种群与进化
Phylogenetic networks generalize phylogenetic trees to evolutionary histories that include reticulate events such as recombination, horizontal gene transfer, and hybridization. Under a Markov model of nucleotide substitution, a phylogenetic…
Evolved sequences can be used to infer the rules of evolution. Orally transmitted folk melodies are evolved sequences whose similarity to protein sequences (one-dimensional, drawn from a limited alphabet) invites application of…
These are lecture notes for an advanced topics course in the master's programme at Bonn University. It aims to give a concise review of some of the work that has been done around the topic of adaptive dynamics from a rigorous stochastic…
Tumor evolution is shaped by cell division, cell death, competition, and constraints imposed by the local microenvironment. Because these dynamics are usually not observed directly, phylogenetic trees inferred from somatic variation in…
Species-specific pest and vector control strategies, including the sterile insect technique, Wolbachia-based interventions, and genetic control technologies, offer powerful alternatives to broad-spectrum chemical control, with applications…
Respiratory syncytial virus (RSV) is a leading cause of bronchiolitis and other lower respiratory tract infections in infants. Increased viral circulation in the post-COVID era and heterogeneous prevention strategies across regions have…
The Moran process with selection and recurrent mutation is a classical model in population genetics, yet how the placement of selection within the update rule shapes the stationary distribution has received little attention. We study a…
We extend the standard susceptible-infected-recovered framework to incorporate natural immune boosting during a short-scale outbreak. By deriving closed-form final size relations, we analytically link total attack rates to boosting dynamics…
\textbf{Background:} In Costa Rica, dengue is reported and controlled at the canton level, and outbreaks in one canton are often followed by outbreaks in others. Climate models describe where conditions favor transmission but not how dengue…
Phylogenetic trees are rooted trees with branch lengths that record genetic divergence or elapsed time, and quantifying differences between them is central to a wide range of evolutionary and epidemiological analyses. Graph-polynomial…
We propose and analyse a mathematical model of evolutionary adaptation for non-degenerate (permanent) replicator systems, in which the fitness landscape matrix evolves on a slow timescale -- the evolutionary time -- while the species…
We mathematically model the dynamics of the number of migratory fish observed at a fixed location along a river in a random environment. Particularly, as a new approach, we construct a stochastic differential equation that incorporates the…
How can a species persist in an environment where it is always outcompeted? Using a minimal predator-prey model with environment-dependent parameters, we show that a predator driven to extinction in each of two static environments can…
Estimating peak prevalence is a central problem in epidemic modeling because it determines the period of greatest infectious burden and is closely linked to health-care demand. In multistage SIR models, however, peak prevalence is generally…
Population immunity carried over from past epidemics of an antigenically variable pathogen influences the epidemic of new variants based on their antigenic similarity to the previous ones. We develop a recurrent SIR model where a population…
In multispecies birth-death processes, how population regulation -- through suppressed replication, elevated mortality, or both -- affects macroscopic stochastic dynamics has escaped detailed analysis. Here, we show that the distribution of…
This work addresses an optimal control problem for a SI epidemic model incorporating heterogeneities in resistance and viral load at the population level. Building upon the heterogeneous SI framework developed in [1], a minimization problem…
This study presents a comprehensive analysis of bird diversity across Sri Lanka by integrating spatial, temporal, and environmental data. Bird observation records were combined with environmental variables, including weather conditions, air…
Multi-level selection and senescence do not at first sight have much in common. Here, we demonstrate that the emergent mortality patterns generated by demographic senescence can be understood as the product of multi-level selection. We…
The coalescing colony model provides a minimal framework for biological invasions with long-range dispersion. In its standard formulation, the dispersion range is assumed independent of the size of the invading population. Here, we relax…