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 ($\beta=0.29(4)$) and of its fluctuation ($\gamma=0.34(6)$) 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 $N$ 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, $\ell(t)\sim t^\alpha$, where $\alpha=3/4$ (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, ${\cal L}(t)\sim t^\beta$, with $\beta=1$ and 2/3 for N=3 and 4, respectively. For $N\geq 5$, 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 20–30 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: “The total number of bud scars is equal to the total number of cells.” 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 $S_q= \frac{1- \sum_ip_i^q}{q-1}$ $(S_1=-\sum_i p_i \ln p_i)$. This finiteness only occurs for $q=0.5$ for the $d=2$ growth mode (growing droplet), and for $q=0$ for the $d=1$ 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