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Ecological Modelling 248 (2013) 1– 10

Contents lists available at SciVerse ScienceDirect

Ecological Modelling

jo ur n al homep ag e: www.elsev ier .com/ locate /eco lmodel

eview

nterdisciplinary linkages of biophysical processes and resilience theory:ursuing predictability

hris Zell a,1, Jason A. Hubbartb,∗

University of Missouri, School of Natural Resources, Department of Forestry, Interdisciplinary Hydrology Laboratory, Columbia, MO, USAUniversity of Missouri, School of Natural Resources, Department of Forestry, 203-Q ABNR Building, Columbia, MO 65211, USA

r t i c l e i n f o

rticle history:eceived 14 May 2012eceived in revised form3 September 2012ccepted 25 September 2012vailable online 9 November 2012

eywords:esilienceiophysicscosystem, Stability, Energy balance

a b s t r a c t

The global value of ecosystem services is approximately $33 trillion per year. Given the economic value,it is not surprising that billions of dollars are spent annually to protect, preserve, restore and conservenatural resources. Resilience describes the ability of ecological systems to recover from disturbance.Resilient ecosystems remain productive and thus maintain services including biophysical processes thatare important for human well-being. Four system-wide characteristics, or biophysical signatures arereviewed, at least one of which is required to relate ecosystem structure or function to resilience. Bio-physical signatures include (a) variable material and energy recycling, (b) biodiversity, (c) the rate ofgoverning processes, and (d) bioenergetics. Fast recycling rates encourage ecosystem stability by damp-ening oscillations while slow recycling rates increase resistance by weakly propagating disturbances. Therole of biodiversity in stabilizing ecosystems may be viewed as either a functional redundancy whereincreased diversity resists perturbation by maintaining key ecosystem functions, or as response diver-sity that ensures recovery processes. Governing ecosystem processes that respond slowly, such as thoseinvolving large storage reservoirs, resist perturbation and shift to alternative states. Several observational

resilience studies featured bioenergetics as both the perturbation force (i.e., predation, food supply) andthe thermodynamic orientor that organizes recovery (i.e., maximizing exergy storage). An energy bal-ance approach is proposed as a possible method to assess ecosystem stability. Validating a mechanisticresilience model against high resolution data collected from a system undergoing regime shift is neededto advance theory toward practical application. As physical requirements bound the possibility space forecosystems, it is not surprising that biophysical processes play a central role in resilience theory.

© 2012 Elsevier B.V. All rights reserved.

ontents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22. Biophysical processes as essential services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Biophysical signatures of stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1. Recycling rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2. Diversity and complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.3. Governing rate processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.4. Stability as bioenergetic goal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4. Assessing stability: an energy balance approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75. Future research needs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

∗ Corresponding author. Tel.: +1 573 884 7732; fax: +1 573 882 1932.E-mail address: HubbartJ@Missouri.edu (J.A. Hubbart).

1 Tel.: +1 573 884 7732.

304-3800/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.ecolmodel.2012.09.021

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. Introduction

The global monetary value of ecosystem services has been esti-ated to be approximately $33 trillion per year (Costanza et al.,

997). It is therefore not surprising that sustaining ecosystemervices amidst multiple stressors or perturbations is a goal ofcosystem managers (Palmer et al., 2004; Vitousek et al., 1997).nsuccessful attempts to manage the human–ecosystem relation-

hip can result in ecosystem collapse. Ecosystem collapse occurshen stress and perturbation is severe enough to reduce or elim-

nate ecosystem services and threaten human welfare (Dobsont al., 2006). Previous examples of collapse include significanteclines in honey bee (Apis mellifera) pollination services discussedy Harries-Jones (2009) and deterioration of marine food and sportsheries (Jackson et al., 2001). Certainly, the five great mass extinc-ions represent the extreme of ecosystem collapse (Hallam, 2004).iven increasing human population pressures and the implica-

ions of ecosystem collapse for supporting the human population, aramework for predicting ecosystem collapse is increasingly desir-ble. Resilience theory (Holling, 1973) is gaining acceptance incological literature as a framework for interpreting ecosystemesponse to perturbation and characterizing conditions leading toollapse.

Resilience was introduced by Holling (1973) who later definedt in ecological terms (Holling, 1996) to describe the amount oferturbation or disturbance an ecological system can absorb with-ut transitioning to an alternate state or condition. The concept ofesilience derives from the observation that a given ecosystem canxist in multiple stable states (May, 1972, 1977) as systems evolvend adapt through time. Stable states that persist over time mayepresent conditions that are beneficial to human welfare such asoodplain ecosystems that are nourished by annual floods (Bayley,995) or detrimental such as loss of bottomland hardwood forestnd consequently floodplain flood attenuation capacity (Hubbartt al., 2011). Ecological resilience is contrasted with engineeringesilience which represents the return time between disturbancend a return to an original state or condition (Holling, 1996). Engi-eering resilience assumes the existence of a single (vs. multiple orlternative) stable state (Gunderson, 2000).

A ball and cup heuristic model (Fig. 1) is frequently used to illus-

rate the following descriptors of resilience theory (Carpenter et al.,001; Folke et al., 2004; Gunderson, 2000):

ig. 1. Ball and cup representation of ecosystem stability across the stability land-cape. Stability domains are represented by valleys.

implified from Folke et al. (2004).

Modelling 248 (2013) 1– 10

Adaptive Capacity – processes that shape the stability (i.e., returntime) and resilience of an ecosystem. With reference to Fig. 1,adaptive capacity is the net result of processes that determine theshape of the cup (e.g., slope, width, depth, volume). Also called thestability landscape.Persistence – qualities of a stability domain (i.e., cup in Fig. 1) thatresist changes in state, or shifts in regime. In the context of Fig. 1,persistence can be thought of as the arc length, height, or frictionforce within a single cup or stability domain.Precariousness – the proximity or trajectory of ecosystem state toa threshold that if crossed will result in regime shift. An ecosys-tem would be precariously positioned near a local maximum thatdifferentiates the two cups in Fig. 1.Regime Shift – the term regime shift is analogous to a shift in sta-bility domain. The length between adjacent local minima could beconsidered the regime wavelength in Fig. 1.Resilience – an ecosystem quality that describes how much dis-turbance can be absorbed without changing to an alternate state.Resilience can be thought of as the width of the cup in Fig. 1.Resistance – the magnitude of external forces needed to displace anecosystem a given amount. Resistance serves as a compliment toresilience in describing the ability of a system to absorb perturba-tion or remain stable. An ecosystem that is very resistant (difficultto move ball in Fig. 1) but low in resilience (narrow cup) may beas effective in preventing regime shift as a wider cup (i.e., greaterresilience) with moderate resistance.Stability – persistence of an ecosystem near or close to an equilib-rium state. A system is more likely to be stable when persistencefactors (e.g., cup height, arc length, etc.) are maximized.

While there appears to be widespread evidence that ecosys-tems can exist in multiple stable states, linking qualitative theory toquantitative application has been infrequently achieved (Carpenteret al., 2001; Scheffer and Carpenter, 2003; Groffman et al., 2006).A fundamental test in science is the ability of theory or conceptto predict outcomes in the general and specific sense (Hilbornand Mangel, 1997). To achieve such predictions, many studieshave applied mathematical models that are not calibrated againstdata from systems undergoing regime shift Therefore, a quantita-tive framework for integrating resilience theory into managementdecisions based on measurable ecosystem variables is needed tounderstand the principles that yield regime shift. The need forsuch a framework is pressing as undesirable stable states can beirreversible (Carpenter et al., 1999). An avenue of inquiry that holdspromise in predicting regime shift is the lens of biophysical pro-cesses.

Biophysical processes have been described or hypothesizedby some investigators as agents or surrogates for determiningresilience (Alberti, 2004; Carpenter et al., 2001). Biophysical pro-cesses describe the mechanisms whereby mass or energy exchangeinfluences biological systems. Cited biophysical–resilience rela-tionships include rainfall and grazing regimes that influence plantcommunities in savanna rangelands (Gunderson, 2000), transportof soil phosphorus in shaping transparency of freshwater lakes(Carpenter et al., 2001) and macroinvertebrate diversity statesinfluenced by the patchiness of energy and organic matter flowsin urban landscapes (Alberti, 2004).

Many biological populations exhibit cyclic behavior in responseto resource limitation and predation (Caughley and Sinclair, 1994).It is thus not surprising that Holling’s (2001) adaptive cycle model(Fig. 3) that characterizes the phases of resilience follows a sinu-soidal pattern. While certainly descriptive and insightful with

respect to socioecological interactions, the adaptive cycle modelis presently qualitative and thus not falsifiable in the predictivesense. Assembly of governing processes is a fundamental step inmodel development. Moving resilience theory toward quantitative

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se by environmental managers necessitates a predictive model.herefore, the overall objective of this brief review is to describeiophysical processes and linkages associated with resilience the-ry as a step in the model development process. To support thisbjective, we (a) describe ecosystem services (i.e., objective func-ions) maintained by resilient systems, (b) identify four biophysicalignatures associated with resilience case studies, (c) propose aelatively simple physically based method for ecosystem stabil-ty assessment, and (d) discuss research needs to further modelevelopment.

. Biophysical processes as essential services

The macroscale dependence of ecosystems on biophysical pro-esses may best be illustrated from the critical services perspective.ll 17 ecosystem services (see synopsis, Table 1) listed by Costanzat al. (1997), involve distinctly biophysical or biologically mediatedhysical processes. As will be shown later, the control of biologicalystems and trophic dynamics may be constrained by physical pro-esses (Hubbart, 2007). Presently however, a discussion of servicesost important to survival is warranted to underscore the impor-

ance of biophysical processes. These services include the qualitynd availability of food, water, and air supplies within a climateegime that supports biological activity.

Conversion of radiant energy into biomass (chemical poten-ial energy) via photosynthesis (i.e., primary production) formshe foundation of terrestrial and aquatic food webs (Townsendt al., 2000). Photosynthesis in green plants fixes CO2 and produces2. Physical atmospheric mixing, turbulence, and surface shearrocesses provide a steady supply of CO2 to support primary pro-uction in terrestrial and aquatic ecosystems. Atmospheric physicsovern transport of water vapor and production of precipitationeeded to support terrestrial vegetation (Dingman, 2002). Theseiophysical processes yield energy as food, and provide physicalabitat for consumers and higher ecosystem trophic levels.

The air and land phases of the hydrologic cycle produce precip-tation, surface, and groundwater supplies. Astrobiologists believe

ater may be the singularly most important determinant of bio-ogical life (Motti et al., 2007). Liquid water serves as an essential

able 1iophysical processes as ecosystem services.

Ecosystem service Biophysical description

Gas regulation Atmospheric balance of O2, CO2, NOX ,Climate regulation Biologically mediated temperature an

and soil moisture balances.Disturbance regulation and biologic control Reduce impact and recovery times fro

flows mediated by biological processeWater regulation and supply Biophysically coupled hydrologic cyclErosion control Soil retention by reducing rainfall kin

stress) as a result of vegetative densitSoil formation Weathering of parent material as conNutrient cycling Biologically mediated oxidation–redu

phosphorus, iron, and silicon.Waste treatment and water quality Biologically mediated reactions that dPollination Direct transport by wind of floral gam

frequent pollination contacts.Refugia Soil formation processes, vegetative d

development support habitats for terrFood production Conversion of solar energy into bioma

ecosystems.Raw materials Plant materials used as raw materials

processed plant material for paper.Genetic resources Physical environment needed to suppCultural resources Esthetic, artistic, and spiritual uses su

Maintenance of hydrologic and nutrieRecreation Includes healthy environment to supp

processes.

Modelling 248 (2013) 1– 10 3

medium for biochemical reactions and transport mechanism fornutrients (Voet et al., 2008). Terrestrial vegetation affects theland phase distribution of precipitation inputs through biophysi-cal processes including interception, root uptake, infiltration, andevapotranspiration (Arora, 2002). It can therefore be concludedthat water supplied by aquifers and streamflow to support humanwell-being is often modulated by plant physiologic requirementsand mechanisms. Biophysical pathways that regulate climate arenumerous and complex. These include absorption of greenhousegases where photosynthetic fixation of CO2 by terrestrial (IPCC,2001) and lotic (Downing et al., 2008) producers act as sinks ofcarbon. Sensible and latent heat fluxes produce turbulent mixingof the planetary boundary layer (West et al., 2011). Atmosphericmixing is necessary to provide a steady supply of oxygen for aero-bic metabolism and CO2 for primary photosynthesis (Campbell andNorman, 1998). Changes in these fluxes due to land use alteration(i.e., increased albedo and reduced evapotranspiration from defor-estation) can also influence regional temperature and precipitationpatterns (Gerten et al., 2004). Clearly, terrestrial vegetation, thehydrologic cycle, and regional climates are complex interconnectedbiophysical systems.

Climate regulation along with food, water, and energy suppliesare considered essential because these services are fundamen-tally coupled with homeostasis. The homeostasis concept suggeststhat organisms, communities, and ecosystems seek a stable state(Odum, 1969; Costanza, 1992; Reynolds, 2002). A homeosta-sis example at the organismal level is thermoregulation wheremetabolic and behavior modifications are used to maintain bodytemperatures within an acceptable physiological range termedthe thermal neutral zone (Young et al., 1989). An exampleof community-level homeostasis was identified by Ernest andBrown (2001) who investigated the bistability of a Kangaroorat (Dipodomys) community living in resource-limited condi-tions. Increased rainfall (water supply) changed the vegetationcommunity (biophysical process) such that several rat species

decreased in abundance or locally went extinct. Local colonizationby new rat species took the place of extirpated taxa (i.e., compen-satory dynamics) in the ecosystem energy flow thus exemplifyingecosystem-level stability and resilience (Reynolds, 2002).

etc. by photosynthesis, respiration, nitrification, etc. via turbulent transport.d precipitation regimes via greenhouse effects, transpiration, vegetation albedo,

m disturbance. The focus of this paper. Ecosystem energy and stoichiometrys that occur within homeostatic tolerance intervals.e as needed for drinking water, irrigation, fisheries maintenance.etic energy (interception) and increasing surface roughness (and critical sheary.trolled by climate and biological activity producing organic matter and acids.ction reactions for major elements including carbon, nitrogen, sulfur,

egrade harmful pollutants or uptake into removable biomass.etes, bioenergetics of insect pollinators require frequent feeding and thus

evelopment, woody debris transfers, photic zone maintenance, coral reefestrial and aquatic communities.ss via photosynthesis provides the energy foundation for terrestrial and aquatic

such as lumber, aged detritus as fuel, weathered parent material for roadways,

ort growth and propagation of medicinal plants and genetic materials.pported by biologically mediated attenuation and cleansing processes.nt cycles.ort eco-tourism, sport fishing, hiking, sailing, etc. Numerous biophysical

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. Biophysical signatures of stability

Biophysical processes serve as both the perturbation mecha-ism causing shifts among stable states as well as negative feedback

oops that maintain stability (Table 2). For example, temperatehallow lakes tend to exist in two alternate states, as clear waterr in turbid phase (Carpenter et al., 2001). Clear water transi-ions to the turbid phase as nutrient loading increases and rooted

acrophytes are replaced by phytoplankton. Nutrient loads (per-urbation) ultimately delivered to a lake are transported fromatershed source areas undergoing biologically mediated trans-

ormations and uptake in transport.Resilience of the clear water phase is provided by two biophys-

cal processes representing negative feedbacks. The first is waterolumn light attenuation, described by Beer’s law (Chapra, 1997),here rooted macrophytes light-limit phytoplankton and there-

ore better compete for available nutrient resources (Carpentert al., 2001). The second biophysical feedback is the build-up ofoil phosphorus in contributing watersheds. Soils may act as reser-oirs or sinks for imported nutrients, thus acting as a buffer againsterpetuated nutrient loading (Carpenter et al., 2001). Under contin-ous loading and fertilization, soils may reach nutrient saturationnd then serve as a positive feedback that drives transition to theurbid water phase (Taylor and Pionke, 2000). Nutrient saturatedoils along with internal nutrient cycling (Carpenter et al., 2001;urnberg, 1984) may then act as negative feedbacks to maintain

he turbid water state. The clear and turbid stable lake states featurehree commonalities or signatures of resilient states reported in theiterature (Table 2). These signatures include increased recyclingates, maintenance of diversity (Folke et al., 2004; Peterson et al.,998) and slow rates of processes governing transition betweentates (Bennett et al., 2005; Carpenter et al., 2001).

Bioenergetics broadly includes the study of energy flows, energyransformation, and thermodynamics in biological systems. In

any of the resilience examples listed in Table 2, the need for foodchemical potential energy) to support growth, reproduction, and

aintenance may act as the perturbation or stressor to a partic-lar trophic level. For example, livestock grazing pressures that

nfluence shrub versus grassland states in the Australian range-ands are driven by food needs of livestock and human populations.lternatively, boreal fir defoliation by spruce budworm is modu-

ated by density-dependent increases in avian predators that feedn the budworm (Peterson et al., 1998). The biotic response toerturbation or stress can similarly be considered a biophysicaleallocation of resources between organism energy budget com-artments (Congdon et al., 2001; Maltby, 1999).

The linkage between bioenergetics and ecosystem stability andevelopment was proposed by Lotka (1922) as the hypothesis ofaximum energy throughput. That is, ecosystems seek maximum

nergy throughput, and by inference, are more stable as the goalunction increases. The question could be asked: how does ecosys-em development theory relate to resilience? The simple answers that unstable systems lacking sufficient adaptive capacity ande facto resilience do not exist (Jorgensen and Svirezhev, 2004).his simple observation represents deep information content givenhat wildland ecosystems evolved over hundreds to thousands (or

ore) of years. Thus, resilient processes and mechanisms have beenistilled over time for us to observe and measure.

.1. Recycling rates

In a simulation of 18 different marine ecosystems, Vasconcellos

t al. (1997) identified Finn’s Cycling Index (FCI) as most correlatednegatively) to return time from fishing pressure (population, state-ariable) perturbations. The FCI measures the fraction of ecosystemhroughput that is recycled. Thus, short return times correspond

Modelling 248 (2013) 1– 10

with a greater proportion of recycled energy. Internal nutrientcycling is a dominant biophysical process in maintaining a turbidwater state in shallow temperate lakes (Carpenter et al., 2001). Inthe eutrophic lake example, the turbid state is resistant to reduc-tions in external nutrient load due to storage of nutrients in thesediment. In both the turbid water and marine ecosystem exam-ples, a large proportion of energy and nutrient throughput comingfrom detritus reservoirs or storage compartments support a stablestate. In a broad review of nutrient recycling dynamics, DeAngeliset al. (1989) supported the role of detritus storage compartmentsin stabilizing ecosystems as follows:

“The nutrient turnover time (Tr) in a nutrient-limited modelsystem is a good approximation of the return time (T), neededfor a system to reach the steady state following a perturbation. . .. Finally, a large detritus compartment can buffer and increasethe resilience of a system to perturbations to living components,but the system would be slow to recover from perturbationsaffecting the detritus.”

Both Loreau (1994) and Vallina and LeQuere (2011) describedthe contribution of recycling to stability as increasing resistanceto perturbation rather than recovery from perturbation. Put inanother way, increased recycling rates tend to increase the rateof recovery (i.e., dampen chaotic oscillations) of a system oncedisplaced, but systems with slow recycling rates typically resistdisplacement due to adaptation to slow nutrient and energy trans-fer rates. These relationships have been recognized by researchersseeking to unify ecological goal functions where maximizingenergy storage results in longer residence times or slower cyclingrates (Jørgensen et al., 2000; Fath et al., 2001). The work of Vallinaand LeQuere (2011) provides a compelling analysis showing thatecosystem stability in response to climatic (biophysical) perturba-tion is more closely linked with resistance and slow cycling ratherthan resilience. It follows that chaotic oscillations produce a pulse ofdetritus that would otherwise not occur at steady state (Daufresneand Loreau, 2001). Under conditions not limited by light, water,or other metabolic limitations, additional detritus production mayresult in a surge of primary production. The additional mass of pri-mary production will eventually dampen oscillation and thereforerepresents a negative feedback (DeAngelis et al., 1989) for sys-tems already perturbed (resilience mechanism). Alternatively, slowcycling rates weakly propagate disturbances through the trophicnetwork thereby promoting stability through resistance. It followsthat k-selected species (MacArthur and Wilson, 1967; Pianka, 1972)are associated with stable environments, slower cycling rates, andby inference local maxima along and across adaptive cycles (Fig. 3).

3.2. Diversity and complexity

Species diversity is an axiom for system stability among manyecologists. Empirical studies positively correlated measures ofspecies diversity with ecosystem stability (MacArthur, 1955; Ivesand Carpenter, 2007). May (1972) initiated the ‘diversity versus sta-bility’ debate stemming from extensive numerical simulations thatsuggested that increasing species richness could lead to destabiliza-tion and lower resilience (i.e., Lyapunov stability). Yodzis (1981)suggested that random (rather than skewed or favored) interac-tion strengths between species and trophic levels initiated May’sinstability. Additional synthesis by McCann (2000) suggested thatreduced interaction strength (i.e., less density dependence betweenspecies) may lead to stability. Doak et al. (1998) argued that weakinteraction strength is statistically inevitable, thereby reducing the

probability that oscillations might occur. The subject of interactionstrength as it relates to ecosystem stability and resilience continuesto be evaluated in the literature, including interactions across scales(Peterson et al., 1998; Allen et al., 2005). At present, two hypotheses

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Table 2Examples of biophysical processes associated with stability and regime shifts.

Author(s) Ecosystem description Stable state 1 Stable state 2 Perturbation Biophysical description Signature

Vasconcellos et al. (1997) Marine fisheries (n = 18) Stable intermediate‘waist’ trophic level

N/A studyevaluated stability

Simulated excessive fishingpressure

Bioenergetics, foodrequirements

Finn’s cycling index – correlated withrecovery time

Chavez and Michaelian (2011) Simulated 3 hypotheticalspecies

Steady-statethermodynamicequilibrium

N/A studyevaluated stability

1. Increase population2. Changes in initialpopulation ratio3. Change in externalconstrains

Bioenergetics 1. Perturbation timing can causecollapse2. Stable population ratios exist withinenvelopes bounded by thermodynamiclaw3. Oscillation orbit passes closer tozero, increase precariousness

Ernest and Brown (2001) Desert rodent community Grassland rodentspecies

Shrubland rodentspecies

Change in rainfall Species compensation inresponse to changes inhydrology

Ecosystem stability from competition.Species diversity is homeostaticallyregulated

Coppex et al. (2004) Simulated Lotka–Volterra,two trophic levels

Balanced system(no extinctions)

N/A evaluatedcollapse dynamics

Changes in prey growthrate

Bioenergetics Periods with abundant prey had higherrates of extinction

Reynolds (2002) Eutrophic orhypereutrophic lake

Stable mesotrophy Hypereutrophy External nutrient loading Low oxygen hypolimnionreleases nutrients (internalloading)

Recycling causes eutrophic state topersist. Recycling adds to exergy buffer

Carpenter et al. (2001) Lake District, WI Clear water phase Turbid water phase External phosphorusloading

Low oxygen hypolimnionreleases nutrients (internalloading). Also,Beer–Lambert lightattenuation

Limited recycling prevents jumps inproduction. Phytoplankton replacemacrophytes

Carpenter et al. (2001) Australian rangelands Grassland Shrubland Grazing pressure, firefrequency

Bioenergetics, Speciesreplacement followingtemperature disturbance

Measures of resilience tend to changeslow in comparison to perturbationsthat move faster

Peterson et al. (1998) New Brunswick, CA Boreal fir forest N/A – evaluatedstability

Defoliation by sprucebudworm

Bioenergetics Functional redundancy of avianpredators that eat bud worms

Dobson et al. (2006) Little Rock Lake, WI Balanced trophicdistribution

N/A Studyingstability andcollapse

Experimental acidification Reduced habitat quality,osmo regulation

Collapse or declines more rapid athigher trophic levels

Elmqvist et al. (2003) Western Polynesia Presence of fruittree population

N/A Studyingstability

Cyclones and fire Bioenergetics Some species resistant to perturbation,seed dispersal response diversity

Folke et al. (2004) Tropical Lakes Free floating plants Submerged plants Nutrient Inputs Light attenuation,bioenergetics (nutrientuptake competition)

Nutrient supply gradient, also slowermoving variable

Folke et al. (2004) Everglades, FL Sawgrass Cattail Nutrient loading Soil Phosphorus build-upand loading

Nutrient supply gradient, slowermoving variable

Folke et al. (2004) Carribean Coral Reefs Brown Algae Excessive fishing pressure,exacerbated by hurricanes

Bioenergetics, physicalclimatic accentuation

Resilience lost when overfishingreduces grazing that prevents algaedominance and colonization by corallarvae

Walker and Salt (2006) Aleutian Archipelago Fligh Density Kelp Low Density Kelp Sea Otter Harvesting Bioenergetics High biomass of upper level predator(otter) maintained low numbers ofprimary consumer (sea urchin) andhigh kelp (producer) density

Walker and Salt (2006) Australian rangelands Productive nativerangelands

Dryland salinity Removal of nativevegetation

Introduced plant speciesnot adapted to hydrologicregime. Vadoze zone waterbalance

Removal of native vegetation increasedrecharge and salt intrusion dynamics

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C. Zell, J.A. Hubbart / Ecolo

ominate the discussion relating diversity to ecosystem sta-ility; functional redundancy and response diversity (McCann,000).

The concept of functional redundancy relates stability to theaintenance of critical ecosystem functions. Originally credited

o MacArthur (1955), functional redundancy infers that stabilityncreases as additional species support the same critical ecosys-em function, i.e., redundancy engineering (Naeem, 1998). Petersont al. (1998) and Allen et al. (2005) offer further refinement ofhe functional redundancy hypothesis by suggesting that greateredundancy across space and time scales are characteristic ofesilient systems. Maximizing functional redundancy across timecales (e.g., mixture of fast and slow adaptive cycles, groups, or foodebs) as a stability objective function is likely related to signatures

lsewhere in this paper (i.e., fast and slow recycling rates). Addi-ional research is needed to quantify the compatibility of temporaledundancy and system-wide recycling rates as cohesive stabilityignatures.

In addition to functional diversity, response diversity (Elmqvistt al., 2003) suggests that stability is achieved by diverse perturba-ion tolerances of species that support critical ecosystem services.esponse diversity is sometimes metaphorically described as an

nsurance policy where critical services are maintained followingignificant perturbation (Elmqvist et al., 2003). Response diversityay be most connected with the homeostasis concept whereby

ncrease in species and environmental tolerances result in a bufferhat counters threats to critical functions. Species with wide envi-onmental tolerances, geographic distributions, and responses (i.e.,eurytopic’) are expected to persist following extinction-level per-urbations (Hallam, 2004). Both of these diversity hypothesesoint to the stability through resistance conclusion of Vallina andeQuere (2011). That is, biodiversity supports stability by maintain-ng functional relationships and energy flow against perturbationhereby preventing chaotic oscillation. The rates of energy flow andther biophysical processes represent a third signature of resilientystems.

.3. Governing rate processes

By definition, stable states change slowly (Holling, 1973). From systems model view, stability is likely to result when governingrocesses controlling the state or ecosystem service of interestove slowly (Bennett et al., 2005; Carpenter et al., 2001; Scheffer

t al., 2001). A frequently cited example (mentioned earlier) of thisffect is the build-up of soil phosphorus within catchments host-ng eutrophic lakes (Carpenter et al., 2001). To move from a turbido clear water phase in a eutrophic lake requires an increase inet nutrient export (i.e., loss of storage). Increases in net export areesisted due to high soil phosphorus and internal nutrient recyclingCarpenter et al., 1999). Similarly, Gunderson (2000) noted that

onversion of the everglades from sawgrass to a cattail dominatedcosystem also resulted from a build-up in soil-P, a biophysicalrocess. While linkages between stability, diversity, and recyclingre more theoretical, application of the limiting process concept

ig. 2. Simplified mass or energy transfer diagram. Note output rate (O) can be reduced bf differential equations, each composed of mass or energy difference between compartm

Modelling 248 (2013) 1– 10

is amenable to practical application as a proxy surrogate (Bennettet al., 2005).

By describing the system of interest with mathematics, gover-ning rate processes (including nested feedbacks) can be evaluatedfor response time and sensitivity (Bennett et al., 2005). Manage-ment for stability then becomes an exercise of slowing down thedominant rate process for the ecosystem characteristic, or state,of interest. Once decelerated, the rate process can serve as asurrogate for resilience. Although referred to as a slow ‘rate’ inreferences (Carpenter et al., 2001; Gunderson, 2000; and others)the intent is apparently to describe slow net transfer of mass orenergy. The simplest form of a mass or energy transfer system(Fig. 2) consists of an input transfer rate, a storage compart-ment, and output transfer rate (Oloman, 2009). In reference toFig. 2, decreasing net transfer from one ecological compartment(Shevtsov et al., 2009) to another may result from either a reductionof inputs or increase in storage. A pair of interesting connectionscan be made from either of these scenarios. Reductions in over-all net transfer rates are linked with the diversity and stabilityrelationship where lower cycling rates minimize the probabilityof network oscillations (i.e., resistance mechanism). Dampeningof oscillations, once induced, is the result of energy releasedfrom storage (i.e., resilience mechanism). Changes in storage arealso connected with several bioenergetic goal functions (Fathet al., 2001), including the principle of maximum exergy storage(Fig. 3).

3.4. Stability as bioenergetic goal functions

Several investigators proposed bioenergetic orientors or goalfunctions (Muller and Leupelt, 1998) that hypothesize a consis-tent pattern of ecosystem response and development. Presumingthat ecosystems develop toward a stable state, goal functions offerpromise in better understanding response to perturbation (i.e.,resilience behavior). Lotka (1922) is often credited with the firstgoal function from the suggestions that ecosystems seek maxi-mum energy throughput. Odum and Pinkerton (1955) formalizedthe throughput hypothesis into the maximum power principle(MPP) that proposes biological systems seek maximum power(i.e., increase in biomass density per unit time converted to freeenergy) to perform work. As explained by Jorgensen and Svirezhev(2004), the MPP was later caveated by Odum and Hall (1995) whostated that systems maximize power to perform useful work orexergy.

One of the more popular goal functions, exergy, is the energyabove some reference level that is available to do useful work(Ahern, 1980). In ecological systems, the reference level for exergyis often heat lost to the environment as maintenance respirationand metabolism, or thermodynamic equilibrium (Jorgensen, 2000).The concept of energy above maintenance is considered exergy

storage and conceptually may be related to Holling’s (2001) adap-tive cycle (Fig. 3). In addition to exergy, several additional goalfunctions have been proposed (Table 3) that by inference leadto stability. One of those goal functions is resilience (Cropp and

y either reducing input (I) or increasing storage (S). Rates are described by a systements multiplied by an intrinsic rate constant or conductance.

C. Zell, J.A. Hubbart / Ecological Modelling 248 (2013) 1– 10 7

Fig. 3. Conceptual relationship between popular bioenergetic goal functions (a) (Fath et al., 2001; Reynolds, 2002) and Holling’s (2001) adaptive cycle (b). Adaptive cycler n resom stabiliS

GmptmwsFwscuadra

index to complex physical process based models (Hubbart, 2007).

TE

epresented as a function of storage where greater adaptive capacity occurs wheinimum where the rate of change of storage is zero (maximum storage) whereas

virezhev (2004).

abric, 2002; Kristensen et al., 2003). Application of resilience (i.e.,inimized return time) as an explicit goal function was found to

roduce the highest concordance (i.e., measure of mutual optimiza-ion) against several popular goal functions in 21 of 24 foodweb

odels and scenarios (Kristensen et al., 2003). That is, resilienceas the single best measure that optimized all goal functions con-

idered. In another search for unification among 10 goal functions,ath et al. (2001) concluded that minimized specific dissipationas a slightly more robust goal function than maximizing specific

torage (Table 3). The search for a single bioenergetic theory thatohesively predicts the response of ecosystems to perturbation isnfinished and incomplete. Both Morowitz (1992) and Jorgensennd Svirezhev (2004) proposed a tentative 4th Law of Thermo-ynamics as a unifying theory that merits testing, especially as itelates to explaining stability, diversity, nutrient cycling, and stor-ge concepts as follows:

Perturbations to ecosystems are disruptions of energy flowthat change the position of ecosystems with respect to ther-modynamic equilibrium. The response to perturbations tend tomaximize the time derivative of exergy, choose paths that yield

the most work, and thus seek a position furthest from thermo-dynamic equilibrium (i.e., maximize gradients). In maximizinggradients, growth can occur as biomass, trophic structure, or

able 3cological goal functions as orienteer’s following perturbation.

Source Goal function

Ulanowicz (1997) Maximum ascendency

Bastianoni and Marchettini (1997) Minimize empower toexergy ratio

Jorgensen and Svirezhev (2004) Maximum exergystorage

Morowitz (1968), Finn (1976) Maximum cycling

Schneider and Kay (1995) Maximize dissipation

Odum and Hall (1995) and others Maximum power

Cheslak and Lamarra (1981) Maximum residencetime

Cropp and Gabric (2002), Kristensen et al. (2003) Maximum resilience

Prigogine (1955) Minimum specificdissipation

urces above maintenance needs are incorporated into storage. Resilience is at aty and resistance may be maximal. Relationship also determined by Jorgensen and

information content (e.g., complexity, genomes, feedbacks, con-nectivity etc.).

The concept of maximized gradients producing potential energyis deeply rooted in physical transport laws including Fickian dif-fusion, Darcy’s Law, and Ohm’s Law among others (Campbell andNorman, 1998; Bonan, 2002). It follows that energy flows neededfor ecosystems to respond to perturbation is optimal when energy(exergy) gradients are maximal. While founded on thermody-namic and biophysical principles, such a proposed law is not wellsuited for ecosystem managers seeking to predict specific out-comes. Rather, a more quantitative framework is needed to moveresilience toward useful prediction to explain signatures describedabove.

4. Assessing stability: an energy balance approach

The surface energy balance (SEB) concept may provide a methodfor quantitative modeling and assessment of ecosystem stability.Surface energy balance models range from simple temperature

An appropriately instrumented meteorological station strategicallyplaced to monitor a point of interest can provide necessary data todrive such models. Multiple stations placed in different land use

Description

Ecosystems maximize organizational power (ascendency) system powermultiplied by mutual information contentEcosystems tend to minimize the amount of throughflow (as exergy) used toproduce organizationEcosystems maximize distance from thermodynamic equilibrium by storingenergy (i.e., exergy) available to do useful workMaximize the percentage ecosystem fluxes or throughput that is derived fromcyclingEcosystems seek to maximize dissipation (entropy production) of availableenergy and gain from work performed at the system levelEcosystems seek maximum power as defined as the increase of biomassdensity per unit timeMaximize the residence time of energy. Can be computed as the fraction ofsystem throughput in storageEcosystems seek minimum return times. Numerically, resilience would beconsidered the lowest eigenvalue following perturbationEcosystem seek to minimize energy dissipation per unit biomass

8 C. Zell, J.A. Hubbart / Ecological Modelling 248 (2013) 1– 10

Fig. 4. Hypothetical time series of change in energy storage (�S) where time mayvary depending on available information, where amplitude and wavelength areanalogous to ecosystem persistence and resilience of stability, respectively, and arn

tea

�

wvctwbseaTtacotbHafamfoflflTnbdiowpopp

Fig. 5. A case study example of average daily change in storage (�S) (based on hourly

egime shift would be inferred from a change in �S from one wavelength to theext, as per Figure 1.

ypes could provide comparative assessment (e.g., forest vs. no for-st, open field vs. urban center). The SEB equation is stated simplys follows:

S = Rnet + H + LvE + G + M (1.0)

here Rnet is net radiation, H is sensible heat, LvE is latent heat ofaporization, G is surface heat, M is advected energy, and �S is thehange in storage (positive or negative, net energy) for any givenime interval. Various surfaces of interest (e.g., grass, canopy, soil,ater) can variably affect local climates and thus surface energy

alance components. In addition, various land use types and/ortages of succession can be quantitatively characterized by consid-ring the energy balance terms (Gates, 1980; Grace, 1983; Monteithnd Unsworth, 1990; Campbell and Norman, 1998; Bonan, 2002).he �S term of the SEB indicates a net gain or loss of energy fromhe system of interest and could thus be used to assess stabilitycross defined time, space, and organizational scales. The equationan be easily manipulated to solve for any of the parameters inrder to suit a system of interest (e.g., the sensible heats (H) wateremperature, soil temperature, etc.). Conceivably, ecosystem sta-ility would be achieved when all energy requirements are met.owever, all energy requirements are usually unknown, therefore,s long as �S is always as least negligibly positive (i.e., net exergy)or any time interval it could be assumed all energy requirementsre met, and the ecosystem is thus stable. Notably, while ther-odynamic equilibrium implies stability, stability does not exist

or long in nature. Equilibrium may therefore be better assessedver longer time intervals (multiple years) since normal ecosystemuctuations in net energy and mass storage could add importantuctuations to ecosystem productivity and species composition.herefore, for many ecosystems a short time period approach mayot be sufficient to assess long-term ecosystem stability questions,ut would provide an instantaneous assessment of current con-itions. Hence the need for long-term data sets. This approach is

dealized graphically in Fig. 4 where wavelength amplitude (anal-gous to resistance, Fig. 1) could approach equilibrium (�S ≈ 0.0)ithout risking ecosystem collapse. Longer time periods (i.e., multi-

le wavelengths, or perturbation-recovery cycles) can be composedf longer or shorter wavelengths (i.e., climate anomalies, humanerturbations) and greater wave peaks and troughs (analogous toersistence, Fig. 1) assuming there is available time for recovery

time series) for an agricultural field and an old growth bottomland hardwood forest(BHF) located in the central U.S. for the month of July 2011.

from over- or under-abundance of mass or energy inputs. In thisregard, the energy balance modeling scenario is analogous to theball and cup heuristic model (Fig. 1) described earlier (Carpenteret al., 2001; Folke et al., 2004; Gunderson, 2000). As discussed,“fast recycling rates encourage ecosystem stability by dampen-ing oscillations while slow recycling rates increase resistance byweakly propagating disturbance”. To apply these concepts to theenergy balance model, an ecosystem that is very resistant, but lowin resilience may have a more narrow wave length and may be lesseffective in preventing a regime shift at a higher frequency (greaterresilience) thus showing less resistance. This argument furtherimplies that these relationships may not be linear or necessarilytwo-dimensional since energy, or mass balance, fluctuations occurboth spatially and temporally, and in response to climate stochas-ticity, catastrophic events, or anthropogenic stressors. The energybalance method is also a natural follow on to Holling’s (2001)adaptive cycle model that characterizes the phases of resiliencein a sinusoidal pattern, and thus may provide a mode of assemblyof governing physical processes, and validation for similar theo-retical models. Fig. 5 shows a case study representative exampleof average daily (based on hourly time series) �S for an agricul-tural field and an old growth bottomland hardwood forest (BHF)located in the central U.S. for the month of July 2011. Each sitewas under the respective management for at least a century atthe time of this analysis. To learn more about the study sites thereader is referred to Hubbart et al. (2011). Using the procedure pre-sented above, average daily �S for the agriculture and BHF site was163 and 72 W/m2 respectively (SD: Ag = 50 W/m2, BHF = 56 W/m2).Minimum daily �S for the agriculture and BHF site was 18 and−46 W/m2 respectively, while maximum daily �S for the agricul-ture and BHF site was 219 and 164 W/m2 respectively. Thus, giventhe argument above, the BHF site is closer to energy equilibrium,and therefore may be more stable relative to the agricultural sitewhich exhibits much higher average �S as well as higher daily min-ima and maxima. Admittedly, one month is a temporal snapshot,and future studies should seek to analyze multi-year data sets to notonly validate the method, but to better understand annual, seasonaland diurnal stability fluctuations.

Given this discussion, the energy balance approach may providea mechanism to link qualitative theory to quantitative application.As a further example, an old-growth forest could be considered to

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C. Zell, J.A. Hubbart / Ecolo

e a particularly resistant system in-part due to complex speciesomposition and a great deal of energy stored in biomass (abovend below ground), and may therefore not exchange the energyt the rate of another, less resistant system. A less resistant butore resilient system may be a recently clear cut forest exhibit-

ng faster rates of energy exchange (i.e., governing rate processes)or tree re-establishment. In the case of the old-growth forest, theenergy capital” created by the long-term storage of biomass (car-on, etc.) supplies resistance through energy storage. In the case ofhe clear cut, the lack of biomass (carbon, etc.) supplies a sink fornergy resulting in reduced resistance to additional perturbation.his example, and the case study example provided above (Fig. 5)rovides a mechanism by which observational assessments can beade to qualitatively assess resilience of an ecosystem of interest

nd resistance to a new condition.

. Future research needs

In keeping with the observation made by Ives and Carpenter2007) with regard to diversity, there seems to be few studies avail-ble in the literature that includes fitting of empirical data from

single system undergoing regime shift by a process-based sta-ility model. Among a few notable exceptions include fitting ofimodal (e.g., two stable states detected in measured system timeeries) soil moisture data to assess bistability of evapotranspirationnd precipitation feedbacks by D’Odorico et al. (2004). Additionaltudies utilizing observational data to support modeled scenariosnclude the interesting evaluation of Peterson (2009) that demon-trated multiple hydrologic steady-states may arise from a singlearameter set as influenced by biophysically dissimilar initial con-itions (i.e., two paired watersheds) and others by Rennermalmt al. (2010) and D’Odorico et al. (2011). At present, ‘confrontingodels with data’ (Hilborn and Mangel, 1997) remains the most

ressing need to move the understanding of ecosystem resilienceorward. Notwithstanding issues of scale and representativeness,btaining the high frequency, multi-trophic data needed to cali-rate a stability model may best be attempted at the bench-scale.acteria microcosm studies summarized by Botton et al. (2006)nd bench-scale aquatic experiments by Steiner et al. (2006) andee and Brown (2011) set forth designs capable of generating datat daily timesteps. It may thus be unrealistic to pursue field scalenderstanding of resilience until analyses are reliable in less com-licated settings.

There remains an ongoing effort to solicit mathematical mod-ls that are not calibrated against data from systems undergoingegime shift (i.e., variable of interest collected from a single sys-em before, during, and after regime shift) to answer our questionsbout resilience. While certainly insightful, many numerical effortsre either overly simplified or utilize a weight of evidence approachather than long-term direct measurement to posit ecologicalistability. Real systems experience several perturbations acrossultiple trophic levels on a periodic or stochastic basis. A proposed

ext step in theoretical resilience modeling is to introduce moreealistic perturbation regimes and parameterize trophic levelsith biophysical tolerances (i.e., temperature, moisture, nutrient,

nd energy thresholds) to climatic, pathogenic, and contaminanttressors.

. Conclusions

Natural resource commodities are critical for human sur-

ival. Disruptions to key biophysical processes such as pri-ary production are implicated in historical mass-extinctions

escribed by Hallam (2004). If perturbations (i.e., global warming)ausing unfavorable shifts are to be better understood and avoided,

Modelling 248 (2013) 1– 10 9

improved understanding of ecosystem resilience and stabilitymechanisms is necessary to support deliberate managementstrategies. Empirical evidence and modeling studies suggest thatbiophysical phenomena including diversity, recycling rates, sen-sitivity of governing processes, and bioenergetics play key rolesin determining ecosystem stability over time. Large-scale per-turbations have shaped ecosystem development and evolution.Therefore, intrinsic bioenergetic goal functions that orient recov-ery processes may offer insights into resilience behavior acrossecosystems. Ecosystem stability may be interpreted as the inter-play between resistance mechanisms (homeostatic feedbacks) andresilience (i.e., recovery) processes that speed recovery. The util-ity of theoretical resilience models would benefit from validationagainst high resolution data. As physical requirements bound thepossibility space for biological systems, it is not surprising thatbiophysical processes play a central role in resilience theory.

Acknowledgements

The authors are grateful for comments provided by John Schulzand anonymous reviewers whose insights improved the quality ofthe article.

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