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Journal ArticleDOI

Experimentally induced transitions in the dynamic behaviour of insect populations

TL;DR: A simple model describing population growth in the flour beetle Tribolium was developed and it was predicted that changes in adult mortality would produce substantial shifts in population dynamic behaviour, and changes in the dynamics from stable fixed points to periodic cycles to aperiodic oscillations were observed.
Abstract: SIMPLE nonlinear models can generate fixed points, periodic cycles and aperiodic oscillations in population abundance without any external environmental variation Another familiar theoretical result is that shifts in demographic parameters (such as survival or fecundity) can move a population from one of these behaviours to another1–4 Unfortunately, empirical evidence to support these theoretical possibilities is scarce5–15 We report here a joint theoretical and experimental study to test the hypothesis that changes in demographic parameters cause predictable changes in the nature of population fluctuations Specifically, we developed a simple model describing population growth in the flour beetle Tribolium16 We then predicted, using standard mathematical techniques to analyse the model, that changes in adult mortality would produce substantial shifts in population dynamic behaviour Finally, by experimentally manipulating the adult mortality rate we observed changes in the dynamics from stable fixed points to periodic cycles to aperiodic oscillations that corresponded to the transitions forecast by the mathematical model
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Book
07 Nov 1996
TL;DR: One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.
Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.

1,924 citations

Reference EntryDOI
25 Apr 2001
TL;DR: The most exotic form of nonlinear dynamics is Chaos as mentioned in this paper, in which deterministic interactions produce apparently irregular fluctuations, and small changes in the initial state of the system are magnified through time.
Abstract: Nonlinear dynamics deals with more-or-less regular fluctuations in system variables caused by feedback intrinsic to the system (as opposed to external forces). Chaos is the most exotic form of nonlinear dynamics, in which deterministic interactions produce apparently irregular fluctuations, and small changes in the initial state of the system are magnified through time.7 Keywords: chaos; population cycles; population dynamics; nonlinear time-series analysis

1,190 citations


Cites background or methods from "Experimentally induced transitions ..."

  • ...For example, Constantino et al. (1995) induced transitions between equilibrium and cyclic dynamics in laboratory populations of the flour beetle (Tribolium castaneum) by artificially increasing the adult mortality rate....

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  • ...The Tribolium study used a mechanistic model to make predictions (which were sometimes confirmed) about the qualitative changes in dynamics as the mortality rate was varied (Constantino et al., 1995)....

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  • ...For example, Constantino et al. (1995) induced transitions between equilibrium and cyclic dynamics in laboratory populations of the flour beetle (Tribolium castaneum) by artificially increasing the adult mortality rate. In contrast, Nicholson stabilized the blowfly cycles by increasing the juvenile death rate. Krebs et al. (1995) added food and reduced predation on snowshoe hares in 1 km(2) enclosures during the course of a cycle....

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Journal ArticleDOI
Mario Bunge1
TL;DR: In this paper, the authors elucidate the notions of explanation and mechanism, in particular of the social kind, and explain macro-micro-micro micro-macro social relations.
Abstract: The aim of this article is to elucidate the notions of explanation and mechanism, in particular of the social kind. A mechanism is defined as what makes a concrete system tick, and it is argued that to propose an explanation proper is to exhibit a lawful mechanism. The so-called covering law model is shown to exhibit only the logical aspect of explanation: it just subsumes particulars under universals. A full or mechanismic explanation involves mechanismic law statements, not purely descriptive ones such as functional relations and rate equations. Many examples from the natural, biosocial, and social sciences are examined. In particular, macro-micro-micro-macro social relations are shown to explain other wise puzzling macro-macro links. The last part of the article relates the author's progress, over half a century, toward understanding mechanism and explanation.

443 citations


Cites background from "Experimentally induced transitions ..."

  • ...For example, chaos has recently been induced experimentally by deliberately varying the mortality rate in an insect population (Costantino et al. 1995)....

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Journal ArticleDOI
TL;DR: The cause and implication of changes in population cycles in voles, grouse and insects in Europe are discussed, which are expected to imply collapses of important ecosystem functions, such as the pulsed flows of resources and disturbances.
Abstract: During the past two decades population cycles in voles, grouse and insects have been fading out in Europe. Here, we discuss the cause and implication of these changes. Several lines of evidence now point to climate forcing as the general underlying cause. However, how climate interacts with demography to induce regime shifts in population dynamics is likely to differ among species and ecosystems. Herbivores with high-amplitude population cycles, such as voles, lemmings, snowshoe hares and forest Lepidoptera, form the heart of terrestrial food web dynamics. Thus, collapses of these cycles are also expected to imply collapses of important ecosystem functions, such as the pulsed flows of resources and disturbances.

396 citations

Journal ArticleDOI
17 Jan 1997-Science
TL;DR: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior.
Abstract: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior. With the adult mortality rate experimentally set high, the dynamics of animal abundance changed from equilibrium to quasiperiodic cycles to chaos as adult-stage recruitment rates were experimentally manipulated. These transitions in dynamics corresponded to those predicted by the mathematical model. Phase-space graphs of the data together with the deterministic model attractors provide convincing evidence of transitions to chaos.

395 citations

References
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Journal ArticleDOI
10 Jun 1976-Nature
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Abstract: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

6,118 citations

Book
01 Jan 1990
TL;DR: Non-linear least-squares prediction based on non-linear models and case studies and an introduction to dynamical systems.
Abstract: Preface Acknowlegement Introduction 1. An introduction to dynamical systems 2. Some non-linear time series models 3. Probability structure 4. Statistical aspects 5. Non-linear least-squares prediction based on non-linear models 6. Case studies

2,209 citations

Book
01 Jan 1968

1,481 citations

Journal ArticleDOI
15 Nov 1974-Science
TL;DR: This paper presents a dynamical regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur.
Abstract: Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between 2 population points, to stable cycles with 4, 8, 16, . . . points, through to a chaotic regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur. This rich dynamical structure is overlooked in conventional linearized analyses; its existence in such fully deterministic nonlinear difference equations is a fact of considerable mathematical and ecological interest.

1,456 citations