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We consider a time-continuous branching random walk on a one-dimensional lattice on which there is one center (lattice point) of particle generation, called branching source. The generation of particles in the branching source is described…
In this paper we review some recent results that shed light on a fundamental question in molecular systematics: how much phylogenetic `signal' can we expect from characters that have evolved under some Markov process? There are many sides…
The theory of large random matrices has proved an invaluable tool for the study of systems with disordered interactions in many quite disparate research areas. Widely applicable results, such as the celebrated elliptic law for dense random…
A phylogenetic tree is a way to organize a finite set of species, individuals or other sources of related data. The species for which we have existing DNA data make up the set of leaves of the tree. The balanced minimal evolution method of…
We consider catalytic branching populations. They consist of a catalyst population evolving according to a critical binary branching process in continuous time with a constant branching rate and a reactant population with a branching rate…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the…
In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…
Representations of population models in terms of countable systems of particles are constructed, in which each particle has a `type', typically recording both spatial position and genetic type, and a level. For finite intensity models, the…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the Random Energy Model…
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…
In the present article the recent works to formulate laws in Darwinian evolutionary dynamics are discussed. Although there is a strong consensus that general laws in biology may exist, opinions opposing such suggestion are abundant. Based…
Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly…
Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa…
The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The…
This study presents the approach to analyzing the evolution of an arbitrary complex system whose behavior is characterized by a set of different time-dependent factors. The key requirement for these factors is only that they must contain an…
Molecular phylogenetic and phylogeographic reconstructions generally assume time-homogeneous substitution processes. Motivated by computational convenience, this assumption sacrifices biological realism and offers little opportunity to…