611 research outputs found
Food Quality in Producer-Grazer Models: A Generalized Analysis
Stoichiometric constraints play a role in the dynamics of natural
populations, but are not explicitly considered in most mathematical models.
Recent theoretical works suggest that these constraints can have a significant
impact and should not be neglected. However, it is not yet resolved how
stoichiometry should be integrated in population dynamical models, as different
modeling approaches are found to yield qualitatively different results. Here we
investigate a unifying framework that reveals the differences and commonalities
between previously proposed models for producer-grazer systems. Our analysis
reveals that stoichiometric constraints affect the dynamics mainly by
increasing the intraspecific competition between producers and by introducing a
variable biomass conversion efficiency. The intraspecific competition has a
strongly stabilizing effect on the system, whereas the variable conversion
efficiency resulting from a variable food quality is the main determinant for
the nature of the instability once destabilization occurs. Only if the food
quality is high an oscillatory instability, as in the classical paradox of
enrichment, can occur. While the generalized model reveals that the generic
insights remain valid in a large class of models, we show that other details
such as the specific sequence of bifurcations encountered in enrichment
scenarios can depend sensitively on assumptions made in modeling stoichiometric
constraints.Comment: Online appendixes include
Spatiotemporal complexity of a ratio-dependent predator-prey system
In this paper, we investigate the emergence of a ratio-dependent
predator-prey system with Michaelis-Menten-type functional response and
reaction-diffusion. We derive the conditions for Hopf, Turing and Wave
bifurcation on a spatial domain. Furthermore, we present a theoretical analysis
of evolutionary processes that involves organisms distribution and their
interaction of spatially distributed population with local diffusion. The
results of numerical simulations reveal that the typical dynamics of population
density variation is the formation of isolated groups, i.e., stripelike or
spotted or coexistence of both. Our study shows that the spatially extended
model has not only more complex dynamic patterns in the space, but also chaos
and spiral waves. It may help us better understand the dynamics of an aquatic
community in a real marine environment.Comment: 6pages, revtex
Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes
Spatial variation in population densities across a landscape is a feature of many ecological systems, from
self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of
environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of
populations. However the ways in which abiotic and biotic factors interact to determine the existence
and nature of spatial patterns in population density remain poorly understood. Here we present a new
approach to studying this question by analysing a predator–prey patch-model in a heterogenous
landscape. We use analytical and numerical methods originally developed for studying nearest-
neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns
emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a
rich and highly complex array of coexisting stable patterns, located within an enormous number of
unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable
basins of attraction, making them significant in applications. We are able to identify mechanisms for
these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby
landscape heterogeneity can modulate the spatial scales at which these processes operate to structure
the populations
Generalized models as a universal approach to the analysis of nonlinear dynamical systems
We present a universal approach to the investigation of the dynamics in
generalized models. In these models the processes that are taken into account
are not restricted to specific functional forms. Therefore a single generalized
models can describe a class of systems which share a similar structure. Despite
this generality, the proposed approach allows us to study the dynamical
properties of generalized models efficiently in the framework of local
bifurcation theory. The approach is based on a normalization procedure that is
used to identify natural parameters of the system. The Jacobian in a steady
state is then derived as a function of these parameters. The analytical
computation of local bifurcations using computer algebra reveals conditions for
the local asymptotic stability of steady states and provides certain insights
on the global dynamics of the system. The proposed approach yields a close
connection between modelling and nonlinear dynamics. We illustrate the
investigation of generalized models by considering examples from three
different disciplines of science: a socio-economic model of dynastic cycles in
china, a model for a coupled laser system and a general ecological food web.Comment: 15 pages, 2 figures, (Fig. 2 in color
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