294 research outputs found
Deleting species from model food webs
We use food webs generated by a model to investigate the effects of deleting
species on other species in the web and on the web as a whole. The model
incorporates a realistic population dynamics, adaptive foragers and other
features which allow for the construction of model webs which resemble
empirical food webs. A large number of simulations were carried out to produce
a substantial number of model webs on which deletion experiments could be
performed. We deleted each species in four hundred distinct model webs and
determined, on average, how many species were eliminated from the web as a
result. Typically only a small number of species became extinct; in no instance
was the web close to collapse. Next, we examined how the the probability of
extinction of a species depended on its relationship with the deleted species.
This involved the exploration of the concept of indirect predator and prey
species and the extent that the probability of extinction depended on the
trophic level of the two species. The effect of deletions on the web itself was
studied by searching for keystone species, whose removal caused a major
restructuring of the community, and also by looking at the correlation between
a number of food web properties (number of species, linkage density, fraction
of omnivores, degree of cycling and redundancy) and the stability of the web to
deletions. With the exception of redundancy, we found little or no correlation.
In particular, we found no evidence that complexity in terms of increased
species number or links per species is destabilising.Comment: 30 pages, 9 figure
Species assembly in model ecosystems, I: Analysis of the population model and the invasion dynamics
Recently we have introduced a simplified model of ecosystem assembly (Capitan
et al., 2009) for which we are able to map out all assembly pathways generated
by external invasions in an exact manner. In this paper we provide a deeper
analysis of the model, obtaining analytical results and introducing some
approximations which allow us to reconstruct the results of our previous work.
In particular, we show that the population dynamics equations of a very general
class of trophic-level structured food-web have an unique interior equilibrium
point which is globally stable. We show analytically that communities found as
end states of the assembly process are pyramidal and we find that the
equilibrium abundance of any species at any trophic level is approximately
inversely proportional to the number of species in that level. We also find
that the per capita growth rate of a top predator invading a resident community
is key to understand the appearance of complex end states reported in our
previous work. The sign of these rates allows us to separate regions in the
space of parameters where the end state is either a single community or a
complex set containing more than one community. We have also built up
analytical approximations to the time evolution of species abundances that
allow us to determine, with high accuracy, the sequence of extinctions that an
invasion may cause. Finally we apply this analysis to obtain the communities in
the end states. To test the accuracy of the transition probability matrix
generated by this analytical procedure for the end states, we have compared
averages over those sets with those obtained from the graph derived by
numerical integration of the Lotka-Volterra equations. The agreement is
excellent.Comment: 16 pages, 8 figures. Revised versio
Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients
We present a convergence analysis of a cell-based finite volume (FV)
discretization scheme applied to a problem of control in the
coefficients of a generalized Laplace equation modelling, for
example, a steady state heat conduction.
Such problems arise in applications dealing with geometric optimal
design, in particular shape and topology optimization, and are most
often solved numerically utilizing a finite element approach.
Within the FV framework for control in the coefficients problems
the main difficulty we face is the need to analyze the convergence
of fluxes defined on the faces of cells, whereas the
convergence of the coefficients happens only with respect to the
âvolumetricâ Lebesgue measure.
Additionally,
depending on whether the stationarity conditions are stated for the
discretized or the original continuous problem, two distinct
concepts of stationarity at a discrete level arise.
We provide characterizations of limit points, with respect to FV
mesh size, of globally optimal solutions and two types of
stationary points to the discretized problems.
We illustrate the practical behaviour of our cell-based FV
discretization algorithm on a numerical example
Googling Food Webs: Can an Eigenvector Measure Species' Importance for Coextinctions?
A major challenge in ecology is forecasting the effects of species' extinctions, a pressing problem given current human impacts on the planet. Consequences of species losses such as secondary extinctions are difficult to forecast because species are not isolated, but interact instead in a complex network of ecological relationships. Because of their mutual dependence, the loss of a single species can cascade in multiple coextinctions. Here we show that an algorithm adapted from the one Google uses to rank web-pages can order species according to their importance for coextinctions, providing the sequence of losses that results in the fastest collapse of the network. Moreover, we use the algorithm to bridge the gap between qualitative (who eats whom) and quantitative (at what rate) descriptions of food webs. We show that our simple algorithm finds the best possible solution for the problem of assigning importance from the perspective of secondary extinctions in all analyzed networks. Our approach relies on network structure, but applies regardless of the specific dynamical model of species' interactions, because it identifies the subset of coextinctions common to all possible models, those that will happen with certainty given the complete loss of prey of a given predator. Results show that previous measures of importance based on the concept of âhubsâ or number of connections, as well as centrality measures, do not identify the most effective extinction sequence. The proposed algorithm provides a basis for further developments in the analysis of extinction risk in ecosystems
Optimal Homogenization of Perfusion Flows in Microfluidic Bio-Reactors: A Numerical Study
In recent years, the interest in small-scale bio-reactors has increased dramatically. To ensure homogeneous conditions within the complete area of perfused microfluidic bio-reactors, we develop a general design of a continually feed bio-reactor with uniform perfusion flow. This is achieved by introducing a specific type of perfusion inlet to the reaction area. The geometry of these inlets are found using the methods of topology optimization and shape optimization. The results are compared with two different analytic models, from which a general parametric description of the design is obtained and tested numerically. Such a parametric description will generally be beneficial for the design of a broad range of microfluidic bioreactors used for, e.g., cell culturing and analysis and in feeding bio-arrays
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