22,688 research outputs found
Selected topics on reaction-diffusion-advection models from spatial ecology
We discuss the effects of movement and spatial heterogeneity on population
dynamics via reaction-diffusion-advection models, focusing on the persistence,
competition, and evolution of organisms in spatially heterogeneous
environments. Topics include Lokta-Volterra competition models, river models,
evolution of biased movement, phytoplankton growth, and spatial spread of
epidemic disease. Open problems and conjectures are presented
Plant clonal morphologies and spatial patterns as self-organized responses to resource-limited environments
We propose here to interpret and model peculiar plant morphologies (cushions,
tussocks) observed in the Andean altiplano as localized structures. Such
structures resulting in a patchy, aperiodic aspect of the vegetation cover are
hypothesized to self-organize thanks to the interplay between facilitation and
competition processes occurring at the scale of basic plant components
biologically referred to as 'ramets'. (Ramets are often of clonal origin.) To
verify this interpretation, we applied a simple, fairly generic model (one
integro-differential equation) emphasizing via Gaussian kernels non-local
facilitative and competitive feedbacks of the vegetation biomass density on its
own dynamics. We show that under realistic assumptions and parameter values
relating to ramet scale, the model can reproduce some macroscopic features of
the observed systems of patches and predict values for the inter-patch distance
that match the distances encountered in the reference area (Sajama National
Park in Bolivia). Prediction of the model can be confronted in the future to
data on vegetation patterns along environmental gradients as to anticipate the
possible effect of global change on those vegetation systems experiencing
constraining environmental conditions.Comment: 14 pages, 6figure
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Robust permanence for ecological equations with internal and external feedbacks.
Species experience both internal feedbacks with endogenous factors such as trait evolution and external feedbacks with exogenous factors such as weather. These feedbacks can play an important role in determining whether populations persist or communities of species coexist. To provide a general mathematical framework for studying these effects, we develop a theorem for coexistence for ecological models accounting for internal and external feedbacks. Specifically, we use average Lyapunov functions and Morse decompositions to develop sufficient and necessary conditions for robust permanence, a form of coexistence robust to large perturbations of the population densities and small structural perturbations of the models. We illustrate how our results can be applied to verify permanence in non-autonomous models, structured population models, including those with frequency-dependent feedbacks, and models of eco-evolutionary dynamics. In these applications, we discuss how our results relate to previous results for models with particular types of feedbacks
Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms
We study the existence of non-trivial, non-negative periodic solutions for
systems of singular-degenerate parabolic equations with nonlocal terms and
satisfying Dirichlet boundary conditions. The method employed in this paper is
based on the Leray-Schauder topological degree theory. However, verifying the
conditions under which such a theory applies is more involved due to the
presence of the singularity. The system can be regarded as a possible model of
the interactions of two biological species sharing the same isolated territory,
and our results give conditions that ensure the coexistence of the two species.Comment: 39 page
Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales
In this paper, we consider the almost periodic dynamics of a multispecies
Lotka-Volterra mutualism system with time varying delays on time scales. By
establishing some dynamic inequalities on time scales, a permanence result for
the model is obtained. Furthermore, by means of the almost periodic functional
hull theory on time scales and Lyapunov functional, some criteria are obtained
for the existence, uniqueness and global attractivity of almost periodic
solutions of the model. Our results complement and extend some scientific work
in recent years. Finally, an example is given to illustrate the main results.Comment: 31page
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