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6 papers
Mathematical modeling of evolution of horizontally transferred genes
Artem S. Novozhilov, Georgy P. Karev, Eugene V. Koonin
We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model descri…
Modeling the dynamics of inhomogeneous natural rotifer populations under toxicant exposure
Georgy P. Karev, Artem S. Novozhilov, Faina S. Berezovskaya
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to…
Biological applications of the theory of birth-and-death processes
Artem S. Novozhilov, Georgy P. Karev, Eugene V. Koonin
In this review, we discuss the applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principle…
Simple stochastic birth and death models of genome evolution: Was there enough time for us to evolve?
Georgy P. Karev, Yuri I. Wolf, Eugene V. Koonin
We show that simple stochastic models of genome evolution lead to power law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation…
Modeling genome evolution with a diffusion approximation of a birth-and-death process
Georgy P. Karev, Faina S. Berezovskaya, Eugene V. Koonin
In our previous studies, we developed discrete-space Birth, Death and Innovation Models (BDIM) of genome evolution. These models explain the origin of the characteristic Pareto dis…
Traveling wave solutions of Fitzhugh model with cross-diffusion
F. Berezovskaya, E. Camacho, S. Wirkus +1
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the…