3,874 research outputs found
Bistability induced by generalist natural enemies can reverse pest invasions
Reaction-diffusion analytical modeling of predator-prey systems has shown
that specialist natural enemies can slow, stop and even reverse pest invasions,
assuming that the prey population displays a strong Allee effect in its growth.
Few additional analytical results have been obtained for other spatially
distributed predator-prey systems, as traveling waves of non-monotonous systems
are notoriously difficult to obtain. Traveling waves have indeed recently been
shown to exist in predator-prey systems, but the direction of the wave, an
essential item of information in the context of the control of biological
invasions, is generally unknown. Preliminary numerical explorations have hinted
that control by generalist predators might be possible for prey populations
displaying logistic growth. We aimed to formalize the conditions in which
spatial biological control can be achieved by generalists, through an
analytical approach based on reaction-diffusion equations. The population of
the focal prey - the invader - is assumed to grow according to a logistic
function. The predator has a type II functional response and is present
everywhere in the domain, at its carrying capacity, on alternative hosts.
Control, defined as the invader becoming extinct in the domain, may result from
spatially independent demographic dynamics or from a spatial extinction wave.
Using comparison principles, we obtain sufficient conditions for control and
for invasion, based on scalar bistable partial differential equations (PDEs).
The searching efficiency and functional response plateau of the predator are
identified as the main parameters defining the parameter space for prey
extinction and invasion. Numerical explorations are carried out in the region
of those control parameters space between the super-and subso-lutions, in which
no conclusion about controllability can be drawn on the basis of analytical
solutions. The ability of generalist predators to control prey populations with
logistic growth lies in the bis-table dynamics of the coupled system, rather
than in the bistability of prey-only dynamics as observed for specialist
predators attacking prey populations displaying Allee effects. The
consideration of space in predator-prey systems involving generalist predators
with a parabolic functional response is crucial. Analysis of the ordinary
differential equations (ODEs) system identifies parameter regions with
monostable (extinction) and bistable (extinction or invasion) dynamics. By
contrast, analysis of the associated PDE system distinguishes different and
additional regions of invasion and extinction. Depending on the relative
positions of these different zones, four patterns of spatial dynamics can be
identified : traveling waves of extinction and invasion, pulse waves of
extinction and heterogeneous stationary positive solutions of the Turing type.
As a consequence, prey control is predicted to be possible when space is
considered in additional situations other than those identified without
considering space. The reverse situation is also possible. None of these
considerations apply to spatial predator-prey systems with specialist natural
enemies
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
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
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
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
Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth
Allee effect in population dynamics has a major impact in suppressing the
paradox of enrichment through global bifurcation, and it can generate highly
complex dynamics. The influence of the reproductive Allee effect, incorporated
in the prey's growth rate of a prey-predator model with Beddington-DeAngelis
functional response, is investigated here. Preliminary local and global
bifurcations are identified of the temporal model. Existence and non-existence
of heterogeneous steady-state solutions of the spatio-temporal system are
established for suitable ranges of parameter values. The spatio-temporal model
satisfies Turing instability conditions, but numerical investigation reveals
that the heterogeneous patterns corresponding to unstable Turing eigen modes
acts as a transitory pattern. Inclusion of the reproductive Allee effect in the
prey population has a destabilising effect on the coexistence equilibrium. For
a range of parameter values, various branches of stationary solutions including
mode-dependent Turing solutions and localized pattern solutions are identified
using numerical bifurcation technique. The model is also capable to produce
some complex dynamic patterns such as travelling wave, moving pulse solution,
and spatio-temporal chaos for certain range of parameters and diffusivity along
with appropriate choice of initial conditions Judicious choices of
parametrization for the Beddington-DeAngelis functional response help us to
infer about the resulting patterns for similar prey-predator models with
Holling type-II functional response and ratio-dependent functional response
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