相关论文: Generalized Urn Models of Evolutionary Processes
Despite the increase in observational data on exoplanets, the processes that lead to the formation of planets are still not well understood. But thanks to the high number of known exoplanets, it is now possible to look at them as a…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
We study a new class of time inhomogeneous P\'olya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma…
The utilization of populations is one of the most important features of evolutionary algorithms (EAs). There have been many studies analyzing the impact of different population sizes on the performance of EAs. However, most of such studies…
An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the…
This paper proposes a non-phenomenological model of population growth that is based on the interactions between the individuals that compose the system. It is assumed that the individuals interact cooperatively and competitively. As a…
The stage of evolution is the population of reproducing individuals. The structure of the population is know to affect the dynamics and outcome of evolutionary processes, but analytical results for generic random structures have been…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
We consider a generalized two-color Polya urn (black and withe balls) first introduced by Hill, Lane, Sudderth where the urn composition evolves as follows: let $\pi:\left[0,1\right]\rightarrow\left[0,1\right]$, and denote by $x_{n}$ the…
Modern population genetics studies typically involve genome-wide genotyping of individuals from a diverse network of ancestries. An important, unsolved problem is how to formulate and estimate probabilistic models of observed genotypes that…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
Research in quantitative evolutionary genomics and systems biology led to the discovery of several universal regularities connecting genomic and molecular phenomic variables. These universals include the log-normal distribution of the…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…