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- Georgy P Karev, Yuri I Wolf, Andrey Y Rzhetsky, Faina S Berezovskaya, Eugene V Koonin
- BMC evolutionary biology
- 2002

BACKGROUND
Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in… (More)

BACKGROUND
The size distribution of gene families in a broad range of genomes is well approximated by a generalized Pareto function. Evolution of ensembles of gene families can be described with Birth, Death, and Innovation Models (BDIMs). Analysis of the properties of different versions of BDIMs has the potential of revealing important features of genome… (More)

- Georgy P Karev, Artem S Novozhilov, Faina S Berezovskaya, Adams, M R And Sornborger, A T +1 other
- 2009

Selection systems and the corresponding replicator equations model the evolution of repli-cators with a high level of abstraction. In this paper we apply novel methods of analysis of selection systems to the replicator equations. To be suitable for the suggested algorithm the interaction matrix of the replicator equation should be transformed; in particular… (More)

A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from the biological standpoint. This regime corresponds to the presence of a family of homoclinics to the origin, so-called… (More)

BACKGROUND
Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction.
RESULTS
A complete parametric analysis of… (More)

- Faina Berezovskaya, Georgy Karev, Terry W Snell, Faina S Berezovskaya
- 2005

A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase–parametric portrait of the model was… (More)

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… (More)

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 modeling heterogeneous populations with discrete evolutionary time step. The theory is applied to population dynamics of natural rotifer populations. We show that under… (More)

Selection systems and the corresponding replicator equations model the evolution of replicators with a high level of abstraction. In this paper, we apply novel methods of analysis of selection systems to the replicator equations. To be suitable for the suggested algorithm, the interaction matrix of the replicator equation should be transformed; in… (More)