8,543 research outputs found
Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution
In the theoretical biology framework one fundamental problem is the so-called
error catastrophe in Darwinian evolution models. We reexamine Eigen's
fundamental equations by mapping them into a polymer depinning transition
problem in a ``genotype'' space represented by a unitary hypercubic lattice.
The exact solution of the model shows that error catastrophe arises as a direct
consequence of the equations involved and confirms some previous qualitative
results. The physically relevant consequence is that such equations are not
adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors.
[email protected] (e-mail address
Error threshold in the evolution of diploid organisms
The effects of error propagation in the reproduction of diploid organisms are
studied within the populational genetics framework of the quasispecies model.
The dependence of the error threshold on the dominance parameter is fully
investigated. In particular, it is shown that dominance can protect the
wild-type alleles from the error catastrophe. The analysis is restricted to a
diploid analogue of the single-peaked landscape.Comment: 9 pages, 4 Postscript figures. Submitted to J. Phy. A: Mat. and Ge
Molecular Evolution in Time Dependent Environments
The quasispecies theory is studied for dynamic replication landscapes. A
meaningful asymptotic quasispecies is defined for periodic time dependencies.
The quasispecies' composition is constantly changing over the oscillation
period. The error threshold moves towards the position of the time averaged
landscape for high oscillation frequencies and follows the landscape closely
for low oscillation frequencies.Comment: 5 pages, 3 figures, Latex, uses Springer documentclass llncs.cl
Anderson Localization, Non-linearity and Stable Genetic Diversity
In many models of genotypic evolution, the vector of genotype populations
satisfies a system of linear ordinary differential equations. This system of
equations models a competition between differential replication rates (fitness)
and mutation. Mutation operates as a generalized diffusion process on genotype
space. In the large time asymptotics, the replication term tends to produce a
single dominant quasispecies, unless the mutation rate is too high, in which
case the populations of different genotypes becomes de-localized. We introduce
a more macroscopic picture of genotypic evolution wherein a random replication
term in the linear model displays features analogous to Anderson localization.
When coupled with non-linearities that limit the population of any given
genotype, we obtain a model whose large time asymptotics display stable
genotypic diversityComment: 25 pages, 8 Figure
Equilibrium Distribution of Mutators in the Single Fitness Peak Model
This paper develops an analytically tractable model for determining the
equilibrium distribution of mismatch repair deficient strains in unicellular
populations. The approach is based on the single fitness peak (SFP) model,
which has been used in Eigen's quasispecies equations in order to understand
various aspects of evolutionary dynamics. As with the quasispecies model, our
model for mutator-nonmutator equilibrium undergoes a phase transition in the
limit of infinite sequence length. This "repair catastrophe" occurs at a
critical repair error probability of , where denotes the length of the genome controlling viability, while
denotes the overall length of the genome. The repair catastrophe therefore
occurs when the repair error probability exceeds the fraction of deleterious
mutations. Our model also gives a quantitative estimate for the equilibrium
fraction of mutators in {\it Escherichia coli}.Comment: 4 pages, 2 figures (included as separate PS files
Genetic Polymorphism in Evolving Population
We present a model for evolving population which maintains genetic
polymorphism. By introducing random mutation in the model population at a
constant rate, we observe that the population does not become extinct but
survives, keeping diversity in the gene pool under abrupt environmental
changes. The model provides reasonable estimates for the proportions of
polymorphic and heterozygous loci and for the mutation rate, as observed in
nature
The Tangled Nature model as an evolving quasi-species model
We show that the Tangled Nature model can be interpreted as a general
formulation of the quasi-species model by Eigen et al. in a frequency dependent
fitness landscape. We present a detailed theoretical derivation of the mutation
threshold, consistent with the simulation results, that provides a valuable
insight into how the microscopic dynamics of the model determine the observed
macroscopic phenomena published previously. The dynamics of the Tangled Nature
model is defined on the microevolutionary time scale via reproduction, with
heredity, variation, and natural selection. Each organism reproduces with a
rate that is linked to the individuals' genetic sequence and depends on the
composition of the population in genotype space. Thus the microevolutionary
dynamics of the fitness landscape is regulated by, and regulates, the evolution
of the species by means of the mutual interactions. At low mutation rate, the
macro evolutionary pattern mimics the fossil data: periods of stasis, where the
population is concentrated in a network of coexisting species, is interrupted
by bursts of activity. As the mutation rate increases, the duration and the
frequency of bursts increases. Eventually, when the mutation rate reaches a
certain threshold, the population is spread evenly throughout the genotype
space showing that natural selection only leads to multiple distinct species if
adaptation is allowed time to cause fixation.Comment: Paper submitted to Journal of Physics A. 13 pages, 4 figure
Error Thresholds on Dynamic Fittness-Landscapes
In this paper we investigate error-thresholds on dynamics fitness-landscapes.
We show that there exists both lower and an upper threshold, representing
limits to the copying fidelity of simple replicators. The lower bound can be
expressed as a correction term to the error-threshold present on a static
landscape. The upper error-threshold is a new limit that only exists on dynamic
fitness-landscapes. We also show that for long genomes on highly dynamic
fitness-landscapes there exists a lower bound on the selection pressure needed
to enable effective selection of genomes with superior fitness independent of
mutation rates, i.e., there are distinct limits to the evolutionary parameters
in dynamic environments.Comment: 5 page
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