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Self-adjustment of parameters can significantly improve the performance of evolutionary algorithms. A notable example is the $(1+(\lambda,\lambda))$ genetic algorithm, where the adaptation of the population size helps to achieve the linear…
We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica…
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values…
The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
The purpose of this article is to study some asymptotic properties of the \Lambda-Wright-Fisher process with selection. This process represents the frequency of a disadvantaged allele. The resampling mechanism is governed by a finite…
The expansion of deleted mitochondrial DNA (mtDNA) molecules has been linked to ageing, particularly in skeletal muscle fibres; its mechanism has remained unclear for three decades. Previous accounts assigned a replicative advantage to the…
The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
We investigate the fitness advantage associated with the robustness of a phenotype against deleterious mutations using deterministic mutation-selection models of quasispecies type equipped with a mesa shaped fitness landscape. We obtain…
Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
Recently van der Meer et al. studied the breakdown of a granular cluster (Phys. Rev. Lett. {\bf 88}, 174302 (2002)). We reexamine this problem using an urn model, which takes into account fluctuations and finite-size effects. General…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
The bit-string model of biological aging is used to simulate the catastrophic senescence of Pacific Salmon. We have shown that reproduction occuring only once and at a fixed age is the only ingredient needed to explain the catastrophic…
Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $\alpha$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic…
The time evolution of galaxy cluster abundance is used to constrain cosmological parameters in dark matter models containing a fraction of hot particles (massive neutrino). We test the modified MDM models with cosmic gravitational waves…
Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…
Since its proposition in 1995, the Heumann-Hotzel model has remained as an obscure model of biological aging. The main arguments used against it were its apparent inability to describe populations with many age intervals and its failure to…