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A minimal model of fire-vegetation feedbacks and disturbance stochasticity generates

alternative stable states in grassland–shrubland–woodland systems

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2015 Environ. Res. Lett. 10 034018

(http://iopscience.iop.org/1748-9326/10/3/034018)

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Environ. Res. Lett. 10 (2015) 034018 doi:10.1088/1748-9326/10/3/034018

LETTER

Aminimal model of fire-vegetation feedbacks and disturbancestochasticity generates alternative stable states in grassland–shrubland–woodland systems

Enric Batllori1,2,3, DavidDAckerly4 andMaxAMoritz3

1 CEMFOR—CTFC, InForest Joint ResearchUnit, CSIC-CTFC-CREAF, Solsona, E-25280, Spain2 CREAF, Cerdanyola del Vallès, E-08193, Spain3 Department of Environmental Science, Policy, andManagement, University of California Berkeley, California, USA4 Department of Integrative Biology and JepsonHerbarium,University of California Berkeley, California, USA

E-mail: [email protected]

Keywords: alternative stable states, fire, fire-vegetation feedbacks, flammability, mediterranean-type ecosystems, stochasticity, systembehavior

Supplementarymaterial for this article is available online

AbstractAltered disturbance regimes in the context of global change are likely to have profound consequencesfor ecosystems. Interactions betweenfire and vegetation are of particular interest, asfire is amajordriver of vegetation change, and vegetation properties (e.g., amount,flammability) alterfire regimes.Mediterranean-type ecosystems (MTEs) constitute a paradigmatic example of temperate fire-pronevegetation. Although these ecosystemsmay be heavily impacted by global change, disturbance regimeshifts and the implications offire-vegetation feedbacks in the dynamics of such biomes are still poorlycharacterized.We developed aminimalmodeling framework incorporating key aspects offire ecologyand successional processes to evaluate the relative influence of extrinsic and intrinsic factors ondisturbance and vegetation dynamics in systems composed of grassland, shrubland, andwoodlandmosaics, which characterizemanyMTEs. In this theoretical investigation, we performed extensivesimulations representing different background rates of vegetation succession and disturbance regime(fire frequency and severity) processes that reflect a broad range ofMTE environmental conditions.Varying fire-vegetation feedbacks can lead to different critical points in underlying processes ofdisturbance and sudden shifts in the vegetation state of grassland–shrubland–woodland systems,despite gradual changes in ecosystemdrivers as defined by the environment. Vegetation flammabilityand disturbance stochasticity effectivelymodify systembehavior, determining its heterogeneity andthe existence of alternative stable states inMTEs. Small variations in systemflammability andfirerecurrence induced by climate or vegetation changesmay trigger sudden shifts in the state of suchecosystems. The existence of threshold dynamics, alternative stable states, and contrasting systemresponses to environmental change has broad implications forMTEmanagement.

Introduction

Understanding and predicting ecological responses toenvironmental change, which can be modulated bystochastic processes such as disturbances, are keychallenges in environmental research.Mediterranean-type ecosystems (MTEs) are a prime example oftemperate vegetation where climate and the regularoccurrence of fire as a natural disturbance haveinfluenced plant traits and the structure, composition,

and diversity of vegetation (Callaway and Davis 1993,Keeley et al 2012). Nevertheless, climates ofMTEsmaychange dramatically over the century (Klausmeyer andShaw 2009), and it is unclear how alterations in fireactivity (e.g., Batllori et al 2013) will affect theircomposition and function.

Models of varying complexity have been devel-oped for prediction of MTE vegetation dynamics,many of which include fire as a key process. Except fora few physiological process-based and dynamic

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vegetation models (e.g., Mouillot et al 2002, Kelleyet al 2014), most recent approaches use landscape fire-successionmodels (e.g., Syphard et al 2007,Millingtonet al 2009, Loepfe et al 2011, Brotons et al 2013). Land-scape models emphasize spatially explicit dynamicsand allow for simulation of realistic landscape patternsinduced from past fire regimes (i.e., area burned andfire recurrence). However, such detailed and highlyparameterized approaches are not designed to identifygeneral fire ecology principles and predictions relatedto environmental change (Zinck andGrimm2009).

Simple and generalized fire models capture keyprocesses that explain properties and patternsobserved in real ecosystems on large spatial and tem-poral scales (e.g., Zinck and Grimm 2009, Pueyoet al 2010). In semi-arid, fire-prone ecosystems such assavannas, minimal models have been used to examinethe stability of tree/grass dominance as a result of sto-chastic fire–vegetation interactions (D’Odoricoet al 2006) or associated with percolation dynamicsand fire spread (Staver and Levin 2012); fire has beensuggested to promote alternative stable states and eco-system shifts due to crossing of critical thresholds oraltered system feedbacks (Hoffmann et al 2012).Although fire can strongly influence the distributionof grass and woody cover in MTEs (e.g., Callaway andDavis 1993, Vilà et al 2001, Koniak and Noy-Meir 2009), the study of regime shifts and system feed-backs and their implications in these ecosystems is stillvery limited. Characterizing ecosystem behavior toidentify sensitive thresholds and their causes in MTEsis an indispensable first step towards the specificationofmanagement and conservation scenarios.

Conceptual models such as state-and-transitionmodeling frameworks (STMs) reflect our under-standing of ecosystem dynamics and can be easilyadjusted to include new knowledge and/or specificlandscape and climate conditions (Westoby et al 1989,Bestelmeyer et al 2004). Such approaches have beenwidely used to analyze restoration actions and man-agement benchmarks. Our objective was to develop aminimal STM incorporating key aspects offire ecologyto evaluate the relative influence of environment, dis-turbance stochasticity, and plant traits on the dynam-ics of ecosystem types dominated by grassland–shrubland–woodland (G–S–W) mosaics, character-istic of many MTEs. The model incorporates: (i) therate of vegetation succession in the absence of dis-turbance; (ii) the probability of fire and the severity offire, including feedback effects of vegetation onflammability; and (iii) stochasticity infire return inter-vals. The influence of both environment and vegeta-tion on fire and the inclusion of disturbancestochasticity make our STM framework a novelapproach towards better understanding basic ecologi-cal mechanisms constraining G–S–W dynamics infire-prone vegetation such as MTEs, and lays thegroundwork for investigations of global changeinfluences.

We used coastal California ecosystems dominatedby three vegetation types (mosaics of woodlands,shrublands, and grasslands) as an example of MTEvegetation and as a reference system formodel develop-ment and to define the parameter space used in this the-oretical study. We assess: (a) whether gradual variationin succession rates, disturbance frequency or dis-turbance severity (e.g., due to external ecosystem dri-vers such as climate) can promote threshold changes inMTE vegetation composition; (b) whether alternativestable states exist, andwhat factors drive systembifurca-tions; and (c) how disturbance stochasticity and fire-vegetation feedbacks influence system responses.

Material andmethods

Model and simulation runs overviewOur STM framework (figure 1) corresponds to a semi-Markov model based on discrete-time theory (Scan-lan 1994). The systemmoves fromone vegetation stateto another in a successional sequence and fire sets backvegetation to earlier succession stages as defined by fireseverity. Fire is incorporated as a stochastic processinfluenced by vegetation flammability, and the succes-sion rate of vegetation is temporally constrained onthe basis of time since disturbance (Hobbs 1994;figure 1). The rate of succession among vegetationtypes and the strength of fire-vegetation feedbackscapture the importance of productivity and fuelstructure, respectively, for fire activity in fire-proneecosystems (e.g., Krawchuk and Moritz 2011, Pausasand Paula 2012), whereas altered fire probabilities andfire severities across changing conditions reflect cli-mate–fire interactions (e.g., Marlon et al 2008, vanMantgem et al 2013).

The model was built in R (R Development CoreTeam 2013) and implemented as a bi-dimensional lat-tice. Each cell in the lattice presents a state defined bythe proportion of three vegetation types: grassland(G), shrubland (S), and woodland (W), and by a timesince fire (TSF). By defining the cells’ vegetation as G–S–Wfractions, flammability effects and different levelsof fire severity (e.g., proportion of W and S set back toG) can be easily implemented. Fire spread is implicitlycaptured by assuming that cells burn entirely whenignition occurs, impacting all vegetation types, butamong-cell connectivity is not incorporated in themodel. Therefore, each cell in this implementation isassumed to experience independent fire probability,successional dynamics, and state transitions. This sim-plified framework allows us to keep the number ofmodel parameters and associated uncertainty at aminimum, while also retaining the capacity for simu-lating underlying spatial gradients in a STM frame-work (Bestelmeyer et al 2011).

For this theoretical study, we defined a simulationdomain of 300 vegetated cells (i.e., no empty spaces).Geographic cell size is not fixed, but following

2

Environ. Res. Lett. 10 (2015) 034018 EBatllori et al

ecological site descriptions (ESDs; Brown 2010), cor-responds to an area of homogeneous climatic andedaphic conditions large enough (e.g., 2 × 2 km2) toencompass patches of multiple vegetation types (e.g.,G–S–W) with shared capabilities to respond to man-agement or disturbance. Coastal California ecologicaland fire literature (table S1 in the supplementary data,available at stacks.iop.org/ERL/10/034018/mmedia),descriptions of ecosystem processes in ESDs, andLANDFIRE National Vegetation Dynamics Models(LANDFIRE 2010) were used to infer parameter ran-ges for succession rate, fire probability, and fire sever-ity. The parameters required for the simulationspresented here, however, are not available from anyone site and we thus used general rates representativeof ecosystem types where fire defines the extent of G–S–W (e.g., California blue oak or coastal live oakwoodlands and savannas; Brown 2010, Landfire 2010,Keeley et al 2012). Consequently, model results cannotbe directly compared to specific historical dynamics orlandscape patterns but to general ecosystem featuresand trends.

In this initial investigation, the environment wasset as spatially homogeneous and initial model para-meters were thus the same across the system. The lat-tice of 300 cells thus provided multiple realizations ofthe model’s processes at the same time, allowing us todetermine whether all cells follow similar dynamicsfor a given set of model parameters, or whether diver-gent vegetation trajectories occur due to stochasticdynamics or local feedbacks.

We performed a set of simulations representative ofecosystem processes in Mediterranean-climate Cali-fornia; grasslands are primarily annual grasses, which

are highly flammable in the summer dry season of theMediterranean-type climate. Dense and continuousshrub cover characterizes the shrublands, which arecomprised offire-resilient, chaparral dominated speciesthat both resprout after fire and have fire-stimulatedseed germination. Woodlands are primarily oak wood-lands dominated by fire resistant species that present athick bark and ability for basal and epicormic resprout-ing. Throughout the simulations, the broad range ofparameter’ values evaluated reflect different environ-mental conditions. Higher fire probabilities would cor-respond to climatic conditions associated with higherfire risk (e.g., warmer-drier conditions), and/or couldbe regarded as a function of ignition probability (e.g.,reflecting human-induced fires, or conversely, fire sup-pression). Low and high succession rates of vegetationwould represent productivity gradients (e.g., linked toprecipitation or soil fertility) translating into slow orfast successional changes towards woodlands, respec-tively, and higher fire severities would reflect moreextreme climatic conditions (e.g., extended periods ofdrought) which increase fire intensity and the prob-ability that burned vegetation is unable to regenerate, oralternatively can represent plant communities com-posed of less resilient taxa. Variation of vegetationflammability and persistence following fire incorpo-rates the varying importance of feedbacks from vegeta-tion indriving systemdynamics.

Model processesThe state of each cell is modified in discrete time steps(i.e., one year) following a probability β of changingstate due to succession (change from G–S and S–W)and a probability F for a cell to be struck by an ignition

Figure 1.Representation of themain processes of the state and transitionmodeling (STM) framework reproducing the dynamics ofgrassland–shrubland–woodland systems (G–S–W). Themodel incorporates a coupled set of three vegetation STM sub-systemsdescribing vegetation succession on the basis of time since fire (TSF−top row−), the effects offire on vegetation (fire severity−upperright−), and differential flammability among the three vegetation types (flammability frameworks−bottom right−). Flammabilityincorporates the influence of strong (left) ormoderate (right) fire-vegetation feedbacks in themodel: ternary plots depict the effectivefire probability of a cell after accounting for theflammability of each vegetation type in a scenariowhereG burnsmore than S, which inturn burnsmore thanW (see text for details). The green-red-yellow ternary plot at the bottom left shows the color scale used insubsequent figures to represent a given proportion of G–S–W.

3


http://stacks.iop.org/ERL/10/034019/mmedia

source. When fire occurs, the entire cell is consideredeffective fuel (i.e., it burns when ignited), but fireseverity α defines state transitions to earlier succes-sional states (proportion changing from W to S or G,or from S to G). Parameters β, F, and α are jointlydetermined by the environmental conditions and cellvegetation characteristics and thus themodel incorpo-rates fire-vegetation feedbacks.

The successional process at the cell-level is expres-sed as Ci(t+1) = βI ·Ci(t), where Ci(t+1) and Ci(t) are vec-tors whose elements are proportions of G–S–Wwithincells, which are also characterized by a state i of 3 pos-sible TSF: TSF⩽ 5 years, TSF from 6 to⩽ 15 years, andTSF> 15 years (figure 1; Landfire 2010). Sensitivityanalyses of themodel using accelerated or delayed TSFintervals exhibit qualitatively similar results (see sup-plementary data). Parameter βi corresponds to asquare matrix composed of probabilities representingthe proportion of vegetation in one state (e.g., G)changing to another (e.g., S) at a given time step;values of such succession probabilities depend on TSF.Therefore, βi incorporates time lags and different ratesof vegetation change after disturbance. Cell-level suc-cessional dynamics are thus described by

ββ β

β

=

= −

−

+

+

CWSG

1 0

0 1

0 0 1

WSG

, (1)

i t

i t

s i

s i g i

g i i t

( 1)

( 1)

,

, ,

, ( )

⎛⎝⎜⎜

⎞⎠⎟⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

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where βg,i and βs,i define the rate of succession from Gto S and from S toW, respectively, contingent on cells’TSF state i (figure 1). Direct succession of G to W andadditional factors (e.g., shallow soils) constrainingsuccession from S to W are not considered in thisstudy; S are thus a transient state between G and W(table S1, Landfire 2010), though they could persist formany years prior to succession to W (e.g.,Keeley 1992).

Changes in vegetation are also influenced by fire.At each time step it is determined whether each cellburns or not on the basis of its fire probability F, whichis defined by both baseline fire probability f (capturingenvironmental or human influence) and vegetationflammability v (see below). Because in this para-meterization the fire season peaks in late summer andearly fall (Davis and Borchert 2006), fire was computa-tionally implemented after the successional change ofvegetation at each time step. Cells cannot burn morethan once in a given time step.

Cells burn entirely but this does not cause statetransitions of all the vegetation. Fire severity α, whichis jointly modulated by environmental conditions andvegetation type, determines the proportion of a cell’svegetation to be set back to earlier successionalstates by burning (figure 1). Vegetation remaining inthe same state captures the capacity of many

Mediterranean-climate plant species of California toregenerate and persist through fire events (Keeleyet al 2012).

The flammability v of each vegetation type influ-ences fire occurrence which, together with the differ-ing capacity of each vegetation type to persist throughfire, defines fire-vegetation feedbacks in the model.This is implemented by modifying the baseline fireprobability (f) and fire severity (α) factors of each cellon the basis of its G–S–W abundance. The dynamicrole of vegetation in fire-vegetation feedbacks wasincorporated through two alternative flammabilityframeworks (figure 1): a) the dominant vegetation rulewhere the cell’s baseline fire probability is modulatedby the flammability of the dominant vegetation type(strong or nonlinear feedbacks) and b) the weightedaverage rule where the baseline fire probability isweighted in accordance to the relative abundance ofeach vegetation type (moderate or linear feedbacks).

The dominant vegetation rule represents a sce-nario in which changes in the abundance of the non-dominant vegetation types may have little impact onthe resulting fire probability until a threshold isreached (i.e., change in vegetation dominance), whenfire probability changes abruptly (e.g., Staver andLevin 2012). On the other hand, the weighted averagerule represents a scenario where small changes in theabundance of vegetation types have a proportionalimpact on the resulting fire probability (e.g., D’Anto-nio and Vitousek 1992). We considered G the mostflammable vegetation type and expressed S and Wflammability as a percentage of G flammability andindependent from each other.

Implementation of the STM frameworkThe simulation loop forming the core of the modelconsists of the following rules:

Rule 1—successional processThe TSF in all cells within the system (lattice of 300cells) is increased by one year. Vegetation dynamicsdue to succession at the system-level is described as:

∑β=+=

LN

C1

, (2)tj

N

i ij t( 1)

1

( )

where Cij(t) corresponds to cell j (of N= 300) in TSFstate i (of three possible TSF states) at a given time t,and βi is the succession matrix as defined by each TSFstate (see equation (1)). L is thus a vector whoseelements are system-level proportions of G–S–W; theparameter 1/N is introduced so that vegetation pro-portions in L sum to one.

Rule 2—vegetation flammability feedbacksSelection of the flammability framework (i.e., strongor moderate feedbacks) and modification of cells’baseline fire probability. Feedbacks are implementedat the cell-level as:

4


∑==

F p f v , (3)k

N

k k

1

where F is the effective fire probability of a cell, fcorresponds to the baseline fire probability defined bythe environment, and pk and vk are the proportion andflammability of vegetation type k (of N= 3; G, S, andW), respectively. When strong feedbacks operate, vk ofthe non-dominant vegetation types is set to 0. Notethat v is a unitless modifier of f that is always smallerthan or equal to 1.

Rule 3—ignitionRandom ignitions based on each cell’s effective fireprobability (F) at each time step; TSF for burned cellsis reset to 0. Ignitions are implemented at the cell-levelusing the beta andBernoulli probability distributions:

r F

r

~ Beta (2, )

Ignition ~ Bernoulli ( ). (4)

j t

j t j t

,

, ,

In temperate fire-prone vegetation, many tree andshrub species have the ability to resprout and grassbiomass approaches pre-burn levels quickly followingfire. Additionally, much of the area burned in thisCalifornia implementation exhibitsminimal influenceof vegetation age on fire probabilities (e.g., Mor-itz 2003). Therefore, for our initial investigation weapproximate fire as a stochastic process in which theprobability of burning is independent of the time sincelast burn. This is a simplifying assumption that can beexplored in more detail in future versions of themodel. Note, however, that due to the influence ofvegetation types on F, the observed time elapsedbetween fires will vary among cells for a given f (e.g.,cells dominated by grasslands will experience morefrequent fire under either flammability feedback rule).

Rule 4—fire severity effectsIn cells that burn, fire severity determines vegetationtransitions to earlier successional states. Severityeffects at the system-level are described as:

∑α α==

p , (5)j k

N

jk k

, 1

where α is the amount of vegetation set back to earlierstates due to burning, pjk corresponds to the propor-tion of vegetation type k (of N= 2; W and S) of cell j(see equation (2)), and αk is the severity of fire onvegetation type k; αk can vary from 0 (no change in Wand S proportion due to fire) to 1 (all W and Sexperiencing state type-conversion as a result ofburning). In this study, G is not type-converted by fireand, for simplification to avoid the inclusion ofanother model parameter, type-conversion for W isequally split to S and G; this has no qualitative impacton themodel, though itmay influence the quantitativebehavior of the systemunder some parameterizations.

The complete functioning of the model (figure 1)is formalized as:

β

βα

α

β β

β β

αα

α

β β

= − −

− − + +

= − − − −

+ − + −

+ −

= −

+ − + −

+

+

+

G G GF

GF

WF S

F

S S SF

SF

GF

GF

WF S

F

W W WF

SF

SF

11

11

1

2

1,

11

11

11

11

1

2

1,

1

11

11

,

t t g

g

w t

s t

t t s s

g g

w t

s t

t t w t

s s

1 2 2

3 3

1 2 2 3 3

2 2 3 3

1

2 2 3 3

⎜ ⎟

⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎜ ⎟ ⎜ ⎟

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎛⎝

⎞⎠

⎛⎝

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⎞⎠

⎛⎝

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⎛⎝

⎞⎠

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⎞⎠

where G, S, W corresponds to frequency distributionof grasslands, shrublands, and woodlands across thesimulation domain at each time step (t), respectively.The coefficients β, which define succession rates fromone vegetation type to another, are contingent onvegetation type (βg and βs) andTSF (subscripts 2 and 3—from 6 to⩽ 15 years, and > 15 years, respectively;equation (1)). Vegetation type does not change due tosuccession during the first 5 years following fire (allβ= 0). Effective fire probability (the likelihood ofburning at each time step; equation (3)) is defined byF, and α defines fire severity (the amount of type-conversion to earlier successional stateswhen burning;equation (5)). Fire-vegetation feedbacks are incorpo-rated through the influence of vegetation on both Fand α. All model parameters are independent amongcells and thus there can be spatial heterogeneity at thesystem-level. Each cell is characterized by a TSF and aG–S–W proportion, so full characterization of thesystem’s vegetation state is represented by a 9-cellmatrix including proportions of G–S–W in three ageclasses (defined by TSF).

Simulation experimentsWe conducted a comprehensive set of simulationexperiments (parameter scenarios) to evaluate howthe coupled effects of environmental conditions(influencing β, α, and F) and fire-vegetation feedbacks(influencing α and F) determine the dynamics of G–S–W systems (table 1). In each simulation run, weassumed homogeneous and constant (i.e., no tem-poral change) conditions over the simulation domain:there were no spatial differences in succession rate, fireprobability, fire severity, and vegetation flammabilityacross the system. These background model para-meters were therefore reduced to a common set ofinitial values for all cells, though their effective valuescould change in time and space due to within-cellsfire-vegetation feedbacks. Through the simulationexperiments, model processes were systematicallymodified two at a time while setting the rest at baselinelevels to evaluate system behavior and the implicationsof such processes in G–S–Wdynamics. The parameter

5


Table 1.Parameter settings of themodel (see figure 1) for the simulation experiments (parameter scenarios) conducted to evaluate the effects of succession rate of vegetation (β),fire probability (f), vegetation flammability (v), andfireseverity (α) on the dynamics of grassland–shrubland–woodland systems. Each scenario consisted in themodification of two of themodel processes at a time (highlighted in bold) whilefixing the others at baseline values: scenario 1—variation offire probability and succession rate (number of simulationsN= 2240); scenario 2—variation offire probability and fire severity (number of simulationsN= 2240); scenario 3—variation offire severity onwoodlands andshrublands (number of simulationsN=1092); scenario 4—variation of vegetation flammability (number of simulationsN= 14 112). In each scenario,model parameterizationwas homogeneous among cells, and an initial random timesincefire between 1 and 100 years,fixed across all simulations, was used for each cell.

Scenario 1 Scenario 2 Scenario 3 Scenario 4

Succession rate (β) (proportion/year)

βg2 (Grass→ shrub 6–15 yr after fire) 0.5 βg3 0.5 βg3 0.5 βg3 0.5 βg3βs2 (Shrub→wood 6–15 yr after fire) 0.05 βg3 0.05 βg3 0.05 βg3 0.05 βg3βg3 (Grass→ shrub>15 yr afterfire) 0.01–0.2 (by +0.01; n= 20) 0.05 0.05 0.05βs3 (Shrub→wood>15 yr afterfire) 0.1 βg3 0.1 βg3 0.1 βg3 0.1 βg3

Baselinefire probability (f) (1/fire frequency)

0.01–0.685 (by + 0.025; n= 28) 0.01–0.685 (by + 0.025; n= 28) 0.1 0.05, 0.1, 0.2, 0.3 (n= 4)

Vegetationflammability (v) (unitlessmodifier offire

probability)

vg(Grasslandflammability) 1 1 1 1

vs (Shrublandflammability) 1*vg 1*vg 1*vg 0.01*vg–1*vg(by + 0.05; n= 21)

vw (Woodland flammability) 1*vg 1*vg 1*vg 0.01*vg–1*vg(by + 0.05; n= 21)

Fire severity (α) (proportion set back to earlier vegetation stages)

αS (Fire severity on shrubland) 0.25 0.05–0.5 (by + 0.05; n= 20) 0.05–0.55 (by + 0.02;n= 21) 0.25αW (Fire severity onwoodland) 0.1αS 0.1αS 0.005–0.125 (by + 0.02; n= 13) 0.1αS

Initial cells composition 100%W, 100%S, 100%G,mixed 100%W, 100%S, 100%G,mixed 100%W, 100%S, 100%G,mixed 100%W, 100%S, 100%G,mixed

Flammability rule — — — Weighted/ dominant

Total number of parameter combinations 2240 2240 1092 14 112

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Environ.R

es.Lett.10(2015)

034018EBatllorietal

space evaluated in this theoretical study encompasses awide range of empirical observations (table S1) andreference conditions (e.g., ESDs) on vegetation succes-sion and fire occurrence in Mediterranean-climateCalifornia; within this range, a total of 19684 differentcombinations of model parameters were evaluated(table 1).

Model runsSimulation runs on each background set of parameterswere performed on four initial, spatially homogeneousvegetation conditions: 100% dominance of eachvegetation type in all cells (i.e., G, S, W), plus a systemwhere all cells were initiated with equal proportion ofG–S–W. Cells were assigned an initial random TSFbetween 1 and 100 years fixed through all model runs.Each individual simulation comprised 10 000 modelsteps to ensure the system reached a stable state orequilibrium, which was defined as a de-trendedproportion of G–S–W over time. That is, even if thesystem is dynamic because the proportion of eachvegetation type may fluctuate through time, at equili-brium such fluctuations are centered on a certain leveland the long-term proportions of G–S–W do notincrease or decrease.

During the simulations, the proportion covered byeach vegetation type and the age (i.e., TSF) of each cellwere reported at each time step and integrated acrossthe entire system (i.e., frequency distribution of G, S,and W across all cells). System-level stability (propor-tion of area not exhibiting vegetation transitions dueto fire or succession) and heterogeneity (Shannondiversity index on the proportion of G–S–W) werecomputed at each time step. Results for each simula-tion were then expressed as 1000-year averages (underequilibrium conditions). Variation in the frequencydistribution of vegetation types at the cell-level wasalso examined to test for internal bifurcations intoalternative states that would bemasked by consideringonly system-level statistics.

Results

Vegetation dynamics across parameter spaceWhen different vegetation types have the same prob-ability of burning (i.e., no vegetation feedbacks thatalter fire probabilities; parameter scenarios 1–3), thesystem exhibits a single stable state for a given set ofmodel parameters irrespective of its initial vegetationstate (figure 2 and S1). As expected, fire probabilityexerts a strong influence on vegetation composition,determining major patterns of G, S, andW abundanceat the system-level. Regardless of the succession rate ofvegetation orfire severity,Wdominates at low levels offire (static system), whereas G dominate under highfire occurrence (dynamic system). At intermediate firefrequencies S are most abundant, and they are

associated with higher system-level vegetation hetero-geneity (figure 2 and S2).

Drastic changes in G–S–W dominance can occurover narrow ranges of the parameter space (figure 2),especially with changes in fire probability. Similarly,over a limited range of fire probability values, the suc-cession rate of vegetation and fire severity stronglyinfluence the abundance of W, S, and G at equili-brium: faster succession rates and lower fire severitylead to increased W dominance. Given the transientnature of S in this study, shrublands only becomedominant when fire severity is higher on W than on S(figure 2). The dominance or relatively high presenceof S is generally associated with higher temporal varia-tion in within-cell vegetation proportions that resultin larger system-level fluctuations of G–S–W abun-dancewhen equilibrium is reached (figure S3).

Alternative stable statesWhenG, S, andWexperience a different probability ofburning because of their flammability, the systemexhibits two alternative stable states (bistability) undercertain parameter combinations (figure 3). The natureof fire-vegetation feedbacks induced by vegetationflammability determines whether alternative stablestates exist or not. Bistability in system behavior ariseswhen the flammability of G> S>W and the effectivefire probability of a cell is determined by strongfeedbacks (figure 1). In this case, given a baseline fireprobability, fire severity, and flammability of G andW,increasing the flammability of S leads to high Gdominance when the initial cell vegetation is notdominated by W (figure 4(A)). However, increased Sflammability does not result in G dominance when theflammability of W is low and cells are initiallydominated by W. When moderate fire-vegetationfeedbacks operate (figure 1) the system still showsnonlinear changes in G–S–W dominance, but onlyone stable equilibrium exists for any given condition,irrespective of initial vegetation composition(figure S4).

Regardless of the existence of one or two stablestates, the abundance of G, S, and W vegetation statescan respond in different ways to changing conditionsand thus to altered levels of system processes (succes-sion rate, flammability, fire probability, and fire sever-ity; figures 2, 3, and S1). Changes in the abundance ofG andW are coupled (with opposite trends) and exhi-bit both gradual and threshold-type responsesdepending on the process that is governing such chan-ges. However, S shows in some cases a differentialresponse fromW and G, and it displays hump-shapedrelationships with fire probability and severity(figures 2 and 3). The high sensitivity of G–S–Wdom-inance to changes in fire probability is related tothreshold-type responses of G and W abundance tothis process. In addition, for a limited range of condi-tions andwhen strong fire-vegetation feedbacks occur,

7


vegetation proportions can be insensitive to parameterchange (figure 3).

Divergent vegetation trajectoriesTo better characterize alternative stable states in thedynamics of the system, we performed additionalsimulations to evaluate whether the entire system (i.e.,all 300 cells) settles eventually to the same vegetationstate irrespective of the initial vegetation composition.We tested different model parameterizations (homo-geneous among cells) defined by different combina-tions of G–S–W flammability and strong fire-vegetation feedbacks; in each case 441 initial condi-tions defined by cells’ G–S–W proportion wereevaluated (N= 7056 simulations). Results corroboratethe existence of two major basins of attraction at thesystem-level where vegetation in all cells is eitherdominated by W or G, but also the presence ofintermediate stability attractors between them(figures 4(B) and S6). Such intermediate attractors aredetermined by high levels of among-cell vegetationheterogeneity (figure 4(C)): combinations of contrast-ing vegetation states among individual cells averageout to define the stable vegetation state at the system-level.

The mechanisms that determine the dynamics ofG–S–W vegetation and which basin of attraction thesystem will follow depend both on factors extrinsicand intrinsic to the system (figure 5). System-leveltransitions to different stable states can be driven byextrinsic factors such as the environment (e.g., differ-ent fire probability; figure 5(A)), but also by intrinsic

fire-vegetation feedbacks under a given environment(e.g., different vegetation composition; figures 5(B)and (C)). On the other hand, under some parametercombinations, stochastically driven transitions in thevegetation state of some cells, together with the effectsof post-disturbance dynamics, result in contrastingstable states at the cell-level and thus increased systemheterogeneity (figures 5(D)–(F)).

Discussion

High rates of vegetation succession, low flammability,and low severity (or high capacity of vegetation topersist through fire) promote rather static systemsdominated by woodlands. However, because of therelatively slow dynamics of vegetation successionalchange (years to decades), high fire frequenciesinevitably lead to a single stable state dominated bygrasslands. The interplay of factors extrinsic andintrinsic to the system determines the nature oftransitions between vegetation states. As evidenced bythe dynamics of ecosystems representative ofMediter-ranean-climate California, transitions between grass-lands and woodlands in G–S–W systems canencompass a continuum of possible behavior, includ-ing continuous responses (gradual or threshold-like)and catastrophic shifts (alternative stable states).

Dynamics of california ecosystemsAlthough a direct quantitative model validation wasnot possible, the modeling framework presented here

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Fire probabilityFire probability

Fire probability Fire probability

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shru

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Figure 2.Equilibriumproportion of grassland, shrubland, andwoodland in relation tofire probability, succession rate, and fireseverity; A, B, andC correspond to parameter scenarios 1, 2, and 3, respectively−see table 1. The lower panels (line plots) illustrate themodeled response of the system to changes inmodel parameters across the selected conditions (1)–(7), which aremarked by dottedlines and the same number in the upper plots; solid gray lines represent the equilibriumproportion of each vegetation type. Alldepicted cases represent stable states at the system-level.

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Figure 3.Equilibriumproportion of grassland, shrubland, andwoodland in relation to differential vegetation flammability(parameter scenario 4; see table 1) and initial system conditions: A—cells dominated by equal proportions of each vegetation type, andB—cells dominated bywoodlands. The lower panels (line plots) illustrate themodeled response of the system to changes inmodelparameters across the selected conditions (1)–(6), which aremarked by dotted lines and the samenumber in the upper plots; solidgray lines represent the equilibriumproportion of each vegetation type.Note that the systempresents two alternative stable statesunder the same conditions—(1) and (4)—which are contingent on vegetation flammability and the initial vegetation state of thesystem. All depicted cases represent stable states at the system-level.

Figure 4.Modeled response of woodland vegetation to increasing shrubland flammability (A) and example of alternative stable statesinduced by fire-vegetation feedbacks (B) in grassland–shrubland–woodland (G–S–W) systems. In (A) the dashed line representsunstable equlibria points and corresponds to the border between basins of attraction of the two alternative states (solid lines)representing woodland or grassland dominance. Over the range of shrubland flammability where these alternative stable states exist,the initial vegetation composition of the systemdetermines towardswhich alternative stable state the system settles as shown in (B). In(B) the initial vegetation conditions of the system,which are homogeneous among all cells, aremarked by the origin of each gray linein the ternary plot; the black dots depict the equilibrium state reached in each case. Equilibrium states are characterized by aG–S–Wproportion at the system-level, but as shown in (C), the among-cell variability in vegetation composition in thefinal equilibria variessubstantially in each case. Therefore, contrasted vegetation states among cells average out to define the intermediate stability attractorsat the system-level illustrated in (B).

9


successfully captures major ecosystem features andtrends observed in recent decades over Californialandscapes. For instance, the model can reproduce thedominance of oak woodlands reported under firefrequencies of ∼10 years associated with ground firesbefore the implementation of fire suppression policiesin the 1930s (Sugihara et al 2006). This can bemodeled

by implementing low fire severities thus reducing therate of vegetation conversion driven by fire. Incontrast, the dynamics of forests of fire-sensitivespecies (e.g., Douglas-fir, Lazzeri-Aerts and Rus-sell 2014) are captured over a range of fire frequencieswhen high fire severities are implemented. On theother hand, landscapes dominated by shrublands

Figure 5. Summary of themechanisms that determine the equilibriumproportions of each vegetation type in grassland–shrubland–woodland systems (G–S–W). Panels A, B–C,D, and E–F represent four different sets of simulations related to 4major processes infire-prone ecosystems. In each ternary plot, the gray and colored big-dots correspond to the initial and final system-level vegetationstate, respectively. System-level states are characterized by aG–S–Wproportion, which depends on theG–S–Wproportion of the cellsintegrating the system. In all cases (A through F), the initial vegetation state of all cells coincide with the system initial state (i.e., graybig-dot), whereas cells’final vegetation state is represented by the black small-dots. In panel A simulations, the four ternary plotsrepresent four environments with their corresponding baseline fire probability f; the rest ofmodel parameters are the same acrossenvironments (succession rate of vegetation, time since disturbance –TSF–, vegetation flammability, and fire severity). Similarly,initial G–S–Wproportion differs between simulations B andC,whereas the initial TSF is the only parameter that differ between E andF.

10


under a fire return interval of∼30–40 years, character-istic of chaparral (Sugihara et al 2006, table S1), wereobserved under relatively high fire severity consistentwith the crown-fire regime of such communities.

Despite the often assumed high fire resilience ofMTE vegetation, our approach reinforces that suchecosystems can be very sensitive to altered fire fre-quency and severity. Our results show that fire returnintervals under five years result in grass-dominatedsystems irrespective of the succession rate of vegeta-tion. This is consistent with trends observed in recentdecades over Mediterranean-climate California (e.g.,Minnich and Dezzani 1998, Sugihara et al 2006) andwith anthropological knowledge regarding NativeAmerican burning practices over central coastal Cali-fornia (e.g., Lightfoot et al 2013). On the other hand,reduced ignition rates allow buildup of fuels and suc-cession from grassland to shrubland or from shrub-land to woodland, as observed over California afterimplementation of fire suppression policies (e.g., Rus-sell and McBride 2003, Meentemeyer et al 2008). Ourmodel does not have fuel buildup effects on severity,so we do not address the question of whether suppres-sion will contribute to extreme or uncharacteristicfires (see Keeley et al 1999), nor do we model extremefire weather effects that can overwhelm inherent vege-tationflammability characteristics (Moritz 2003).

Feedbacks, bistability and disturbance stochasticitySwitches between contrasting stable vegetation statesin G–S–W systems may occur as a result of smallvariations in extrinsic ecosystemdrivers of disturbance(climate) or in fire-vegetation feedbacks (e.g., invasivespecies). Such switches are triggered by the existenceof critical points in underlying processes of distur-bance linked to external drivers (Beisner et al 2003).Phase transitions may also result, however, fromvariation in processes that are not dependent on orinduced by disturbance such as succession rate ofvegetation. In these cases, system behavior is notdetermined by feedbacks, and state dynamics aregoverned by gradual or threshold changes (Suding andHobbs 2009).

In our model, the inclusion of moderate fire-vege-tation feedbacks successfully reproduce the observedself-reinforcing grass-fire cycle (D’Antonio andVitousek 1992), whereas alternative stable states (bist-ability) and hysteresis emerge when strong fire-vegeta-tion feedbacks operate (Scheffer et al 2001). In bothcases, feedbacks induced by differential vegetationflammability drive the behavior of the system by effec-tively modifying environmental drivers (e.g., fireprobability). Plant traits that modulate fire-vegetationfeedbacks are thus key in determining the nature andlocation of critical thresholds in the dynamics of fire-prone G–S–W systems. Other studies point to theimportance of plant life history strategies (e.g., Saura-Mas et al 2010), self-reinforcing combustion

properties (e.g., Odion et al 2010), and vegetationtraits related to flammability (e.g., Hoffmannet al 2012) in generating feedbacks and conditions thatallow long-termpersistence of vegetation states.

The analysis presented in this theoretical studyindicates that threshold responses in the probability offire (induced by fire-vegetation feedbacks) and dis-turbance stochasticity may be strong enough mechan-isms to generate system bistability in fire-prone G–S–Wsystems such asMTEs. Suchmechanisms have beenassociated with alternative stable states in other fire-prone ecosystems (D’Odorico et al 2006). Our frame-work, however, emphasizes that these mechanismsoperate at different scales; disturbance stochasticitycan generate spatial heterogeneity (i.e., state changeonly at local scales) as opposed to system-wide shiftsmodulated by strong fire-vegetation feedbacks. Whenstrong feedbacks operate, system-level alteration inthe abundance of one ecosystem component (e.g.,grass) can be expected to permanently change the nat-ure of system interactions and the dynamics of vegeta-tion towards a different stable state (Suding andHobbs 2009, Staver and Levin 2012). However, if suchchanges occur when the state of the system is close tobifurcation points (Scheffer 2009), then disturbancestochasticity can effectively modulate shifts across thebifurcation threshold. For instance, locally delayed (orexpedited) fire occurrence may allow (or prevent)vegetation successional changes that can override sys-tem-level feedback switches and thus determine tra-jectory towards one state or the other at the local scale.Overall, our findings suggest that, under some condi-tions, disturbance stochasticity may translate intomore gradual responses of the system as a whole toaltered conditions even when strong feedbacksoperate.

Framework limitations and implicationsClearly, extrinsic ecosystem drivers such as climate arenot spatially homogeneous, and extreme events andclimate fluctuations can be particularly important inmodulating system dynamics and stability throughtime. Similarly, additional spatially heterogeneousdrivers (e.g., herbivory, nutrient cycling, hydrology,edaphic factors or humans) might prevent some sitesfrom vegetation succession during disturbance-freeintervals (e.g., Callaway and Davis 1993, Land-fire 2010). Even though our model can incorporateenvironmental gradients and other spatially explicitecosystem drivers (figure S7), these factors are notimplemented in the simulations presented here, whichaim to evaluate basic fire-vegetation mechanismsunderlying the behavior of G–S–W systems. Thefuture inclusion of climate fluctuations into a spatiallyinformed STM (e.g., incorporating patterns of soiltypology and climate gradients; Bestelmeyeret al 2011) will allow a more sophisticated predictiveapproach for characterizing dynamics and

11


understanding general pattern-process relationshipsacross scales infire-prone communities.

It is encouraging that a simple STMmodel like theone presented here can approximate some of thehuman and environmental influences in the dynamicsofMTE fire regimes. Refinedmodels representing spe-cific ecosystems are needed to be able to assess if,when, and where drastic shifts may occur in reality.The possibility of abrupt and non-reversible statechanges in such ecosystems, however, evidences theuncertainty and unpredictability that can be associatedwith their management. Comprehensive under-standing of system behavior is needed to infer feed-back mechanisms, identify system thresholds, anddetermine biotic and abiotic factors that affect the resi-lience of ecosystems (e.g., van de Koppel et al 2002,Suding and Hobbs 2009). Identifying thresholds rela-ted to collapse and recovery is a first step that can helpprioritize adaptive management efforts to sustaindesired states and associated ecosystem services (Folkeet al 2004, Bestelmeyer 2006). We believe our con-ceptual framework could thus represent a useful start-ing point for specifying management scenarios basedon refined predictive local models and assessingthreshold responses and disequilibrium dynamicsderived from ongoing land-use and climate changes.This may help resolve under which fire modeling orscales of analysis the inclusion of feedback effects iscritical to capture MTEs dynamics, and to assess whenand where drastic ecosystem shifts may occur underfuture MTE climates so that conditions resulting instate changes can be attenuated via resilience-basedmanagement.

Conclusion

Our minimal dynamic framework provides deepermechanistic understanding of how certain aspects of adisturbance regime (fire recurrence, severity, andstochasticity), vegetation characteristics (successionrate and flammability), and fire-vegetation feedbacksdetermine system composition and dynamics in G–S–W systems, which characterize many temperate fire-prone vegetation. Our findings strongly suggest thatvegetation alteration inMTEsmay not only occur afterextreme fire events (e.g., Rodrigo et al 2004), contrast-ing states in such ecosystems may be driven by smallvariation in ecosystem processes such as fire recur-rence and system flammability. Plant traits thatmodulate system feedbacks effectively modify thebehavior of MTEs and determine the nature andlocation of critical thresholds in their dynamics. Theexistence of alternative stable states and of contrastedMTEs response to environmental change has broadimplications for theirmanagement.

Acknowledgments

We are grateful to Katharine Suding, Mathieu Buoro,and two anonymous referees for their helpful com-ments. Thanks to iPlant Collaborative and to theNational Center for Ecological Analysis and Synthesis,the University of California, Santa Barbara, for com-puting resources. Funding for this work was providedby the Gordon and Betty Moore Foundation throughthe Berkeley Initiative inGlobal Change Biology.

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IntroductionMaterial and methodsModel and simulation runs overviewModel processesImplementation of the STM frameworkRule 1—successional processRule 2—vegetation flammability feedbacksRule 3—ignitionRule 4—fire severity effects

Simulation experimentsModel runs

ResultsVegetation dynamics across parameter spaceAlternative stable statesDivergent vegetation trajectories

DiscussionDynamics of california ecosystemsFeedbacks, bistability and disturbance stochasticityFramework limitations and implications

ConclusionAcknowledgmentsReferences

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