Ecological outbreak dynamics and the cusp catastrophe

Rose, Michael R.; Harmsen, R.

doi:10.1007/bf00051769

Cited by 26 publications

(13 citation statements)

References 20 publications

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“…Insect outbreaks (Harmsen et al, 1976;Ludwig et al, 1978;Rose & Harmsen, 1981) and transitions between clear and turbid states in shallow lakes (Scheffer, 1990;Scheffer et al, 1993) are known to be good examples for the application of the catastrophe theory in ecology. Our model has suggested that the catastrophe theory is also applicable to the vertical pattern formation of phytoplankton especially when there exists a well-defined seasonal thermocline.…”

Section: Applicability Of Catastrophe Theory For Vertical Distributiomentioning

confidence: 98%

Catastrophic Transition in Vertical Distributions of Phytoplankton: Alternative Equilibria in a Water Column

Yoshiyama

Nakajima

2002

Journal of Theoretical Biology

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Section: Applicability Of Catastrophe Theory For Vertical Distributiomentioning

confidence: 98%

Catastrophic Transition in Vertical Distributions of Phytoplankton: Alternative Equilibria in a Water Column

Yoshiyama

Nakajima

2002

Journal of Theoretical Biology

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“…1989; Bazely & Jefferies 1996; Rietkerk & Van de Koppel 1997). When vegetation change is a non‐linear process with apparent discontinuities (Rose & Harmsen 1981), or a series of threshold responses between meta‐stable states (Westoby et al . 1989; Rietkerk & Van de Koppel 1997), restoration efforts require knowledge of the various variables that need to be manipulated in order to achieve state transitions (Hobbs 1994; Hobbs & Norton 1996).…”

Section: Introductionmentioning

confidence: 99%

Patterns of vegetation change and the recovery potential of degraded areas in a coastal marsh system of the Hudson Bay lowlands

2002

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Summary 1In recent decades, foraging by increasing numbers of lesser snow geese has led to loss of vegetation and changes in soil conditions in marshes on the Hudson Bay coast. 2 Changes in species composition were recorded in areas unprotected from goose foraging and in exclosures of varying age (5-15 years) erected in intact swards and on bare sediments where foraging had occurred at La Pérouse Bay, Manitoba. 3 In the supratidal marsh, plants failed to establish naturally in either open or exclosed (15 years) plots in bare areas. In moist intertidal soils, vegetative fragments of the asexual species Puccinellia phryganodes readily established and formed a mat in exclosures (5 years). 4 Changes in species assemblages occurred over 11 years in exclosed and adjacent open plots in intertidal and supratidal marshes. Loss of vegetation cover and species richness, particularly dicotyledonous species, and the reversion of later successional plant assemblages to earlier successional assemblages occurred in open plots. In the absence of foraging, late successional graminoids and willow species replaced early successional graminoids. 5 Late successional grasses of the upper intertidal marsh died when transplanted into degraded soils but still survived after one season in control plots, suggesting that an early successional template is needed for establishment. 6 In the absence of goose foraging, natural re-vegetation by clonal propagation can occur only where edaphic conditions are suitable. Within exclosures, vegetation changes resemble those in undamaged areas where goose foraging pressure is still moderate. We propose a state and transition model for vegetation change in the system based on succession patterns, alternative vegetation states and geomorphological events.

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“…Large-scale outbreaks and similar oscillations, particularly of pest species, are seen as undesirable, in part because of their economic implications. This is the context of papers by Jones (1977), Rose and Harmsen (1981) and Casti (1982). The last, relating (as does Jones' analysis) to the spruce budworm, is notable for its conclusion that the sought-for goal is not always attainable.…”

Section: Ecological Studiesmentioning

confidence: 99%

Catastrophe modelling in the biological sciences

Deakin

1990

Acta Biotheor

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Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional "physical" way, it could also be applied in a new "metaphysical" way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology. Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised. This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.

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Ecological outbreak dynamics and the cusp catastrophe

Cited by 26 publications

References 20 publications

Catastrophic Transition in Vertical Distributions of Phytoplankton: Alternative Equilibria in a Water Column

Catastrophic Transition in Vertical Distributions of Phytoplankton: Alternative Equilibria in a Water Column

Patterns of vegetation change and the recovery potential of degraded areas in a coastal marsh system of the Hudson Bay lowlands

Catastrophe modelling in the biological sciences

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