2010
DOI: 10.3354/meps08691
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Multiple stable states and relationship between thresholds in processes and states

Abstract: The concept of thresholds is applied broadly in ecology to both processes and states that exhibit step-like behavior. Thresholds are observed in parameters, equilibrium states, and in states over time, but presence or absence of thresholds at any of these levels does not provide information about the occurrence of thresholds at the other levels. Here we explore the relationship between thresholds and theory of multiple stable states. We present a 2-species Lotka-Volterra model of competition to illustrate that… Show more

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Cited by 51 publications
(31 citation statements)
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References 59 publications
(98 reference statements)
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“…Ecologists have tended to emphasize phase shifts in time, especially for cases in which environmental changes, perhaps accrued over time, have caused abrupt and dramatic changes in species composition. An important example is the transition from corals to macroalgae observed on some coral reefs (Hughes 1994, Petraitis & Hoffman 2010. The essential feature characterizing a phase shift is that the shift in the community assemblage is caused by a persistent change or trend in the environment, because under each specified set of environmental conditions, there is only a single attractor, or equilibrial community.…”
Section: Phase Shiftsmentioning
confidence: 99%
See 1 more Smart Citation
“…Ecologists have tended to emphasize phase shifts in time, especially for cases in which environmental changes, perhaps accrued over time, have caused abrupt and dramatic changes in species composition. An important example is the transition from corals to macroalgae observed on some coral reefs (Hughes 1994, Petraitis & Hoffman 2010. The essential feature characterizing a phase shift is that the shift in the community assemblage is caused by a persistent change or trend in the environment, because under each specified set of environmental conditions, there is only a single attractor, or equilibrial community.…”
Section: Phase Shiftsmentioning
confidence: 99%
“…Petraitis & Latham (1999) described hypothetical scenarios in which a pulse of recruitment or mortality might move the system between basins of attraction in the absence of environmental variability. Lewontin (1969) and May (1977) (May 1977) or threshold curve (Petraitis & Hoffman 2010). The environments over which multiple stable equilibria exist determine hysteresis in the system.…”
Section: Alternative Stable Statesmentioning
confidence: 99%
“…It is worth emphasizing that, at either patch or ecosystem scale, such patterns in space and state shifts in time can exist in an environment otherwise characterized by smooth spatial gradients and smooth temporal change in background environmental conditions. Crossing thresholds in environmental conditions is not required [104]. Also, multiple states apparent at one scale are not necessarily dependent upon or transferrable to other scales [156].…”
Section: Significance Of Multiple Stable States In Observation and Mamentioning
confidence: 99%
“…As depicted, the conditions for the two states are not mutually exclusive: Within a range of values of the environmental parameter both states are possible. These are termed "alternative stable states" or "multiple stable states" (the two terms have been used interchangeably in the literature, e.g., see [101,104]). …”
Section: Theory Of Multiple Stable Ecosystem Statesmentioning
confidence: 99%
“…Wilson and Agnew 1992). However, this hypothesis is not universally accepted (e.g., Petraitis and Hoffman 2010).…”
Section: Discussionmentioning
confidence: 99%