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Morozov A, Feudel U, Hastings A, Abbott KC, Cuddington K, Heggerud CM, Petrovskii S. Long-living transients in ecological models: Recent progress, new challenges, and open questions. Phys Life Rev 2024; 51:423-441. [PMID: 39581175 DOI: 10.1016/j.plrev.2024.11.004] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2024] [Accepted: 11/08/2024] [Indexed: 11/26/2024]
Abstract
Traditionally, mathematical models in ecology placed an emphasis on asymptotic, long-term dynamics. However, a large number of recent studies highlighted the importance of transient dynamics in ecological and eco-evolutionary systems, in particular 'long transients' that can last for hundreds of generations or even longer. Many models as well as empirical studies indicated that a system can function for a long time in a certain state or regime (a 'metastable regime') but later exhibits an abrupt transition to another regime not preceded by any parameter change (or following the change that occurred long before the transition). This scenario where tipping occurs without any apparent source of a regime shift is also referred to as 'metastability'. Despite considerable evidence of the presence of long transients in real-world systems as well as models, until recently research into long-living transients in ecology has remained in its infancy, largely lacking systematisation. Within the past decade, however, substantial progress has been made in creating a unifying theory of long transients in deterministic as well as stochastic systems. This has considerably accelerated further studies on long transients, in particular on those characterised by more complicated patterns and/or underlying mechanisms. The main goal of this review is to provide an overview of recent research on long transients and related regime shifts in models of ecological dynamics. We pay special attention to the role of environmental stochasticity, the effect of multiple timescales (slow-fast systems), transient spatial patterns, and relation between transients and spatial synchronisation. We also discuss current challenges and open questions in understanding transients with applications to ecosystems dynamics.
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Affiliation(s)
- Andrew Morozov
- School of Computing and Mathematical Sciences, University of Leicester, LE1 7RH, UK; Institute of Ecology and Evolution, Russian Academy of Sciences, Moscow, Russia
| | - Ulrike Feudel
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Oldenburg, Germany
| | - Alan Hastings
- Department of Environmental Science and Policy, University of California, Davis, USA; Santa Fe Institute, Santa Fe, New Mexico, USA
| | - Karen C Abbott
- Department of Biology, Case Western Reserve University, Cleveland, OH 44106, USA
| | - Kim Cuddington
- Department of Biology, University of Waterloo, Waterloo, Ontario, Canada
| | | | - Sergei Petrovskii
- School of Computing and Mathematical Sciences, Institute for Environmental Futures, University of Leicester, LE1 7RH, UK; Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia.
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Ghislain M, Bonnet T, Godeau U, Dehorter O, Gimenez O, Henry PY. Synchrony in adult survival is remarkably strong among common temperate songbirds across France. Ecology 2024; 105:e4305. [PMID: 38679955 DOI: 10.1002/ecy.4305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 11/06/2023] [Accepted: 02/19/2024] [Indexed: 05/01/2024]
Abstract
Synchronous variation in demographic parameters across species increases the risk of simultaneous local extinction, which lowers the probability of subsequent recolonization. Synchrony therefore tends to destabilize meta-populations and meta-communities. Quantifying interspecific synchrony in demographic parameters, like abundance, survival, or reproduction, is thus a way to indirectly assess the stability of meta-populations and meta-communities. Moreover, it is particularly informative to identify environmental drivers of interspecific synchrony because those drivers are important across species. Using a Bayesian hierarchical multisite multispecies mark-recapture model, we investigated temporal interspecific synchrony in annual adult apparent survival for 16 common songbird species across France for the period 2001-2016. Annual adult survival was largely synchronous among species (73%, 95% credible interval [47%-94%] of the variation among years was common to all species), despite species differing in ecological niche and life history. This result was robust to different model formulations, uneven species sample sizes, and removing the long-term trend in survival. Synchrony was also shared across migratory strategies, which suggests that environmental forcing during the 4-month temperate breeding season has a large-scale, interspecific impact on songbird survival. However, the strong interspecific synchrony was not easily explained by a set of candidate weather variables we defined a priori. Spring weather variables explained only 1.4% [0.01%-5.5%] of synchrony, while the contribution of large-scale winter weather indices may have been stronger but uncertain, accounting for 12% [0.3%-37%] of synchrony. Future research could jointly model interspecific variation and covariation in breeding success, age-dependent survival, and age-dependent dispersal to understand when interspecific synchrony in abundance emerges and destabilizes meta-communities.
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Affiliation(s)
- Manon Ghislain
- Mécanismes adaptatifs et évolution (MECADEV UMR 7179), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Brunoy, France
- Centre de Recherches sur la Biologie des Populations d'Oiseaux (CRBPO), Centre d'Ecologie et des Sciences de la Conservation (CESCO UMR 7204), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Sorbonne Université, CP135, Paris, France
- PatriNat (OFB-MNHN-CNRS-IRD), Centre d'expertise et de données sur le patrimoine naturel, Muséum national d'Histoire naturelle, Paris, France
| | - Timothée Bonnet
- Division of Ecology and Evolution, Research School of Biology, ANU College of Science, The Australian National University, Canberra, ACT, Australia
- Centre d'Études Biologiques de Chizé (CEBC UMR 7372), Centre National de la Recherche Scientifique, Villiers en Bois, France
| | - Ugoline Godeau
- Mécanismes adaptatifs et évolution (MECADEV UMR 7179), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Brunoy, France
- Centre de Recherches sur la Biologie des Populations d'Oiseaux (CRBPO), Centre d'Ecologie et des Sciences de la Conservation (CESCO UMR 7204), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Sorbonne Université, CP135, Paris, France
- Institut national de Recherche en Sciences et Technologies pour l'Environnement et l'Agriculture, Ecosystèmes Forestiers (UR EFNO), Domaine des Barres, Nogent-Sur-Vernisson, France
- Institut National de Recherche pour l'Agriculture l'Alimentation et l'Environnement, UR 406 Abeilles et Environnement, Avignon, France
| | - Olivier Dehorter
- Centre de Recherches sur la Biologie des Populations d'Oiseaux (CRBPO), Centre d'Ecologie et des Sciences de la Conservation (CESCO UMR 7204), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Sorbonne Université, CP135, Paris, France
| | - Olivier Gimenez
- Centre d'Ecologie Fonctionnelle et Evolutive (CEFE UMR 5175), Centre National de la Recherche Scientifique, Université de Montpellier, Université Paul-Valéry Montpellier, Ecole Pratique des Hautes Études, Montpellier Cedex 5, France
| | - Pierre-Yves Henry
- Mécanismes adaptatifs et évolution (MECADEV UMR 7179), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Brunoy, France
- Centre de Recherches sur la Biologie des Populations d'Oiseaux (CRBPO), Centre d'Ecologie et des Sciences de la Conservation (CESCO UMR 7204), Muséum National d'Histoire Naturelle, Centre National de la Recherche Scientifique, Sorbonne Université, CP135, Paris, France
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Emery SE, Klapwijk M, Sigvald R, Bommarco R, Lundin O. Cold winters drive consistent and spatially synchronous 8-year population cycles of cabbage stem flea beetle. J Anim Ecol 2023; 92:594-605. [PMID: 36484622 DOI: 10.1111/1365-2656.13866] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Accepted: 11/29/2022] [Indexed: 12/14/2022]
Abstract
Population cycles have been observed in mammals as well as insects, but consistent population cycling has rarely been documented in agroecosystems and never for a beetle. We analysed the long-term population patterns of the cabbage stem flea beetle Psylliodes chrysocephala in winter oilseed rape over 50 years. Psylliodes chrysocephala larval density from 3045 winter oilseed rape fields in southern Sweden showed strong 8-year population cycles in regional mean density. Fluctuations in larval density were synchronous over time across five subregional populations. Subregional mean environmental variables explained 90.6% of the synchrony in P. chrysocephala populations at the 7-11 year time-scale. The number of days below -10°C showed strong anti-phase coherence with larval densities in the 7-11 year time-scale, such that more cold days resulted in low larval densities. High levels of the North Atlantic Oscillation weather system are coherent and anti-phase with cold weather in Scania, Sweden. At the field-scale, later crop planting date and more cold winter days were associated with decreased overwintering larval density. Warmer autumn temperatures, resulting in greater larval accumulated degree days early in the season, increased overwintering larval density. Despite variation in environmental conditions and crop management, 8-year cycles persisted for cabbage stem flea beetle throughout the 50 years of data collection. Moran effects, influenced by the North Atlantic Oscillation weather patterns, are the primary drivers of this cycle and synchronicity. Insect pest data collected in commercial agriculture fields is an abundant source of long-term data. We show that an agricultural pest can have the same periodic population cycles observed in perennial and unmanaged ecosystems. This unexpected finding has implications for sustainable pest management in agriculture and shows the value of long-term pest monitoring projects as an additional source of time-series data to untangle the drivers of population cycles.
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Affiliation(s)
- Sara E Emery
- Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden.,Department of Wildlife Fish and Conservation Biology, University of California Davis, Davis, California, USA
| | - Maartje Klapwijk
- Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Roland Sigvald
- Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Riccardo Bommarco
- Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden
| | - Ola Lundin
- Department of Ecology, Swedish University of Agricultural Sciences, Uppsala, Sweden
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Payo-Payo A, Igual JM, Sanz-Aguilar A, Real E, Genovart M, Oro D, Tavecchia G. Interspecific synchrony on breeding performance and the role of anthropogenic food subsidies. PLoS One 2022; 17:e0275569. [PMID: 36223369 PMCID: PMC9555664 DOI: 10.1371/journal.pone.0275569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2022] [Accepted: 09/20/2022] [Indexed: 11/07/2022] Open
Abstract
Synchrony can have important consequences for long-term metapopulations persistence, community dynamics and ecosystems functioning. While the causes and consequences of intra-specific synchrony on population size and demographic rates have received considerable attention only a few factors that may affect inter-specific synchrony have been described. We formulate the hypothesis that food subsidies can buffer the influence of environmental stochasticity on community dynamics, disrupting and masking originally synchronized systems. To illustrate this hypothesis, we assessed the consequences of European policies implementation affecting subsidy availability on the temporal synchrony of egg volume as a proxy of breeding investment in two sympatric marine top predators with differential subsidy use. We show how 7-year synchrony appears on egg volume fluctuations after subsidy cessation suggesting that food subsidies could disrupt interspecific synchrony. Moreover, cross correlation increased after subsidy cessation and environmental buffering seems to act during synchronization period. We emphasize that subsidies dynamics and waste management provide novel insights on the emergence of synchrony in natural populations.
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Affiliation(s)
- Ana Payo-Payo
- School of Biological Sciences, University of Aberdeen, Aberdeen, United Kingdom
- IMEDEA (CSIC-UIB), Esporles, Spain
- * E-mail:
| | - José-Manuel Igual
- IMEDEA (CSIC-UIB), Esporles, Spain
- Animal Demography and Ecology Unit (GEDA), IMEDEA (CSIC-UIB), Esporles, Spain
| | - Ana Sanz-Aguilar
- Animal Demography and Ecology Unit (GEDA), IMEDEA (CSIC-UIB), Esporles, Spain
- Applied Zoology and Conservation Group, University of Balearic Islands, Palma, Spain
| | - Enric Real
- Animal Demography and Ecology Unit (GEDA), IMEDEA (CSIC-UIB), Esporles, Spain
- Instituto Español de Oceanografía, Centre Oceanográfico de Baleares, Palma, Spain
| | | | - Daniel Oro
- IMEDEA (CSIC-UIB), Esporles, Spain
- CEAB (CSIC), Blanes, Spain
| | - Giacomo Tavecchia
- Animal Demography and Ecology Unit (GEDA), IMEDEA (CSIC-UIB), Esporles, Spain
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Barraquand F, Picoche C, Aluome C, Carassou L, Feigné C. Looking for compensation at multiple scales in a wetland bird community. Ecol Evol 2022; 12:e8876. [PMID: 35784078 PMCID: PMC9163198 DOI: 10.1002/ece3.8876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2021] [Revised: 11/21/2021] [Accepted: 12/09/2021] [Indexed: 11/30/2022] Open
Abstract
Compensatory dynamics, during which community composition shifts despite a near-constant total community size, are usually rare: Synchronous dynamics prevail in natural communities. This is a puzzle for ecologists, because of the key role of compensation in explaining the relation between biodiversity and ecosystem functioning. However, most studies so far have considered compensation in either plants or planktonic organisms, so that evidence for the generality of such synchrony is limited. Here, we extend analyses of community-level synchrony to wetland birds. We analyze a 35-year monthly survey of a community where we suspected that compensation might occur due to potential competition and changes in water levels, favoring birds with different habitat preferences. We perform both year-to-year analyses by season, using a compensation/synchrony index, and multiscale analyses using a wavelet-based measure, which allows for both scale- and time-dependence. We analyze synchrony both within and between guilds, with guilds defined either as tightknit phylogenetic groups or as larger functional groups. We find that abundance and biomass compensation are rare, likely due to the synchronizing influence of climate (and other drivers) on birds, even after considering several temporal scales of covariation (during either cold or warm seasons, above or below the annual scale). Negative covariation in abundance at the guild or community level did only appear at the scale of a few months or several years. We also found that synchrony varies with taxonomic and functional scale: The rare cases where compensation appeared consistently in year-to-year analyses were between rather than within functional groups. Our results suggest that abundance compensation may have more potential to emerge between broad functional groups rather than between species, and at relatively long temporal scales (multiple years for vertebrates), above that of the dominant synchronizing driver.
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Affiliation(s)
- Frédéric Barraquand
- Institute of Mathematics of BordeauxUniversity of Bordeaux and CNRSTalenceFrance
- Integrative and Theoretical EcologyLabEx COTEUniversity of BordeauxPessacFrance
| | - Coralie Picoche
- Institute of Mathematics of BordeauxUniversity of Bordeaux and CNRSTalenceFrance
- Integrative and Theoretical EcologyLabEx COTEUniversity of BordeauxPessacFrance
| | - Christelle Aluome
- Integrative and Theoretical EcologyLabEx COTEUniversity of BordeauxPessacFrance
- ISPABordeaux Sciences Agro & INRAEVillenave d'OrnonFrance
| | - Laure Carassou
- Integrative and Theoretical EcologyLabEx COTEUniversity of BordeauxPessacFrance
- EABXINRAECestasFrance
| | - Claude Feigné
- Teich Ornithological ReservePNR Landes GascogneLe TeichFrance
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6
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Liebhold AM, Björkman C, Roques A, Bjørnstad ON, Klapwijk MJ. Outbreaking forest insect drives phase synchrony among sympatric folivores: Exploring potential mechanisms. POPUL ECOL 2020. [DOI: 10.1002/1438-390x.12060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Andrew M. Liebhold
- USDA Forest Service Northern Research Station Morgantown West Virginia
- Czech University of Life Sciences Prague, Faculty of Forestry and Wood Sciences Suchdol Prague Czech Republic
| | - Christer Björkman
- Department of Ecology Swedish University of Agricultural Sciences Uppsala Sweden
| | - Alain Roques
- INRAE, UR 0633, Zoologie Forestière Orléans France
| | - Ottar N. Bjørnstad
- Departments of Entomology and Biology Pennsylvania State University University Park Pennsylvania
| | - Maartje J. Klapwijk
- Department of Ecology Swedish University of Agricultural Sciences Uppsala Sweden
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Ward SF, Aukema BH, Fei S, Liebhold AM. Warm temperatures increase population growth of a nonnative defoliator and inhibit demographic responses by parasitoids. Ecology 2020; 101:e03156. [PMID: 32740922 DOI: 10.1002/ecy.3156] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Revised: 06/01/2020] [Accepted: 06/19/2020] [Indexed: 11/06/2022]
Abstract
Changes in thermal regimes that disparately affect hosts and parasitoids could release hosts from biological control. When multiple natural enemy species share a host, shifts in host-parasitoid dynamics could depend on whether natural enemies interact antagonistically vs. synergistically. We investigated how biotic and abiotic factors influence the population ecology of larch casebearer (Coleophora laricella), a nonnative pest, and two imported parasitoids, Agathis pumila and Chrysocharis laricinellae, by analyzing (1) temporal dynamics in defoliation from 1962 to 2018, and (2) historical, branch-level data on densities of larch casebearer and parasitism rates by the two imported natural enemies from 1972 to 1995. Analyses of defoliation indicated that, prior to the widespread establishment of parasitoids (1962 to ~1980), larch casebearer outbreaks occurred in 2-6 yr cycles. This pattern was followed by a >15-yr period during which populations were at low, apparently stable densities undetectable via aerial surveys, presumably under control from parasitoids. However, since the late 1990s and despite the persistence of both parasitoids, outbreaks exhibiting unstable dynamics have occurred. Analyses of branch-level data indicated that growth of casebearer populations, A. pumila populations, and within-casebearer densities of C. laricinellae-a generalist whose population dynamics are likely also influenced by use of alternative hosts-were inhibited by density dependence, with high intraspecific densities in one year slowing growth into the next. Casebearer population growth was also inhibited by parasitism from A. pumila, but not C. laricinellae, and increased with warmer autumnal temperatures. Growth of A. pumila populations and within-casebearer densities of C. laricinellae increased with casebearer densities but decreased with warmer annual maximum temperatures. Moreover, parasitism by A. pumila was associated with increased growth of within-casebearer densities of C. laricinellae without adverse effects on its own demographics, indicating a synergistic interaction between these parasitoids. Our results indicate that warming can be associated with opposing effects between trophic levels, with deleterious effects of warming on one natural enemy species potentially being exacerbated by similar impacts on another. Coupling of such parasitoid responses with positive responses of hosts to warming might have contributed to the return of casebearer outbreaks to North America.
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Affiliation(s)
- Samuel F Ward
- Department of Forestry and Natural Resources, Purdue University, West Lafayette, Indiana, 47907, USA
| | - Brian H Aukema
- Department of Entomology, University of Minnesota, Saint Paul, Minnesota, 55108, USA
| | - Songlin Fei
- Department of Forestry and Natural Resources, Purdue University, West Lafayette, Indiana, 47907, USA
| | - Andrew M Liebhold
- USDA Forest Service, Northern Research Station, Morgantown, West Virginia, 26505, USA.,Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, CZ 165 21, Praha 6-Suchdol, Czech Republic
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Dallas TA, Antão LH, Pöyry J, Leinonen R, Ovaskainen O. Spatial synchrony is related to environmental change in Finnish moth communities. Proc Biol Sci 2020; 287:20200684. [PMID: 32453988 DOI: 10.1098/rspb.2020.0684] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Spatially distinct pairs of sites may have similarly fluctuating population dynamics across large geographical distances, a phenomenon called spatial synchrony. However, species rarely exist in isolation, but rather as members of interactive communities, linked with other communities through dispersal (i.e. a metacommunity). Using data on Finnish moth communities sampled across 65 sites for 20 years, we examine the complex synchronous/anti-synchronous relationships among sites using the geography of synchrony framework. We relate site-level synchrony to mean and temporal variation in climatic data, finding that colder and drier sites-and those with the most drastic temperature increases-are important for spatial synchrony. This suggests that faster-warming sites contribute most strongly to site-level estimates of synchrony, highlighting the role of a changing climate to spatial synchrony. Considering the spatial variability in climate change rates is therefore important to understand metacommunity dynamics and identify habitats which contribute most strongly to spatial synchrony.
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Affiliation(s)
- Tad A Dallas
- Department of Biological Science, Louisiana State University, Baton Rouge, LA, USA.,Organismal and Evolutionary Biology Research Programme, University of Helsinki, PO Box 65, FI-00014, Finland
| | - Laura H Antão
- Organismal and Evolutionary Biology Research Programme, University of Helsinki, PO Box 65, FI-00014, Finland
| | - Juha Pöyry
- Finnish Environment Institute (SYKE), Biodiversity Centre, Latokartanonkaari 11, FI-00790 Helsinki, Finland
| | - Reima Leinonen
- Kainuu Centre for Economic Development, Transport and the Environment, PO Box 115, FI-87101 Kajaani, Finland
| | - Otso Ovaskainen
- Organismal and Evolutionary Biology Research Programme, University of Helsinki, PO Box 65, FI-00014, Finland.,Centre for Biodiversity Dynamics, Department of Biology, Norwegian University of Science and Technology, 7491 Trondheim, Norway
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Temporal patterns of dispersal-induced synchronization in population dynamics. J Theor Biol 2020; 490:110159. [PMID: 31954109 DOI: 10.1016/j.jtbi.2020.110159] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Revised: 01/08/2020] [Accepted: 01/10/2020] [Indexed: 11/24/2022]
Abstract
The mechanisms and properties of synchronization of oscillating ecological populations attract attention because it is a fairly common phenomenon and because spatial synchrony may elevate a risk of extinction and may lead to other environmental impacts. Conditions for stable synchronization in a system of linearly coupled predator-prey oscillators have been considered in the past. However, the spatial dispersal coupling may be relatively weak and may not necessarily lead to a stable, complete synchrony. If the coupling between oscillators is too weak to induce a stable synchrony, oscillators may be engaged into intermittent synchrony, when episodes of synchronized dynamics are interspersed with the episodes of desynchronized dynamics. In the present study we consider the temporal patterning of this kind of intermittent synchronized dynamics in a system of two dispersal-coupled Rosenzweig-MacArthur predator-prey oscillators. We consider the properties of the distributions of durations of desynchronized intervals and their dependence on the model parameters. We show that the temporal patterning of synchronous dynamics (an ecological network phenomenon) may depend on the properties of individual predator-prey patch (individual oscillator) and may vary independently of the strength of dispersal. We also show that if the dynamics of predator is slow relative to the dynamics of the prey (a situation that may promote brief but large outbreaks), dispersal-coupled predator-prey oscillating populations exhibit numerous short desynchronizations (as opposed to few long desynchronizations) and may require weaker dispersal in order to reach strong synchrony.
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