150 research outputs found
Multiple-line inference of selection on quantitative traits
Trait differences between species may be attributable to natural selection.
However, quantifying the strength of evidence for selection acting on a
particular trait is a difficult task. Here we develop a population-genetic test
for selection acting on a quantitative trait which is based on multiple-line
crosses. We show that using multiple lines increases both the power and the
scope of selection inference. First, a test based on three or more lines
detects selection with strongly increased statistical significance, and we show
explicitly how the sensitivity of the test depends on the number of lines.
Second, a multiple-line test allows to distinguish different lineage-specific
selection scenarios. Our analytical results are complemented by extensive
numerical simulations. We then apply the multiple-line test to QTL data on
floral character traits in plant species of the Mimulus genus and on
photoperiodic traits in different maize strains, where we find a signatures of
lineage-specific selection not seen in a two-line test.Comment: 21 pages, 11 figures; to appear in Genetic
Evolutionary games and quasispecies
We discuss a population of sequences subject to mutations and
frequency-dependent selection, where the fitness of a sequence depends on the
composition of the entire population. This type of dynamics is crucial to
understand the evolution of genomic regulation. Mathematically, it takes the
form of a reaction-diffusion problem that is nonlinear in the population state.
In our model system, the fitness is determined by a simple mathematical game,
the hawk-dove game. The stationary population distribution is found to be a
quasispecies with properties different from those which hold in fixed fitness
landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact
solution for the hawks-dove game is provide
Vicinal Surfaces and the Calogero-Sutherland Model
A miscut (vicinal) crystal surface can be regarded as an array of meandering
but non-crossing steps. Interactions between the steps are shown to induce a
faceting transition of the surface between a homogeneous Luttinger liquid state
and a low-temperature regime consisting of local step clusters in coexistence
with ideal facets. This morphological transition is governed by a hitherto
neglected critical line of the well-known Calogero-Sutherland model. Its exact
solution yields expressions for measurable quantities that compare favorably
with recent experiments on Si surfaces.Comment: 4 pages, revtex, 2 figures (.eps
On Growth, Disorder, and Field Theory
This article reviews recent developments in statistical field theory far from
equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic
surface growth and its mathematical relatives, namely the stochastic Burgers
equation in fluid mechanics and directed polymers in a medium with quenched
disorder. At strong stochastic driving -- or at strong disorder, respectively
-- these systems develop nonperturbative scale-invariance. Presumably exact
values of the scaling exponents follow from a self-consistent asymptotic
theory. This theory is based on the concept of an operator product expansion
formed by the local scaling fields. The key difference to standard Lagrangian
field theory is the appearance of a dangerous irrelevant coupling constant
generating dynamical anomalies in the continuum limit.Comment: review article, 50 pages (latex), 10 figures (eps), minor
modification of original versio
Universality of Long-Range Correlations in Expansion-Randomization Systems
We study the stochastic dynamics of sequences evolving by single site
mutations, segmental duplications, deletions, and random insertions. These
processes are relevant for the evolution of genomic DNA. They define a
universality class of non-equilibrium 1D expansion-randomization systems with
generic stationary long-range correlations in a regime of growing sequence
length. We obtain explicitly the two-point correlation function of the sequence
composition and the distribution function of the composition bias in sequences
of finite length. The characteristic exponent of these quantities is
determined by the ratio of two effective rates, which are explicitly calculated
for several specific sequence evolution dynamics of the universality class.
Depending on the value of , we find two different scaling regimes, which
are distinguished by the detectability of the initial composition bias. All
analytic results are accurately verified by numerical simulations. We also
discuss the non-stationary build-up and decay of correlations, as well as more
complex evolutionary scenarios, where the rates of the processes vary in time.
Our findings provide a possible example for the emergence of universality in
molecular biology.Comment: 23 pages, 15 figure
A minimal stochastic model for influenza evolution
We introduce and discuss a minimal individual-based model for influenza
dynamics. The model takes into account the effects of specific immunization
against viral strains, but also infectivity randomness and the presence of a
short-lived strain transcending immunity recently suggested in the literature.
We show by simulations that the resulting model exhibits substitution of viral
strains along the years, but that their divergence remains bounded. We also
show that dropping any of these features results in a drastically different
behavior, leading either to the extinction of the disease, to the proliferation
of the viral strains, or to their divergence
Dynamical Anomalies and Intermittency in Burgers Turbulence
We analyze the field theory of fully developed Burgers turbulence. Its key
elements are shock fields, which characterize the singularity statistics of the
velocity field. The shock fields enter an operator product expansion describing
intermittency. The latter is found to be constrained by dynamical anomalies
expressing finite dissipation in the inviscid limit. The link between dynamical
anomalies and intermittency is argued to be important in a wider context of
turbulence.Comment: revised version, 4 pp., 1 fig., to appear in PR
A Solvable Sequence Evolution Model and Genomic Correlations
We study a minimal model for genome evolution whose elementary processes are
single site mutation, duplication and deletion of sequence regions and
insertion of random segments. These processes are found to generate long-range
correlations in the composition of letters as long as the sequence length is
growing, i.e., the combined rates of duplications and insertions are higher
than the deletion rate. For constant sequence length, on the other hand, all
initial correlations decay exponentially. These results are obtained
analytically and by simulations. They are compared with the long-range
correlations observed in genomic DNA, and the implications for genome evolution
are discussed.Comment: 4 pages, 4 figure
Quantized Scaling of Growing Surfaces
The Kardar-Parisi-Zhang universality class of stochastic surface growth is
studied by exact field-theoretic methods. From previous numerical results, a
few qualitative assumptions are inferred. In particular, height correlations
should satisfy an operator product expansion and, unlike the correlations in a
turbulent fluid, exhibit no multiscaling. These properties impose a
quantization condition on the roughness exponent and the dynamic
exponent . Hence the exact values for two-dimensional
and for three-dimensional surfaces are derived.Comment: 4 pages, revtex, no figure
Ring Migration Topology Helps Bypassing Local Optima
Running several evolutionary algorithms in parallel and occasionally
exchanging good solutions is referred to as island models. The idea is that the
independence of the different islands leads to diversity, thus possibly
exploring the search space better. Many theoretical analyses so far have found
a complete (or sufficiently quickly expanding) topology as underlying migration
graph most efficient for optimization, even though a quick dissemination of
individuals leads to a loss of diversity. We suggest a simple fitness function
FORK with two local optima parametrized by and a scheme for
composite fitness functions. We show that, while the (1+1) EA gets stuck in a
bad local optimum and incurs a run time of fitness evaluations
on FORK, island models with a complete topology can achieve a run time of
by making use of rare migrations in order to explore the
search space more effectively. Finally, the ring topology, making use of rare
migrations and a large diameter, can achieve a run time of
, the black box complexity of FORK. This shows that the
ring topology can be preferable over the complete topology in order to maintain
diversity.Comment: 12 page
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