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The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. We consider a Moran model describing the evolution of a population of size $m$ of chromosomes of length $\ell$ over…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
Suppose an initial state is coupled to a continuum of energy states. The population of the initial state is expected to decrease with time, but is the decrease monotonic? The occupation probability of the initial state is the survival…
The tempo and mode of an adaptive process is strongly determined by the structure of the fitness landscape that underlies it. In order to be able to predict evolutionary outcomes (even on the short term), we must know more about the nature…
Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…
A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation. Biologically motivated by the influence of seasons or the variation of drug concentration during medical treatment,…
The Bak-Sneppen model displaying punctuated equilibria in biological evolution is studied on random complex networks. By using the rate equation and the random walk approaches, we obtain the analytic solution of the fitness threshold $x_c$…
Quasispecies theory provides the conceptual and theoretical bases for describing the dynamics of biological information of replicators subject to large mutation rates. This theory, initially conceived within the framework of prebiotic…
We consider Evolution Strategies operating only with isotropic Gaussian mutations on positive quadratic objective functions, and investigate the covariance matrix when constructed out of selected individuals by truncation. We prove that the…
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 argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
We consider the parabolic Anderson model $\frac{\partial}{\partial t} v_n=\kappa\Delta_n v_n + \xi_n v_n$ on the $n$-dimensional hypercube $\{-1,+1\}^n$ with random i.i.d. potential $\xi_n$. We parametrize time by volume and study $v_n$ at…
There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to…
Developmental dynamics of multicellular organism is a process that takes place in a multi-stable system in which each attractor state represents a cell type and attractor transitions correspond to cell differentiation paths. This new…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
Identifying and quantifying the benefits of sex and recombination is a long standing problem in evolutionary theory. In particular, contradictory claims have been made about the existence of a benefit of recombination on high dimensional…
We discuss fitness landscapes and how they can be modified to account for co-evolution. We are interested in using the landscape as a way to model rational decision making in a toy economic system. We develop a model very similar to the…
A microscopic model is developed, within the frame of the theory of quantitative traits, to study both numerically and analytically the combined effect of competition and assortativity on the sympatric speciation process, i.e. speciation in…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…