A birth, death, and diffusion process

Modeling genome evolution with a diffusion approximation of a birth-and-death process

MOTIVATION In our previous studies, we developed discrete-space birth, death and innovation models (BDIMs) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and model parameters that provide for the evolution of these distributions within a realistic time frame have been identified. However, extracting the ...

Birth, death and diffusion of interacting particles

Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrat...

A Birth-Death Process for Feature Allocation

We propose a Bayesian nonparametric prior over feature allocations for sequential data, the birthdeath feature allocation process (BDFP). The BDFP models the evolution of the feature allocation of a set of N objects across a covariate (e.g. time) by creating and deleting features. A BDFP is exchangeable, projective, stationary and reversible, and its equilibrium distribution is given by the Ind...

The Z-transform Applied to a Birth-death Process Having Varying Birth and Death Rates

The analysis of a birth-death process using the z-transform was recently reported for processes having fixed transition probabilities between states. The current report extends that analysis to processes having transition probabilities that can differ from state to state. It is then shown that the model can be used to study practical queuing and birth-death systems where the arrival, birth, ser...

Stationary Distribution of a Perturbed Quasi-birth-and-death Process