Phase locking: another cause of synchronicity in predator–prey systems

Jansen, Vincent A. A.

doi:10.1016/s0169-5347(99)01654-7

Cited by 49 publications

(47 citation statements)

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“…Instead, we found only short periods where there is phase locking. For the cyclic communities, our study confirms previous observations that migration between cyclic communities can lead to phase-locked dynamics and that the intrinsic cyclical behaviour persists 11,12,35,37 . Interestingly, we did not find the driver and response population cycling in-phase as has been shown in another experimental predator-prey system 11 , instead we found out-phase cycles.…”

Section: Discussionsupporting

confidence: 89%

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: Discussionsupporting

confidence: 89%

Different types of synchrony in chaotic and cyclic communities

Becks

Arndt

2013

Nat Commun

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“…The benefits of dispersal come with a potential cost, however, as dispersing individuals may synchronize predator-prey dynamics across patches. If local dynamics are cyclical, for example classic predator-prey cycles, dispersal can synchronize patches in ''phase lock'' (local dynamics are synchronized with 0-time lag) (Jansen 1999). As a result, all subpopulations will be small, and thus susceptible to demographic stochasticity, at the same time (Earn et al 2000, Hastings 2001).…”

Section: Introductionmentioning

confidence: 99%

“…Most models of predator-prey metapopulations are based on deterministic equations, particularly ordinary differential equations (ODEs), which show that any amount of dispersal by 1 E-mail: jls468@cornell.edu either trophic level will eventually synchronize local dynamics unless patches differ in quality (Murdoch et al 1992, Jansen 1999, Hastings 2001. Although ODE models provide a tractable starting point and useful deterministic comparison, they cannot directly speak to the effects of demographic stochasticity.…”

Section: Introductionmentioning

confidence: 99%

Demographic stochasticity reduces the synchronizing effect of dispersal in predator–prey metapopulations

Simonis

2012

Ecology

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Abstract. Dispersal may affect predator-prey metapopulations by rescuing local sink populations from extinction or by synchronizing population dynamics across the metapopulation, increasing the risk of regional extinction. Dispersal is likely influenced by demographic stochasticity, however, particularly because dispersal rates are often very low in metapopulations. Yet the effects of demographic stochasticity on predator-prey metapopulations are not well known. To that end, I constructed three models of a twopatch predator-prey system. The models constitute a hierarchy of complexity, allowing direct comparisons. Two models included demographic stochasticity (pure jump process [PJP] and stochastic differential equations [SDE]), and the third was deterministic (ordinary differential equations [ODE]). One stochastic model (PJP) treated population sizes as discrete, while the other (SDE) allowed population sizes to change continuously. Both stochastic models only produced synchronized predator-prey dynamics when dispersal was high for both trophic levels. Frequent dispersal by only predators or prey in the PJP and SDE spatially decoupled the trophic interaction, reducing synchrony of the non-dispersive species. Conversely, the ODE generated synchronized predator-prey dynamics across all dispersal rates, except when initial conditions produced anti-phase transients. These results indicate that demographic stochasticity strongly reduces the synchronizing effect of dispersal, which is ironic because demographic stochasticity is often invoked post hoc as a driver of extinctions in synchronized metapopulations.

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“…The crucial question thus is whether asynchronous fluctuations in the local densities are to be expected in metapopulations. Migration couples local populations in a metapopulation (Hanski, 1991) but it also tends to reduce differences between local populations (Murray, 1993;Sole and Gamarra, 1998;Jansen, 1999). When no differences between the local populations exist, the local patches proceed in phase and are phase locked.…”

Section: Introductionmentioning

confidence: 99%

“…There has been some debate about whether phase locking can offer an alternative explanation for synchronized population dynamics (Jansen, 1999;Ranta et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

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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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Phase locking: another cause of synchronicity in predator–prey systems

Cited by 49 publications

References 4 publications

Different types of synchrony in chaotic and cyclic communities

Different types of synchrony in chaotic and cyclic communities

Demographic stochasticity reduces the synchronizing effect of dispersal in predator–prey metapopulations

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

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