Wave of Chaos: New Mechanism of Pattern Formation in Spatio-temporal Population Dynamics

Petrovskii, Sergei; Malchow, Horst

doi:10.1006/tpbi.2000.1509

Cited by 205 publications

(125 citation statements)

References 38 publications

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“…In a number of previous studies, self-organized patchiness and spatiotemporal chaos in predator-prey systems (with apparent application to plankton dynamics) have been reported [e.g., 7,24,32]. On one hand, the results of the present study potentially give an extension of the conceptual results of those studies onto a three-species model plankton system.…”

Section: Discussionsupporting

confidence: 52%

“…However, because the dispersals of the species in a planktonic system are due to turbulent mixing, an assumption of unequal diffusivity might be unlikely. Moreover, Turing instability results in stationary and regular patterns, whereas, in a real-world plankton community, the spatial patterns observed are nonstationary and irregular [7,24]. Following these observations, it is fair to investigate the dynamics of NTP-TPP species under equal diffusivity assumptions…”

Section: A Reaction-diffusion Model Of Two Ntp Species and A Tpp Speciesmentioning

confidence: 94%

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Spatial Interaction Among Nontoxic Phytoplankton, Toxic Phytoplankton, and Zooplankton: Emergence in Space and Time

Roy

2008

J Biol Phys

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In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity-a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reactiondiffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

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Section: Discussionsupporting

confidence: 52%

Section: A Reaction-diffusion Model Of Two Ntp Species and A Tpp Speciesmentioning

confidence: 94%

Spatial Interaction Among Nontoxic Phytoplankton, Toxic Phytoplankton, and Zooplankton: Emergence in Space and Time

Roy

2008

J Biol Phys

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“…For D 1, the model describes pattern formation: the initial conditions evolve to a function with a complicated, multi-peak structure (see Fig. 21c), smaller values of D result in a larger number of peaks in the domain [123,124].…”

Section: Evaluation Of Population Abundance On Coarse Gridsmentioning

confidence: 99%

“…either smooth patterns in space (e.g. periodical) combined with periodical oscillations in time or spatiotemporal chaos [123], the latter also being known as the "biological turbulence" [88].…”

Section: Ipm Tacticsmentioning

confidence: 99%

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Petrovskii

Petrovskaya

Bearup

2014

Physics of Life Reviews

104

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Pest insects pose a significant threat to food production worldwide resulting in annual losses worth hundreds of billions of dollars. Pest control attempts to prevent pest outbreaks that could otherwise destroy a sward. It is good practice in integrated pest management to recommend control actions (usually pesticides application) only when the pest density exceeds a certain threshold. Accurate estimation of pest population density in ecosystems, especially in agro-ecosystems, is therefore very important, and this is the overall goal of the pest insect monitoring. However, this is a complex and challenging task; providing accurate information about pest abundance is hardly possible without taking into account the complexity of ecosystems' dynamics, in particular, the existence of multiple scales. In the case of pest insects, monitoring has three different spatial scales, each of them having their own scale-specific goal and their own approaches to data collection and interpretation. In this paper, we review recent progress in mathematical models and methods applied at each of these scales and show how it helps to improve the accuracy and robustness of pest population density estimation.

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“…An alternative mechanism is sometimes referred to as biological turbulence 1 or a wave of chaos (Petrovskii and Malchow 2001) which becomes possible when the dynamics of the interacting species are oscillatory. From a theoretical perspective, this is usually related to the existence of a stable limit cycle, e.g.…”

Section: Introductionmentioning

confidence: 99%

Delay driven spatiotemporal chaos in single species population dynamics models

Jankovic

Petrovskii

Banerjee

2016

Theoretical Population Biology

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Questions surrounding the prevalence of complex population dynamics form one of the central themes in ecology. Limit cycles and spatiotemporal chaos are examples that have been widely recognised theoretically, although their importance and applicability to natural populations remains debatable. The ecological processes underlying such dynamics are thought to be numerous, though there seems to be consent as to delayed density dependence being one of the main driving forces. Indeed, time delay is a common feature of many ecological systems and can signi cantly in uence population dynamics. In general, time delays may arise from interand intra-speci c trophic interactions or population structure, however in the context of single species populations they are linked to more intrinstic biological phenomena such as gestation or resource regeneration. In this paper, we consider theoretically the spatiotemporal dynamics of a single species population using two di erent mathematical formulations. Firstly, we revisit the di usive logistic equation in which the per capita growth is a function of some speci ed delayed argument. We then modify the model by incorporating a spatial convolution which results in a biologically more viable integro-di erential model. Using the combination of analytical and numerical techniques, we investigate the e ect of time delay on pattern formation. In particular, we show that for su ciently large values of time delay the system's dynamics are indicative to spatiotemporal chaos. The chaotic dynamics arising in the wake of a travelling population front can be preceded by either a plateau corresponding to dynamical stabilisation of the unstable equilibrium or by periodic oscillations.

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Wave of Chaos: New Mechanism of Pattern Formation in Spatio-temporal Population Dynamics

Cited by 205 publications

References 38 publications

Spatial Interaction Among Nontoxic Phytoplankton, Toxic Phytoplankton, and Zooplankton: Emergence in Space and Time

Spatial Interaction Among Nontoxic Phytoplankton, Toxic Phytoplankton, and Zooplankton: Emergence in Space and Time

Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks

Delay driven spatiotemporal chaos in single species population dynamics models

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