2,970 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
Random copying in space
Random copying is a simple model for population dynamics in the absence of
selection, and has been applied to both biological and cultural evolution. In
this work, we investigate the effect that spatial structure has on the
dynamics. We focus in particular on how a measure of the diversity in the
population changes over time. We show that even when the vast majority of a
population's history may be well-described by a spatially-unstructured model,
spatial structure may nevertheless affect the expected level of diversity seen
at a local scale. We demonstrate this phenomenon explicitly by examining the
random copying process on small-world networks, and use our results to comment
on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference
on "Cultural Evolution in Spatially Structured Populations" at UCL, September
2010. To appear in ACS - Advances in Complex System
L-band Microwave Remote Sensing and Land Data Assimilation Improve the Representation of Prestorm Soil Moisture Conditions for Hydrologic Forecasting
Recent advances in remote sensing and land data assimilation purport to improve the quality of antecedent soil moisture information available for operational hydrologic forecasting. We objectively validate this claim by calculating the strength of the relationship between storm-scale runoff ratio (i.e., total stream flow divided by total rainfall accumulation in depth units) and pre-storm surface soil moisture estimates from a range of surface soil moisture data products. Results demonstrate that both satellite-based, L-band microwave radiometry and the application of land data assimilation techniques have significantly improved the utility of surface soil moisture data sets for forecasting stream flow response to future rainfall events
Exact Solution for the Time Evolution of Network Rewiring Models
We consider the rewiring of a bipartite graph using a mixture of random and
preferential attachment. The full mean field equations for the degree
distribution and its generating function are given. The exact solution of these
equations for all finite parameter values at any time is found in terms of
standard functions. It is demonstrated that these solutions are an excellent
fit to numerical simulations of the model. We discuss the relationship between
our model and several others in the literature including examples of Urn,
Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem
and some models of zero range processes. Our model is also equivalent to those
used in various applications including cultural transmission, family name and
gene frequencies, glasses, and wealth distributions. Finally some Voter models
and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E
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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
Adaptive evolution of molecular phenotypes
Molecular phenotypes link genomic information with organismic functions,
fitness, and evolution. Quantitative traits are complex phenotypes that depend
on multiple genomic loci. In this paper, we study the adaptive evolution of a
quantitative trait under time-dependent selection, which arises from
environmental changes or through fitness interactions with other co-evolving
phenotypes. We analyze a model of trait evolution under mutations and genetic
drift in a single-peak fitness seascape. The fitness peak performs a
constrained random walk in the trait amplitude, which determines the
time-dependent trait optimum in a given population. We derive analytical
expressions for the distribution of the time-dependent trait divergence between
populations and of the trait diversity within populations. Based on this
solution, we develop a method to infer adaptive evolution of quantitative
traits. Specifically, we show that the ratio of the average trait divergence
and the diversity is a universal function of evolutionary time, which predicts
the stabilizing strength and the driving rate of the fitness seascape. From an
information-theoretic point of view, this function measures the
macro-evolutionary entropy in a population ensemble, which determines the
predictability of the evolutionary process. Our solution also quantifies two
key characteristics of adapting populations: the cumulative fitness flux, which
measures the total amount of adaptation, and the adaptive load, which is the
fitness cost due to a population's lag behind the fitness peak.Comment: Figures are not optimally displayed in Firefo
Exploiting Soil Moisture, Precipitation and Streamflow Observations to Evaluate Soil Moisture/Runoff Coupling in Land Surface Models
Accurate partitioning of precipitation into infiltration and runoff is a fundamental objective of land surface models tasked with characterizing the surface water and energy balance. Temporal variability in this partitioning is due, in part, to changes in prestorm soil moisture, which determine soil infiltration capacity and unsaturated storage. Utilizing the National Aeronautics and Space Administration Soil Moisture Active Passive Level4 soil moisture product in combination with streamflow and precipitation observations, we demonstrate that land surface models (LSMs) generally underestimate the strength of the positive rank correlation between prestorm soil moisture and event runoff coefficients (i.e., the fraction of rainfall accumulation volume converted into stormflow runoff during a storm event). Underestimation is largest for LSMs employing an infiltrationexcess approach for stormflow runoff generation. More accurate coupling strength is found in LSMs that explicitly represent subsurface stormflow or saturationexcess runoff generation processes
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