1,957 research outputs found
The Role of Behavioral Dynamics in Determining the Patch Distributions of Interacting Species
The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species–two-patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection
Ideal Free Distributions, Evolutionary Games, and Population Dynamics in Multiple-Species Environments
In this article, we develop population game theory, a theory that combines the dynamics of animal behavior with population dynamics. In particular, we study interaction and distribution of two species in a two-patch environment assuming that individuals behave adaptively (i.e., they maximize Darwinian fitness). Either the two species are competing for resources or they are in a predator-prey relationship. Using some recent advances in evolutionary game theory, we extend the classical ideal free distribution (IFD) concept for single species to two interacting species. We study population dynamical consequences of two-species IFD by comparing two systems: one where individuals cannot migrate between habitats and one where migration is possible. For single species, predator-prey interactions, and competing species, we show that these two types of behavior lead to the same population equilibria and corresponding species spatial distributions, provided interspecific competition is patch independent. However, if differences between patches are such that competition is patch dependent, then our predictions strongly depend on whether animals can migrate or not. In particular, we show that when species are settled at their equilibrium population densities in both habitats in the environment where migration between habitats is blocked, then the corresponding species spatial distribution need not be an IFD. Thus, when species are given the opportunity to migrate, they will redistribute to reach an IFD (e.g., under which the two species can completely segregate), and this redistribution will also influence species population equilibrial densities. Alternatively, we also show that when two species are distributed according to the IFD, the corresponding population equilibrium can be unstable
Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
We study the general properties of stochastic two-species models for
predator-prey competition and coexistence with Lotka-Volterra type interactions
defined on a -dimensional lattice. Introducing spatial degrees of freedom
and allowing for stochastic fluctuations generically invalidates the classical,
deterministic mean-field picture. Already within mean-field theory, however,
spatial constraints, modeling locally limited resources, lead to the emergence
of a continuous active-to-absorbing state phase transition. Field-theoretic
arguments, supported by Monte Carlo simulation results, indicate that this
transition, which represents an extinction threshold for the predator
population, is governed by the directed percolation universality class. In the
active state, where predators and prey coexist, the classical center
singularities with associated population cycles are replaced by either nodes or
foci. In the vicinity of the stable nodes, the system is characterized by
essentially stationary localized clusters of predators in a sea of prey. Near
the stable foci, however, the stochastic lattice Lotka-Volterra system displays
complex, correlated spatio-temporal patterns of competing activity fronts.
Correspondingly, the population densities in our numerical simulations turn out
to oscillate irregularly in time, with amplitudes that tend to zero in the
thermodynamic limit. Yet in finite systems these oscillatory fluctuations are
quite persistent, and their features are determined by the intrinsic
interaction rates rather than the initial conditions. We emphasize the
robustness of this scenario with respect to various model perturbations.Comment: 19 pages, 11 figures, 2-column revtex4 format. Minor modifications.
Accepted in the Journal of Statistical Physics. Movies corresponding to
Figures 2 and 3 are available at
http://www.phys.vt.edu/~tauber/PredatorPrey/movies
Red Queen Coevolution on Fitness Landscapes
Species do not merely evolve, they also coevolve with other organisms.
Coevolution is a major force driving interacting species to continuously evolve
ex- ploring their fitness landscapes. Coevolution involves the coupling of
species fit- ness landscapes, linking species genetic changes with their
inter-specific ecological interactions. Here we first introduce the Red Queen
hypothesis of evolution com- menting on some theoretical aspects and empirical
evidences. As an introduction to the fitness landscape concept, we review key
issues on evolution on simple and rugged fitness landscapes. Then we present
key modeling examples of coevolution on different fitness landscapes at
different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and
Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.).
Springer Series in Emergence, Complexity, and Computation, 201
Intransitivity and coexistence in four species cyclic games
Intransitivity is a property of connected, oriented graphs representing
species interactions that may drive their coexistence even in the presence of
competition, the standard example being the three species Rock-Paper-Scissors
game. We consider here a generalization with four species, the minimum number
of species allowing other interactions beyond the single loop (one predator,
one prey). We show that, contrary to the mean field prediction, on a square
lattice the model presents a transition, as the parameter setting the rate at
which one species invades another changes, from a coexistence to a state in
which one species gets extinct. Such a dependence on the invasion rates shows
that the interaction graph structure alone is not enough to predict the outcome
of such models. In addition, different invasion rates permit to tune the level
of transitiveness, indicating that for the coexistence of all species to
persist, there must be a minimum amount of intransitivity.Comment: Final, published versio
Competing associations in six-species predator-prey models
We study a set of six-species ecological models where each species has two
predators and two preys. On a square lattice the time evolution is governed by
iterated invasions between the neighboring predator-prey pairs chosen at random
and by a site exchange with a probability Xs between the neutral pairs. These
models involve the possibility of spontaneous formation of different defensive
alliances whose members protect each other from the external invaders. The
Monte Carlo simulations show a surprisingly rich variety of the stable spatial
distributions of species and subsequent phase transitions when tuning the
control parameter Xs. These very simple models are able to demonstrate that the
competition between these associations influences their composition. Sometimes
the dominant association is developed via a domain growth. In other cases
larger and larger invasion processes preceed the prevalence of one of the
stable asociations. Under some conditions the survival of all the species can
be maintained by the cyclic dominance occuring between these associations.Comment: 8 pages, 9 figure
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