615 research outputs found
Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?
Motivated by the results of recent laboratory experiments (Yoshida et al.
Nature, 424, 303-306 (2003)) as well as many earlier field observations that
evolutionary changes can take place in ecosystems over relatively short
ecological time scales, several ``unified'' mathematical models of evolutionary
ecology have been developed over the last few years with the aim of describing
the statistical properties of data related to the evolution of ecosystems.
Moreover, because of the availability of sufficiently fast computers, it has
become possible to carry out detailed computer simulations of these models. For
the sake of completeness and to put these recent developments in the proper
perspective, we begin with a brief summary of some older models of ecological
phenomena and evolutionary processes. However, the main aim of this article is
to review critically these ``unified'' models, particularly those published in
the physics literature, in simple language that makes the new theories
accessible to wider audience.Comment: 28 pages, LATEX, 4 eps figure
Modelling Food Webs
We review theoretical approaches to the understanding of food webs. After an
overview of the available food web data, we discuss three different classes of
models. The first class comprise static models, which assign links between
species according to some simple rule. The second class are dynamical models,
which include the population dynamics of several interacting species. We focus
on the question of the stability of such webs. The third class are species
assembly models and evolutionary models, which build webs starting from a few
species by adding new species through a process of "invasion" (assembly models)
or "speciation" (evolutionary models). Evolutionary models are found to be
capable of building large stable webs.Comment: 34 pages, 2 figures. To be published in "Handbook of graphs and
networks" S. Bornholdt and H. G. Schuster (eds) (Wiley-VCH, Berlin
Generalized Lotka-Volterra Systems with Time Correlated Stochastic Interactions
The dynamics of species communities are typically modelled considering fixed
parameters for species interactions. The problem of over-parameterization that
ensues when considering large communities has been overcome by sampling species
interactions from a probability distribution. However, species interactions are
not fixed in time, but they can change on a time scale comparable to population
dynamics. Here we investigate the impact of time-dependent species interactions
using the generalized Lotka-Volterra model, which serves as a paradigmatic
theoretical framework in several scientific fields. In this work we model
species interactions as stochastic colored noise. Assuming a large number of
species and a steady state, we obtain analytical predictions for the species
abundance distribution, which matches well empirical observations. In
particular, our results suggest the absence of extinctions, unlike scenarios
with fixed species interactions.Comment: 4 Figure
Evolutionary ecology in-silico:evolving foodwebs, migrating population and speciation
We have generalized our ``unified'' model of evolutionary ecology by taking
into account the possible movements of the organisms from one ``patch'' to
another within the same eco-system. We model the spatial extension of the
eco-system (i.e., the geography) by a square lattice where each site
corresponds to a distinct ``patch''. A self-organizing hierarchical food web
describes the prey-predator relations in the eco-system. The same species at
different patches have identical food habits but differ from each other in
their reproductive characteristic features. By carrying out computer
simulations up to time steps, we found that, depending on the values of
the set of parameters, the distribution of the lifetimes of the species can be
either exponential or a combination of power laws. Some of the other features
of our ``unified'' model turn out to be robust against migration of the
organisms.Comment: 12 pages of PS file, including LATEX text and 9 EPS figure
Spectral dimension reduction of complex dynamical networks
Dynamical networks are powerful tools for modeling a broad range of complex
systems, including financial markets, brains, and ecosystems. They encode how
the basic elements (nodes) of these systems interact altogether (via links) and
evolve (nodes' dynamics). Despite substantial progress, little is known about
why some subtle changes in the network structure, at the so-called critical
points, can provoke drastic shifts in its dynamics. We tackle this challenging
problem by introducing a method that reduces any network to a simplified
low-dimensional version. It can then be used to describe the collective
dynamics of the original system. This dimension reduction method relies on
spectral graph theory and, more specifically, on the dominant eigenvalues and
eigenvectors of the network adjacency matrix. Contrary to previous approaches,
our method is able to predict the multiple activation of modular networks as
well as the critical points of random networks with arbitrary degree
distributions. Our results are of both fundamental and practical interest, as
they offer a novel framework to relate the structure of networks to their
dynamics and to study the resilience of complex systems.Comment: 16 pages, 8 figure
Reconciling cooperation, biodiversity and stability in complex ecological communities
Empirical observations show that ecological communities can have a huge
number of coexisting species, also with few or limited number of resources.
These ecosystems are characterized by multiple type of interactions, in
particular displaying cooperative behaviors. However, standard modeling of
population dynamics based on Lotka-Volterra type of equations predicts that
ecosystem stability should decrease as the number of species in the community
increases and that cooperative systems are less stable than communities with
only competitive and/or exploitative interactions. Here we propose a stochastic
model of population dynamics, which includes exploitative interactions as well
as cooperative interactions induced by cross-feeding. The model is exactly
solved and we obtain results for relevant macro-ecological patterns, such as
species abundance distributions and correlation functions. In the large system
size limit, any number of species can coexist for a very general class of
interaction networks and stability increases as the number of species grows.
For pure mutualistic/commensalistic interactions we determine the topological
properties of the network that guarantee species coexistence. We also show that
the stationary state is globally stable and that inferring species interactions
through species abundance correlation analysis may be misleading. Our
theoretical approach thus show that appropriate models of cooperation naturally
leads to a solution of the long-standing question about complexity-stability
paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure
AI-Assisted Discovery of Quantitative and Formal Models in Social Science
In social science, formal and quantitative models, such as ones describing
economic growth and collective action, are used to formulate mechanistic
explanations, provide predictions, and uncover questions about observed
phenomena. Here, we demonstrate the use of a machine learning system to aid the
discovery of symbolic models that capture nonlinear and dynamical relationships
in social science datasets. By extending neuro-symbolic methods to find compact
functions and differential equations in noisy and longitudinal data, we show
that our system can be used to discover interpretable models from real-world
data in economics and sociology. Augmenting existing workflows with symbolic
regression can help uncover novel relationships and explore counterfactual
models during the scientific process. We propose that this AI-assisted
framework can bridge parametric and non-parametric models commonly employed in
social science research by systematically exploring the space of nonlinear
models and enabling fine-grained control over expressivity and
interpretability.Comment: 19 pages, 4 figure
Gang Confrontation: The case of Medellin (Colombia)
Protracted conflict is one of the largest human challenges that have
persistently undermined economic and social progress. In recent years, there
has been increased emphasis on using statistical and physical science models to
better understand both the universal patterns and the underlying mechanics of
conflict. Whilst macroscopic power-law fractal patterns have been shown for
death-toll in wars and self-excitation models have been shown for roadside
ambush attacks, very few works deal with the challenge of complex dynamics
between gangs at the intra-city scale. Here, based on contributions to the
historical memory of the conflict in Colombia, Medellin's
gang-confrontation-network is presented. It is shown that socio-economic and
violence indexes are moderate to highly correlated to the structure of the
network. Specifically, the death-toll of conflict is strongly influenced by the
leading eigenvalues of the gangs' conflict adjacency matrix, which serves a
proxy for unstable self-excitation from revenge attacks. The distribution of
links based on the geographic distance between gangs in confrontation leads to
the confirmation that territorial control is a main catalyst of violence and
retaliation among gangs. Additionally, the Boltzmann-Lotka-Volterra (BLV)
dynamic interaction network analysis is applied to quantify the spatial
embeddedness of the dynamic relationship between conflicting gangs in Medellin,
results suggest that more involved and comprehensive models are needed to
described the dynamics of Medellin's armed conflict.Comment: 18 pages, 9 figures. Statistical analysis was largely improved. arXiv
admin note: text overlap with arXiv:1107.0539 by other author
Evolutionary games on graphs
Game theory is one of the key paradigms behind many scientific disciplines
from biology to behavioral sciences to economics. In its evolutionary form and
especially when the interacting agents are linked in a specific social network
the underlying solution concepts and methods are very similar to those applied
in non-equilibrium statistical physics. This review gives a tutorial-type
overview of the field for physicists. The first three sections introduce the
necessary background in classical and evolutionary game theory from the basic
definitions to the most important results. The fourth section surveys the
topological complications implied by non-mean-field-type social network
structures in general. The last three sections discuss in detail the dynamic
behavior of three prominent classes of models: the Prisoner's Dilemma, the
Rock-Scissors-Paper game, and Competing Associations. The major theme of the
review is in what sense and how the graph structure of interactions can modify
and enrich the picture of long term behavioral patterns emerging in
evolutionary games.Comment: Review, final version, 133 pages, 65 figure
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