Fluctuation Domains in Adaptive Evolution

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource

Aging and Energy Landscapes: Application to Liquids and Glasses

The equation of state for a liquid in equilibrium, written in the potential energy landscape formalism, is generalized to describe out-of-equilibrium conditions. The hypothesis that during aging the system explores basins associated to equilibrium configurations is the key ingredient in the derivation. Theoretical predictions are successfully compared with data from molecular dynamics simulations of different aging processes, such as temperature and pressure jumps.Comment: RevTeX4, 4 pages, 5 eps figure

Ripple and kink dynamics

We propose a relevant modification of the Nishimori-Ouchi model [{\em Phys. Rev. Lett.} {\bf 71}, 197 (1993)] for granular landscape erosion. We explicitly introduce a new parameter: the angle of repose $\theta_r$, and a new process: avalanches. We show that the $\theta_r$ parameter leads to an asymmetry of the ripples, as observed in natural patterns. The temporal evolution of the maximum ripple height $h_{max}$ is limited and not linear, according to recent observations. The ripple symmetry and the kink dynamics are studied and discussed.Comment: 7 pages, 10 figure, RevTe

A model for evolution and extinction

We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions against the fossil record. The model indicates that a possible mechanism for mass extinction is the coincidence of a large coevolutionary avalanche in the ecosystem with a severe environmental disturbance.Comment: Postscript (compressed etc. using uufiles), 16 pages, with 15 embedded figure