34 research outputs found
Finite-size scaling of the quasiespecies model
We use finite-size scaling to investigate the critical behavior of the
quasiespecies model of molecular evolution in the single-sharp-peak replication
landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where
Q is the probability of exact replication of a molecule of length L and a is
the selective advantage of the master string.
We investigate the sharpness of the threshold and find that its
characteristic persist across a range of Q of order L^(-1) about Q_c.
Furthermore, using the data collapsing method we show that the normalized mean
Hamming distance between the master string and the entire population, as well
as the properly scaled fluctuations around this mean value, follow universal
forms in the critical region.Comment: 8 pages,tex. Submitted to Physical Review
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.
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
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
Error threshold in finite populations
A simple analytical framework to study the molecular quasispecies evolution
of finite populations is proposed, in which the population is assumed to be a
random combination of the constiyuent molecules in each generation,i.e.,
linkage disequilibrium at the population level is neglected. In particular, for
the single-sharp-peak replication landscape we investigate the dependence of
the error threshold on the population size and find that the replication
accuracy at threshold increases linearly with the reciprocal of the population
size for sufficiently large populations. Furthermore, in the deterministic
limit our formulation yields the exact steady-state of the quasispecies model,
indicating then the population composition is a random combination of the
molecules.Comment: 14 pages and 4 figure
Field theory for a reaction-diffusion model of quasispecies dynamics
RNA viruses are known to replicate with extremely high mutation rates. These
rates are actually close to the so-called error threshold. This threshold is in
fact a critical point beyond which genetic information is lost through a
second-order phase transition, which has been dubbed the ``error catastrophe.''
Here we explore this phenomenon using a field theory approximation to the
spatially extended Swetina-Schuster quasispecies model [J. Swetina and P.
Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape.
In analogy with standard absorbing-state phase transitions, we develop a
reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model.
The field theory representation of the reaction-diffusion system is
constructed. The proposed field theory belongs to the same universality class
than a conserved reaction-diffusion model previously proposed [F. van Wijland
{\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we
obtain the full set of exponents that characterize the critical behavior at the
error threshold. Our results present the error catastrophe from a new point of
view and suggest that spatial degrees of freedom can modify several mean field
predictions previously considered, leading to the definition of characteristic
exponents that could be experimentally measurable.Comment: 13 page
Finite-size scaling of the error threshold transition in finite population
The error threshold transition in a stochastic (i.e. finite population)
version of the quasispecies model of molecular evolution is studied using
finite-size scaling. For the single-sharp-peak replication landscape, the
deterministic model exhibits a first-order transition at , where is the probability of exact replication of a molecule of length , and is the selective advantage of the master string. For
sufficiently large population size, , we show that in the critical region
the characteristic time for the vanishing of the master strings from the
population is described very well by the scaling assumption \tau = N^{1/2} f_a
\left [ \left (Q - Q_c) N^{1/2} \right ] , where is an -dependent
scaling function.Comment: 8 pages, 3 ps figures. submitted to J. Phys.
Schwinger Boson Formulation and Solution of the Crow-Kimura and Eigen Models of Quasispecies Theory
We express the Crow-Kimura and Eigen models of quasispecies theory in a
functional integral representation. We formulate the spin coherent state
functional integrals using the Schwinger Boson method. In this formulation, we
are able to deduce the long-time behavior of these models for arbitrary
replication and degradation functions.
We discuss the phase transitions that occur in these models as a function of
mutation rate. We derive for these models the leading order corrections to the
infinite genome length limit.Comment: 37 pages; 4 figures; to appear in J. Stat. Phy
Maximum principle and mutation thresholds for four-letter sequence evolution
A four-state mutation-selection model for the evolution of populations of
DNA-sequences is investigated with particular interest in the phenomenon of
error thresholds. The mutation model considered is the Kimura 3ST mutation
scheme, fitness functions, which determine the selection process, come from the
permutation-invariant class. Error thresholds can be found for various fitness
functions, the phase diagrams are more interesting than for equivalent
two-state models. Results for (small) finite sequence lengths are compared with
those for infinite sequence length, obtained via a maximum principle that is
equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 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