536 research outputs found
Metastability and anomalous fixation in evolutionary games on scale-free networks
We study the influence of complex graphs on the metastability and fixation
properties of a set of evolutionary processes. In the framework of evolutionary
game theory, where the fitness and selection are frequency-dependent and vary
with the population composition, we analyze the dynamics of snowdrift games
(characterized by a metastable coexistence state) on scale-free networks. Using
an effective diffusion theory in the weak selection limit, we demonstrate how
the scale-free structure affects the system's metastable state and leads to
anomalous fixation. In particular, we analytically and numerically show that
the probability and mean time of fixation are characterized by stretched
exponential behaviors with exponents depending on the network's degree
distribution.Comment: 5 pages, 4 figures, to appear in Physical Review Letter
Phosphorylation of pRb: mechanism for RB pathway inactivation in MYCN-amplified retinoblastoma.
A small, but unique subgroup of retinoblastoma has been identified with no detectable mutation in the retinoblastoma gene (RB1) and with high levels of MYCN gene amplification. This manuscript investigated alternate pathways of inactivating pRb, the encoded protein in these tumors. We analyzed the mutation status of the RB1 gene and MYCN copy number in a series of 245 unilateral retinoblastomas, and the phosphorylation status of pRb in a subset of five tumors using immunohistochemistry. There were 203 tumors with two mutations in RB1 (RB1(-/-) , 83%), 29 with one (RB1(+/-) , 12%) and 13 with no detectable mutations (RB1(+/+) , 5%). Eighteen tumors carried MYCN amplification between 29 and 110 copies: 12 had two (RB1(-/-) ) or one RB1 (RB1(+/-) ) mutations, while six had no mutations (RB1(+/+) ). Immunohistochemical staining of tumor sections with antibodies against pRb and phosphorylated Rb (ppRb) displayed high levels of pRb and ppRb in both RB1(+/+) and RB1(+/-) tumors with MYCN amplification compared to no expression of these proteins in a classic RB1(-/-) , MYCN-low tumor. These results establish that high MYCN amplification can be present in retinoblastoma with or without coding sequence mutations in the RB1 gene. The functional state of pRb is inferred to be inactive due to phosphorylation of pRb in the MYCN-amplified retinoblastoma without coding sequence mutations. This makes inactivation of RB1 by gene mutation or its protein product, pRb, by protein phosphorylation, a necessary condition for initiating retinoblastoma tumorigenesis, independent of MYCN amplification
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
We present a general framework to describe the evolutionary dynamics of an
arbitrary number of types in finite populations based on stochastic
differential equations (SDE). For large, but finite populations this allows to
include demographic noise without requiring explicit simulations. Instead, the
population size only rescales the amplitude of the noise. Moreover, this
framework admits the inclusion of mutations between different types, provided
that mutation rates, , are not too small compared to the inverse
population size 1/N. This ensures that all types are almost always represented
in the population and that the occasional extinction of one type does not
result in an extended absence of that type. For this limits the use
of SDE's, but in this case there are well established alternative
approximations based on time scale separation. We illustrate our approach by a
Rock-Scissors-Paper game with mutations, where we demonstrate excellent
agreement with simulation based results for sufficiently large populations. In
the absence of mutations the excellent agreement extends to small population
sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review
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
Evolutionary dynamics on degree-heterogeneous graphs
The evolution of two species with different fitness is investigated on
degree-heterogeneous graphs. The population evolves either by one individual
dying and being replaced by the offspring of a random neighbor (voter model
(VM) dynamics) or by an individual giving birth to an offspring that takes over
a random neighbor node (invasion process (IP) dynamics). The fixation
probability for one species to take over a population of N individuals depends
crucially on the dynamics and on the local environment. Starting with a single
fitter mutant at a node of degree k, the fixation probability is proportional
to k for VM dynamics and to 1/k for IP dynamics.Comment: 4 pages, 4 figures, 2 column revtex4 format. Revisions in response to
referee comments for publication in PRL. The version on arxiv.org has one
more figure than the published PR
Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion
We study the voter model and related random-copying processes on arbitrarily
complex network structures. Through a representation of the dynamics as a
particle reaction process, we show that a quantity measuring the degree of
order in a finite system is, under certain conditions, exactly governed by a
universal diffusion equation. Whenever this reduction occurs, the details of
the network structure and random-copying process affect only a single parameter
in the diffusion equation. The validity of the reduction can be established
with considerably less information than one might expect: it suffices to know
just two characteristic timescales within the dynamics of a single pair of
reacting particles. We develop methods to identify these timescales, and apply
them to deterministic and random network structures. We focus in particular on
how the ordering time is affected by degree correlations, since such effects
are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and
simulation results to appear in J Phys
Pupil mobility, attainment and progress in secondary school
This paper is the second of two articles arising from a study of the association between pupil mobility and attainment in national tests and examinations in an inner London borough. The first article (Strand & Demie, 2006) examined the association of pupil mobility with attainment and progress during primary school. It concluded that pupil mobility had little impact on performance in national tests at age 11, once pupils’ prior attainment at age 7 and other pupil background factors such as age, sex, special educational needs, stage of fluency in English and socio-economic disadvantage were taken into account. The present article reports the results for secondary schools (age 11-16). The results indicate that pupil mobility continues to have a significant negative association with performance in public examinations at age 16, even after including statistical controls for prior attainment at age 11 and other pupil background factors. Possible reasons for the contrasting results across school phases are explored. The implications for policy and further research are discussed
Stochastic slowdown in evolutionary processes
We examine birth--death processes with state dependent transition
probabilities and at least one absorbing boundary. In evolution, this describes
selection acting on two different types in a finite population where
reproductive events occur successively. If the two types have equal fitness the
system performs a random walk. If one type has a fitness advantage it is
favored by selection, which introduces a bias (asymmetry) in the transition
probabilities. How long does it take until advantageous mutants have invaded
and taken over? Surprisingly, we find that the average time of such a process
can increase, even if the mutant type always has a fitness advantage. We
discuss this finding for the Moran process and develop a simplified model which
allows a more intuitive understanding. We show that this effect can occur for
weak but non--vanishing bias (selection) in the state dependent transition
rates and infer the scaling with system size. We also address the Wright-Fisher
model commonly used in population genetics, which shows that this stochastic
slowdown is not restricted to birth-death processes.Comment: 8 pages, 3 figures, accepted for publicatio
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
Adaptive walks on time-dependent fitness landscapes
The idea of adaptive walks on fitness landscapes as a means of studying
evolutionary processes on large time scales is extended to fitness landscapes
that are slowly changing over time. The influence of ruggedness and of the
amount of static fitness contributions are investigated for model landscapes
derived from Kauffman's landscapes. Depending on the amount of static
fitness contributions in the landscape, the evolutionary dynamics can be
divided into a percolating and a non-percolating phase. In the percolating
phase, the walker performs a random walk over the regions of the landscape with
high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.
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