723 research outputs found
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
The Clumping Transition in Niche Competition: a Robust Critical Phenomenon
We show analytically and numerically that the appearance of lumps and gaps in
the distribution of n competing species along a niche axis is a robust
phenomenon whenever the finiteness of the niche space is taken into account. In
this case depending if the niche width of the species is above or
below a threshold , which for large n coincides with 2/n, there are
two different regimes. For the lumpy pattern emerges
directly from the dominant eigenvector of the competition matrix because its
corresponding eigenvalue becomes negative. For the lumpy
pattern disappears. Furthermore, this clumping transition exhibits critical
slowing down as is approached from above. We also find that the number
of lumps of species vs. displays a stair-step structure. The positions
of these steps are distributed according to a power-law. It is thus
straightforward to predict the number of groups that can be packed along a
niche axis and it coincides with field measurements for a wide range of the
model parameters.Comment: 16 pages, 7 figures;
http://iopscience.iop.org/1742-5468/2010/05/P0500
Number of Common Sites Visited by N Random Walkers
We compute analytically the mean number of common sites, W_N(t), visited by N
independent random walkers each of length t and all starting at the origin at
t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct
regimes for the asymptotic large t growth of W_N(t). These three regimes are
separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane.
For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the
prefactor). For 2<d<d_c(N), W_N(t)\sim t^{\nu} where the exponent \nu=
N-d(N-1)/2 varies with N and d. For d>d_c(N), W_N(t) approaches a constant as
t\to \infty. Exactly at the critical dimensions there are logaritmic
corrections: for d=2, we get W_N(t)\sim t/[\ln t]^N, while for d=d_c(N),
W_N(t)\sim \ln t for large t. Our analytical predictions are verified in
numerical simulations.Comment: 5 pages, 3 .eps figures include
Stochastic models in population biology and their deterministic analogs
In this paper we introduce a class of stochastic population models based on
"patch dynamics". The size of the patch may be varied, and this allows one to
quantify the departures of these stochastic models from various mean field
theories, which are generally valid as the patch size becomes very large. These
models may be used to formulate a broad range of biological processes in both
spatial and non-spatial contexts. Here, we concentrate on two-species
competition. We present both a mathematical analysis of the patch model, in
which we derive the precise form of the competition mean field equations (and
their first order corrections in the non-spatial case), and simulation results.
These mean field equations differ, in some important ways, from those which are
normally written down on phenomenological grounds. Our general conclusion is
that mean field theory is more robust for spatial models than for a single
isolated patch. This is due to the dilution of stochastic effects in a spatial
setting resulting from repeated rescue events mediated by inter-patch
diffusion. However, discrete effects due to modest patch sizes lead to striking
deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure
The shape of ecological networks
We study the statistics of ecosystems with a variable number of co-evolving
species. The species interact in two ways: by prey-predator relationships and
by direct competition with similar kinds. The interaction coefficients change
slowly through successful adaptations and speciations. We treat them as
quenched random variables. These interactions determine long-term topological
features of the species network, which are found to agree with those of
biological systems.Comment: 4 pages, 2 figure
Unstable decay and state selection II
The decay of unstable states when several metastable states are available for
occupation is investigated using path-integral techniques. Specifically, a
method is described which allows the probabilities with which the metastable
states are occupied to be calculated by finding optimal paths, and fluctuations
about them, in the weak noise limit. The method is illustrated on a system
described by two coupled Langevin equations, which are found in the study of
instabilities in fluid dynamics and superconductivity. The problem involves a
subtle interplay between non-linearities and noise, and a naive approximation
scheme which does not take this into account is shown to be unsatisfactory. The
use of optimal paths is briefly reviewed and then applied to finding the
conditional probability of ending up in one of the metastable states, having
begun in the unstable state. There are several aspects of the calculation which
distinguish it from most others involving optimal paths: (i) the paths do not
begin and end on an attractor, and moreover, the final point is to a large
extent arbitrary, (ii) the interplay between the fluctuations and the leading
order contribution are at the heart of the method, and (iii) the final result
involves quantities which are not exponentially small in the noise strength.
This final result, which gives the probability of a particular state being
selected in terms of the parameters of the dynamics, is remarkably simple and
agrees well with the results of numerical simulations. The method should be
applicable to similar problems in a number of other areas such as state
selection in lasers, activationless chemical reactions and population dynamics
in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.
The species diversity × fire severity relationship is hump-shaped in semiarid yellow pine and mixed conifer forests
The combination of direct human influences and the effects of climate change are resulting in altered ecological disturbance regimes, and this is especially the case for wildfires. Many regions that historically experienced low–moderate severity fire regimes are seeing increased area burned at high severity as a result of interactions between high fuel loads and climate warming with a number of negative ecological effects. While ecosystem impacts of altered fire regimes have been examined in the literature, little is known of the effects of changing fire regimes on forest understory plant diversity even though understory taxa comprise the vast majority of forest plant species and play vital roles in overall ecosystem function. We examined understory plant diversity across gradients of wildfire severity in eight large wildfires in yellow pine and mixed conifer temperate forests of the Sierra Nevada, California, USA. We found a generally unimodal hump-shaped relationship between local (alpha) plant diversity and fire severity. High-severity burning resulted in lower local diversity as well as some homogenization of the flora at the regional scale. Fire severity class, post-fire litter cover, and annual precipitation were the best predictors of understory species diversity. Our research suggests that increases in fire severity in systems historically characterized by low and moderate severity fire may lead to plant diversity losses. These findings indicate that global patterns of increasing fire size and severity may have important implications for biodiversity
Evaluating the discriminatory power of EQ-5D, HUI2 and HUI3 in a US general population survey using Shannon’s indices
OBJECTIVES: To compare quantitatively the discriminatory power of the EQ-5D, HUI2 and HUI3 in terms of absolute and relative informativity, using Shannon's indices. METHODS: EQ-5D and HUI2/3 data completed by a sample of the general adult US population (N = 3,691) were used. Five dimensions allowed head-to-head comparison of informativity: Mobility/Ambulation; Anxiety/Depression/Emotion; Pain/Discomfort (EQ-5D; HUI2; HUI3); Self-Care (EQ-5D; HUI2); and Cognition (HUI2; HUI3). Shannon's index and Shannon's Evenness index were used to assess absolute and relative informativity, both by dimension and by instrument as a whole. RESULTS: Absolute informativity was highest for HUI3, with the largest differences in Pain/Discomfort and Cognition. Relative informativity was highest for EQ-5D, with the largest differences in Mobility/Ambulation and Anxiety/Depression/Emotion. Absolute informativity by instrument was consistently highest for HUI3 and lowest for EQ-5D, and relative informativity was highest for EQ-5D and lowest for HUI3. DISCUSSION: Performance in terms of absolute and relative informativity of the common dimensions of the three instruments varies over dimensions. Several dimensions are suboptimal: Pain/Discomfort (EQ-5D) seems too crude with only 3 levels, and the level descriptions of Ambulation (HUI3) and Self-Care (HUI2) could be improved. In absence of a formal measure, Shannon's indices provide useful measures for assessing discriminatory power of utility instrument
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