64 research outputs found
Phase transition and selection in a four-species cyclic Lotka-Volterra model
We study a four species ecological system with cyclic dominance whose
individuals are distributed on a square lattice. Randomly chosen individuals
migrate to one of the neighboring sites if it is empty or invade this site if
occupied by their prey. The cyclic dominance maintains the coexistence of all
the four species if the concentration of vacant sites is lower than a threshold
value. Above the treshold, a symmetry breaking ordering occurs via growing
domains containing only two neutral species inside. These two neutral species
can protect each other from the external invaders (predators) and extend their
common territory. According to our Monte Carlo simulations the observed phase
transition is equivalent to those found in spreading models with two equivalent
absorbing states although the present model has continuous sets of absorbing
states with different portions of the two neutral species. The selection
mechanism yielding symmetric phases is related to the domain growth process
whith wide boundaries where the four species coexist.Comment: 4 pages, 5 figure
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
Evolutionary prisoner's dilemma games with optional participation
Competition among cooperators, defectors, and loners is studied in an
evolutionary prisoner's dilemma game with optional participation. Loners are
risk averse i.e. unwilling to participate and rather rely on small but fixed
earnings. This results in a rock-scissors-paper type cyclic dominance of the
three strategies. The players are located either on square lattices or random
regular graphs with the same connectivity. Occasionally, every player
reassesses its strategy by sampling the payoffs in its neighborhood. The loner
strategy efficiently prevents successful spreading of selfish, defective
behavior and avoids deadlocks in states of mutual defection. On square
lattices, Monte Carlo simulations reveal self-organizing patterns driven by the
cyclic dominance, whereas on random regular graphs different types of
oscillatory behavior are observed: the temptation to defect determines whether
damped, periodic or increasing oscillations occur. These results are compared
to predictions by pair approximation. Although pair approximation is incapable
of distinguishing the two scenarios because of the equal connectivity, the
average frequencies as well as the oscillations on random regular graphs are
well reproduced.Comment: 6 pages, 7 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
Studying non-alcoholic fatty liver disease with zebrafish: a confluence of optics, genetics, and physiology
A facile incorporation of the aldehyde function into DNA: 3-formylindole nucleoside as an aldehyde-containing universal nucleoside
A dielectric-sensitive fluorescent DNA probe for monitoring polarities on the interior of a DNA-binding protein
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