# The emergence of phase asynchrony and frequency modulation in metacommunities

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## Abstract

Spatial synchrony can summarize complex patterns of population abundance. Studies of phase synchrony predict that limited dispersal can drive either in-phase or out-of-phase synchrony, characterized by a constant phase difference among populations. We still lack an understanding of ecological processes leading to the loss of phase synchrony. Here, we study the role of limited dispersal as a cause of phase asynchrony defined as fluctuating phase differences among populations. We adopt a minimal predator-prey model allowing for dispersal-induced phase asynchrony, and show its dependence on species traits. We show that phase asynchrony in a homogeneous metacommunity requires a minimum of three communities and is characterized by the emergence of regional frequency modulation of population fluctuations. This frequency modulation results in spectral signatures in local time series that can be used to infer the causes and properties of metacommunity dynamics. Dispersal-induced phase asynchrony extends the application of ecological theories of synchrony to nonstationary time series, and is consistent with observed spatiotemporal patterns in marine metacommunities.

## Keywords

Phase synchrony Metacommunities Spatial dynamics Predator-prey dynamics Self-organization Weakly coupled oscillators## Notes

### Acknowledgments

F.G. and F.L. wish to thank the Natural Science and Engineering Research Council (NSERC) of Canada for their support through the Discovery Program.

### Funding information

This study is financially supported by the NSF of China (No. 11601386). We also wish to acknowledge financial support from the Centre de Recherches Mathématiques (CRM) and from the Canadian Healthy Ocean Network (CHONe).

## References

- Abbott KC (2011) A dispersal-induced paradox: synchrony and stability in stochastic metapopulations. Ecol Lett 14(11):1158–1169CrossRefGoogle Scholar
- Allstadt AJ, Liebhold A, Johnson DM, Davis RE, Haynes KJ (2015) Temporal variation in the synchrony of weather and its consequences for spatiotemporal population dynamics. Ecology 96(11):2935–2946CrossRefGoogle Scholar
- Arumugam R, Dutta PS, Banerjee T (2015) Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig–MacArthur model. Chaos 25(10). https://doi.org/10.1063/1.4933300
- Ashwin P, King G, Swift JW (1990) Three identical oscillators with symmetric coupling. Nonlinearity 3(3):585–601CrossRefGoogle Scholar
- Baesens C, Guckenheimer J, Kim S, MacKay R (1991) Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos. Physica D: Nonlinear Phenom 49(3):387–475CrossRefGoogle Scholar
- Bjørnstad ON, Ims RA, Lambin X (1999) Spatial population dynamics: analyzing patterns and processes of population synchrony. Trends Ecol Evol 14(11):427–432CrossRefGoogle Scholar
- Blasius B, Huppert A, Stone L (1999) Complex dynamics and phase synchronization in spatially extended ecological systems. Nature 399:354–359CrossRefGoogle Scholar
- Boashash B (2016) Time-frequency signal analysis and processing, 2nd edn. Elsevier, New YorkGoogle Scholar
- Cavanaugh KC, Kendall BE, Siegel DA, Reed DC, Alberto F, Assis J (2013) Synchrony in dynamics of giant kelp forests is driven by both local recruitment and regional environmental controls. Ecology 94 (2):499–509CrossRefGoogle Scholar
- Cazelles B, Bottani S, Stone L (2001) Unexpected coherence and conservation. Proc R Soc B 268 (1485):2595–2602CrossRefGoogle Scholar
- Cazelles B, Boudjema G (2001) The Moran effect and phase synchronization in complex spatial community dynamics. Am Nat 157(6):670–676CrossRefGoogle Scholar
- Cazelles B, Chavez M, Berteaux D, Ménard F, Vik JO, Jenouvrier S, Stenseth NC (2008) Wavelet analysis of ecological time series. Oecol 156(2):287–304CrossRefGoogle Scholar
- Emelianova YP, Kuznetsov A, Sataev I, Turukina L (2013) Synchronization and multi-frequency oscillations in the low-dimensional chain of the self-oscillators. Physica D: Nonlinear Phenom 244(1):36–49CrossRefGoogle Scholar
- Ermentrout B (2002) Simulating, analyzing and animating dynamical systems: a guide to XPPAUT for researchers and students. SIAM, PhiladelphiaCrossRefGoogle Scholar
- Goldwyn EE, Hastings A (2007) When can dispersal synchronize populations? Theor Pop Biol 73:395–402CrossRefGoogle Scholar
- Goldwyn EE, Hastings A (2009) Small heterogeneity has large effects on synchronization of ecological oscillators. Bull Math Biol 71(1):130–144CrossRefGoogle Scholar
- Goldwyn EE, Hastings A (2011) The roles of the Moran affect and dispersal in synchronizing oscillating populations. J Theor Biol 289:237–246CrossRefGoogle Scholar
- Gouhier TC, Guichard F (2014) Synchrony: quantifying variability in space and time. Meth Ecol Evol 5 (6):524–533CrossRefGoogle Scholar
- Gouhier TC, Guichard F, Menge BA (2010) Ecological processes can synchronize marine population dynamics over continental scales. Proc Natl Acad Sci U S A 107(18):8281–8286CrossRefGoogle Scholar
- Grainger TN, Gilbert B (2016) Dispersal and diversity in experimental metacommunities: linking theory and practice. Oikos 125(9):1213–1223CrossRefGoogle Scholar
- Guichard F, Gouhier TC (2014) Non-equilibrium spatial dynamics of ecosystems. Math Biosci 255:1–10CrossRefGoogle Scholar
- Hastings A (2001) Transient dynamics and persistence of ecological systems. Ecol Lett 4:215–220CrossRefGoogle Scholar
- Hastings A (2004) Transients: the key to long-term ecological understanding? Trends Ecol Evol 19(1):39–45CrossRefGoogle Scholar
- Haydon DT, Greenwood PE (2000) Spatial coupling in cyclic population dynamics: models and data. Theor Pop Biol 58(3):239–254CrossRefGoogle Scholar
- Henden JA, Ims RA, Yoccoz NG (2009) Nonstationary spatio-temporal small rodent dynamics: evidence from long-term norwegian fox bounty data. J An Ecol 78(3):636–645CrossRefGoogle Scholar
- Holland MD, Hastings A (2008) Strong effect of dispersal network structure on ecological dynamics. Nature 456(7223):792–794CrossRefGoogle Scholar
- Hoppensteadt FC, Izhikevech EM (1997) Weakly connected neural networks. Springer, New YorkCrossRefGoogle Scholar
- Hoppensteadt FC, Izhikevich EM (1998) Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use fm radio principles? Biosystems 48:85–94CrossRefGoogle Scholar
- Jansen VA, de Roos A (2000) The role of space in reducing predator–prey cycles. In: The geometry of ecological interactions: simplifying spatial complexity, eds. Cambridge University Press, pp 183–201Google Scholar
- Jassby AD, Powell TM (1990) Detecting changes in ecological time series. Ecology pp 2044–2052Google Scholar
- Kim S, Kook H, Lee SG, Park MH (1998) Synchronization and clustering in a network of three globally coupled neural oscillators. Int J Bif Chaos 8(04):731–739CrossRefGoogle Scholar
- Koelle K, Vandermeer J (2005) Dispersal-induced desynchronization: from metapopulations to metacommunities. Ecol Lett 8(2):167–175CrossRefGoogle Scholar
- Lampert A, Hastings A (2016) Stability and distribution of predator–prey systems: local and regional mechanisms and patterns. Ecol Lett 19(3):279–288CrossRefGoogle Scholar
- Lande, Engen, Sæther (1999) Spatial scale of population synchrony: environmental correlation versus dispersal and density regulation. Am Nat 154(3):271–281CrossRefGoogle Scholar
- Liebhold A, Koenig WD, Bjørnstad ON (2004) Spatial synchrony in population dynamics. Ann Rev Ecol Evol Syst 35:467–490CrossRefGoogle Scholar
- Louca S, Doebeli M (2014) Distinguishing intrinsic limit cycles from forced oscillations in ecological time series. Theor Ecol 7(4):381–390CrossRefGoogle Scholar
- Marleau JN, Guichard F, Loreau M (1777) Meta-ecosystem dynamics and functioning on finite spatial networks. Proc R Soc B 281:20132094CrossRefGoogle Scholar
- Montbrió E, Kurths J, Blasius B (2004) Synchronization of two interacting populations of oscillators. Phys Rev E 70:056125CrossRefGoogle Scholar
- Morton ES (1975) Ecological sources of selection on avian sounds. Am Nat 109:17–34CrossRefGoogle Scholar
- Ruxton G, Doebeli M (1996) Spatial self-organization and persistence of transients in a metapopulation model. Proc R Soc B 263(1374):1153–1158CrossRefGoogle Scholar
- Truax B (2001) Handbook of acoustic ecology. Comput Mus J 25:93–94CrossRefGoogle Scholar
- Turchin P (2003) Complex population dynamics: a theoretical/empirical synthesis, vol 35 of monographs in population biology. Princeton University Press, PrincetonGoogle Scholar
- Wall E, Guichard F, Humphries AR (2013) Synchronization in ecological systems by weak dispersal coupling with time delay. Theor Ecol 6(4):405–418CrossRefGoogle Scholar
- Zhang Y, Lutscher F, Guichard F (2015) How robust is dispersal-induced spatial synchrony? Chaos 25(036402). https://doi.org/10.1063/1.4906951