9,191 research outputs found
Self-organizing patterns maintained by competing associations in a six-species predator-prey model
Formation and competition of associations are studied in a six-species
ecological model where each species has two predators and two prey. Each site
of a square lattice is occupied by an individual belonging to one of the six
species. The evolution of the spatial distribution of species is governed by
iterated invasions between the neighboring predator-prey pairs with species
specific rates and by site exchange between the neutral pairs with a
probability . This dynamical rule yields the formation of five associations
composed of two or three species with proper spatiotemporal patterns. For large
a cyclic dominance can occur between the three two-species associations
whereas one of the two three-species associations prevails in the whole system
for low values of in the final state. Within an intermediate range of
all the five associations coexist due to the fact that cyclic invasions between
the two-species associations reduce their resistance temporarily against the
invasion of three-species associations.Comment: 6 pages, 8 figure
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
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
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
Eigen model as a quantum spin chain: exact dynamics
We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465
(1971)] into a one-dimensional quantum spin model with non-Hermitean
Hamiltonian. Based on such a connection, we derive exact relaxation periods for
the Eigen model to approach static energy landscape from various initial
conditions. We also study a simple case of dynamic fitness function.Comment: 10 pages. Physical Revew E vol. 69, in press (2004
Complex noise in diffusion-limited reactions of replicating and competing species
We derive exact Langevin-type equations governing quasispecies dynamics. The
inherent multiplicative noise has both real and imaginary parts. The numerical
simulation of the underlying complex stochastic partial differential equations
is carried out employing the Cholesky decomposition for the noise covariance
matrix. This noise produces unavoidable spatio-temporal density fluctuations
about the mean field value. In two dimensions, the fluctuations are suppressed
only when the diffusion time scale is much smaller than the amplification time
scale for the master species.Comment: 10 pages, 2 composite figure
Differentiation and Replication of Spots in a Reaction Diffusion System with Many Chemicals
The replication and differentiation of spots in reaction diffusion equations
are studied by extending the Gray-Scott model with self-replicating spots to
include many degrees of freedom needed to model systems with many chemicals. By
examining many possible reaction networks, the behavior of this model is
categorized into three types: replication of homogeneous fixed spots,
replication of oscillatory spots, and differentiation from `m ultipotent
spots'. These multipotent spots either replicate or differentiate into other
types of spots with different fixed-point dynamics, and as a result, an
inhomogeneous pattern of spots is formed. This differentiation process of spots
is analyzed in terms of the loss of chemical diversity and decrease of the
local Kolmogorov-Sinai entropy. The relevance of the results to developmental
cell biology and stem cells is also discussed.Comment: 8 pages, 12 figures, Submitted to EP
Growth states of catalytic reaction networks exhibiting energy metabolism
All cells derive nutrition by absorbing some chemical and energy resources
from the environment; these resources are used by the cells to reproduce the
chemicals within them, which in turn leads to an increase in their volume. In
this study, we introduce a protocell model exhibiting catalytic reaction
dynamics, energy metabolism, and cell growth. Results of extensive simulations
of this model show the existence of four phases with regard to the rates of
both the influx of resources and the cell growth. These phases include an
active phase with high influx and high growth rates, an inefficient phase with
high influx but low growth rates, a quasi-static phase with low influx and low
growth rates, and a death phase with negative growth rate. A mean field model
well explains the transition among these phases as bifurcations. The
statistical distribution of the active phase is characterized by a power law
and that of the inefficient phase is characterized by a nearly equilibrium
distribution. We also discuss the relevance of the results of this study to
distinct states in the existing cells.Comment: 21 pages, 5 figure
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
Non-Gaussian statistics and extreme waves in a nonlinear optical cavity
A unidirectional optical oscillator is built by using a liquid crystal
light-valve that couples a pump beam with the modes of a nearly spherical
cavity. For sufficiently high pump intensity, the cavity field presents a
complex spatio-temporal dynamics, accompanied by the emission of extreme waves
and large deviations from the Gaussian statistics. We identify a mechanism of
spatial symmetry breaking, due to a hypercycle-type amplification through the
nonlocal coupling of the cavity field
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