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Gene drives have the potential to rapidly replace a harmful wild-type allele with a gene drive allele engineered to have desired functionalities. However, an accidental or premature release of a gene drive construct to the natural…

This paper is concerned with a reaction--diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has…

Gene drive alleles bias their own inheritance to offspring. They can fix in a wild-type population in spite of a fitness cost, and even lead to the eradication of the target population if the fitness cost is high. However, this outcome may…

Despite the advent of several novel, synthetic gene drive mechanisms and their potential to one-day control a number of devastating diseases, among other applications, practical use of these systems remains contentious and risky. In…

Understanding the temporal spread of gene drive alleles -- alleles that bias their own transmission -- through modeling is essential before any field experiments. In this paper, we present a deterministic reaction-diffusion model describing…

The pace and unpredictability of evolution are critically relevant in a variety of modern challenges: combating drug resistance in pathogens and cancer, understanding how species respond to environmental perturbations like climate change,…

The spread of synthetic gene drives is often discussed in the context of panmictic populations connected by gene flow and described with simple deterministic models. Under such assumptions, an entire species could be altered by releasing a…

We consider evolution of a large population, where fitness of each organism is defined by many phenotypical traits. These traits result from expression of many genes. We propose a new model of gene regulation, where gene expression is…

Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because…

We use fitness graphs, or directed cube graphs, for analyzing evolutionary reversibility. The main application is antimicrobial drug resistance. Reversible drug resistance has been observed both clinically and experimentally. If drug…

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…

Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…

In genetic drift of small population, it is well known that even when the ratio of alleles is 0.5, specific genes are fixed in or disappear from the population. It seems the reason why inbreeding is avoided. On the other hand, this…

Under the effects of strong genetic drift, it is highly probable to observe gene fixation or loss in a population, shown by divergent probability density functions, or infinite adaptive peaks on a landscape. It is then interesting to ask…

Antimicrobial resistance is an emerging global health crisis that is undermining advances in modern medicine and, if unmitigated, threatens to kill 10 million people per year worldwide by 2050. Research over the last decade has demonstrated…

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or…

We present a new method for constraining the mass transfer evolution of low mass X-ray binaries (LMXBs) - a reverse population synthesis technique. This is done using the detailed 1D stellar evolution code MESA (Modules for Experiments in…

We are interested in predator-prey dynamics on infinite trees, which can informally be seen as particular two-type branching processes where individuals may die (or be infected) only after their parent dies (or is infected). We study two…

Reaction-diffusion analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. Few…

Spatially resolved genetic data is increasingly used to reconstruct the migrational history of species. To assist such inference, we study, by means of simulations and analytical methods, the dynamics of neutral gene frequencies in a…