301 research outputs found
Climate Change and World Food Security: A New Assessment
Building on previous work, quantitative estimates of climate change impacts on global food production have been made for the UK Hadley Centre's HadCM2 greenhouse gas only ensemble experiment and the more recent HadCM3 experiment (Hume et al., 1999). The consequences for world food prices and the number of people at risk of hunger as defined by the Food and Agriculture Organization (FAO, 1998) have also been assessed. Climate change is expected to increase yields at high and mid-latitudes, and lead to decreases at lower latitudes. This pattern becomes more pronounced as time progresses. The food system may be expected to accommodate such regional variations at the global level, with production, prices and the risk of hunger being relatively unaffected by the additional stress of climate change. By the 2080s the additional number of people at risk of hunger due to climate change is about 80 million (+/- 10 million depending on which of the four HadCM2 ensemble members are selected). However, some regions (particularly the arid and sub-humid tropics) will be adversely affected. A particular example is Africa, which is expected to experience marked reduction in yield, decreases in production, and increases in the risk of hunger as a result of climate change. The continent can expect to have between 55 and 65 million extra people at risk of hunger by the 2080s under the HadCM2 climate scenario. Under the HadCM3 climate scenario, the effect is even more severe, producing an estimated additional 70+ million people at risk of hunger in Africa
Compact support probability distributions in random matrix theory
We consider a generalization of the fixed and bounded trace ensembles introduced by Bronk and Rosenzweig up to an arbitrary polynomial potential. In the large-N limit we prove that the two are equivalent and that their eigenvalue distribution coincides with that of the "canonical" ensemble with measure exp[-Tr V(M)]. The mapping of the corresponding phase boundaries is illuminated in an explicit example. In the case of a Gaussian potential we are able to derive exact expressions for the one- and two-point correlator for finite , having finite support
Density of states for almost diagonal random matrices
We study the density of states (DOS) for disordered systems whose spectral
statistics can be described by a Gaussian ensemble of almost diagonal Hermitian
random matrices. The matrices have independent random entries with small off-diagonal elements: . Using the recently suggested method of a {\it virial expansion in
the number of interacting energy levels} (Journ.Phys.A {\bf 36}, 8265), we
calculate the leading correction to the Poissonian DOS in the cases of the
Gaussian Orthogonal and Unitary Ensembles. We apply the general formula to the
critical power-law banded random matrices and the unitary
Moshe-Neuberger-Shapiro model and compare DOS of these models.Comment: submitted to Phys. Rev.
Some Universal Properties for Restricted Trace Gaussian Orthogonal, Unitary and Symplectic Ensembles
Consider fixed and bounded trace Gaussian orthogonal, unitary and symplectic
ensembles, closely related to Gaussian ensembles without any constraint. For
three restricted trace Gaussian ensembles, we prove universal limits of
correlation functions at zero and at the edge of the spectrum edge. In
addition, by using the universal result in the bulk for fixed trace Gaussian
unitary ensemble, which has been obtained by Gtze and Gordin, we also
prove universal limits of correlation functions for bounded trace Gaussian
unitary ensemble.Comment: 19pages,bounded trace Gaussian ensembles are adde
Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps
file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised
version, to appear in PRD, minor modifications and corrected typos, Fig.4
revise
Does Conservation Planning Matter in a Dynamic and Uncertain World?
We show that while comprehensive reserve network design is best when the entire network can be implemented immediately, when conservation investments must be staged over years, such solutions actually may be sub-optimal in the context of biodiversity loss and uncertainty
New directions in island biogeography
Aim: Much of our current understanding of ecological and evolutionary processes comes from island research. With the increasing availability of data on distributions and phylogenetic relationships and new analytical approaches to understanding the processes that shape species distributions and interactions, a re-evaluation of this ever-interesting topic is timely.
Location: Islands globally.
Methods: We start by arguing that the reasons why island research has achieved so much in the past also apply to the future. We then critically assess the current state of island biogeography, focusing on recent changes in emphasis, including research featured in this special issue of Global Ecology and Biogeography. Finally, we suggest promising themes for the future. We cover both ecological and evolutionary topics, although the greater emphasis on island ecology reflects our own backgrounds and interests.
Results: Much ecological theory has been directly or indirectly influenced by research on island biotas. Currently, island biogeography is renascent, with research focusing on, among other things, patterns and processes underlying species interaction networks, species coexistence and the assembly of island communities through ecological and evolutionary time. Continuing island research should provide additional insight into biological invasions and other impacts of human activities, functional diversity and ecosystem functioning, extinction and diversification, species pools and more. Deeper understanding of the similarities and differences between island and mainland systems will aid transferability of island theory to continental regions.
Main conclusions: As research in biogeography and related fields expands in new directions, islands continue to provide opportunities for developing insights, both as natural laboratories for ecology and evolution and because of the exceptions islands often present to the usual ârulesâ of ecology. New data collection initiatives are needed on islands world-wide and should be directed towards filling gaps in our knowledge of within-island distributions of species, as well as the functional traits and phylogenetic relationships of island species
Species abundance distributions: moving beyond single prediction theories to integration within an ecological framework
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75247/1/j.1461-0248.2007.01094.x.pd
Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models
Both community ecology and conservation biology seek further understanding of
factors governing the advance of an invasive species. We model biological
invasion as an individual-based, stochastic process on a two-dimensional
landscape. An ecologically superior invader and a resident species compete for
space preemptively. Our general model includes the basic contact process and a
variant of the Eden model as special cases. We employ the concept of a
"roughened" front to quantify effects of discreteness and stochasticity on
invasion; we emphasize the probability distribution of the front-runner's
relative position. That is, we analyze the location of the most advanced
invader as the extreme deviation about the front's mean position. We find that
a class of models with different assumptions about neighborhood interactions
exhibit universal characteristics. That is, key features of the invasion
dynamics span a class of models, independently of locally detailed demographic
rules. Our results integrate theories of invasive spatial growth and generate
novel hypotheses linking habitat or landscape size (length of the invading
front) to invasion velocity, and to the relative position of the most advanced
invader.Comment: The original publication is available at
www.springerlink.com/content/8528v8563r7u2742
Sensitivity analysis of reactive ecological dynamics
Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Bulletin of Mathematical Biology 70 (2008): 1634-1659, doi:10.1007/s11538-008-9312-7.Ecological systems with asymptotically stable equilibria may exhibit significant transient
dynamics following perturbations. In some cases, these transient dynamics include
the possibility of excursions away from the equilibrium before the eventual return; systems
that exhibit such amplification of perturbations are called reactive. Reactivity is
a common property of ecological systems, and the amplification can be large and long-lasting.
The transient response of a reactive ecosystem depends on the parameters of
the underlying model. To investigate this dependence, we develop sensitivity analyses
for indices of transient dynamics (reactivity, the amplification envelope, and the optimal
perturbation) in both continuous- and discrete-time models written in matrix form.
The sensitivity calculations require expressions, some of them new, for the derivatives
of equilibria, eigenvalues, singular values, and singular vectors, obtained using matrix
calculus. Sensitivity analysis provides a quantitative framework for investigating the
mechanisms leading to transient growth. We apply the methodology to a predator-prey
model and a size-structured food web model. The results suggest predator-driven and
prey-driven mechanisms for transient amplification resulting from multispecies interactions.Financial support provided by NSF grant DEB-0343820, NOAA grant NA03-NMF4720491,
the Ocean Life Institute of the Woods Hole Oceanographic Institution, and the Academic
Programs Office of the MIT-WHOI Joint Program in Oceanography
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