7,667 research outputs found
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
Survival benefits in mimicry: a quantitative framework
Mimicry is a resemblance between species that benefits at least one of the
species. It is a ubiquitous evolutionary phenomenon particularly common among
prey species, in which case the advantage involves better protection from
predation. We formulate a mathematical description of mimicry among prey
species, to investigate benefits and disadvantages of mimicry. The basic setup
involves differential equations for quantities representing predator behavior,
namely, the probabilities for attacking prey at the next encounter. Using this
framework, we present new quantitative results, and also provide a unified
description of a significant fraction of the quantitative mimicry literature.
The new results include `temporary' mutualism between prey species, and an
optimal density at which the survival benefit is greatest for the mimic. The
formalism leads naturally to extensions in several directions, such as the
evolution of mimicry, the interplay of mimicry with population dynamics, etc.
We demonstrate this extensibility by presenting some explorations on
spatiotemporal pattern dynamics.Comment: 9 pages, 7 figure
Modelling chemotaxis of microswimmers: from individual to collective behavior
We discuss recent progress in the theoretical description of chemotaxis by
coupling the diffusion equation of a chemical species to equations describing
the motion of sensing microorganisms. In particular, we discuss models for
autochemotaxis of a single microorganism which senses its own secretion leading
to phenomena such as self-localization and self-avoidance. For two
heterogeneous particles, chemotactic coupling can lead to predator-prey
behavior including chase and escape phenomena, and to the formation of active
molecules, where motility spontaneously emerges when the particles approach
each other. We close this review with some remarks on the collective behavior
of many particles where chemotactic coupling induces patterns involving
clusters, spirals or traveling waves.Comment: to appear as a contribution to the book "Chemical kinetics beyond the
textbook
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