161 research outputs found
Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models
The most general nonuniform reaction-diffusion models on a one-dimensional
lattice with boundaries, for which the time evolution equations of corre-
lation functions are closed, are considered. A transfer matrix method is used
to find the static solution. It is seen that this transfer matrix can be
obtained in a closed form, if the reaction rates satisfy certain conditions. We
call such models superautonomous. Possible static phase transitions of such
models are investigated. At the end, as an example of superau- tonomous models,
a nonuniform voter model is introduced, and solved explicitly.Comment: 14 page
Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain
The one-dimensional Ising model is easily generalized to a \textit{genuinely
nonequilibrium} system by coupling alternating spins to two thermal baths at
different temperatures. Here, we investigate the full time dependence of this
system. In particular, we obtain the evolution of the magnetisation, starting
with arbitrary initial conditions. For slightly less general initial
conditions, we compute the time dependence of all correlation functions, and
so, the probability distribution. Novel properties, such as oscillatory decays
into the steady state, are presented. Finally, we comment on the relationship
to a reaction-diffusion model with pair annihilation and creation.Comment: Submitted to J. Phys. A (Letter to the editor
When does cyclic dominance lead to stable spiral waves?
Species diversity in ecosystems is often accompanied by characteristic spatio-temporal patterns. Here, we consider a generic two-dimensional population model and study the spiraling patterns arising from the combined effects of cyclic dominance of three species, mutation, pair-exchange and individual hopping. The dynamics is characterized by nonlinear mobility and a Hopf bifurcation around which the system's four-phase state diagram is inferred from a complex Ginzburg-Landau equation derived using a perturbative multiscale expansion. While the dynamics is generally characterized by spiraling patterns, we show that spiral waves are stable in only one of the four phases. Furthermore, we characterize a phase where nonlinearity leads to the annihilation of spirals and to the spatially uniform dominance of each species in turn. Away from the Hopf bifurcation, when the coexistence fixed point is unstable, the spiraling patterns are also affected by the nonlinear diffusion
Exactly solvable reaction diffusion models on a Cayley tree
The most general reaction-diffusion model on a Cayley tree with
nearest-neighbor interactions is introduced, which can be solved exactly
through the empty-interval method. The stationary solutions of such models, as
well as their dynamics, are discussed. Concerning the dynamics, the spectrum of
the evolution Hamiltonian is found and shown to be discrete, hence there is a
finite relaxation time in the evolution of the system towards its stationary
state.Comment: 9 pages, 2 figure
Evolution of cooperation driven by zealots
Recent experimental results with humans involved in social dilemma games
suggest that cooperation may be a contagious phenomenon and that the selection
pressure operating on evolutionary dynamics (i.e., mimicry) is relatively weak.
I propose an evolutionary dynamics model that links these experimental findings
and evolution of cooperation. By assuming a small fraction of (imperfect)
zealous cooperators, I show that a large fraction of cooperation emerges in
evolutionary dynamics of social dilemma games. Even if defection is more
lucrative than cooperation for most individuals, they often mimic cooperation
of fellows unless the selection pressure is very strong. Then, zealous
cooperators can transform the population to be even fully cooperative under
standard evolutionary dynamics.Comment: 5 figure
Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability (EV) thus shapes the long-time population dynamics, notably by influencing the ability of different strains of microorganisms to coexist. Inspired by the evolution of antimicrobial resistance, we study the dynamics of a community consisting of two competing strains subject to twofold EV. The level of toxin varies in time, favouring the growth of one strain under low drug concentration and the other strain when the toxin level is high. We also model time-changing resource abundance by a randomly switching carrying capacity that drives the fluctuating size of the community. While one strain dominates in a static environment, we show that species coexistence is possible in the presence of EV. By computational and analytical means, we determine the environmental conditions under which long-lived coexistence is possible and when it is almost certain. Notably, we study the circumstances under which environmental and demographic fluctuations promote, or hinder, the strains coexistence. We also determine how the make-up of the coexistence phase and the average abundance of each strain depend on the EV
Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance
There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in large populations and static environments. This picture is, however, greatly altered by the fluctuations arising in volatile environments, in which microbial communities commonly evolve. Here, we study the eco-evolutionary dynamics of a population consisting of an antimicrobial-resistant strain and microbes sensitive to antimicrobial drugs in a time-fluctuating environment, modelled by a carrying capacity randomly switching between states of abundance and scarcity. We assume that antimicrobial resistance (AMR) is a shared public good when the number of resistant cells exceeds a certain threshold. Eco-evolutionary dynamics is thus characterised by demographic noise (birth and death events) coupled to environmental fluctuations which can cause population bottlenecks. By combining analytical and computational means, we determine the environmental conditions for the long-lived coexistence and fixation of both strains, and characterise a fluctuation-driven AMR eradication mechanism, where resistant microbes experience bottlenecks leading to extinction. We also discuss the possible applications of our findings to laboratory-controlled experiments
Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations
Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability (EV) thus shapes the long-time population dynamics, notably by influencing the ability of different strains of microorganisms to coexist. Inspired by the evolution of antimicrobial resistance, we study the dynamics of a community consisting of two competing strains subject to twofold EV. The level of toxin varies in time, favouring the growth of one strain under low drug concentration and the other strain when the toxin level is high. We also model time-changing resource abundance by a randomly switching carrying capacity that drives the fluctuating size of the community. While one strain dominates in a static environment, we show that species coexistence is possible in the presence of EV. By computational and analytical means, we determine the environmental conditions under which long-lived coexistence is possible and when it is almost certain. Notably, we study the circumstances under which environmental and demographic fluctuations promote, or hinder, the strains coexistence. We also determine how the make-up of the coexistence phase and the average abundance of each strain depend on the EV
Large Fluctuations and Fixation in Evolutionary Games
We study large fluctuations in evolutionary games belonging to the
coordination and anti-coordination classes. The dynamics of these games,
modeling cooperation dilemmas, is characterized by a coexistence fixed point
separating two absorbing states. We are particularly interested in the problem
of fixation that refers to the possibility that a few mutants take over the
entire population. Here, the fixation phenomenon is induced by large
fluctuations and is investigated by a semi-classical WKB
(Wentzel-Kramers-Brillouin) theory generalized to treat stochastic systems
possessing multiple absorbing states. Importantly, this method allows us to
analyze the combined influence of selection and random fluctuations on the
evolutionary dynamics \textit{beyond} the weak selection limit often considered
in previous works. We accurately compute, including pre-exponential factors,
the probability distribution function in the long-lived coexistence state and
the mean fixation time necessary for a few mutants to take over the entire
population in anti-coordination games, and also the fixation probability in the
coordination class. Our analytical results compare excellently with extensive
numerical simulations. Furthermore, we demonstrate that our treatment is
superior to the Fokker-Planck approximation when the selection intensity is
finite.Comment: 17 pages, 10 figures, to appear in JSTA
Commitment versus persuasion in the three-party constrained voter model
In the framework of the three-party constrained voter model, where voters of
two radical parties (A and B) interact with "centrists" (C and Cz), we study
the competition between a persuasive majority and a committed minority. In this
model, A's and B's are incompatible voters that can convince centrists or be
swayed by them. Here, radical voters are more persuasive than centrists, whose
sub-population consists of susceptible agents C and a fraction zeta of centrist
zealots Cz. Whereas C's may adopt the opinions A and B with respective rates
1+delta_A and 1+delta_B (with delta_A>=delta_B>0), Cz's are committed
individuals that always remain centrists. Furthermore, A and B voters can
become (susceptible) centrists C with a rate 1. The resulting competition
between commitment and persuasion is studied in the mean field limit and for a
finite population on a complete graph. At mean field level, there is a
continuous transition from a coexistence phase when
zeta=
Delta_c. In a finite population of size N, demographic fluctuations lead to
centrism consensus and the dynamics is characterized by the mean consensus time
tau. Because of the competition between commitment and persuasion, here
consensus is reached much slower (zeta=Delta_c) than
in the absence of zealots (when tau\simN). In fact, when zeta<Delta_c and there
is an initial minority of centrists, the mean consensus time asymptotically
grows as tau\simN^{-1/2} e^{N gamma}, where gamma is determined. The dynamics
is thus characterized by a metastable state where the most persuasive voters
and centrists coexist when delta_A>delta_B, whereas all species coexist when
delta_A=delta_B. When zeta>=Delta_c and the initial density of centrists is
low, one finds tau\simln N (when N>>1). Our analytical findings are
corroborated by stochastic simulations.Comment: 25 pages, 6 figures. Final version for the Journal of Statistical
Physics (special issue on the "applications of statistical mechanics to
social phenomena"
- …