3,115 research outputs found
Phase Diagrams of Quasispecies Theory with Recombination and Horizontal Gene Transfer
We consider how transfer of genetic information between individuals
influences the phase diagram and mean fitness of both the Eigen and the
parallel, or Crow-Kimura, models of evolution. In the absence of genetic
transfer, these physical models of evolution consider the replication and point
mutation of the genomes of independent individuals in a large population. A
phase transition occurs, such that below a critical mutation rate an
identifiable quasispecies forms. We generalize these models of quasispecies
evolution to include horizontal gene transfer. We show how transfer of genetic
information changes the phase diagram and mean fitness and introduces
metastability in quasispecies theory, via an analytic field theoretic mapping.Comment: 5 pages, 1 figure, to appear in Physics Review Letter
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
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
Voter Model with Time dependent Flip-rates
We introduce time variation in the flip-rates of the Voter Model. This type
of generalisation is relevant to models of ageing in language change, allowing
the representation of changes in speakers' learning rates over their lifetime
and may be applied to any other similar model in which interaction rates at the
microscopic level change with time. The mean time taken to reach consensus
varies in a nontrivial way with the rate of change of the flip-rates, varying
between bounds given by the mean consensus times for static homogeneous (the
original Voter Model) and static heterogeneous flip-rates. By considering the
mean time between interactions for each agent, we derive excellent estimates of
the mean consensus times and exit probabilities for any time scale of flip-rate
variation. The scaling of consensus times with population size on complex
networks is correctly predicted, and is as would be expected for the ordinary
voter model. Heterogeneity in the initial distribution of opinions has a strong
effect, considerably reducing the mean time to consensus, while increasing the
probability of survival of the opinion which initially occupies the most slowly
changing agents. The mean times to reach consensus for different states are
very different. An opinion originally held by the fastest changing agents has a
smaller chance to succeed, and takes much longer to do so than an evenly
distributed opinion.Comment: 16 pages, 6 figure
Stochasticity and evolutionary stability
In stochastic dynamical systems, different concepts of stability can be
obtained in different limits. A particularly interesting example is
evolutionary game theory, which is traditionally based on infinite populations,
where strict Nash equilibria correspond to stable fixed points that are always
evolutionarily stable. However, in finite populations stochastic effects can
drive the system away from strict Nash equilibria, which gives rise to a new
concept for evolutionary stability. The conventional and the new stability
concepts may apparently contradict each other leading to conflicting
predictions in large yet finite populations. We show that the two concepts can
be derived from the frequency dependent Moran process in different limits. Our
results help to determine the appropriate stability concept in large finite
populations. The general validity of our findings is demonstrated showing that
the same results are valid employing vastly different co-evolutionary
processes
Fixation and consensus times on a network: a unified approach
We investigate a set of stochastic models of biodiversity, population
genetics, language evolution and opinion dynamics on a network within a common
framework. Each node has a state, 0 < x_i < 1, with interactions specified by
strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for
the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a
case relevant to language change this time is independent of the network
structure.Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted
by Phys. Rev. Let
Reduction of a metapopulation genetic model to an effective one island model
We explore a model of metapopulation genetics which is based on a more
ecologically motivated approach than is frequently used in population genetics.
The size of the population is regulated by competition between individuals,
rather than by artificially imposing a fixed population size. The increased
complexity of the model is managed by employing techniques often used in the
physical sciences, namely exploiting time-scale separation to eliminate fast
variables and then constructing an effective model from the slow modes.
Remarkably, an initial model with 2 variables, where
is the number of islands in the metapopulation, can be reduced to a model with
a single variable. We analyze this effective model and show that the
predictions for the probability of fixation of the alleles and the mean time to
fixation agree well with those found from numerical simulations of the original
model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure
Evaluation and Application of Remotely Sensed Soil Moisture Products
Whereas in-situ measurements of soil moisture are very accurate, achieving accurate regional soil moisture estimates derived solely from point measurements is difficult because of the dependence upon the density of the gauge network and the proper upkeep of these instruments, which can be costly. Microwave remote sensing is the only technology capable of providing timely direct measurements of regional soil moisture in areas that are lacking in-situ networks. Soil moisture remote sensing technology is well established has been successfully applied in many fashions to Earth Science applications. Since the microwave emission from the soil surface has such a high dependency upon the moisture content within the soil, we can take advantage of this relationship and combined with physically-based models of the land surface, derive accurate regional estimates of the soil column water content from the microwave brightness temperature observed from satellite-based remote sensing instruments. However, there still remain many questions regarding the most efficient methodology for evaluating and applying satellite-based soil moisture estimates. As discussed below, we to use satellite-based estimates of soil moisture dynamics to improve the predictive capability of an optimized hydrologic model giving more accurate root-zone soil moisture estimates
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