Complex dynamics and phase synchronization in spatially extended ecological systems

Abstract

Population cycles that persist in time and are synchronized over space pervade ecological systems, but their underlying causes remain a long-standing enigma. Here we examine the synchronization of complex population oscillations in networks of model communities and in natural systems, where phenomena such as unusual '4- and 10-year cycle' of wildlife are often found. In the proposed spatial model, each local patch sustains a three-level trophic system composed of interacting predators, consumers and vegetation. Populations oscillate regularly and periodically in phase, but with irregular and chaotic peaks together in abundance-twin realistic features that are not found in standard ecological models. In a spatial lattice of patches, only small amounts of local migration are required to induce broad-scale 'phase synchronization, with all populations in the lattice phase-locking to the same collective rhythm. Peak population abundances, however, remain chaotic and largely uncorrelated. Although synchronization is often perceived as being detrimental to spatially structured populations, phase synchronization leads to the emergence of complex chaotic travelling-wave structures which may be crucial for species persistence.

Different types of synchrony in chaotic and cyclic communities

“…Because wavelet analysis can generically create spurious 'on'-'off ' spots (short periods of synchronization interrupted by periods with no significant phase relations) 32 , as we find for the chaotic response communities, we used a second method to examine the relations between the phases of driver and response communities 7,33 (see Methods). Again, we find clear differences between cyclic and chaotic communities.…”

“…In our study, migration was unidirectional, corresponding to external or forced synchronization simulating , for example, unidirectional dispersal due to predominating winds or water flow. Almost all the theory on synchronized community and population dynamics in chaotic systems is developed for bidirectional dispersal or as reaction-diffusion model allowing for mutual synchronization 7,44,45 . One condition for phase locking of forced chaotic systems (that is, unidirectional dispersal) is that the mismatch between the instantaneous phase of the driver and response population is relatively small 46 .…”

“…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 .…”

“…Synchronization between populations may be caused by migration or dispersal between populations, fluctuating abiotic parameters affecting multiple populations (Moran effect), or trophic interactions with synchronized predators or food resources 5 . Until now, synchronization has been observed for lynx 6,7 , voles 8 , measles 9,10 , microbes 11 and mussel populations 12 . Synchronization of biological phenomena, such as periodic dynamics of populations, physiological activities or reproductive behavior, have been shown and one principal conclusion of these studies is that synchronization and phase locking can have a fundamental role 11,13,14 .…”

“…Beside in-phase synchronization between spatially separated populations, where populations cycle in tune, a more subtle form, phase locking, has been suggested by ecological models for periodic and chaotically oscillating populations 7,11,[25][26][27] . Phase locking occurs when one (or more) oscillator influences a second oscillator in such a way that their phases oscillate in tune but that there is a constant difference in the phase of two oscillators 1,2 .…”