Related papers: Mutation and Random Matrix Theory
We explore the connection between evolution and large-deviation theory. To do so, we study evolutionary dynamics in which individuals experience mutations, reproduction, and selection using variants of the Moran model. We show that, in the…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
Two quantum systems, each described as a random-matrix ensemble. are coupled to each other via a number of transition states. Each system is strongly coupled to a large number of channels. The average transmission probability is the product…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
The current theory of evolution is almost the one Darwin and Wallace proposed two centuries ago and the following discoveries e.g., Mendelian genetics and neutral mutation theory have not made significant modifications. The current…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Applying the concepts and formalisms from Evolutionary Game Theory to the data regime, the fundamental paradigms of Evolutionary Data Theory are introduced. Interpreting data in matrix form as evolutionary entities, input data is mapped to…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
Mutations are typically classified by their effects on the nucleotide sequence and by their size. Here, we argue that if our main aim is to understand the effect of mutations on evolutionary outcomes (such as adaptation or speciation), we…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
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…
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described.…
Kingman's House-of-Cards model is a simple and celebrated model to describe the evolution of population under the competition of selection and mutation. Letting mutation probabilities vary on generations makes the model more realistic and…
Evolution occurs in populations of reproducing individuals. It is well known that population structure can affect evolutionary dynamics. Traditionally, natural selection is studied between mutants that differ in reproductive rate, but are…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…