10,049 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
Host-Parasite Co-evolution and Optimal Mutation Rates for Semi-conservative Quasispecies
In this paper, we extend a model of host-parasite co-evolution to incorporate
the semi-conservative nature of DNA replication for both the host and the
parasite. We find that the optimal mutation rate for the semi-conservative and
conservative hosts converge for realistic genome lengths, thus maintaining the
admirable agreement between theory and experiment found previously for the
conservative model and justifying the conservative approximation in some cases.
We demonstrate that, while the optimal mutation rate for a conservative and
semi-conservative parasite interacting with a given immune system is similar to
that of a conservative parasite, the properties away from this optimum differ
significantly. We suspect that this difference, coupled with the requirement
that a parasite optimize survival in a range of viable hosts, may help explain
why semi-conservative viruses are known to have significantly lower mutation
rates than their conservative counterparts
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
A Population Genetic Approach to the Quasispecies Model
A population genetics formulation of Eigen's molecular quasispecies model is
proposed and several simple replication landscapes are investigated
analytically. Our results show a remarcable similarity to those obtained with
the original kinetics formulation of the quasispecies model. However, due to
the simplicity of our approach, the space of the parameters that define the
model can be explored. In particular, for the simgle-sharp-peak landscape our
analysis yelds some interesting predictions such as the existence of a maximum
peak height and a mini- mum molecule length for the onset of the error
threshold transition.Comment: 16 pages, 4 Postscript figures. Submited to Phy. Rev.
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
Self-organizing patterns maintained by competing associations in a six-species predator-prey model
Formation and competition of associations are studied in a six-species
ecological model where each species has two predators and two prey. Each site
of a square lattice is occupied by an individual belonging to one of the six
species. The evolution of the spatial distribution of species is governed by
iterated invasions between the neighboring predator-prey pairs with species
specific rates and by site exchange between the neutral pairs with a
probability . This dynamical rule yields the formation of five associations
composed of two or three species with proper spatiotemporal patterns. For large
a cyclic dominance can occur between the three two-species associations
whereas one of the two three-species associations prevails in the whole system
for low values of in the final state. Within an intermediate range of
all the five associations coexist due to the fact that cyclic invasions between
the two-species associations reduce their resistance temporarily against the
invasion of three-species associations.Comment: 6 pages, 8 figure
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
Error threshold in simple landscapes
We consider the quasispecies description of a population evolving in both the
"master sequence" landscape (where a single sequence is evolutionarily
preferred over all others) and the REM landscape (where the fitness of
different sequences is an independent, identically distributed, random
variable). We show that, in both cases, the error threshold is analogous to a
first order thermodynamical transition, where the overlap between the average
genotype and the optimal one drops discontinuously to zero.Comment: 10 pages and 2 figures, Plain LaTe
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