9,504 research outputs found
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.
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
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
Global Fits of the CKM Matrix
We report upon the present status of global fits to Cabibbo-Kobayashi-Maskawa
matrix.Comment: 3 pages, 3 figures invited talk presented at EPS conference, Aachen
July 17-2
Group selection models in prebiotic evolution
The evolution of enzyme production is studied analytically using ideas of the
group selection theory for the evolution of altruistic behavior. In particular,
we argue that the mathematical formulation of Wilson's structured deme model
({\it The Evolution of Populations and Communities}, Benjamin/Cumings, Menlo
Park, 1980) is a mean-field approach in which the actual environment that a
particular individual experiences is replaced by an {\it average} environment.
That formalism is further developed so as to avoid the mean-field approximation
and then applied to the problem of enzyme production in the prebiotic context,
where the enzyme producer molecules play the altruists role while the molecules
that benefit from the catalyst without paying its production cost play the
non-altruists role. The effects of synergism (i.e., division of labor) as well
as of mutations are also considered and the results of the equilibrium analysis
are summarized in phase diagrams showing the regions of the space of parameters
where the altruistic, non-altruistic and the coexistence regimes are stable. In
general, those regions are delimitated by discontinuous transition lines which
end at critical points.Comment: 22 pages, 10 figure
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