Chaotic Dynamics in an Insect Population

Costantino, R. F.; Desharnais, Robert A.; Cushing, J. M.; Dennis, B. R.

doi:10.1126/science.275.5298.389

Cited by 394 publications

(331 citation statements)

References 12 publications

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“…The LPA model has been validated by means of a number of experiments, and has been used successfully to predict transitions between equilibria, periodic cy-cles, invariant loops, and chaos, as well as saddle phenomena and phase switching in population cycles (see Costantino et al, 1995Costantino et al, , 1997Costantino et al, , 1998Cushing et al, 1996Cushing et al, , 1998Dennis et al, 1995Dennis et al, , 1997Desharnais et al, 1997;Beniot et al, 1998;Henson et al, 1998). Henson and Cushing (1997) and Costantino et al (1998) modified the autonomous LPA model (1) to account for the periodic flour volume.…”

Section: The Modelmentioning

confidence: 99%

“…The α = 0 or constant 20 g habitat is commonly used in our laboratory and the projected 2-cycles are well documented (Moffa and Costantino, 1977;Desharnais and Costantino, 1980;Jillson, 1980;Costantino et al, 1995Costantino et al, , 1997. The α = 0.6 alternating 32-8 g habitat was used in the experiment conducted by Jillson (1980) and recently analysed by Henson and Cushing (1997) and Costantino et al (1998).…”

Section: Experimental Protocolmentioning

confidence: 99%

“…To explain this phenomenon, the discrete LPA Tribolium model of Dennis et al (1995Dennis et al ( , 1997 and Costantino et al (1995Costantino et al ( , 1997 was modified by Henson and Cushing (1997) and Costantino et al (1998) to account for the periodic flour volume. Cannibalism between life cycle stages is the nonlinear mechanism driving flour beetle dynamics in these experiments (Park et al, 1970).…”

Section: Introductionmentioning

confidence: 99%

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Multiple Attractors, Saddles, and Population Dynamics in Periodic Habitats

Henson

Costantino

Cushing

et al. 1999

Bulletin of Mathematical Biology

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1122 S. M. Henson et al.periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic habitats of fluctuating flour volume. Predictions included multiple (2-cycle) attractors, resonance and attenuation phenomena, and saddle influences. Stochasticity, combined with the deterministic effects of an unstable 'saddle cycle' separating the two stable cycles, is used to explain the observed transients and final states of the experimental cultures. In experimental regimes containing multiple attractors, the presence of unstable invariant sets, as well as stochasticity and the nature, location, and size of basins of attraction, are all central to the interpretation of data.

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Section: The Modelmentioning

confidence: 99%

Section: Experimental Protocolmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiple Attractors, Saddles, and Population Dynamics in Periodic Habitats

Henson

Costantino

Cushing

et al. 1999

Bulletin of Mathematical Biology

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“…Understanding the aspects and tendencies of complex population dynamics observed in natural ecosystems (Ellner and Turchin, 1995;Ranta et al, 1995;Widdicombe et al, 2010) as well as in the laboratory (Costantino et al, 1997;Yoshida et al, 2003;Becks et al 2005) is important for both theoretical and practical reasons, and indeed it has been a central point of ecological research for several decades (Nicholson, 1954;Luckinbill, 1974;Turchin, 2003;Odum and Barrett, 2004;Begon et al, 2005). Whilst empirical studies provide invaluable information such as, for instance, examples of different dynamics (Becks et al 2005;Yoshida et al, 2003), a theoretical approach is necessary in order to generalize and systematize the results of field observations or lab experiments.…”

Section: Introductionmentioning

confidence: 99%

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Морозов

Banerjee

Petrovskii

2016

Journal of Theoretical Biology

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Traditionally, mathematical modelling in population ecology is mainly focused on asymptotical behaviour of the model, i.e. as given by the system attractors. Recently, however, transient regimes and especially long-term transients have been recognized as playing a crucial role in the dynamics of ecosystems. In particular, long-term transients are a potential explanation of ecological regime shifts, when an apparently healthy population suddenly collapses and goes extinct.In this paper, we show that the interplay between delay in maturation and a strong Allee effect can result in long-term transients in a single species system. We first derive a simple 'conceptual' model of the population dynamics that incorporates both a strong Allee effect and maturation delay. Unlike much of the previous work, our approach is not empirical since our model is derived from basic principles. We show that the model exhibits a high complexity in its asymptotic dynamics including multi-periodic and chaotic attractors. We then show the existence of long-term transient dynamics in the system, when the population size oscillates for a long time between locally stable stationary states before it eventually settles either at the persistence equilibrium or goes extinct. The parametric space of the model is found to have a complex structure with the basins of attraction corresponding to the persistence and extinction states being of a complicated shape. This impedes the prediction of the eventual fate of the population, as a small variation in the maturation delay or the initial population size can either bring the population to extinction or ensure its persistence.3

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“…Although chaotic dynamics have not been reported for natural populations, there is now accumulating evidence from laboratory studies [18][19][20] and theory [21][22][23][24] underlining the potential role of chaos. In trying to understand the meaning of chaos for population dynamics, it is necessary to critically evaluate theoretical predictions by manipulative experiments and compare it with systems with cyclic dynamics.…”

mentioning

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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Chaotic Dynamics in an Insect Population

Cited by 394 publications

References 12 publications

Multiple Attractors, Saddles, and Population Dynamics in Periodic Habitats

Multiple Attractors, Saddles, and Population Dynamics in Periodic Habitats

Long-term transients and complex dynamics of a stage-structured population with time delay and the Allee effect

Different types of synchrony in chaotic and cyclic communities

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