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Transient compartments have been recently shown to be able to maintain functional replicators in the context of prebiotic studies. Here, we show that a broad class of selection dynamics is able to achieve this goal. We identify two key parameters, the relative amplification of nonactive replicators (parasites) and the size of compartments. These parameters account for competition and diversity, and the results are relevant to similar multilevel selection problems, such as those found in virus-host ecology and trait group selection.

Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly deleterious mutations can reach large frequencies in the newly colonized regions, as if they were surfing the front of the range expansion. These findings raise the question of how frequently beneficial mutations successfully surf at shifting range margins, thereby promoting adaptation towards a range-expansion phenotype. Here, we use individual-based simulations to study the surfing statistics of recurrent beneficial mutations on wave-like range expansions in linear habitats. We show that the rate of surfing depends on two strongly antagonistic factors, the probability of surfing given the spatial location of a novel mutation and the rate of occurrence of mutations at that location. The surfing probability strongly increases towards the tip of the wave. Novel mutations are unlikely to surf unless they enjoy a spatial head start compared to the bulk of the population. The needed head start is shown to be proportional to the inverse fitness of the mutant type, and only weakly dependent on the carrying capacity. The precise location dependence of surfing probabilities is derived from the non-extinction probability of a branching process within a moving field of growth rates. The second factor is the mutation occurrence which strongly decreases towards the tip of the wave. Thus, most successful mutations arise at an intermediate position in the front of the wave. We present an analytic theory for the tradeoff between these factors that allows to predict how frequently substitutions by beneficial mutations occur at invasion fronts. We find that small amounts of genetic drift increase the fixation rate of beneficial mutations at the advancing front, and thus could be important for adaptation during species invasions.

We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical properties of a modified dynamics, and since they no longer involve rare events, can be evaluated efficiently and over a wider ranges of values. We illustrate the method with the current fluctuations of the Totally Asymmetric Exclusion Process and with the work distribution of a driven Lorentz gas.

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.

We simulate asexually and sexually reproducing model populations evolving in a rugged fitness landscape where fit and unfit genotypes are distributed at random, and where all fit genotypes have the same a priori probability of reproduction. Varying the fraction chi of unfit genotypes at a fixed mutation rate we observe a strikingly different behavior for the two reproduction mechanisms. For the asexually reproducing population, the effective mutation rate lambda decreases roughly proportionally to (1-chi), and the fraction delta of sterile individuals--processing an unfit genotype--accordingly increases roughly proportionally to chi. On the other hand, lambda remains approximately constant (and delta increases proportionally to chi) for small values of chi:but, at a critical value chi*, both lambda and delta suddenly drop. This corresponds to the transition to an adaptive regime where the average fitness of the population is enhanced. We show how this transition can be interpreted in terms of an improvement of the collective fitness of the population.

We consider a population of fixed size and reproducing asexually, evolving in a rugged fitness landscape. Selection takes place only via the elimination of individuals with unfit genomes. Unfit genotypes are distributed at random in genotypic space. The genetic structure of the population and the speed of genetic drift are explicitly computed in the infinite genome limit.

We introduce a simple model of molecular evolution, with a fixed population and a rugged fitness function. We exhibit the analogy between the crossover from a neutralist to an adaptative evolutionary behavior and the percolation transition in genome space.