Related papers: The Evolutionary Unfolding of Complexity
Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
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 study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to…
The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical…
We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes…
Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against "unconditional" dispersal in spatially heterogeneous environments. "Unconditional" means individuals disperse at…
The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
Due to the conventional distinction between ecological (rapid) and evolutionary (slow)timescales, ecological and population models to date have typically ignored the effects of evolution. Yet the potential for rapid evolutionary change has…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in various contexts. Here we propose a generative model to capture the dynamics of survival analysis,…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and…
We study the asymptotic behavior of an integro-dierential equation describing the evolutionary adaptation of a population structured by a phenotypic trait. The model takes into account mutation, selection, horizontal gene transfer and…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…