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This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
We introduce a simple computational model that, with a microscopic dynamics driven by natural selection and mutation alone, allows the description of true speciation events. A statistical analysis of the so generated evolutionary tree…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
This paper studies the entropy of tree-shifts of finite type with and without boundary conditions. We demonstrate that computing the entropy of a tree-shift of finite type is equivalent to solving a system of nonlinear recurrence equations.…
We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a…
We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
Mitochondrial and nuclear genomes must be co-adapted to ensure proper cellular respiration and energy production. Mito-nuclear incompatibility reduces individual fitness and induces hybrid infertility, suggesting a possible role in…
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the…
In this paper, we consider $n$-type Markov branching processes with immigration and resurrection. The uniqueness criteria are first established. Then, a new method is found and the explicit expression of extinction probability is…
Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…
Global environmental change is affecting species distribution and their interactions with other species. In particular, the main drivers of environmental change strongly affect the strength of interspecific interactions with considerable…
Phenotypic plasticity and its evolution may help evolutionary rescue in a novel and stressful environment, especially if environmental novelty reveals cryptic genetic variation that enables the evolution of increased plasticity. However,…
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 consider a discrete-time Markov chain, called fragmentation process, that describes a specific way of successively removing objects from a linear arrangement. The process arises in population genetics and describes the ancestry of the…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
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…
We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We present and rigorously analyze a model describing a mixed…