2,422 research outputs found
Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics
The enigmatic stability of population oscillations within ecological systems
is analyzed. The underlying mechanism is presented in the framework of two
interacting species free to migrate between two spatial patches. It is shown
that that the combined effects of migration and noise cannot account for the
stabilization. The missing ingredient is the dependence of the oscillations'
frequency upon their amplitude; with that, noise-induced differences between
patches are amplified due to the frequency gradient. Migration among
desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of
the homogenous manifold. A simple model of diffusively coupled oscillators
allows the derivation of quantitative results, like the functional dependence
of the desynchronization upon diffusion strength and frequency differences. The
oscillations' amplitude is shown to be (almost) noise independent. The results
are compared with a numerical integration of the marginally stable
Lotka-Volterra equations. An unstable system is extinction-prone for small
noise, but stabilizes at larger noise intensity
Synchronization and Stability in Noisy Population Dynamics
We study the stability and synchronization of predator-prey populations
subjected to noise. The system is described by patches of local populations
coupled by migration and predation over a neighborhood. When a single patch is
considered, random perturbations tend to destabilize the populations, leading
to extinction. If the number of patches is small, stabilization in the presence
of noise is maintained at the expense of synchronization. As the number of
patches increases, both the stability and the synchrony among patches increase.
However, a residual asynchrony, large compared with the noise amplitude, seems
to persist even in the limit of infinite number of patches. Therefore, the
mechanism of stabilization by asynchrony recently proposed by R. Abta et. al.,
combining noise, diffusion and nonlinearities, seems to be more general than
first proposed.Comment: 3 pages, 3 figures. To appear in Phys. Rev.
Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication
We employ partial integro-differential equations to model trophic interaction
in a spatially extended heterogeneous environment. Compared to classical
reaction-diffusion models, this framework allows us to more realistically
describe the situation where movement of individuals occurs on a faster time
scale than the demographic (population) time scale, and we cannot determine
population growth based on local density. However, most of the results reported
so far for such systems have only been verified numerically and for a
particular choice of model functions, which obviously casts doubts about these
findings. In this paper, we analyse a class of integro-differential
predator-prey models with a highly mobile predator in a heterogeneous
environment, and we reveal the main factors stabilizing such systems. In
particular, we explore an ecologically relevant case of interactions in a
highly eutrophic environment, where the prey carrying capacity can be formally
set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient
of the growth rate is due to abiotic factors only, and (ii) the local growth
rate depends on the global density distribution across the environment (e.g.
due to non-local self-shading). For an arbitrary spatial gradient of the prey
growth rate, we analytically investigate the possibility of the predator-prey
equilibrium in such systems and we explore the conditions of stability of this
equilibrium. In particular, we demonstrate that for a Holling type I (linear)
functional response, the predator can stabilize the system at low prey density
even for an 'unlimited' carrying capacity. We conclude that the interplay
between spatial heterogeneity in the prey growth and fast displacement of the
predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin
of Mathematical Biolog
Complex dynamics in coevolution models with ratio-dependent functional response
We explore the complex dynamical behavior of two simple predator-prey models
of biological coevolution that on the ecological level account for
interspecific and intraspecific competition, as well as adaptive foraging
behavior. The underlying individual-based population dynamics are based on a
ratio-dependent functional response [W.M. Getz, J. Theor. Biol. 108, 623
(1984)]. Analytical results for fixed-point population sizes in some simple
communities are derived and discussed. In long kinetic Monte Carlo simulations
we find quite robust, approximate 1/f noise in species diversity and population
sizes, as well as power-law distributions for the lifetimes of individual
species and the durations of periods of relative evolutionary stasis. Adaptive
foraging enhances coexistence of species and produces a metastable
low-diversity phase and a stable high-diversity phase.Comment: 19 page
Predation effects on mean time to extinction under demographic stochasticity
Methods for predicting the probability and timing of a species' extinction
are typically based on a combination of theoretical models and empirical data,
and focus on single species population dynamics. Of course, species also
interact with each other, forming more or less complex networks of
interactions. Models to assess extinction risk often lack explicit
incorporation of these interspecific interactions. We study a birth and death
process in which the death rate includes an effect from predation. This
predation rate is included via a general nonlinear expression for the
functional response of predation to prey density. We investigate the effects of
the foraging parameters (e.g. attack rate and handling time) on the mean time
to extinction. Mean time to extinction varies by orders of magnitude when we
alter the foraging parameters, even when we exclude the effects of these
parameters on the equilibrium population size. In particular we observe an
exponential dependence of the mean time to extinction on handling time. These
findings clearly show that accounting for the nature of interspecific
interactions is likely to be critically important when estimating extinction
risk.Comment: 11 pages, 4 figures; Typos removed. For further discussion about the
paper go to http://purl.org/net/extinctio
Effects of rapid prey evolution on predator-prey cycles
We study the qualitative properties of population cycles in a predator-prey
system where genetic variability allows contemporary rapid evolution of the
prey. Previous numerical studies have found that prey evolution in response to
changing predation risk can have major quantitative and qualitative effects on
predator-prey cycles, including: (i) large increases in cycle period, (ii)
changes in phase relations (so that predator and prey are cycling exactly out
of phase, rather than the classical quarter-period phase lag), and (iii)
"cryptic" cycles in which total prey density remains nearly constant while
predator density and prey traits cycle. Here we focus on a chemostat model
motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003]
with algae (prey) and rotifers (predators), in which the prey exhibit rapid
evolution in their level of defense against predation. We show that the effects
of rapid prey evolution are robust and general, and furthermore that they occur
in a specific but biologically relevant region of parameter space: when traits
that greatly reduce predation risk are relatively cheap (in terms of reductions
in other fitness components), when there is coexistence between the two prey
types and the predator, and when the interaction between predators and
undefended prey alone would produce cycles. Because defense has been shown to
be inexpensive, even cost-free, in a number of systems [Andersson and Levin
1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be
reproduced in other model systems, and in nature. Finally, some of our key
results are extended to a general model in which functional forms for the
predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure
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