136 research outputs found
Emergent spatial correlations in stochastically evolving populations
We study the spatial pattern formation and emerging long range correlations
in a model of three species coevolving in space and time according to
stochastic contact rules. Analytical results for the pair correlation
functions, based on a truncation approximation and supported by computer
simulations, reveal emergent strategies of survival for minority agents based
on selection of patterns. Minority agents exhibit defensive clustering and
cooperative behavior close to phase transitions.Comment: 11 pages, 4 figures, Adobe PDF forma
Application of the Limit Cycle Model to Star Formation Histories in Spiral Galaxies: Variation among Morphological Types
We propose a limit-cycle scenario of star formation history for any
morphological type of spiral galaxies. It is known observationally that the
early-type spiral sample has a wider range of the present star formation rate
(SFR) than the late-type sample. This tendency is understood in the framework
of the limit-cycle model of the interstellar medium (ISM), in which the SFR
cyclically changes in accordance with the temporal variation of the mass
fraction of the three ISM components. When the limit-cycle model of the ISM is
applied, the amplitude of variation of the SFR is expected to change with the
supernova (SN) rate. Observational evidence indicates that the early-type
spiral galaxies show smaller rates of present SN than late-type ones. Combining
this evidence with the limit-cycle model of the ISM, we predict that the
early-type spiral galaxies show larger amplitudes in their SFR variation than
the late-types. Indeed, this prediction is consistent with the observed wider
range of the SFR in the early-type sample than in the late-type sample. Thus,
in the framework of the limit-cycle model of the ISM, we are able to interpret
the difference in the amplitude of SFR variation among the morphological
classes of spiral galaxies.Comment: 12 pages LaTeX, to appear in A
Population Uncertainty in Model Ecosystem: Analysis by Stochastic Differential Equation
Perturbation experiments are carried out by contact process and its
mean-field version. Here, the mortality rate is increased or decreased
suddenly. It is known that the fluctuation enhancement (FE) occurs after the
perturbation, where FE means a population uncertainty. In the present paper, we
develop a new theory of stochastic differential equation. The agreement between
the theory and the mean-field simulation is almost perfect. This theory enables
us to find much stronger FE than reported previously. We discuss the population
uncertainty in the recovering process of endangered species.Comment: 16 pages, 4 figure, submitted to J. Phys. Soc. Jp
Competing associations in six-species predator-prey models
We study a set of six-species ecological models where each species has two
predators and two preys. On a square lattice the time evolution is governed by
iterated invasions between the neighboring predator-prey pairs chosen at random
and by a site exchange with a probability Xs between the neutral pairs. These
models involve the possibility of spontaneous formation of different defensive
alliances whose members protect each other from the external invaders. The
Monte Carlo simulations show a surprisingly rich variety of the stable spatial
distributions of species and subsequent phase transitions when tuning the
control parameter Xs. These very simple models are able to demonstrate that the
competition between these associations influences their composition. Sometimes
the dominant association is developed via a domain growth. In other cases
larger and larger invasion processes preceed the prevalence of one of the
stable asociations. Under some conditions the survival of all the species can
be maintained by the cyclic dominance occuring between these associations.Comment: 8 pages, 9 figure
Vortex dynamics in a three-state model under cyclic dominance
The evolution of domain structure is investigated in a two-dimensional voter
model with three states under cyclic dominance. The study focus on the dynamics
of vortices, defined by the points where three states (domains) meet. We can
distinguish vortices and antivortices which walk randomly and annihilate each
other. The domain wall motion can create vortex-antivortex pairs at a rate
which is increased by the spiral formation due to the cyclic dominance. This
mechanism is contrasted with a branching annihilating random walk (BARW) in a
particle antiparticle system with density dependent pair creation rate.
Numerical estimates for the critical indices of the vortex density
() and of its fluctuation () improve an earlier
Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the
three-state cyclic voter model in two dimensions.Comment: 5 pages, 6 figures, to appear in PR
Spatial organization in cyclic Lotka-Volterra systems
We study the evolution of a system of interacting species which mimics
the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5
species, spatial inhomogeneities develop spontaneously in initially homogeneous
systems. The arising spatial patterns form a mosaic of single-species domains
with algebraically growing size, , where
(1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4,
respectively. The domain distribution also exhibits a self-similar spatial
structure which is characterized by an additional length scale, , with and 2/3 for N=3 and 4, respectively. For
, the system quickly reaches a frozen state with non interacting
neighboring species. We investigate the time distribution of the number of
mutations of a site using scaling arguments as well as an exact solution for
N=3. Some possible extensions of the system are analyzed.Comment: 18 pages, 10 figures, revtex, also available from
http://arnold.uchicago.edu/~ebn
Defensive alliances in spatial models of cyclical population interactions
As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in
space, cyclical interaction models of six mutating species are studied on a
square lattice, in which each species is supposed to have two dominant, two
subordinated and a neutral interacting partner. Depending on their interaction
topologies, these systems can be classified into four (isomorphic) groups
exhibiting significantly different behaviors as a function of mutation rate. On
three out of four cases three (or four) species form defensive alliances which
maintain themselves in a self-organizing polydomain structure via cyclic
invasions. Varying the mutation rate this mechanism results in an ordering
phenomenon analogous to that of magnetic Ising model.Comment: 4 pages, 3 figure
Apoptosis at Inflection Point in Liquid Culture of Budding Yeasts
Budding yeasts are highly suitable for aging studies, because the number of bud
scars (stage) proportionally correlates with age. Its maximum stages are known
to reach at 20â30 stages on an isolated agar medium. However, their stage
dynamics in a liquid culture is virtually unknown. We investigate the population
dynamics by counting scars in each cell. Here one cell division produces one new
cell and one bud scar. This simple rule leads to a conservation law: âThe
total number of bud scars is equal to the total number of cells.â We find
a large discrepancy: extremely fewer cells with over 5 scars than expected.
Almost all cells with 6 or more scars disappear within a short period of time in
the late log phase (corresponds to the inflection point). This discrepancy is
confirmed directly by the microscopic observations of broken cells. This finding
implies apoptosis in older cells (6 scars or more)
Phase Transitions and Oscillations in a Lattice Prey-Predator Model
A coarse grained description of a two-dimensional prey-predator system is
given in terms of a 3-state lattice model containing two control parameters:
the spreading rates of preys and predators. The properties of the model are
investigated by dynamical mean-field approximations and extensive numerical
simulations. It is shown that the stationary state phase diagram is divided
into two phases: a pure prey phase and a coexistence phase of preys and
predators in which temporal and spatial oscillations can be present. The
different type of phase transitions occuring at the boundary of the prey
absorbing phase, as well as the crossover phenomena occuring between the
oscillatory and non-oscillatory domains of the coexistence phase are studied.
The importance of finite size effects are discussed and scaling relations
between different quantities are established. Finally, physical arguments,
based on the spatial structure of the model, are given to explain the
underlying mechanism leading to oscillations.Comment: 11 pages, 13 figure
Nonextensivity of the cyclic Lattice Lotka Volterra model
We numerically show that the Lattice Lotka-Volterra model, when realized on a
square lattice support, gives rise to a {\it finite} production, per unit time,
of the nonextensive entropy . This finiteness only occurs for for the growth mode
(growing droplet), and for for the one (growing stripe). This
strong evidence of nonextensivity is consistent with the spontaneous emergence
of local domains of identical particles with fractal boundaries and competing
interactions. Such direct evidence is for the first time exhibited for a
many-body system which, at the mean field level, is conservative.Comment: Latex, 6 pages, 5 figure
- âŠ