Climatic controls on ecosystem resilience: Postfireregeneration in the Cape Floristic Region ofSouth AfricaAdam M. Wilsona,b,c,1, Andrew M. Latimerd, and John A. Silander Jr.c

aDepartment of Geography, University at Buffalo, Buffalo, NY 14261; bDepartment of Ecology and Evolutionary Biology, Yale University, New Haven,CT 06520-8106; cDepartment of Ecology and Evolutionary Biology, University of Connecticut, Storrs, CT 06269; and dDepartment of Plant Sciences, Universityof California, Davis, CA 95616

Edited by Monica G. Turner, University of Wisconsin-Madison, Madison, WI, and approved June 2, 2015 (received for review September 9, 2014)

Conservation of biodiversity and natural resources in a changingclimate requires understanding what controls ecosystem resilienceto disturbance. This understanding is especially important in thefire-prone Mediterranean systems of the world. The fire frequencyin these systems is sensitive to climate, and recent climate changehas resulted in more frequent fires over the last few decades.However, the sensitivity of postfire recovery and biomass/fuelload accumulation to climate is less well understood than fire fre-quency despite its importance in driving the fire regime. In thisstudy, we develop a hierarchical statistical framework to modelpostfire ecosystem recovery using satellite-derived observationsof vegetation as a function of stand age, topography, and climate.In the Cape Floristic Region (CFR) of South Africa, a fire-prone bio-diversity hotspot, we found strong postfire recovery gradients as-sociated with climate resulting in faster recovery in regions withhigher soil fertility, minimum July (winter) temperature, and meanJanuary (summer) precipitation. Projections using an ensemble of11 downscaled Coupled Model Intercomparison Project Phase 5(CMIP5) general circulation models (GCMs) suggest that warmerwinter temperatures in 2080–2100 will encourage faster postfirerecovery across the region, which could further increase fire fre-quency due to faster fuel accumulation. However, some modelsproject decreasing precipitation in the western CFR, which wouldslow recovery rates there, likely reducing fire frequency throughlack of fuel and potentially driving local biome shifts from fynbosshrubland to nonburning semidesert vegetation. This simple yetpowerful approach to making inferences from large, remotelysensed datasets has potential for wide application to modelingecosystem resilience in disturbance-prone ecosystems globally.

hierarchical Bayesian | ecology | fire | climate | remote sensing

In many ecosystems, climate change will exert its most powerfulimpacts via disturbance, such as outbreaks of forest pests (1),

species invasions (2), and fire (3). A key feature of ecosystems’response to disturbance is the recovery time, the time requiredfor the ecosystem to return to a state similar to its state beforedisturbance [called “engineering resilience” by Peterson et al.(4)]. Rapid recovery from disturbance is associated with highresilience—that is, the ability of the system to return reliably toits previous state (5). Slow recovery can signal an approachingcatastrophic jump to an alternative state (6) or, given frequentdisturbance, chronically lower function (7).Fire is one of the most widespread and important forms of

disturbance globally, occurring as an important feature in morethan 50% of the world’s terrestrial ecosystems (8). However, therisk of climate change is difficult to assess because fires are notwell represented in global ecosystem models (9). There is growingevidence of increased fire frequency, severity, and/or size in manyregions, due in large part to warming and incidence of drought(3, 10–13). In many regions of the world and especially Mediter-ranean climate systems, the frequency and severity of wildfire isexpected to continue to increase in the coming decades due to

warmer and drier weather conditions (14, 15), although someareas may actually see a decrease in frequency due to slower fuelaccumulation (16). Accordingly, resilience to disturbance by firewill strongly influence the response of these regions to climatechange and is central to management; in the western UnitedStates, South Africa, and elsewhere, postfire resilience is a focus ofland management agencies (9).Despite the critical role of resilience to disturbance (and es-

pecially to fire) in the response of ecosystems to climate change,few studies have attempted to quantify and predict patterns ofresilience or to understand the climatic controls on postfire re-covery across a biome. Equally importantly, there has been vir-tually no research at large scales most relevant to ecosystemregime shifts and management (17). The key reasons are logis-tical: it is difficult to measure postdisturbance recovery overrelevant time frames (years to decades) and spatial scales (10s to1,000s of square kilometers).The necessary data and tools are now, however, available. We

have multidecadal, continuous global measurements from sat-ellites including Moderate Resolution Imaging Spectroradi-ometer (MODIS) and LANDSAT that can be used to measurekey ecosystem properties through time (18). High-resolutionhistorical weather data are also now increasingly available (19,20), as are decades of spatially detailed fire records (3, 10). Inthis paper, we develop a relatively simple yet powerful compu-tational approach to make regional-scale inferences and pre-dictions of ecosystem resilience in response to projected climatechange. By incorporating millions of pixels from satellite imageryover the last 15 y, for the first time to our knowledge, it is pos-sible to quantify broad-scale patterns in ecosystem recoveryand identify regional climatic gradients in postfire ecosystem

Significance

The rate at which ecosystems recover from disturbance cangreatly influence their resilience to environmental change. Weused more than a decade of satellite data to model how theextraordinarily biodiverse shrublands of South Africa recoverfollowing fire and how recovery rates vary with temperature andprecipitation across the region. We found that climate stronglyaffects how quickly plant communities can recover after fire. Wealso used global climate models to project ecosystem recoveryinto the future and found that warmer winter temperatures willlikely speed up postfire recovery unless precipitation declines astemperature increases (as some models project).

Author contributions: A.M.W., A.M.L., and J.A.S. designed research; A.M.W. performedresearch; A.M.W. analyzed data; and A.M.W., A.M.L., and J.A.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Data deposition: Fire recovery parameters (maps) are available via figshare at dx.doi.org/10.6084/m9.figshare.1420575.1To whom correspondence should be addressed. Email: adamw@buffalo.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1416710112/-/DCSupplemental.

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dynamics. With relatively simple parametric models fit in a hier-archical Bayesian (HB) framework, we can use large environmentaldatasets to explain these patterns in terms of climatic variation andpredict the effects of climate change on postfire resilience.Remotely sensed vegetation indices have a long tradition in

vegetation monitoring (21–25). Remotely sensed data are com-monly used to assess various attributes of wildfires includinglocations of active fires, fire severity, and identification of burnedareas (see ref. 26 for an excellent review of various tools andmetrics). The majority of these studies use remotely sensed datato monitor fire characteristics rather than postfire recovery. Evenfewer studies have attempted to use biophysical data to modelpostdisturbance recovery rates. For example, Röder et al. (27)used 20 LANDSAT scenes to assess postfire recovery in Spainwith simple linear regression to quantify the increase in vegeta-tion cover as a function of time since fire. However, no attemptwas made to quantitatively estimate the relationship betweenexplanatory variables or construct a predictive model. In anotherstudy, Schroeder, et al. (28) classified forest regrowth into fourcategories (little to no, slow, moderate, and fast) using field dataand then used LANDSAT imagery and a regression tree ap-proach to identify environmental covariates of the recovery rates.However, this method required all pixels to be binned into the fourclasses before analysis and was capable only of making coarse cat-egorical predictions for a fixed time period. Other similar studieshave used various methods to quantify recovery, including object-based image analysis (29), linear regression (30, 31), spatially bin-ning regions and comparing with unburned areas (32), and log-normal regression (33), but none of these methods were able toincorporate environmental covariates directly into the postfire re-covery model or make quantitative recovery predictions.In this study, we develop an HB model that uses climate and

topographical parameters to predict postfire biomass accumu-lation across the fynbos (Mediterranean shrubland) biome (34)in the Cape Floristic Region (CFR) of South Africa (Fig. S1).The CFR alone has over nine thousand vascular plant species,two-thirds of which are endemic to the region (representingnearly half of the 20,000 vascular plant species in all of southernAfrica) and is one of the most biodiverse regions globally (35).The extraordinary biodiversity and speciation rates in combina-tion with the large proportion of transformed habitats have ledto the region’s high conservation priority (36). Fire, which has atypical return time of 10–13 y in the system (37), is recognized asone of the most important factors in developing and maintainingsuch extraordinary biodiversity (38), and therefore, it is criticalthat we understand the climatic controls on the fire regime andpostfire recovery in this system.Our approach draws on detailed fire history records from the

region, a 10-y archive of biweekly MODIS satellite imagery, high-resolution climate and topographical data (Fig. S2), and a hierar-chical model. In fynbos, there is a strong relationship betweenbiomass and the Normalized Difference Vegetation Index (NDVI)(39), so despite its low spectral resolution compared with modernhyperspectral sensors, for long-term continuous monitoring oflarge spatial domains, it remains extremely useful. The modelwas evaluated using 25% holdout cross-validation and compar-ison with a 40-y history of observed fire events. We also used anensemble of 11 Coupled Model Intercomparison Project Phase 5(CMIP5) general circulation models downscaled to the region topredict future change in postfire recovery rates.

ResultsThe full model, which included climate, topography, and soil,had a lower deviance information criterion score (DIC; meandeviance: 3,104,349; effective number of parameters pD: 14,608;DIC: 3,089,741) compared with a model with only topography andsoil (mean deviance: 3,136,752; pD: 15,656; DIC: 3,121,097, ΔDIC = 31,356), indicating extremely strong support (40) for thehypothesis that climate is a key predictor of the postfire NDVItrajectory in this system (model code available in Dataset S1). Themean predicted and observed NDVI values for four fires across

the region illustrate how the model is able to capture the spatialvariability observed in postfire NDVI (Fig. 1; locations shown inFig. S1). To assess the predictive performance across differentpost fire ages, the R2 between the predicted and observed me-dian annual values were calculated for various ages (e.g., 0–2 y,1–3 y, etc.) for every location and time step in the validationdataset. The model can predict approximately half (R2 = 0.47) ofthe variation in NDVI between 2 and 10 y following fire (whichdecreases slightly in older areas; Fig. S3). Furthermore, there isstrong support [ΔAkaike information criterion (AIC) = 229] fora relationship between the estimated recovery time and observedfire return intervals in this system (SI Materials and Methods),suggesting that recovery time can be used to estimate mean firereturn intervals given environmental conditions.

Spatial Variability in Postfire Recovery. Estimated recovery timesranged from <  5 to > 25 y, depending on the environmental con-ditions (Fig. 2). The regression coefficients shown in Table S1represent the association between each predictor (climate, topog-raphy, and soil) and the recovery parameters. Previous work hasshown that satellite derived NDVI is significantly correlated withbiomass in fynbos (39), so these parameters can be used to inferhow climate affects various aspects of postfire biomass accumula-tion across the region. The γ parameter, which represents themaximum increase in NDVI from the initial postfire value (α) tothe asymptotic value (α + γ), is positively correlated with meanJanuary (midsummer) rainfall and minimum temperatures in July(midwinter). In contrast, γ is negatively correlated with maximumJanuary temperature. These relationships suggest that the potentialmaximum NDVI (and, therefore, maximum biomass) is sensitive tothe temperature and precipitation extremes in the region, with lessbiomass accumulation in parts of the region with hot, dry summers(Fig. 2). Furthermore, NDVI increase (γ) is also positively associated

Age (Years)

NDV

I

0.2

0.4

0.6

0 4 8

α

De Hoop

0 4 8

α

Waterval0.2

0.4

0.6

α

α+γ

Baavianskloof

α

Cederberg

PredictedObserved

50% CI

α+γ

α+γα+γ

Fig. 1. Predicted and observed postfire recoveries for four regions across theCFR (see Fig. S1 for locations). The heavy black lines are the mean observed NDVIvalues for all validation pixels from a single fire in each region. The red linesrepresent the mean predicted value (Eq. 3). The horizontal dotted lines illustratethe estimated initial (α) and upper asymptote (α+ γ) of postfire NDVI. The shadedareas represent the 50% highest posterior density (HPD) credible intervals (CIs) ofthe predicted values. Note that the predicted values were estimated using thefitted model (Table S1) and environmental data for each validation pixel asspecified in the model and not fit directly to the observed data plotted here.

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with fine soil texture which has an important influence on soil nu-trients, water holding capacity, and plant water availability (41–44).The recovery rate (λ; which indicates more rapid recovery with

smaller values) was sensitive to midsummer precipitation and pre-cipitation concentration but not mean annual precipitation (TableS1). This result suggests that the growth of young and recoveringplants through the first few years following fire is limited by warmseason moisture availability, as has been observed in detailed studiesof individual plants (43, 45, 46) and population level analyses (47).The association with summer precipitation may also be driven byincreased seedling mortality in drier microsites as observed byMidgley (45) or alternatively by differences in species compositionand community functional traits across the gradient in recoverytime. For example, there is some evidence for higher frequency ofresprouting shrubs in wetter areas (48), which could lead to fasterpostfire recovery of biomass observed from satellite. Recovery rate(λ) is also strongly associated with soil fertility, with faster recoveryoccurring in more nutrient-rich soils (Table S1).The potential maximum NDVI (γ + α) and recovery rate (λ)

have similar (but inverted) spatial patterns indicating lower peakNDVI values and slower recovery (larger λ) in interior arid re-gions (e.g., Cederberg and Waterval) compared with wetter areasalong the coast and in the eastern portion of the region withaseasonal rainfall (e.g., de Hoop and Baviaanskloof; Figs. 1 and 2).The spatial pattern of maximum NDVI (γ + α) shows the overalleffect of elevation is less pronounced than the coastal-interior gra-dient (Fig. 2). The most arid parts of the region (near 20°E, 33°S)have estimated maximum NDVI (γ + α) values near 0.4, indicatingthat the aridity limits biomass below the levels found in wetter areas.The seasonal amplitude (A) is negatively associated with ele-

vation, slope, and mean January (midsummer) precipitation, butpositively associated with soil acidity, maximum January temper-ature, and mean annual precipitation (Table S1). The seasonalityof precipitation (SI Materials and Methods) is also an importantinfluence on A, with less seasonal variability in parts of the region

with more seasonal concentration of rainfall. The counter intuitiverelationship is likely driven by differences in species compositionand functional traits across the region. The most important traitsthat would lead to a seasonal variation in NDVI are deciduousleaves or an annual life cycle, which are more common in partsof the region with aseasonal rainfall (primarily in the east) (49).Model output including maps of λ, γ, A, and the recovery time areavailable at dx.doi.org/10.6084/m9.figshare.1420575.

Climate Projections. The climate models forecast that the region willconsistently warm in the coming century but precipitation is muchless certain, reflecting the climatological complexity in precipitationacross the region. For example, the 2081–2100 RCP8.5 changes(multimodel regional mean± SD) for January maximum tem-perature (3.67± 1.07 °C), and July temperature (3.24± 0.95 °C)are relatively smooth across the region, with higher values in theinland regions (Fig. S4). However, the predictions for mean annualprecipitation (−17.36± 33.76 mm), mean January precipitation(0.16± 5.93 mm), and precipitation seasonality (−0.53± 4.47) havelarge spatial and intermodel variability (Fig. S4). In general, thewestern part of the region is likely to experience decreased meanannual and January precipitation, whereas there may be an increasein winter rainfall in the east.Multimodel mean projections of postfire recovery time show

little change (−1.34± 1.41 y), but predictions vary widely be-tween models and across the region (Fig. 3). Overall, most showdecreasing (faster) recovery time driven primarily by warmerwinter temperatures (Fig. S5). However, precipitation is para-mount in this system and the high uncertainty in projected pre-cipitation change for this region translates to large intermodelvariability even in the sign of the projected postfire recovery rates.Some models (e.g., MIROC5, GFDL-ESM2M) show regionalgradients with slowing recovery in the west (driven by decreasedprecipitation) and faster recovery in the east, while others (e.g.,FGOALSs2) result in faster recovery times (−3.18± 1.76 y) acrossthe region by as much as −12.4 y (Fig. 3).

DiscussionMuch of the focus in the remote sensing literature has been onmapping and monitoring ecosystem patterns (50–52) rather thanunderstanding ecosystem processes and building predictive modelsof spatiotemporal dynamics (53). In this study, we used millions of

34°S

33°S

32°S

31°S

0.6

Maximum NDVI

18°E 20°E 22°E 24°E

34°S

33°S

32°S

31°S

0 10 20 30

Recovery Time (years)

0.4

Fig. 2. Median posterior values of maximum NDVI (γ +α, unitless) and re-covery time (years for NDVI to return to prefire levels; Eq. 10). (Inset) His-togram of the values across the region and serves as a color key to the mapin each panel. Fig. S1 shows the pixels used in model fitting and validation.Note that maximum NDVI is the modeled asymptotic maximum predicteddue to the climate, topography, and soil across the region. Predictions weremade for all areas in the fynbos biome including those currently transformed(e.g., for agriculture), whereas white areas are outside the fynbos biome.

34°S

33°S

32°S

31°S

−10 −5 0

MIROC5

18°E 20°E 22°E 24°E

34°S

33°S

32°S

31°S

−10 −5 0

FGOALSs2

Fig. 3. Median posterior value of predicted change in recovery time (years)under two downscaled CMIP5 general circulation models (FGOALSs2 andMIROC5) with scenario RCP8.5 averaged over 2080–2100. Negative valuesindicate faster postfire recovery, whereas positive values indicate slowerrecovery. See Fig. S5 for all 11 models.

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satellite observations collected over the last two decades to identifyrecovery gradients in postfire ecosystem dynamics. By breakingecosystem recovery into distinct but complementary componentsand quantifying the role of climate, soil, and other topographicalvariables, we also gain the ability to forecast how the ecosystem mayrespond to future climate change. Despite its relative simplicity andease of interpretation, the model performed well in cross-validation,explaining ≈ 50% of the variation in the held-out data.We found that postfire recovery rate varies dramatically across

the region and is significantly associated with climatic gradients(Table S1). Additionally, we found that the estimated postfire re-covery times were a useful predictor of fire return intervals using aseparate survival analysis (SI Materials and Methods and Fig. 4).Recovery time ranges from only a few years on the warmer mesiccoast to more than three decades in the arid interior where fynbosshrubland transitions into desert vegetation (Fig. 2). Eastern coastalregions have the shortest recovery times despite accumulating morebiomass (large γ) due to fast recovery rates (λ< 2). In contrast,vegetation in the more arid west requires decades to recover toprefire conditions even though the maximum NDVI tends to besmaller (γ + α≤ 0.45).Warmer winter temperatures in the future are expected to ac-

celerate postfire recovery across the region, which could furtherincrease fire frequency due to faster fuel accumulation (Fig. 3 andFig. S5). Warmer conditions are known to increase short-term firerisk in the region (10), but the impact of climate change on fuelload accumulation rates had not been previously quantified. Thisknowledge gap is important, because climate affects fire regimesthrough its influence on fuel loads as well as burning conditions.This study is limited to recovery of ecosystem-level above-

ground biomass, which cannot account for changes in functionalor phylogenetic community structure. There are likely to beadditional ecological impacts of shorter fire return times accordingto the regeneration strategies and dispersal capabilities of the

constituent species (54, 55). For example, some fynbos speciesrequire up to 10 y following fire before successfully reproducing(56), which in combination with more frequent fires leads to theaptly named interval squeeze (57). More frequent fires encouragedby both high-risk weather (10) and faster postfire biomass accu-mulation could lead to significant shifts in community compositionby eliminating long-lived, nonsprouting shrubs (as observedexperimentally) (58).However, moisture availability is extremely important in this

region and the climate models exhibit large variability in pro-jected precipitation (Fig. S4). Several climate models project adecrease in precipitation in the western CFR, which would leadto slower recovery rates there and faster recovery in the easternpart of the region (e.g., MIROC5 in Fig. 3). This outcome wouldlikely lead to reduced fire frequency in the west due to lack offuel despite higher temperatures and more frequent high-riskfire weather and could lead to a biome conversion from fynbos tosemidesert vegetation in strongly affected areas.Understanding the spatiotemporal variability of the fire regime

and ecosystem resilience is critical to successfully manage andconserve floral biodiversity in this system. For example, landmanagers in the region currently attempt to maintain intervalsbetween fires long enough for ≥ 50% of the “individuals in apopulation of the slowest-maturing of the obligate reseeding spe-cies to have flowered and developed seed for at least three suc-cessive seasons” (59, 60). In combination with field observations,this modeling framework could be further developed to account forthe phylogenetic and functional composition of plant communitiesto give a more comprehensive perspective on the relationship be-tween climate and ecological resilience in this system.

Materials and MethodsData. Long-term (1950–2000) mean climate data (61) for the region wereextracted, and topographical parameters were calculated using the 30-m

Estimated RecoveryTime (years)

Fire

Ret

urn

Tim

e (y

ears

)

Fire

Pro

babi

lity

(%)

5

10

15

20

25

30

5 10 15 20 25 30

5%

25%

50%

75%

0

20

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Fig. 4. Fire return time distributions estimated from a sur-vival model fit with observed fire return times (SI Materialsand Methods) and the satellite-derived estimated recoverytimes described in this study (Fig. 2). This relationship cor-roborates the utility of the satellite-derived recovery times asa useful proxy for fire return intervals in this system. Colorsindicate the cumulative probability of observing a given firereturn interval (y axis) given the satellite-derived postfirerecovery time estimated in this study (x axis).

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digital elevation model (DEM) from the ASTER project (asterweb.jpl.nasa.gov/gdem.asp) and aggregated to the 500-m grid.

Fire occurrence data include fire boundaries mapped by reserve managersextending back to the 1950s (10) and the remotely sensed burned area productderived from the MODIS satellite sensor. The historical burned area polygonswere then used to resolve the postfire age of each pixel in each time step duringthe MODIS era, with postfire ages ranging from 0 to 59 y. This, in combinationwith the climate data described above, allowed us to extract the multidecadalclimate signal from a single decade of satellite observations. For example,imagine we know from the field data that a pixel burned in both 1980 and 2008.The NDVI observations for that pixel (which are limited to post-2000 MODIS)would start at postfire age 20, continue to 28, and then reset back to age zero(due to the fire in 2008) and increase again until the end of the record. Bycomparing these postfire trajectories with climate rather than weather, we canarrange the data in terms of age rather than date and have a record of recoveryextending back decades before the satellite data are available.

Locations with no NDVI observations from the first 3 y, or with fewer than3 y of data, were removed resulting in ≈ 16,700 pixels across the region, eachwith 225 bimonthly observations of NDVI through time (totaling ≈ 3.7million observations of individual pixels) from the MODIS 500-m resolution16-d gridded NDVI product (MOD13A1). Furthermore, there were 1.4 millionNDVI observations from over 3,000 km2 greater than 10 y old and 375,000observations from 850 km2 greater than 20 y old. This space-for-time sub-stitution extended the ability of the model to infer recovery trajectoriesmuch longer than the duration of the MODIS data. See SI Materials andMethods for a more detailed description of data sources and processing.

Model Design. The postfire NDVI trajectory is modeled as a simple parametricfunction of the environmental variables mentioned above in a HBmodel. Thefirst level of the model fits the trajectory of observed NDVI values as a functiondefined in Eqs. 1–3. The second level regresses each parameter against theenvironmental variables, providing a link between climate and the shape of thepostfire recovery trajectory (Eq. 4). The model was completed by specifyingvague prior distributions on the model hyperparameters (Eqs. 5–9). This ap-proach accomplishes several tasks in a single coherent framework. For learningabout environmental controls on resilience, the parameters of primary interestare the regression coefficients between the environment and the three recoveryfunction parameters. The model provides full posterior distributions for allmodel parameters and avoids complications introduced by stringing togetherseveral disparate models in an ad hoc fashion (e.g., one model to describe thepostfire trajectory of NDVI through time and another to relate the trajectoriesto environmental variables). This approach ensures that uncertainty inherent ineach level of themodel is propagated through to the posterior distributions (62).

The postfireNDVI trajectory is approximated by anexponential function thatincreases to an asymptote similar to the curve described by Dìaz-Delgado andPons (63). We extended this function by adding (i) a sinusoidal component tocapture the seasonality, (ii) a term (ϕ) to adjust the curve for month of fire,and (iii) a term (α) that allows spatial variation in NDVI immediately followingfire (Eq. 3). Let i∈ 1 : I index space (I≈ 16,700), t ∈ 1 : T index time (2000–2010with 225 16-d intervals),m∈ 1 : 12 indicates themonth of the previous fire, andp∈1 : P index the environmental covariates including an intercept.

NDVIi,t ∼N�μi,t ,

1τ

�, [1]

μi,t = αi + γi

�1− e−

agei,tλi

�+ , [2]

Ai sinn2π × agei,t +

hϕ+

π

6

�mi,t − 1

�io. [3]

The spatial recovery parameters (α, γ, λ, and A) are assumed to be constantfor each location (i) and do not vary through time (although the modelcould be extended to include time-varying parameters). The terms of thisequation can be interpreted as follows: α represents the initial postfire NDVI.Because various regions have different postfire reflectance (due to soil,topography, and other factors), this term accounts for this spatial vari-ability in the observed NDVI immediately postfire. See ref. 64 for discus-sion on the impact of different soil types across the region on remotelysensed data. The γ +α term defines the asymptotic upper limit of the curveand thus represents the potential maximum NDVI of the pixel (givenenough time to recover after fire). The parameter λ is the exponentialterm that describes the recovery rate, A describes the amplitude of thesine wave and reflects the magnitude of the seasonality in that location,and ϕ adjusts for month-of-fire (m). The month-of-fire must be taken intoaccount because the fires occurred throughout the year, so age 0 can occurat any phase of the seasonal cycle. Using m− 1 fixes January at ϕ and allowsthe subsequent months to increase by π=6. The term 2π × agei,t sets theseasonal frequency to be one year. Fig. 1 provides an example fit of thisfunction to observed data.

The P environmental variables (soil, climate, topography, etc.; Fig. S2) areused to explain the variation in the spatial recovery parameters γi, λi, and Ai.These parameters are fit as independent variables in multivariate regressionswith the matrix of environmental variables X, an I × P matrix with βγ, βλ, andβA as vectors of length P

ξi ∼ lnN�Xiβξ,

1τξ

�ξ∈ fγ, λ,Ag; i∈ 1 : I. [4]

The NDVI immediately after fire can vary due to soil reflectance, exposedbedrock, and other factors that are not easily explained using climate ortopography. Our uncertainty in the value of this parameter was representedin the model with a relatively vague prior on the α term

μα ∼Nð0.15, 10Þ, [5]

τα ∼Γð0.01, 0.01Þ. [6]

The priors on each of the regression terms (β and τ) were selected to besufficiently noninformative to let the data drive the posterior distributions

βξ,p ∼Nð0,10Þτξ ∼Γð0.01, 0.01Þ

�ξ∈ fγ, λ,Ag; p∈ 1 : P, [7]

αi ∼N�μα,

1τα

�i∈ 1 : I, [8]

ϕ∼Uniformð−π, πÞ. [9]

The parameters can be used to estimate the postfire recovery time (RT) bycalculating the time until the predicted curve approaches γ +α (33). Thisprocess is sensitive to the threshold (especially for larger values of λ whichincrease gradually to the asymptote) but serves as a useful relative metric tocompare the recovery trajectories across the region. Here we define RT to bewhen the exponential component of the model equals γ − 0.005. Therefore,solving γið1− e−agei,t=λi Þ= γ − 0.005 for age, we have

RTi = λi × logð200× γiÞ. [10]

ACKNOWLEDGMENTS. This work was supported by NASA headquarters underNASA Earth and Space Science Fellowship Program Grant NNX09AN82H and aYale Climate & Energy Postdoctoral fellowship (to A.M.W.), as well as NationalScience Foundation (NSF) Grants OISE-0623341, DEB-0516320, and DEB-1046328(to J.A.S.) and NSF Grant DEB-1045985 (to A.M.L.).

1. Haynes KJ, Allstadt AJ, Klimetzek D (2014) Forest defoliator outbreaks under climatechange: Effects on the frequency and severity of outbreaks of five pine insect pests.Glob Change Biol 20(6):2004–2018.

2. Chambers JC, et al. (2014) Resilience to stress and disturbance, and resistance tobromus tectorum l. invasion in cold desert shrublands of western North America.Ecosystems (N Y) 17(2):360–375.

3. Westerling AL, Hidalgo HG, Cayan DR, Swetnam TW (2006) Warming and earlierspring increase western U.S. forest wildfire activity. Science 313(5789):940–943.

4. Peterson G, Allen CR, Holling CS (1998) Ecological resilience, biodiversity, and scale.Ecosystems (N Y) 1(1):6–18.

5. Côté IM, Darling ES (2010) Rethinking ecosystem resilience in the face of climatechange. PLoS Biol 8(7):e1000438.

6. Scheffer M, Carpenter S, Foley J, Folke C, Walker B (2001) Catastrophic shifts in eco-systems RID f-2386-2011. Nature 413(6856):591–596.

7. Mumby PJ, Hastings A, Edwards HJ (2007) Thresholds and the resilience of Caribbean

coral reefs. Nature 450(7166):98–101.8. Shlisky A, Alencar AAC, Nolasco MM, Curran LM (2009) Tropical Fire Ecology.

(Springer, Berlin), pp 65–83.9. Bowman DMJS, et al. (2009) Fire in the Earth system. Science 324(5926):481–484.10. Wilson AM, Latimer AM, Silander JA, Gelfand AE, de Klerk H (2010) A Hierarchical

Bayesian model of wildfire in a mediterranean biodiversity hotspot: Implications ofweather variability and global circulation. Ecol Modell 221(1):106–112.

11. Pausas JG (2004) Changes in fire and climate in the eastern Iberian peninsula (Med-iterranean basin). Clim Change 63(3):337–350.

9062 | www.pnas.org/cgi/doi/10.1073/pnas.1416710112 Wilson et al.

Dow

nloa

ded

by g

uest

on

Mar

ch 2

1, 2

020

12. Seidl R, Schelhaas M, Lexer M (2011) Unraveling the drivers of intensifying forestdisturbance regimes in Europe. Glob Change Biol 17(9):2842–2852.

13. Aldersley A, Murray SJ, Cornell SE (2011) Global and regional analysis of climate andhuman drivers of wildfire. Sci Total Environ 409(18):3472–3481.

14. Gitay H, Brown S, Easterling W, Jallow B (2001) Climate Change 2001: Impacts, Ad-aptation, and Vulnerability: Contribution of Working Group II to the Third Assess-ment Report of the Intergovernmental Panel on Climate Change (Cambridge UnivPress, Cambridge, UK).

15. IPCC-WGI (2013) Climate Change 2013: The Physical Science Basis. Annex i: Atlas ofGlobal and Regional Climate Projections: Final Draft Underlying Scientific-TechnicalAssessment (WMO, Geneva).

16. Batllori E, Parisien MA, Krawchuk MA, Moritz MA (2013) Climate change-inducedshifts in fire for Mediterranean ecosystems. Glob Ecol Biogeogr 22(10):1118–1129.

17. Mace G (2013) Global change: Ecology must evolve. Nature 503(7475):191–192.18. Kennedy RE, et al. (2014) Bringing an ecological view of change to LANDSAT-based

remote sensing. Front Ecol Environ 12(6):339–346.19. Hijmans RJ, et al. (2005) Very high resolution interpolated climate surfaces for global

land areas. Int J Climatol 25(15):1965–1978.20. Wilson AM, Silander JA (2014) Estimating uncertainty in daily weather interpolations:

A Bayesian framework for developing climate surfaces. Int J Climatol 34(8):2573–2584.21. Townshend JR, Goff TE, Tucker CJ (1985) Multitemporal dimensionality of images of

normalized difference vegetation index at continental scales. IEEE Trans Geosci RemSens GE-23(6):888–895.

22. Tucker CJ (1979) Red and photographic infrared linear combinations for monitoringvegetation. Remote Sens Environ 8(2):127–150.

23. Curran P (1980) Multispectral remote sensing of vegetation amount. Prog Phys Geogr4(3):315–341.

24. Zhao M, Running S, Heinsch FA, Nemani R (2011) Land Remote Sensing and GlobalEnvironmental Change, Remote Sensing and Digital Image Processing, eds Ram-achandran B, Justice CO, Abrams MJ (Springer, New York), pp 635–660.

25. Huete A, et al. (2002) Overview of the radiometric and biophysical performance ofthe MODIS vegetation indices. Remote Sens Environ 83(1-2):195–213.

26. Lentile LB, et al. (2006) Remote sensing techniques to assess active fire characteristicsand post-fire effects. Int J Wildland Fire 15(3):319–345.

27. Roder A, Hill J, Duguy B, Alloza J, Vallejo R (2008) Using long time series of landsatdata to monitor fire events and post-fire dynamics and identify driving factors. a casestudy in the ayora region (eastern Spain). Remote Sens Environ 112(1):259–273.

28. Schroeder T, Cohen W, Yang Z (2007) Patterns of forest regrowth following clear-cutting in western oregon as determined from a LANDSAT time-series. For EcolManage 243(2-3):259–273.

29. Mitri GH, Gitas IZ (2013) Mapping post-fire forest regeneration and vegetation re-covery using a combination of very high spatial resolution and hyperspectral satelliteimagery. Int J Appl Earth Obs Geoinf 20:60–66.

30. Hernández Clemente R, Navarro Cerrillo RM, Gitas IZ (2009) Monitoring post-fireregeneration in mediterranean ecosystems by employing multitemporal satelliteimagery. Int J Wildland Fire 18(6):648–658.

31. van Leeuwen WJD (2008) Monitoring the effects of forest restoration treatments onpost-fire vegetation recovery with MODIS multitemporal data. Sensors (Basel Swit-zerland) 8(3):2017–2042.

32. HopeA,Albers N, Bart R (2012) Characterizing post-fire recovery of fynbos vegetation in thewestern cape region of south africa using MODIS data. Int J Remote Sens 33(4):979–999.

33. Gouveia C, DaCamara C, Trigo R (2010) Post-fire vegetation recovery in Portugalbased on spot/vegetation data. Nat Hazards Earth Syst Sci 10:673–684.

34. Cowling RM, Richardson DM, Paterson-Jones C (1995) Fynbos: South Africa’s UniqueFloral Kingdom (Fernwood Press, Vlaeberg, South Africa).

35. Manning J, Goldblatt P (2012) Plants of the Greater Cape Floristic Region, Strelitzia(South African National Biodiversity Institute, Pretoria, South Africa), Vol 1.

36. Forest F, et al. (2007) Preserving the evolutionary potential of floras in biodiversityhotspots. Nature 445(7129):757–760.

37. Van Wilgen BW, et al. (2010) Fire management in Mediterranean climate shrublands:A case study from the Cape Fynbos, South Africa. J Appl Ecol 47(3):631–638.

38. Cowling RM, Pressey RL (2001) Rapid plant diversification: Planning for an evolu-tionary future. Proc Natl Acad Sci USA 98(10):5452–5457.

39. Wilson AM, Silander JA, Gelfand A, Glenn JH (2011) Scaling up: Linking field data andremote sensing with a hierarchical model. Int J Geogr Inf Sci 25(3):509–521.

40. Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A (2002) Bayesian measures ofmodel complexity and fit. J R Stat Soc Series B Stat Methodol 64(4):583–639.

41. Newman BD, et al. (2006) Ecohydrology of water-limited environments: A scientificvision. Water Resour Res 42(6):W06302.

42. Mustart P, Cowling R (1993) Effects of soil and seed characteristics on seed germi-nation and their possible roles in determining field emergence patterns of fouragulhas plain (south africa) proteaceae. Can J Bot 71(10):1363–1368.

43. Lechmere-Oertel R, Cowling R (2001) Abiotic determinants of the fynbos/succulentkaroo boundary, south africa. J Veg Sci 12(1):75–80.

44. Vereecken H, Maes J, Feyen J, Darius P (1989) Estimating the soil moisture retentioncharacteristic from texture, bulk density, and carbon content. Soil Sci 148(6):389–403.

45. Midgley JJ (1988) Mortality of cape proteaceae seedlings during their first summer.South African Forestry J 145:9–12.

46. Bond WJ (1983) Fire survival of cape proteaceae-influence of fire season and seedpredators. Plant Ecol 56(2):65–74.

47. Merow C, et al. (2014) On using integral projection models to generate de-mographically driven predictions of species’ distributions: Development and valida-tion using sparse data. Ecography 37(12):1167–1183.

48. Vlok JHJ, Yeaton RI (2000) The effect of short fire cycles on the cover and density of un-derstorey sprouting species in south african mountain fynbos. Divers Distrib 6(5):233–242.

49. Campbell BM, Werger MJA (1988) Plant form in the mountains of the Cape, SouthAfrica. J Ecol 76(3):637–653.

50. Beck P, Atzberger C, Hogda K, Johansen B, Skidmore A (2006) Improved monitoringof vegetation dynamics at very high latitudes: A new method using MODIS NDVI.Remote Sens Environ 100(3):321–334.

51. Ahl D, et al. (2006) Monitoring spring canopy phenology of a deciduous broadleafforest using MODIS. Remote Sens Environ 104(1):88–95.

52. Zhang XY, et al. (2003) Monitoring vegetation phenology using MODIS. Remote SensEnviron 84(3):471–475.

53. Batt RD, Carpenter SR, Cole JJ, Pace ML, Johnson RA (2013) Changes in ecosystemresilience detected in automated measures of ecosystem metabolism during a whole-lake manipulation. Proc Natl Acad Sci USA 110(43):17398–17403.

54. Buhk C, Meyn A, Jentsch A (2007) The challenge of plant regeneration after fire in themediterranean basin: Scientific gaps in our knowledge on plant strategies and evo-lution of traits. Plant Ecol 192(1):1–19.

55. Thuiller W, Slingsby JA, Privett SDJ, Cowling RM (2007) Stochastic species turnover andstable coexistence in a species-rich, fire-prone plant community. PLoS ONE 2(9):e938.

56. Kruger FJ, Bigalke RC (1984) Ecological Effects of Fire in South African Ecosystems,Ecological Studies, eds Booysen PV, Tainton NM (Springer, Berlin), Vol 48, pp 67–114.

57. Bradstock R, Williams R, Gill A (2012) Flammable Australia: Fire Regimes, Biodiversityand Ecosystems in a Changing World (Csiro Publishing, Clayton, VIC, Australia).

58. van Wilgen BW (1981) Some effects of fire frequency on fynbos plant communitycomposition and structure at Jonkershoek, Stellenbosch. South African Forestry J118(1):42–55.

59. Kruger FJ, Lamb A (1979) Conservation of the Kogelberg State Forest. PreliminaryAssessment of the Effects of Management From 1967 to 1978 (Jonkershoek ForestryResearch Centre, Stellenbosch, South Africa).

60. Forsyth G, van Wilgen B (2008) The recent fire history of the Table Mountain NationalPark, and implications for fire management. Koedoe: African Protected Area ConservSci 50(1):3–9.

61. Schulze RE (2007) The South African Atlas of Agrohydrology and Climatology (WaterResearch Commission, Pretoria, South Africa).

62. Clark JS (2007) Models for Ecological Data: An Introduction (Princeton Univ Press,Princeton).

63. Diaz-Delgado R, Pons X (2001) Spatial patterns of forest fires in Catalonia (NE ofspain) along the period 1975–1995: Analysis of vegetation recovery after fire. For EcolManage 147(1):67–74.

64. DeKlerk H (2008) A pragmatic assessment of the usefulness of the MODIS (terra andaqua) 1-km active fire (MOD14a2 and MYD14a2) products for mapping fires in thefynbos biome. Int J Wildland Fire 17(2):166–178.

65. Province WC (2000) Western Cape Nature Conservation Laws amendment act, 2000(no. 3 of 2000).

66. Forsyth GG, van Wilgen BW (2007) An Analysis of the Fire History Records FromProtected Areas in the Western Cape (CSIR, Stellenbosch, South Africa).

67. De Klerk H, Wilson AM, Steenkamp K (2012) Evaluation of satellite-derived burnedarea products for the fynbos, a Mediterranean shrubland. Int J Wildland Fire 21(1):36–47.

68. Roy D, Boschetti L, Justice C, Ju J (2008) The collection 5 MODIS burned area product–global evaluation by comparison with the MODIS active fire product. Remote SensEnviron 112(9):3690–3707.

69. Roy D, Boschetti L (2008) MODIS Collection 5 Burned Area Product (MCD45) User’sGuide v1.1 (South Dakota State Univ, Brookings, SD).

70. Escuin S, Navarro R, Fernandez P (2008) Fire severity assessment by using NBR (nor-malized burn ratio) and NDVI (normalized difference vegetation index) derived fromLANDSAT TM/ETM images. Int J Remote Sens 29(4):1053–1073.

71. Epting J, Verbyla D (2005) Landscape-level interactions of prefire vegetation, burnseverity, and postfire vegetation over a 16-year period in interior Alaska. Can J ForRes 35(6):1367–1377.

72. Markham CG (1970) Seasonality of precipitation in the United States. Ann Assoc AmGeograph 60(3):593–597.

73. Latimer AM, Wu S, Gelfand AE, Silander JA, Jr (2006) Building statistical models toanalyze species distributions. Ecol Appl 16(1):33–50.

74. Cowling RM (1983) The occurrence of C3 and C4 grasses in fynbos and allied shrub-lands in the south eastern Cape, South Africa. Oecologia 58(1):121–127.

75. Soderberg K, Compton JS (2007) Dust as a nutrient source for fynbos ecosystems,South Africa. Ecosystems 10(4):550–561.

76. Neteler M, Bowman MH, Landa M, Metz M (2012) GRASS GIS: A multi-purpose opensource GIS. Environ Model Softw 31:124–130.

77. Sherman R, Mullen R, Haomin L, Zhendong F, Yi W (2008) Spatial patterns of plantdiversity and communities in alpine ecosystems of the Hengduan mountains, North-west Yunnan, China. J Plant Ecol 1(2):117–136.

78. Dormann CF, et al. (2013) Collinearity: A review of methods to deal with it and asimulation study evaluating their performance. Ecography 36(1):027–046.

79. Kalognomou EA, et al. (2013) A diagnostic evaluation of precipitation in CORDEXmodels over southern Africa. J Clim 26(23):9477–9506.

80. R Development Core Team (2011) R: A Language and Environment for StatisticalComputing (R Development Core Team, Vienna).

81. Plummer M (2011) JAGS (just another Gibbs sampler) open-source, cross-platformengine for the BUGS language. Available at sourceforge.net/projects/mcmc-jags/.Accessed July 15, 2011.

82. Brooks S, Gelman A (1998) General methods for monitoring convergence of iterativesimulations. J Comput Graph Stat 7(4):434–455.

83. Wright D (1986) A note on the construction of highest posterior density intervals.Appl Stat 35(1):49–53.

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