11,029 research outputs found
Evolutionary and Ecological Trees and Networks
Evolutionary relationships between species are usually represented in
phylogenies, i.e. evolutionary trees, which are a type of networks. The
terminal nodes of these trees represent species, which are made of individuals
and populations among which gene flow occurs. This flow can also be represented
as a network. In this paper we briefly show some properties of these complex
networks of evolutionary and ecological relationships. First, we characterize
large scale evolutionary relationships in the Tree of Life by a degree
distribution. Second, we represent genetic relationships between individuals of
a Mediterranean marine plant, Posidonia oceanica, in terms of a Minimum
Spanning Tree. Finally, relationships among plant shoots inside populations are
represented as networks of genetic similarity.Comment: 6 pages, 5 figures. To appear in Proceedings of the Medyfinol06
Conferenc
Macro-evolutionary models and coalescent point processes: The shape and probability of reconstructed phylogenies
Forward-time models of diversification (i.e., speciation and extinction)
produce phylogenetic trees that grow "vertically" as time goes by. Pruning the
extinct lineages out of such trees leads to natural models for reconstructed
trees (i.e., phylogenies of extant species). Alternatively, reconstructed trees
can be modelled by coalescent point processes (CPP), where trees grow
"horizontally" by the sequential addition of vertical edges. Each new edge
starts at some random speciation time and ends at the present time; speciation
times are drawn from the same distribution independently. CPP lead to extremely
fast computation of tree likelihoods and simulation of reconstructed trees.
Their topology always follows the uniform distribution on ranked tree shapes
(URT). We characterize which forward-time models lead to URT reconstructed
trees and among these, which lead to CPP reconstructed trees. We show that for
any "asymmetric" diversification model in which speciation rates only depend on
time and extinction rates only depend on time and on a non-heritable trait
(e.g., age), the reconstructed tree is CPP, even if extant species are
incompletely sampled. If rates additionally depend on the number of species,
the reconstructed tree is (only) URT (but not CPP). We characterize the common
distribution of speciation times in the CPP description, and discuss incomplete
species sampling as well as three special model cases in detail: 1) extinction
rate does not depend on a trait; 2) rates do not depend on time; 3) mass
extinctions may happen additionally at certain points in the past
Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics
The reconstruction of phylogenetic trees based on viral genetic sequence data
sequentially sampled from an epidemic provides estimates of the past
transmission dynamics, by fitting epidemiological models to these trees. To our
knowledge, none of the epidemiological models currently used in phylogenetics
can account for recovery rates and sampling rates dependent on the time elapsed
since transmission.
Here we introduce an epidemiological model where infectives leave the
epidemic, either by recovery or sampling, after some random time which may
follow an arbitrary distribution.
We derive an expression for the likelihood of the phylogenetic tree of
sampled infectives under our general epidemiological model. The analytic
concept developed in this paper will facilitate inference of past
epidemiological dynamics and provide an analytical framework for performing
very efficient simulations of phylogenetic trees under our model. The main idea
of our analytic study is that the non-Markovian epidemiological model giving
rise to phylogenetic trees growing vertically as time goes by, can be
represented by a Markovian "coalescent point process" growing horizontally by
the sequential addition of pairs of coalescence and sampling times.
As examples, we discuss two special cases of our general model, namely an
application to influenza and an application to HIV. Though phrased in
epidemiological terms, our framework can also be used for instance to fit
macroevolutionary models to phylogenies of extant and extinct species,
accounting for general species lifetime distributions.Comment: 30 pages, 2 figure
Time reversal dualities for some random forests
We consider a random forest , defined as a sequence of i.i.d.
birth-death (BD) trees, each started at time 0 from a single ancestor, stopped
at the first tree having survived up to a fixed time . We denote by
the population size process associated
to this forest, and we prove that if the BD trees are supercritical, then the
time-reversed process , has the same
distribution as , the
corresponding population size process of an equally defined forest
, but where the underlying BD trees are subcritical,
obtained by swapping birth and death rates or equivalently, conditioning on
ultimate extinction.
We generalize this result to splitting trees (i.e. life durations of
individuals are not necessarily exponential), provided that the i.i.d.
lifetimes of the ancestors have a specific explicit distribution, different
from that of their descendants. The results are based on an identity between
the contour of these random forests truncated up to and the duality
property of L\'evy processes. This identity allows us to also derive other
useful properties such as the distribution of the population size process
conditional on the reconstructed tree of individuals alive at , which has
potential applications in epidemiology.Comment: 28 pages, 3 figure
Phase transitions in contagion processes mediated by recurrent mobility patterns
Human mobility and activity patterns mediate contagion on many levels,
including the spatial spread of infectious diseases, diffusion of rumors, and
emergence of consensus. These patterns however are often dominated by specific
locations and recurrent flows and poorly modeled by the random diffusive
dynamics generally used to study them. Here we develop a theoretical framework
to analyze contagion within a network of locations where individuals recall
their geographic origins. We find a phase transition between a regime in which
the contagion affects a large fraction of the system and one in which only a
small fraction is affected. This transition cannot be uncovered by continuous
deterministic models due to the stochastic features of the contagion process
and defines an invasion threshold that depends on mobility parameters,
providing guidance for controlling contagion spread by constraining mobility
processes. We recover the threshold behavior by analyzing diffusion processes
mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary
Information; Nature Physics (2011
Radioactive Decays in Geant4
The simulation of radioactive decays is a common task in Monte-Carlo systems
such as Geant4. Usually, a system either uses an approach focusing on the
simulations of every individual decay or an approach which simulates a large
number of decays with a focus on correct overall statistics. The radioactive
decay package presented in this work permits, for the first time, the use of
both methods within the same simulation framework - Geant4. The accuracy of the
statistical approach in our new package, RDM-extended, and that of the existing
Geant4 per-decay implementation (original RDM), which has also been refactored,
are verified against the ENSDF database. The new verified package is beneficial
for a wide range of experimental scenarios, as it enables researchers to choose
the most appropriate approach for their Geant4-based application
Endogenous Versus Exogenous Shocks in Complex Networks: an Empirical Test Using Book Sale Ranking
Are large biological extinctions such as the Cretaceous/Tertiary KT boundary
due to a meteorite, extreme volcanic activity or self-organized critical
extinction cascades? Are commercial successes due to a progressive reputation
cascade or the result of a well orchestrated advertisement? Determining the
chain of causality for extreme events in complex systems requires disentangling
interwoven exogenous and endogenous contributions with either no clear or too
many signatures. Here, we study the precursory and recovery signatures
accompanying shocks, that we test on a unique database of the Amazon sales
ranking of books. We find clear distinguishing signatures classifying two types
of sales peaks. Exogenous peaks occur abruptly and are followed by a power law
relaxation, while endogenous sale peaks occur after a progressively
accelerating power law growth followed by an approximately symmetrical power
law relaxation which is slower than for exogenous peaks. These results are
rationalized quantitatively by a simple model of epidemic propagation of
interactions with long memory within a network of acquaintances. The slow
relaxation of sales implies that the sales dynamics is dominated by cascades
rather than by the direct effects of news or advertisements, indicating that
the social network is close to critical.Comment: 5 pages including 3 figures final version published in Physical
Review Letter
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