761 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
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
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 functional significance of dental and mandibular reduction in Homo: A catarrhine perspective.
The reduction in dental size and mandibular robusticity is regarded as a major trend in human evolution, traditionally considered the result of the peculiar extra-oral food processing skills of Homo. The use of stone tools and fire would have allowed our ancestors to chew softer food in smaller bite size, thus relaxing the selective pressures to keep a large dentition and a robust lower jaw. This perspective assumes that differences in dental size and mandibular robusticity in hominins represent functional dissimilarities. This study uses a catarrhine comparative approach to test this fundamental assumption of the hypotheses on dental and mandibular reduction in Homo. A sample of extant catarrhines and fossil hominins was used to test for correlations between dental size, mandibular robusticity, and dietary proxies, the latter include diet quality, diet heterogeneity, feeding time, and microwear variables. The effects of phylogeny and body size were considered. Findings support the association between technological developments in Homo and reduction in incisor size and mandibular corpus robusticity, though not for premolar, molar size, and symphyseal robusticity. These results challenge the functional interpretation of postcanine reduction and symphyseal changes in the genus Homo
Incorporating fine-scale environmental heterogeneity into broad-extent models
A key aim of ecology is to understand the drivers of ecological patterns, so that we can accurately predict the effects of global environmental change. However, in many cases, predictors are measured at a finer resolution than the ecological response. We therefore require data aggregation methods that avoid loss of information on fine-grain heterogeneity. We present a data aggregation method that, unlike current approaches, reduces the loss of information on fine-grain spatial structure in environmental heterogeneity for use with coarse-grain ecological datasets. Our method contains three steps: (a) define analysis scales (predictor grain, response grain, scale-of-effect); (b) use a moving window to calculate a measure of variability in environment (predictor grain) at the process-relevant scale (scale-of-effect); and (c) aggregate the moving window calculations to the coarsest resolution (response grain). We show the theoretical basis for our method using simulated landscapes and the practical utility with a case study. Our method is available as the grainchanger r package. The simulations show that information about spatial structure is captured that would have been lost using a direct aggregation approach, and that our method is particularly useful in landscapes with spatial autocorrelation in the environmental predictor variable (e.g. fragmented landscapes) and when the scale-of-effect is small relative to the response grain. We use our data aggregation method to find the appropriate scale-of-effect of land cover diversity on Eurasian jay Garrulus glandarius abundance in the UK. We then model the interactive effect of land cover heterogeneity and temperature on G. glandarius abundance. Our method enables us quantify this interaction despite the different scales at which these factors influence G. glandarius abundance. Our data aggregation method allows us to integrate variables that act at varying scales into one model with limited loss of information, which has wide applicability for spatial analyses beyond the specific ecological context considered here. Key ecological applications include being able to estimate the interactive effect of drivers that vary at different scales (such as climate and land cover), and to systematically examine the scale dependence of the effects of environmental heterogeneity in combination with the effects of climate change on biodiversity
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