107 research outputs found
Adaptation in tunably rugged fitness landscapes: The Rough Mount Fuji Model
Much of the current theory of adaptation is based on Gillespie's mutational
landscape model (MLM), which assumes that the fitness values of genotypes
linked by single mutational steps are independent random variables. On the
other hand, a growing body of empirical evidence shows that real fitness
landscapes, while possessing a considerable amount of ruggedness, are smoother
than predicted by the MLM. In the present article we propose and analyse a
simple fitness landscape model with tunable ruggedness based on the Rough Mount
Fuji (RMF) model originally introduced by Aita et al. [Biopolymers 54:64-79
(2000)] in the context of protein evolution. We provide a comprehensive
collection of results pertaining to the topographical structure of RMF
landscapes, including explicit formulae for the expected number of local
fitness maxima, the location of the global peak, and the fitness correlation
function. The statistics of single and multiple adaptive steps on the RMF
landscape are explored mainly through simulations, and the results are compared
to the known behavior in the MLM model. Finally, we show that the RMF model can
explain the large number of second-step mutations observed on a highly-fit
first step backgound in a recent evolution experiment with a microvirid
bacteriophage [Miller et al., Genetics 187:185-202 (2011)].Comment: 43 pages, 12 figures; revised version with new results on the number
of fitness maxim
Multidimensional epistasis and the transitory advantage of sex
Identifying and quantifying the benefits of sex and recombination is a long
standing problem in evolutionary theory. In particular, contradictory claims
have been made about the existence of a benefit of recombination on high
dimensional fitness landscapes in the presence of sign epistasis. Here we
present a comparative numerical study of sexual and asexual evolutionary
dynamics of haploids on tunably rugged model landscapes under strong selection,
paying special attention to the temporal development of the evolutionary
advantage of recombination and the link between population diversity and the
rate of adaptation. We show that the adaptive advantage of recombination on
static rugged landscapes is strictly transitory. At early times, an advantage
of recombination arises through the possibility to combine individually
occurring beneficial mutations, but this effect is reversed at longer times by
the much more efficient trapping of recombining populations at local fitness
peaks. These findings are explained by means of well established results for a
setup with only two loci. In accordance with the Red Queen hypothesis the
transitory advantage can be prolonged indefinitely in fluctuating environments,
and it is maximal when the environment fluctuates on the same time scale on
which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final
versio
Exact Results for Amplitude Spectra of Fitness Landscapes
Starting from fitness correlation functions, we calculate exact expressions
for the amplitude spectra of fitness landscapes as defined by P.F. Stadler [J.
Math. Chem. 20, 1 (1996)] for common landscape models, including Kauffman's
NK-model, rough Mount Fuji landscapes and general linear superpositions of such
landscapes. We further show that correlations decaying exponentially with the
Hamming distance yield exponentially decaying spectra similar to those reported
recently for a model of molecular signal transduction. Finally, we compare our
results for the model systems to the spectra of various experimentally measured
fitness landscapes. We claim that our analytical results should be helpful when
trying to interpret empirical data and guide the search for improved fitness
landscape models.Comment: 13 pages, 5 figures; revised and final versio
Quantitative analyses of empirical fitness landscapes
The concept of a fitness landscape is a powerful metaphor that offers insight
into various aspects of evolutionary processes and guidance for the study of
evolution. Until recently, empirical evidence on the ruggedness of these
landscapes was lacking, but since it became feasible to construct all possible
genotypes containing combinations of a limited set of mutations, the number of
studies has grown to a point where a classification of landscapes becomes
possible. The aim of this review is to identify measures of epistasis that
allow a meaningful comparison of fitness landscapes and then apply them to the
empirical landscapes to discern factors that affect ruggedness. The various
measures of epistasis that have been proposed in the literature appear to be
equivalent. Our comparison shows that the ruggedness of the empirical landscape
is affected by whether the included mutations are beneficial or deleterious and
by whether intra- or intergenic epistasis is involved. Finally, the empirical
landscapes are compared to landscapes generated with the Rough Mt.\ Fuji model.
Despite the simplicity of this model, it captures the features of the
experimental landscapes remarkably well.Comment: 24 pages, 5 figures; to appear in Journal of Statistical Mechanics:
Theory and Experimen
Rare events in population genetics: Stochastic tunneling in a two-locus model with recombination
We study the evolution of a population in a two-locus genotype space, in
which the negative effects of two single mutations are overcompensated in a
high fitness double mutant. We discuss how the interplay of finite population
size, , and sexual recombination at rate affects the escape times
to the double mutant. For small populations demographic noise
generates massive fluctuations in . The mean escape time varies
non-monotonically with , and grows exponentially as beyond a critical value .Comment: 4 pages, 3 figure
Scaling properties of growing noninfinitesimal perturbations in space-time chaos
We study the spatiotemporal dynamics of random spatially distributed
noninfinitesimal perturbations in one-dimensional chaotic extended systems. We
find that an initial perturbation of finite size grows in time
obeying the tangent space dynamic equations (Lyapunov vectors) up to a
characteristic time , where is the largest Lyapunov exponent and
is a constant. For times perturbations exhibit spatial
correlations up to a typical distance . For times larger than
finite perturbations are no longer described by tangent space
equations, memory of spatial correlations is progressively destroyed and
perturbations become spatiotemporal white noise. We are able to explain these
results by mapping the problem to the Kardar-Parisi-Zhang universality class of
surface growth.Comment: 4.5 pages LaTeX (RevTeX4) format, 3 eps figs included. Submitted to
Phys Rev
Structure of characteristic Lyapunov vectors in spatiotemporal chaos
We study Lyapunov vectors (LVs) corresponding to the largest Lyapunov
exponents in systems with spatiotemporal chaos. We focus on characteristic LVs
and compare the results with backward LVs obtained via successive Gram-Schmidt
orthonormalizations. Systems of a very different nature such as coupled-map
lattices and the (continuous-time) Lorenz `96 model exhibit the same features
in quantitative and qualitative terms. Additionally we propose a minimal
stochastic model that reproduces the results for chaotic systems. Our work
supports the claims about universality of our earlier results [I. G. Szendro et
al., Phys. Rev. E 76, 025202(R) (2007)] for a specific coupled-map lattice.Comment: 9 page
Van Kampen's expansion approach in an opinion formation model
We analyze a simple opinion formation model consisting of two parties, A and
B, and a group I, of undecided agents. We assume that the supporters of parties
A and B do not interact among them, but only interact through the group I, and
that there is a nonzero probability of a spontaneous change of opinion (A->I,
B->I). From the master equation, and via van Kampen's Omega-expansion approach,
we have obtained the "macroscopic" evolution equation, as well as the
Fokker-Planck equation governing the fluctuations around the deterministic
behavior. Within the same approach, we have also obtained information about the
typical relaxation behavior of small perturbations.Comment: 17 pages, 6 figures, submited to Europ.Phys.J.
1/f^beta noise in a model for weak ergodicity breaking
In systems with weak ergodicity breaking, the equivalence of time averages
and ensemble averages is known to be broken. We study here the computation of
the power spectrum from realizations of a specific process exhibiting 1/f^beta
noise, the Rebenshtok-Barkai model. We show that even the binned power spectrum
does not converge in the limit of infinite time, but that instead the resulting
value is a random variable stemming from a distribution with finite variance.
However, due to the strong correlations in neighboring frequency bins of the
spectrum, the exponent beta can be safely estimated by time averages of this
type. Analytical calculations are illustrated by numerical simulations.Comment: 10 pages, 7 figures; extended references and summary, smaller
corrections; final versio
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