Related papers: The Laplace Motion in Phylogenetic Comparative Met…
By providing a framework of accounting for the shared ancestry inherent to all life, phylogenetics is becoming the statistical foundation of biology. The importance of model choice continues to grow as phylogenetic models continue to…
Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…
The evolution equations for a plasma comprising multiple species of charged fluids with relativistic bulk and thermal motion are derived. It is shown that a minimal fluid coupling model allows a natural casting of the evolution equations in…
We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the $n$th step is given by a random rotation of one of the previous steps chosen uniformly at random.…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
We introduce a model to study the impact of catastrophes on evolutionary paths. If we do not allow catastrophes the number of changes in the maximum fitness of a population grows logarithmically with respect to time. Allowing catastrophes…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Dynamics near and far away from thermal equilibrium is studied within the framework of Langevin equations. A stochasticity-dissipation relation is proposed to emphasize the equal importance of the stochastic and deterministic forces in…
The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same…
Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and…
Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
In biology and ecology, individuals or communities of individuals living in unpredictable environments often alternate between different evolutionary strategies to spread and reduce risks. Such behavior is commonly referred to as…
In this paper, we study the significance of ecological interactions and separation of birth and death dynamics in stochastic heterogeneous populations via general birth-death processes. Interactions can manifest through the birth dynamics,…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…