# Radial Domany-Kinzel models with mutation and selection.

@article{Lavrentovich2013RadialDM, title={Radial Domany-Kinzel models with mutation and selection.}, author={M. Lavrentovich and K. Korolev and D. Nelson}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2013}, volume={87 1}, pages={ 012103 } }

We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, and so on. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved… Expand

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#### References

SHOWING 1-10 OF 134 REFERENCES

Genetic demixing and evolution in linear stepping stone models.

- Physics, Medicine
- Reviews of modern physics
- 2010

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended and q-allele Potts-like models of gene segregation are considered as well. Expand

LIFE AT THE FRONT OF AN EXPANDING POPULATION

- Mathematics, Biology
- Evolution; international journal of organic evolution
- 2010

A simple model of asexual biological evolution at expanding frontiers finds that beneficial mutations give rise to sectors with an opening angle that depends sensitively on the selective advantage of the mutants, and sets tight constraints on sustainable mutation rates for populations that undergo frequent range expansions. Expand

Range Expansion with Mutation and Selection: Dynamical Phase Transition in a Two-Species Eden Model

- Physics, Biology
- 2011

A two-species Eden growth model is introduced to analyze the interplay between uni-directional (irreversible) mutations and selection at the expanding front and finds that surface roughening has a marked effect on the critical properties of the absorbing state phase transition. Expand

Severe Hindrance of Viral Infection Propagation in Spatially Extended Hosts

- Biology, Medicine
- PloS one
- 2011

This paper investigates in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Expand

A Quantitative Test of Population Genetics Using Spatiogenetic Patterns in Bacterial Colonies

- Biology, Physics
- The American Naturalist
- 2011

This system is a simplification of natural microbial community and it is argued that it constitutes proof of principle that the spatial models of population genetics can quantitatively capture organismal evolution. Expand

Genetic drift at expanding frontiers promotes gene segregation

- Biology, Medicine
- Proceedings of the National Academy of Sciences
- 2007

A comparison of bacterial and yeast colonies suggests that this large-scale genetic sectoring is a generic phenomenon that may provide a detectable footprint of past range expansions. Expand

Selective sweeps in growing microbial colonies.

- Medicine, Biology
- Physical biology
- 2012

A simple deterministic reaction-diffusion model is formulated, which successfully predicts the spatial patterns created by two competing species during colony expansion and connects the microscopic parameters like growth rates and diffusion constants with macroscopic spatial patterns and predicts the relationship between fitness in liquid cultures and on Petri dishes, which is confirmed experimentally. Expand

Quasispecies Made Simple

- Medicine, Biology
- PLoS Comput. Biol.
- 2005

It is argued that the lethal mutagenesis of a viral infection by mutation-inducing drugs is not a true error catastophe, but is an extinction catastrophe, because an error threshold is distinct from an extinction threshold, which is the complete loss of the population through lethal mutations. Expand

The mutational meltdown in asexual populations.

- Biology, Medicine
- The Journal of heredity
- 1993

An overview of the theory of the mutational meltdown is given, showing how the process depends on the demographic properties of a population, the properties of mutations, and the relationship between fitness and number of mutations incurred. Expand

Quasispecies theory in the context of population genetics

- Biology, Medicine
- BMC Evolutionary Biology
- 2005

It is demonstrated for a number of cases that the quasispecies concept is equivalent to the concept of mutation-selection balance developed in population genetics, and that there is no disagreement between the population genetics of haploid, asexually-replicating organisms and quasisPEcies theory. Expand