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Recent studies of in vitro evolution of DNA via protein binding indicate that the evolution behavior is qualitatively different in different parameter regimes. I here present a general theory that is valid for a wide range of parameters,…
We study theoretically the in vitro evolution of a DNA sequence by binding to a transcription factor. Using a simple model of protein-DNA binding and available binding constants for the Mnt protein, we perform large-scale, realistic…
The mutation and selection of regulatory DNA sequences is presented as an ideal model system of molecular evolution where genotype, phenotype, and fitness can be explicitly and independently characterized. In this theoretical study, we…
We study the evolution of recombination using a microscopic model developed within the frame of the theory of quantitative traits. Two components of fitness are considered: a static one that describes adaptation to environmental factors not…
Biological evolution of a population is governed by the fitness landscape, which is a map from genotype to fitness. However, a fitness landscape depends on the organisms environment, and evolution in changing environments is still poorly…
Competition between individuals drives the evolution of whole species. Although the fittest individuals survive the longest and produce the most offspring, in some circumstances the resulting species may not be optimally fit. Here, using…
We investigate the evolution of quiescence within the framework of Adaptive Dynamics for an SIQS (Susceptible - Infected - Quiescent) model with constant environment. In the first part of the paper, the competition of two strains which have…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…
The common understanding of protein evolution has been that neutral or slightly deleterious mutations are fixed by random drift, and evolutionary rate is determined primarily by the proportion of neutral mutations. However, recent studies…
We are living in an uncertain and dynamically changing world, where optimal decision-making under uncertainty is directly linked to the survival of species. However, evolutionary selection pressures that shape value-based decision-making…
Proteins evolve through complex sequence spaces, with fitness landscapes serving as a conceptual framework that links sequence to function. Fitness landscapes can be smooth, where multiple similarly accessible evolutionary paths are…
We present a simple model of adaptive radiations in evolution based on species competition. Competition is found to promote species divergence and branching, and to dampen the net species production. In the model simulations, high taxonomic…
We investigate the equilibrium state of the model of Peng, \textit{et al.} for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular…
In this paper we show that a dynamical description of the protein folding process provides an effective representation of equilibrium properties and it allows for a direct investigation of the mechanisms ruling the approach towards the…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is…
We study a dynamic game with a large population of players who choose actions from a finite set in continuous time. Each player has a state in a finite state space that evolves stochastically with their actions. A player's reward depends…
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates…
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…