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We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
The time-reparametrization-invariant dynamics of a relativistic string is studied in the Dirac generalized Hamiltonian theory by resolving the first class constraints. The reparametrization-invariant evolution parameter is identified with…
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability.…
The evolution of the comoving cosmic merger-rate density of neutron star binaries n_c(z) is calculated using a distribution of their merging times provided by population-synthesis computations of binary stars. We adopt an exponential law…
Using a lattice model based on Monte Carlo simulations, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selection pressure from the environment and random mutations. The…
This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian…
Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well documented to much more tightly than traditionally assumed,…
Population dynamics is constrained by the environment, which needs to obey certain conditions to support population growth. We consider a standard model for the evolution of a single species population density, that includes reproduction,…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
It is known that the evolutionary algorithm $(1+1)$-EA with mutation rate $c/n$ optimises every monotone function efficiently if $c<1$, and needs exponential time on some monotone functions (HotTopic functions) if $c\geq 2.2$. We study the…
We explore a Boltzmann scheme for studying the evolution of compact binary populations of globular clusters. We include processes of compact-binary formation by tidal capture and exchange encounters, binary destruction by dissociation and…
Estimation of molecular evolutionary divergence times requires models of rate change. These vary with regard to the assumption of what quantity is penalized. The possibilities considered are the rate of evolution, the log of the rate of…
When beneficial mutations are rare, they accumulate by a series of selective sweeps. But when they are common, many beneficial mutations will occur before any can fix, so there will be many different mutant lineages in the population…
Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbr\"uck model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for…
Cumulants and moments are closely related to the basic mathematics of continuous and discrete selection (respectively). These relationships generalize Fisher's fundamental theorem of natural selection and also make clear some of its…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This…