this paper we study the evolution of the mutation rate for simple organisms in dynamic environments. A model with multiple fitness coding loci tracking a moving fitness peak is developed and an analytical expression for the optimal…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
To every finitely generated group one can assign the conjugacy growth function that counts the number of conjugacy classes intersecting a ball of radius $n$. Results of Ivanov and Osin show that the conjugacy growth function may be constant…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
We announce the folowing result: Any finitely generated non virtually solvable linear group over a field of characteristic zero has uniform exponential growth.
Let $S^m = \{x_0^2 + x_1^2 + \cdots + x_m^2 = 1\}$ and $P = \{x_0 = x_1 = 0\} \cap S^m$. Suppose that $f$ is a self--map of $S^m$ such that $f^{-1}(P) = P$ and $|\mathrm{deg}(f_{|P})| < |\mathrm{deg}(f)|$. Then, the number of fixed points…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
We study growth limited by packing for irregular objects in two dimensions. We generate packings by seeding objects randomly in time and space and allowing each object to grow until it collides with another object. The objects we consider…
In large asexual populations, beneficial mutations have to compete with each other for fixation. Here, I derive explicit analytic expressions for the rate of substitution and the mean beneficial effect of fixed mutations, under the…