12,955 research outputs found
An exactly solvable coarse-grained model for species diversity
We present novel analytical results about ecosystem species diversity that
stem from a proposed coarse grained neutral model based on birth-death
processes. The relevance of the problem lies in the urgency for understanding
and synthesizing both theoretical results of ecological neutral theory and
empirical evidence on species diversity preservation. Neutral model of
biodiversity deals with ecosystems in the same trophic level where per-capita
vital rates are assumed to be species-independent. Close-form analytical
solutions for neutral theory are obtained within a coarse-grained model, where
the only input is the species persistence time distribution. Our results
pertain: the probability distribution function of the number of species in the
ecosystem both in transient and stationary states; the n-points connected time
correlation function; and the survival probability, definned as the
distribution of time-spans to local extinction for a species randomly sampled
from the community. Analytical predictions are also tested on empirical data
from a estuarine fish ecosystem. We find that emerging properties of the
ecosystem are very robust and do not depend on specific details of the model,
with implications on biodiversity and conservation biology.Comment: 20 pages, 4 figures. To appear in Journal of Statistichal Mechanic
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Replicator equations and space
A reaction--diffusion replicator equation is studied. A novel method to apply
the principle of global regulation is used to write down the model with
explicit spatial structure. Properties of stationary solutions together with
their stability are analyzed analytically, and relationships between stability
of the rest points of the non-distributed replicator equation and distributed
system are shown. A numerical example is given to show that the spatial
variable in this particular model promotes the system's permanence.Comment: 24 page
Statistical mechanics and stability of a model eco-system
We study a model ecosystem by means of dynamical techniques from disordered
systems theory. The model describes a set of species subject to competitive
interactions through a background of resources, which they feed upon.
Additionally direct competitive or co-operative interaction between species may
occur through a random coupling matrix. We compute the order parameters of the
system in a fixed point regime, and identify the onset of instability and
compute the phase diagram. We focus on the effects of variability of resources,
direct interaction between species, co-operation pressure and dilution on the
stability and the diversity of the ecosystem. It is shown that resources can be
exploited optimally only in absence of co-operation pressure or direct
interaction between species.Comment: 23 pages, 13 figures; text of paper modified, discussion extended,
references adde
Analysis of a spatial Lotka-Volterra model with a finite range predator-prey interaction
We perform an analysis of a recent spatial version of the classical
Lotka-Volterra model, where a finite scale controls individuals' interaction.
We study the behavior of the predator-prey dynamics in physical spaces higher
than one, showing how spatial patterns can emerge for some values of the
interaction range and of the diffusion parameter.Comment: 7 pages, 7 figure
Extraordinary Sex Ratios: Cultural Effects on Ecological Consequences
We model sex-structured population dynamics to analyze pairwise competition
between groups differing both genetically and culturally. A sex-ratio allele is
expressed in the heterogametic sex only, so that assumptions of Fisher's
analysis do not apply. Sex-ratio evolution drives cultural evolution of a
group-associated trait governing mortality in the homogametic sex. The two-sex
dynamics under resource limitation induces a strong Allee effect that depends
on both sex ratio and cultural trait values. We describe the resulting
threshold, separating extinction from positive growth, as a function of female
and male densities. When initial conditions avoid extinction due to the Allee
effect, different sex ratios cannot coexist; in our model, greater female
allocation always invades and excludes a lesser allocation. But the culturally
transmitted trait interacts with the sex ratio to determine the ecological
consequences of successful invasion. The invading female allocation may permit
population persistence at self-regulated equilibrium. For this case, the
resident culture may be excluded, or may coexist with the invader culture. That
is, a single sex-ratio allele in females and a cultural dimorphism in male
mortality can persist; a low-mortality resident trait is maintained by
father-to-son cultural transmission. Otherwise, the successfully invading
female allocation excludes the resident allele and culture, and then drives the
population to extinction via a shortage of males. Finally, we show that the
results obtained under homogeneous mixing hold, with caveats, in a spatially
explicit model with local mating and diffusive dispersal in both sexes.Comment: final version, reflecting changes in response to referees' comment
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