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We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
Spatial metapopulation models are fundamental to theoretical ecology, enabling to study how landscape structure influences global species dynamics. Traditional models, including recent generalizations, often rely on the deterministic limit…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…
The optimization of dynamic problems is both widespread and difficult. When conducting dynamic optimization, a balance between reinitialization and computational expense has to be found. There are multiple approaches to this. In parallel…
The dynamics of adaptation is difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from number fluctuations, called genetic drift, arising in the small number of particularly fit…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
With the rapid development of data collection and aggregation technologies in many scientific disciplines, it is becoming increasingly ubiquitous to conduct large-scale or online regression to analyze real-world data and unveil real-world…
The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the…
Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to…
Recurrent mutations are a common phenomenon in population genetics. They may be at the origin of the fixation of a new genotype, if they give a phenotypic advantage to the carriers of the new mutation. In this paper, we are interested in…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
In this era of big data, feature selection techniques, which have long been proven to simplify the model, makes the model more comprehensible, speed up the process of learning, have become more and more important. Among many developed…
Recent studies have consistently inferred high rates of adaptive molecular evolution between Drosophila species. At the same time, the Drosophila genome evolves under different rates of recombination, which results in partial genetic…
We consider the challenges that arise when fitting complex ecological models to 'large' data sets. In particular, we focus on random effect models which are commonly used to describe individual heterogeneity, often present in ecological…
Planning with generative models has emerged as an effective decision-making paradigm across a wide range of domains, including reinforcement learning and autonomous navigation. While continuous replanning at each timestep might seem…
We investigate a multi-locus evolutionary model which is based on the DNA shuffling protocol widely applied in \textit{in vitro} directed evolution. This model incorporates selection, recombination and point mutations. The simplicity of the…
Generative models have fundamentally reshaped the landscape of decision-making, reframing the problem from pure scalar reward maximization to high-fidelity trajectory generation and distribution matching. This paradigm shift addresses…
When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…