Search arXiv⌕ Search

arXiv · nlin/0002032

The Influence of Predator-Prey Population Dynamics on the Long-term Evolution of Food Web Structure

Abstract

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary timescale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organised criticality.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Barbara Drossel, Paul G. Higgs, Alan J. McKane. 2000-02-20. The Influence of Predator-Prey Population Dynamics on the Long-term Evolution of Food Web Structure. https://arxiv.org/abs/nlin/0002032

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Higher-Order Competition as a Minimal Mechanism for Spatial Pattern Diversity in Population Dynamics

We show that negative feedback alone generates the diversity of self-organized shapes usually attributed to scale-dependent activation-inhibition. For a broad class of kernels, pairwise competition models only generate hexagonal spot arrays. Higher-order terms eliminate this restriction and promote stripes and gaps. Combining individual-based simulations and nonlinear analysis, we derive the pattern-selection thresholds and construct the full state diagram, including an unusual spots-stripes-spots sequence. Spot patterns are thus not a reliable indicator of proximity to a tipping point.

nlin.AO↗

From Periodicity to Chaos - Stabilization, Bifurcation, and Synchronization of the Van der Pol Oscillator

This work investigates the dynamics of the van der Pol oscillator, a well-known dynamical model used to represent many naturally occurring phenomena, under both unforced and externally forced conditions, with a focus on its stability characteristics and bifurcation behavior. An approximate analytical solution is derived using the Method of Multiple Scales (MMS) and validated against numerical simulations conducted via the ode45 solver. The evolution of the system's limit cycle is examined as the strength of the nonlinear damping term increased. A range of bifurcation scenarios is explored by systematically varying relevant control parameters. The system's response to external forcing at different damping levels is analyzed to uncover transitions toward chaotic behavior and subsequent phase locking (entrainment). Finally, the relevance of the van der Pol oscillator as a model for naturally occurring rhythmic or periodic processes is discussed, highlighting its applicability in representing biological and physical systems.

nlin.AO↗

Frequency bursts in adaptive delay-coupled oscillators

We report on frequency bursting oscillations in a system of phase oscillators with adaptive and delayed coupling. Adaptation of the coupling strengths is considered slow and depends on the phase shift between the oscillators. We find due to the combined chain of adaptation, collective dynamics, and time delays, the system robustly achieves a state in which the oscillator's frequencies are nearly synchronized but detuned by an integer number of small adaptation frequencies. We demonstrate that this quantization of the detuning is caused by alternating slow and fast transitions. Moreover, the observed motions take the form of bursts of instantaneous frequency, and the number of spikes in each burst corresponds to the quantization level of the detuning. We provide a fast-slow analysis of this phenomenon and explain the mechanisms behind the emergence of bursts. Our findings indicate that these frequency bursting oscillations are robust and exist stably within finite parameter regions.

nlin.AO↗