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Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics…
Competitions can occur on an absolute scale, to be faster or more efficient, or they can occur on a relative scale, to "beat" one's competitor in a zero-sum game. Ecological models have focused on absolute competitions, in which optima…
Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
Cells use genetic switches to shift between alternate stable gene expression states, e.g., to adapt to new environments or to follow a developmental pathway. Conceptually, these stable phenotypes can be considered as attractive states on an…
We study the behaviour of a class of edge-reinforced random walks {on $\mathbb{Z}_+$}, with heterogeneous initial weights, where each edge weight can be updated only when the edge is traversed from left to right. We provide a description…
These notes introduce probabilistic landscape models defined on high-dimensional discrete sequence spaces. The models are motivated primarily by fitness landscapes in evolutionary biology, but links to statistical physics and computer…
Epistatic interactions between mutations add substantial complexity to adaptive landscapes, and are often thought of as detrimental to our ability to predict evolution. Yet, patterns of global epistasis, in which the fitness effect of a…
We develop a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by $S$, and the average Hamming distance between them, denoted by $H$. We argue that a…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
Epistasis occurs when the effect of a mutation depends on its carrier's genetic background. Despite increasing evidence that epistasis for fitness is common, its role during evolution is contentious. Fitness landscapes, mappings of genotype…
We discuss the non-equilibrium time evolution of the phase field in the sine-Gordon model using two very different approaches: the truncated Wigner approximation and the truncated conformal space approach. We demonstrate that the two…
We explore a mechanism of decision-making in Mean Field Games with myopic players. At each instant, agents set a strategy which optimizes their expected future cost by assuming their environment as immutable. As the system evolves, the…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
We critically revisit the evidence for the existence of quasistationary states in the globally coupled XY (or Hamiltonian mean-field) model. A slow-relaxation regime at long times is clearly revealed by numerical realizations of the model,…
The finite sensitivity of instruments or detection methods means that data sets in many areas of astronomy, for example cosmological or exoplanet surveys, are necessarily systematically incomplete. Such data sets, where the population being…