15 research outputs found
Influence of local carrying capacity restrictions on stochastic predator-prey models
We study a stochastic lattice predator-prey system by means of Monte Carlo
simulations that do not impose any restrictions on the number of particles per
site, and discuss the similarities and differences of our results with those
obtained for site-restricted model variants. In accord with the classic
Lotka-Volterra mean-field description, both species always coexist in two
dimensions. Yet competing activity fronts generate complex, correlated
spatio-temporal structures. As a consequence, finite systems display transient
erratic population oscillations with characteristic frequencies that are
renormalized by fluctuations. For large reaction rates, when the processes are
rendered more local, these oscillations are suppressed. In contrast with
site-restricted predator-prey model, we observe species coexistence also in one
dimension. In addition, we report results on the steady-state prey age
distribution.Comment: Latex, IOP style, 17 pages, 9 figures included, related movies
available at http://www.phys.vt.edu/~tauber/PredatorPrey/movies
Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension
The model of competition between densities of two different species, called
predator and prey, is studied on a one dimensional periodic lattice, where each
site can be in one of the four states say, empty, or occupied by a single
predator, or occupied by a single prey, or by both. Along with the pairwise
death of predators and growth of preys, we introduce an interaction where the
predators can eat one of the neighboring prey and reproduce a new predator
there instantly. The model shows a non-equilibrium phase transition into a
unusual absorbing state where predators are absent and the lattice is fully
occupied by preys. The critical exponents of the system are found to be
different from that of the Directed Percolation universality class and they are
robust against addition of explicit diffusion.Comment: 10 pages, 6 figures, to appear in JSTA
Stochastic population oscillations in spatial predator-prey models
It is well-established that including spatial structure and stochastic noise
in models for predator-prey interactions invalidates the classical
deterministic Lotka-Volterra picture of neutral population cycles. In contrast,
stochastic models yield long-lived, but ultimately decaying erratic population
oscillations, which can be understood through a resonant amplification
mechanism for density fluctuations. In Monte Carlo simulations of spatial
stochastic predator-prey systems, one observes striking complex spatio-temporal
structures. These spreading activity fronts induce persistent correlations
between predators and prey. In the presence of local particle density
restrictions (finite prey carrying capacity), there exists an extinction
threshold for the predator population. The accompanying continuous
non-equilibrium phase transition is governed by the directed-percolation
universality class. We employ field-theoretic methods based on the Doi-Peliti
representation of the master equation for stochastic particle interaction
models to (i) map the ensuing action in the vicinity of the absorbing state
phase transition to Reggeon field theory, and (ii) to quantitatively address
fluctuation-induced renormalizations of the population oscillation frequency,
damping, and diffusion coefficients in the species coexistence phase.Comment: 14 pages, 6 figures, submitted to J. Phys C: Conf. Ser. (2011
Symmetry and species segregation in diffusion-limited pair annihilation
We consider a system of q diffusing particle species A_1,A_2,...,A_q that are
all equivalent under a symmetry operation. Pairs of particles may annihilate
according to A_i + A_j -> 0 with reaction rates k_{ij} that respect the
symmetry, and without self-annihilation (k_{ii} = 0). In spatial dimensions d >
2 mean-field theory predicts that the total particle density decays as n(t) ~
1/t, provided the system remains spatially uniform. We determine the conditions
on the matrix k under which there exists a critical segregation dimension
d_{seg} below which this uniformity condition is violated; the symmetry between
the species is then locally broken. We argue that in those cases the density
decay slows down to n(t) ~ t^{-d/d_{seg}} for 2 < d < d_{seg}. We show that
when d_{seg} exists, its value can be expressed in terms of the ratio of the
smallest to the largest eigenvalue of k. The existence of a conservation law
(as in the special two-species annihilation A + B -> 0), although sufficient
for segregation, is shown not to be a necessary condition for this phenomenon
to occur. We work out specific examples and present Monte Carlo simulations
compatible with our analytical results.Comment: latex, 19 pages, 3 eps figures include
Segregation in diffusion-limited multispecies pair annihilation
The kinetics of the q species pair annihilation reaction (A_i + A_j -> 0 for
1 <= i < j <= q) in d dimensions is studied by means of analytical
considerations and Monte Carlo simulations. In the long-time regime the total
particle density decays as rho(t) ~ t^{- alpha}. For d = 1 the system
segregates into single species domains, yielding a different value of alpha for
each q; for a simplified version of the model in one dimension we derive
alpha(q) = (q-1) / (2q). Within mean-field theory, applicable in d >= 2,
segregation occurs only for q < 1 + (4/d). The only physical realisation of
this scenario is the two-species process (q = 2) in d = 2 and d = 3, governed
by an extra local conservation law. For d >= 2 and q >= 1 + (4/d) the system
remains disordered and its density is shown to decay universally with the
mean-field power law (alpha = 1) that also characterises the single-species
annihilation process A + A -> 0.Comment: 35 pages (IOP style files included), 10 figures included (as eps
files
HCV genome-wide genetic analyses in context of disease progression and hepatocellular carcinoma
<div><p>Hepatitis C virus (HCV) is a major cause of hepatitis and hepatocellular carcinoma (HCC) world-wide. Most HCV patients have relatively stable disease, but approximately 25% have progressive disease that often terminates in liver failure or HCC. HCV is highly variable genetically, with seven genotypes and multiple subtypes per genotype. This variation affects HCV’s sensitivity to antiviral therapy and has been implicated to contribute to differences in disease. We sequenced the complete viral coding capacity for 107 HCV genotype 1 isolates to determine whether genetic variation between independent HCV isolates is associated with the rate of disease progression or development of HCC. Consensus sequences were determined by sequencing RT-PCR products from serum or plasma. Positions of amino acid conservation, amino acid diversity patterns, selection pressures, and genome-wide patterns of amino acid covariance were assessed in context of the clinical phenotypes. A few positions were found where the amino acid distributions or degree of positive selection differed between in the HCC and cirrhotic sequences. All other assessments of viral genetic variation and HCC failed to yield significant associations. Sequences from patients with slow disease progression were under a greater degree of positive selection than sequences from rapid progressors, but all other analyses comparing HCV from rapid and slow disease progressors were statistically insignificant. The failure to observe distinct sequence differences associated with disease progression or HCC employing methods that previously revealed strong associations with the outcome of interferon α-based therapy implies that variable ability of HCV to modulate interferon responses is not a dominant cause for differential pathology among HCV patients. This lack of significant associations also implies that host and/or environmental factors are the major causes of differential disease presentation in HCV patients.</p></div