6.3 Ecosystem stability

6.3.1 Scheffer, 2001

“Catastrophic shifts in ecosystems” (Scheffer et al. 2001)

Key contribution: This article focuses on observed large-scale shifts in major ecosystems and their explanations. They provide both a theoretical framework for understanding catastrophic shifts, as well as an overview of results from different ecosystems with highlights of different patterns and implications for management.

Key notes:

Theoretical framework:

Catastrophic shifts occur abruptly, and thus “early-warning signals” of approaching catastrophic change are difficult to gather.

Conceptualization of ecosystem response curve as “folded backwards” implies that for certain environmental conditions, ecosystem may have two alternative stable states that are separated by an unstable equilibrium.

The “catastrophic shift” is the point at which the bifurcation point is passed and the system shifts from a stable state either to an unstable state or to an alternative stable state.

This has large implications for the state at which a system exists in, as well as restorative action to return it to a desired state (as returning conditions to original state may not be sufficient).

“Hysteresis” - memory of the system; the path back to a pre-existing state is not simply achieved through reversing the changes that brought about the shifts in states.

“Resilience” - as defined by Holling is the size of the valley, or basin of attraction around a state, which corresponds to maximum perturbation that can be taken without causing a shift to an alt stable state.

Gradually shifting environmental parameters may not induce a change in state, but may greatly impact the “resilience” of a particular basin of attraction.

Examples:

Lakes - One of the most common examples is loss of water clarity and vegetation due to eutrophication in shallow lakes. A threshold appears to exist in which below that, nutrients have no effect but above it they induce stark state shifts.

Hysteresis can be exemplified here as reduction in nutrient concentrations is not sufficient to reduce vegetation and return clarity to lake water.

Desertification - Presence of desert versus vegetated landscapes may be conceived of as alternative stable states. May occur through time as vegetation promotes more moist conditions and lack of vegetation promotes drier conditions. May have feedbacks with the climate in the Sahel region that produce alternating stable states.

Emerging patterns

The strongest cases for existence of alternative stable states are based on combinations of approaches, e.g., observations of repeated shifts, feedback mechanisms that maintain different states, or models showing mechanisms that plausibly explain field data.

Contrasts in ecosystem states are commonly seen by shifts in dominance of organisms with different life forms.

Feedbacks that stabilize different ecosystem states may involve biological, physical, and/or chemical mechanisms.

Critically, invisible impacts, for example anthropogenic effects, may not induce state shifts but may greatly impact the resilience of particular alternative stable states.

Management implications

Resilience often depends on variables that change slowly over time, and thus may be more easily “managed”. Sharp perturbations are less predictable and thus are more difficult to manage. Thus, maintaining resilience is likely the most pragmatic means of managing ecosystems.

Ultimately, this requires long-term monitoring of a variety of environmental parameters. Detection of EWS may be difficult and thus need long-term datasets to see changes in system behavior.

6.3.2 Beisner et al, 2003

“Alternative stable states in ecology” (Beisner, Haydon, and Cuddington 2003)

Key significance: This article provides a nice review of the theory surrounding alternative stable states as they relate to ecology.

Key notes:

The idea is credited first to Lewontin, 1969, but two other seminal works are Holling, 1973 and May, 1977.

Theoretical ecologists largely view alternative stable states and the pressures on the resilience of systems in two different conceptual ways:

1. Different states exist simultaneously under same conditions and shifts between the two states are due to a sufficiently large perturbation (variable shifts)
2. Change in the parameters that determine behavior of state variables and the ways they interact with each other (parameter shifts)
   • generally occur due to shifts in environmental “drivers” influencing communities

Variable shifts

Perturbations to state variables commonly thought of via two separate “classes” of alternative stable states:

1. Alternative interior states - involves nonlinearity in the transformation of the state such that multiple stable points exist within the system (local stability does not imply global stability)
2. Incorporates boundary states (one or more species may be absent) - if systems of equations are linear, only one stable composition is possible with all species represented… but may have other stable points in which some of the species are missing.

Shifts in parameters

Parameters are defined as “environmental drivers”.

Each state is considered stable but associated dynamics (local stability, population fluctuations) are different given that they correspond to different parameter values.

Given that the “landscape” changes, not all potential alternative stable states exist or may be present at all times.

Hysteresis - the dependence of the state of a system on its history (i.e., memory); “hysteresis is revealed if the return trajectory of the equilibrium point differs from that adopted during its outward journey” <- here the outward journey is influencing the system (i.e., it “remembers” its return) and thus it may be seen that the system exhibits a different return trajectory.

6.3.3 Biggs, 2009

“Turning back from the brink: Detecting an impending regime shift in time to avert it” (Biggs, Carpenter, and Brock 2009)

Key contribution: This article examines the “timing” of an early warning signal. It is motivated under the premise that EWS may occur as a system approaches a bifurcation point, but it is unclear whether or not effective management action may be taken in time to avert a regime shift.

They explore:

1. How close ecosystems can get to ecological thresholds and still avert regime shifts
2. Which regime shift indicators might give warning before “no point of return”

Key notes:

The underlying drivers that reduce resilience in systems are often associated with economic gains and thus there may be considerable long-term or short-term pressure on them.

The findings indicate that if the pressure can be immediately reduced, then action even during the beginning stages of a regime shift might be effective enough to avert the actual shift, or prevent transitioning to alternative stable state. For pressures that take much longer to reduce, then action must be taken considerably before the regime shift begins to occur.

EWS such as increases in variance, skewness, kurtosis and AR1 coefficient occur during “policy window” (i.e., the time in which action is still effective) for fast-actions, but only begin to occur after the policy window for slow actions has already closed.

Regime shifts that occur through slow-change of underlying variables occur via bifurcations: small gradual changes can cause abrupt qualitative changes in long-term behavior due to appearance or disappearance of attractors.

Key finding is that within environmental management, there are key windows in which action must be taken to avert shifts. The authors note that this window and the efficacy of different policies over time are rarely taken into consideration.

In managing ecosystems, likely have variables that can be altered both quickly as well as those that change more slowly with time. Thus, may be able to “buy time” in altering the more reactive variables while progress is made on the slower-moving variables.

Their findings show that some of the EWS indicators from Scheffer, 2009 might not be effective from a time-perspective. They use a spectral density ratio, which can be expressed in absolute terms and may be effective in identifying switches in attractors.

Example provided by authors

The authors provide an example of fisheries management, with different pressures that influence state variables at different time scales:

1. Limit on how much fishing is allowed
2. Preservation of sheltering habitat for juvenile piscivorous fish

For the first, the time-scale over which it may take effect is much faster and thus may be able to use it to “buy time” or alter state conditions such that regime shifts are avoided.

Given the time needed for the second (preserving sheltering habitat), the process is much slower and often times EWS may become apparent at too late of a time for changes in these variables to improve resilience and avoid a regime shift.

6.3.4 Scheffer, 2009

“Early-warning signals for critical transitions” (Scheffer et al. 2009)

Key contribution: This paper follows up on Scheffer 2001 in that it addresses the issue of actually identifying early warning signals. The key issue here is predicting critical transitions, which is no easy task, may be facilitated by certain generic symptoms that occur as a system approaches a critical point.

Key notes:

One of the key ideas behind this article is that there are several “generic” early warning signals that are consistent across systems (finance, health, environment) that may be employed as indicators of potential regime shifts. This study reviews them here as well as provides several key examples.

One other that they do not discuss but has shown up in other literature and may be relevant for intertidal ecosystems is:

1. Self-organized patchiness (see Section 6.5.2).

Bifurcations:

Catastrophic bifurcations - once a threshold is exceeded, a positive feedback propels system through phase of directional change towards contrasting state.

Other important bifurcations include those that mark transitions from stable equilibrium to cyclic or chaotic attractor.

Theory:

“Critical slowing down and its symptoms” - recovery rate of the system as it approaches a critical bifurcation can be used as an indicator of how close the system is to said bifurcation point. The rate of change is the criteria (approaches 0 with increasing proximity to critical bifurcation), and thus there is not a risk of pushing a system into an alternative stable state. Key symptoms are:

1. Slowing down - slowing down leads to increase in autocorrelation in resulting pattern of fluctuations
2. Increased autocorrelation - slowing down causes intrinsic rates of change to decrease, thus state of system increasingly resembles previous state (i.e., memory of system; can be seen through lag-1 autocorrelation)
3. Increased variance - increased variance in pattern of fluctuations; given lagged response time, the effects of shocks become additive, increasing variance.

Although it may be difficult to examine experimentally, we can use the presence of natural perturbations to examine recovery rate.

“Skewness and flickering”:

• Skewness - asymmetry of fluctuations; characterized by the state existing in the unstable side of a bifurcation point longer than the stable side (refers to directionality of approach to bifurcation point)
• Flickering - occurs when stochastic forcing pushes the state back and forth between the basins of attraction; considered early warning because system may permanently shift to alternative stable state

“Cyclic and chaotic systems” - may have transitions from stable systems to oscillatory systems; signaled by critical slowing down characterized by long transient oscillations

“Spatial patterns as warning signals” - may have increased cross-correlation or spatial coherence among units before a critical event (e.g., presence of species in adjacent patch habitats)

Examples:

Climate is one of most commonly examined as a messy “real-world” system. Analyses indicate that EWS may exist for abrupt shifts in climate (from tropical to ice-age). For example, increases in autocorrelation have been found, as well as flicking prior to Younger Dryas cold period.

6.3.5 Boettiger, 2012

“Quantifying limits to detection of early warning for critical transitions” (Boettiger and Hastings 2012)

Key significance: This paper discusses the uncertainty and failures of simple statistical means of EWS in alternative stable state theory. They make the case for a model-based approach, which can help alleviate many of the shortcomings of a purely statistical approach.

Key notes:

Summary statistics approach commonly employs increasing trend in summary stats such as variance, autocorrelation, skew, or spectral ratio.

Shortcomings of summary stats approaches

There are many hidden assumptions that occur with use of summary statistics.

For example, variance may increase for reasons that do not signal approaching transition.

Approaches based on increasing trends in summary stats assume a changing parameter has brought a system closer to a bifurcation. This assumption excludes at least three alternative explanations:

1. A large perturbation of the system state has moved system to alternative basin of attraction
   • this perturbation is exogenous to system and thus would not be expected to be predicted
2. Purely noise-induced transition, chance fluctuation that happens to carry system across the boundary
   • studies have shown it’s unlikely EWS are able to detect these
3. System may pass through saddle-node bifurcation, but in rapid or highly nonlinear way making detection of gradual trends impossible.

Given that we do not have replicate systems in which to examine EWS or regime shifts, often use shifting window applied to single replicate over time. This is an issue as selection of the window size and whether or how much to overlap are arbitrary decsisions.

Quantitative measures of early warning patterns do not exist.

Model-based approach

Read once through, but confused by math… need to go back and read a second time.

6.3.6 Moffett, 2015

“Multiple stable states and catastrophic shifts in coastal wetlands: Progress, challenges, and opportunities in validating theory using remote sensing and other methods” (Moffett et al. 2015)

Key contribution: This provides an overview of using remote sensing to examine different alternative stable states in coastal ecosystems. The article is potentially worth a second read, particularly the examples section in which they provide some details on systems outside of mangroves.

Key notes:

Applying multiple stable state theory

“Multiple stable ecosystem states are created by coupled positive and negative feedbacks that link the ecological, hydrological and geomorphological processes in the coastal wetland environment in a self-reinforcing and relatively resilient manner”

Alternative stable states in observation and management

Several characteristics of alternative stable states make them difficult to observe:

1. Impossible to uniquely define the system state with single observation points in time, but rather need knowledge of history of the system as well
2. Practical issue of scale in a system with potential alternative stable states; thus, need observations that span both time and space

Alternative stable states should give rise to two important and related phenomena:

1. Tendency for contrasting states to persist simultaneously along sharp boundary despite gradual change in underlying environmental conditions (“self-organized ecosystem patterning”)
   • May be induced by scale-dependent feedbacks
2. Ability of system to rapidly and wholly switch from one broad ecosystem state to another (“catastrophic ecosystem shift”)

Alternative stable states in mangroves

“Runaway sedimentation” - One mechanism of forming alternative stable states in mangrove systems; as mangroves expand, they induce sedimentation that may eventually limit their expansion, and thus may reach a new stable state wherein the shoreline is no longer prograding

Notion of alternative stable states may differ depending upon scale:

• At ecosystem scale may be cosnidered as mangroves vs. other coastal vegetated ecosystems
• Alternatively may also consider patch occurrence of different mangrove species or zonation

References

Scheffer, Marten, Steve Carpenter, Jonathan A Foley, Carl Folke, and Brian Walker. 2001. “Catastrophic shifts in ecosystems.” Nature 413: 591–96. doi:10.1038/35098000.

Beisner, Beatrix E, Daniel T Haydon, and Kim Cuddington. 2003. “Alternative Stable States in Ecology.” Frontiers in Ecology and the Environment 1 (7): 376–82. doi:10.1890/1540-9295(2003)001[0376:ASSIE]2.0.CO;2.

Biggs, Reinette, Stephen R Carpenter, and William A Brock. 2009. “Turning back from the brink: Detecting an impending regime shift in time to avert it.” Proceedings of the National Academy of Sciences 106 (3): 1–6.

Scheffer, Marten, Jordi Bascompte, William A Brock, Victor Brovkin, Stephen R Carpenter, Vasilis Dakos, Hermann Held, Egbert H Van Nes, Max Rietkerk, and George Sugihara. 2009. “Early-Warning Signals for Critical Transitions.” Nature 461 (7260): 53–59. doi:10.1038/nature08227.

Boettiger, Carl, and Alan Hastings. 2012. “Quantifying Limits to Detection of Early Warning for Critical Transitions.” Journal of the Royal Society Interface, rsif20120125. doi:10.1098/rsif.2012.0125.

Moffett, Kevan B, William Nardin, Sonia Silvestri, Chen Wang, and Stijn Temmerman. 2015. “Multiple Stable States and Catastrophic Shifts in Coastal Wetlands: Progress, Challenges, and Opportunities in Validating Theory Using Remote Sensing and Other Methods.” Remote Sensing 7 (8): 10184–10226. doi:10.3390/rs70810184.