Noise and determinism in synchronized sheep dynamics

Grenfell, Bryan T.; Wilson, Kenneth; Finkenstädt, Bärbel; Coulson, Tim; Murray, Stuart J.; Albon, S. D.; Pemberton, Josephine M.; Clutton‐Brock, Tim; Crawley, Michael J.

doi:10.1038/29291

Cited by 507 publications

(507 citation statements)

References 27 publications

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“…Examples for synchronization, both in phase and anti-phase, of cyclic communities in natural systems can be found in literature, although the mechanisms (spatial correlation in external parameters or migration) are not always known [6][7][8]10,12,55 . Detailed studies on the dynamics of recurrent epidemics suggest that the form of synchronization (in-phase, out-ofphase, anti-phase) depends on the dynamical behaviour, the coupling strength and the dispersal distance 56 .…”

Section: Discussionmentioning

confidence: 99%

Different types of synchrony in chaotic and cyclic communities

Becks

Arndt

2013

Nat Commun

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Stability and persistence of populations is of great interest for management and conservation purposes. Spatial dynamics can have a crucial role in population stability via synchronization, and beneficial and detrimental effects on population persistence have been shown. Despite a theoretical understanding of synchronization, empirical data on synchrony of populations are restricted to systems that do not display the full spectrum of complex dynamics that may occur in nature (that is, chaos or quasiperiodicity). Here we show in experiments that the qualitative form of dynamic behaviour of chaotic and periodic oscillating communities did not change when unidirectionally coupled to oscillating driver communities. Driver and response populations were phase locked in cyclic communities, whereas chaotic communities showed only short periods of statistical coherencies. Our study provides the first empirical analysis of synchronization of chaotic communities and shows that the likelihood for chaos is not lowered in spatially explicit systems but that cyclic and chaotic systems differ in synchronization.

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Section: Discussionmentioning

confidence: 99%

Different types of synchrony in chaotic and cyclic communities

Becks

Arndt

2013

Nat Commun

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“…There are also well-documented examples of populations with a patchy structure in which the dynamics are highly synchronized (Grenfell et al, 1998;Koenig, 1999, and references therein). The explanation that is predominantly used for synchronized population dynamics is the synchronizing force exerted by correlated environmental noise.…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

151

110

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I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

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“…Thus, K = ln(p/q) + ln q = ln p. The complexity can be obtained by computing the separation rate of nearby trajectories evolving in two different realizations of the noise. In the case of sequences produced by function (14), this is equivalent to using two different θ for which (at n = 0) the trajectories are close. Such procedure exactly corresponds to what happens when experimental data are analyzed with the Wolf et al algorithm [24].…”

Section: Random Sequencesmentioning

confidence: 99%

“…There exists a great controversy in ecology [9,10,11,12,13,14,15] concerning the relative importance of intrinsic factors and external environmental variations in determining populations fluctuations. In this article we address this problem using a recently proposed method [16,17] for studying the complexity of a nonlinear random dynamical system.…”

Section: Introductionmentioning

confidence: 99%

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Intrinsic chaos and external noise in population dynamics

González

Trujillo

Escalante

2003

Physica A: Statistical Mechanics and its Applications

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We address the problem of the relative importance of the intrinsic chaos and the external noise in determining the complexity of population dynamics. We use a recently proposed method for studying the complexity of nonlinear random dynamical systems. The new measure of complexity is defined in terms of the average number of bits per time-unit necessary to specify the sequence generated by the system. This measure coincides with the rate of divergence of nearby trajectories under two different realizations of the noise. In particular, we show that the complexity of a nonlinear time-series model constructed from sheep populations comes completely from the environmental variations. However, in other situations, intrinsic chaos can be the crucial factor. This method can be applied to many other systems in biology and physics.

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Noise and determinism in synchronized sheep dynamics

Cited by 507 publications

References 27 publications

Different types of synchrony in chaotic and cyclic communities

Different types of synchrony in chaotic and cyclic communities

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Intrinsic chaos and external noise in population dynamics

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