102 research outputs found
Dynamic fitness landscapes: Expansions for small mutation rates
We study the evolution of asexual microorganisms with small mutation rate in
fluctuating environments, and develop techniques that allow us to expand the
formal solution of the evolution equations to first order in the mutation rate.
Our method can be applied to both discrete time and continuous time systems.
While the behavior of continuous time systems is dominated by the average
fitness landscape for small mutation rates, in discrete time systems it is
instead the geometric mean fitness that determines the system's properties. In
both cases, we find that in situations in which the arithmetic (resp.
geometric) mean of the fitness landscape is degenerate, regions in which the
fitness fluctuates around the mean value present a selective advantage over
regions in which the fitness stays at the mean. This effect is caused by the
vanishing genetic diffusion at low mutation rates. In the absence of strong
diffusion, a population can stay close to a fluctuating peak when the peak's
height is below average, and take advantage of the peak when its height is
above average.Comment: 19 pages Latex, elsart style, 4 eps figure
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
Template coexistence in prebiotic vesicle models
The coexistence of distinct templates is a common feature of the diverse
proposals advanced to resolve the information crisis of prebiotic evolution.
However, achieving robust template coexistence turned out to be such a
difficult demand that only a class of models, the so-called package models,
seems to have met it so far. Here we apply Wright's Island formulation of group
selection to study the conditions for the coexistence of two distinct template
types confined in packages (vesicles) of finite capacity. In particular, we
show how selection acting at the level of the vesicles can neutralize the
pressures towards the fixation of any one of the template types (random drift)
and of the type with higher replication rate (deterministic competition). We
give emphasis to the role of the distinct generation times of templates and
vesicles as yet another obstacle to coexistence.Comment: 7 pages, 8 figure
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
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
The Error and Repair Catastrophes: A Two-Dimensional Phase Diagram in the Quasispecies Model
This paper develops a two gene, single fitness peak model for determining the
equilibrium distribution of genotypes in a unicellular population which is
capable of genetic damage repair. The first gene, denoted by ,
yields a viable organism with first order growth rate constant if it
is equal to some target ``master'' sequence . The second
gene, denoted by , yields an organism capable of genetic repair
if it is equal to some target ``master'' sequence . This
model is analytically solvable in the limit of infinite sequence length, and
gives an equilibrium distribution which depends on \mu \equiv L\eps , the
product of sequence length and per base pair replication error probability, and
\eps_r , the probability of repair failure per base pair. The equilibrium
distribution is shown to exist in one of three possible ``phases.'' In the
first phase, the population is localized about the viability and repairing
master sequences. As \eps_r exceeds the fraction of deleterious mutations,
the population undergoes a ``repair'' catastrophe, in which the equilibrium
distribution is still localized about the viability master sequence, but is
spread ergodically over the sequence subspace defined by the repair gene. Below
the repair catastrophe, the distribution undergoes the error catastrophe when exceeds \ln k/\eps_r , while above the repair catastrophe, the
distribution undergoes the error catastrophe when exceeds , where denotes the fraction of deleterious mutations.Comment: 14 pages, 3 figures. Submitted to Physical Review
Chance and Necessity in Evolution: Lessons from RNA
The relationship between sequences and secondary structures or shapes in RNA
exhibits robust statistical properties summarized by three notions: (1) the
notion of a typical shape (that among all sequences of fixed length certain
shapes are realized much more frequently than others), (2) the notion of shape
space covering (that all typical shapes are realized in a small neighborhood of
any random sequence), and (3) the notion of a neutral network (that sequences
folding into the same typical shape form networks that percolate through
sequence space). Neutral networks loosen the requirements on the mutation rate
for selection to remain effective. The original (genotypic) error threshold has
to be reformulated in terms of a phenotypic error threshold. With regard to
adaptation, neutrality has two seemingly contradictory effects: It acts as a
buffer against mutations ensuring that a phenotype is preserved. Yet it is
deeply enabling, because it permits evolutionary change to occur by allowing
the sequence context to vary silently until a single point mutation can become
phenotypically consequential. Neutrality also influences predictability of
adaptive trajectories in seemingly contradictory ways. On the one hand it
increases the uncertainty of their genotypic trace. At the same time neutrality
structures the access from one shape to another, thereby inducing a topology
among RNA shapes which permits a distinction between continuous and
discontinuous shape transformations. To the extent that adaptive trajectories
must undergo such transformations, their phenotypic trace becomes more
predictable.Comment: 37 pages, 14 figures; 1998 CNLS conference; high quality figures at
http://www.santafe.edu/~walte
Error thresholds for self- and cross-specific enzymatic replication
The information content of a non-enzymatic self-replicator is limited by
Eigen's error threshold. Presumably, enzymatic replication can maintain higher
complexity, but in a competitive environment such a replicator is faced with
two problems related to its twofold role as enzyme and substrate: as enzyme, it
should replicate itself rather than wastefully copy non-functional substrates,
and as substrate it should preferably be replicated by superior enzymes instead
of less-efficient mutants. Because specific recognition can enforce these
propensities, we thoroughly analyze an idealized quasispecies model for
enzymatic replication, with replication rates that are either a decreasing
(self-specific) or increasing (cross-specific) function of the Hamming distance
between the recognition or "tag" sequences of enzyme and substrate. We find
that very weak self-specificity suffices to localize a population about a
master sequence and thus to preserve its information, while simultaneous
localization about complementary sequences in the cross-specific case is more
challenging. A surprising result is that stronger specificity constraints allow
longer recognition sequences, because the populations are better localized.
Extrapolating from experimental data, we obtain rough quantitative estimates
for the maximal length of the recognition or tag sequence that can be used to
reliably discriminate appropriate and infeasible enzymes and substrates,
respectively.Comment: 23 pages, 7 figures; final version as publishe
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
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