Replica analysis of thep-spin interaction Ising spin-glass model

Rate of environmental variation impacts the predictability in evolution

In the two last decades, we have improved our understanding of the adaptive evolution of natural populations under constant and stable environments. For instance, experimental methods from evolutionary biology have allowed us to explore the structure of fitness landscapes and survey how the landscape properties can constrain the adaptation process. However, understanding how environmental changes can affect adaptation remains challenging. Very little progress has been made with respect to time-varying fitness landscapes. Using the adaptive-walk approximation, we survey the evolutionary process of populations under a scenario of environmental variation. In particular, we investigate how the rate of environmental variation influences the predictability in evolution. We observe that the rate of environmental variation not only changes the duration of adaptive walks towards fitness peaks of the fitness landscape, but also affects the degree of repeatability of both outcomes and evolutionary paths. In general, slower environmental variation increases the predictability in evolution. The accessibility of endpoints is greatly influenced by the ecological dynamics. The dependence of these quantities on the genome size and number of traits is also addressed. To our knowledge, this contribution is the first to use the predictive approach to quantify and understand the impact of the speed of environmental variation on the degree of parallelism of the evolutionary process.

Pressure-induced orientational glass phase in molecular para-hydrogen

We propose a theoretical description of a possible orientational glass transition in solid molecular para-hydrogen and ortho-deuterium under pressure supposing that they are mixtures of J=0 and J=2 states of molecules. The theory uses the basic concepts and methods of standard spin-glass theory. We expect our orientational glass to correspond to the II' phase of the high-pressure hydrogen phase diagram.