Modeling stability and resilience afterslashburning across a sub-boreal to subalpineforest gradient in British Columbia

Evelyn H. Hamilton and Sybille Haeussler

Abstract: Stability and resilience of conifer-dominated vegetation communities following clear-cutting and slashburning incentral British Columbia, were modeled across gradients of resource availability, fire return interval (FRI), and fire se-verity. We hypothesized that high resource availability and long fire-free intervals would enhance stability, whereas highresource availability and short fire-free intervals would confer resilience. Fire weather indices and pre- and post-burn fuelloads were recorded and vegetation regrowth monitored for 5–11 years at 12 sites. Stepwise regression was used to modelrates of revegetation, increases in vascular species richness, and pre- and post-burn similarity of species composition as afunction of the environmental variables. Predicted stability for four sub-boreal to subalpine vegetation communities withcontrasting resource availability and FRI corresponded closely to our hypotheses. Rates of revegetation were more stronglycorrelated with resource availability, whereas composition-based response variables were more strongly correlated with theFRI. Based on revegetation rates, all ecosystems were predicted to have equal resilience. However, based on vegetationcomposition, mesic sub-boreal ecosystems were predicted to be more resilient than mesic subalpine ecosystems becausethe degree of change in species composition was less sensitive to increasing burn severity. More slashburned sites with abroader range of burn severities are needed to verify these preliminary models.

Resume : La stabilite et la resilience des groupements vegetaux domines par des coniferes a la suite d’une coupe a blanc etdu brulage des dechets de coupe dans le centre de la Colombie-Britannique ont ete modelisees en fonction de gradients dedisponibilite des ressources, de l’intervalle entre les feux et de la severite du feu. Nous avons emis l’hypothese que la dispo-nibilite elevee des ressources et de longs intervalles sans feux augmenteraient la stabilite tandis que la disponibilite eleveedes ressources et de courts intervalles sans feux favoriseraient la resilience. L’indice foret-meteo et la charge de combusti-bles avant et apres feu ont ete notes et la vegetalisation a ete suivie pendant cinq a 11 ans dans 12 stations. La regressionpar degres a ete utilisee pour modeliser le taux de vegetalisation, l’augmentation de la richesse en especes vasculaires et lasimilitude de la composition en especes avant et apres le brulage en fonction des variables environnementales. La predictionde la stabilite de quatre groupements vegetaux sub-boreaux a subalpins avec differentes disponibilites des ressources et desintervalles differents entre les feux correspondait etroitement a notre hypothese. Le taux de vegetalisation etait plus etroite-ment correle avec la disponibilite des ressources tandis que les variables de reponse basees sur la composition etaient plusetroitement correlees avec les intervalles entre les feux. Selon les predictions, tous les ecosystemes avaient la meme resil-ience sur la base du taux de vegetalisation. Par contre, sur la base de la composition de la vegetation, les predictions indi-quaient que les ecosystemes sub-boreaux mesiques etaient plus resilients que les ecosystemes subalpins mesiques parceque le degre de changement dans la composition en especes etait moins sensible a l’augmentation de la severite dubrulage. Il faudrait davantage de stations ou les dechets de coupe ont ete brules avec une plus large gamme de sever-ites de brulage pour verifier ces modeles preliminaires.

[Traduit par la Redaction]

Introduction

As forest managers and policy makers become moreaware of the pervasive influence of human activities on for-est ecosystems, they have shown increasing interest inunderstanding and assessing the resilience of ecosystems, a

topic that formerly was of concern mainly to theoreticalecologists (Whiteman et al. 2004; Drever et al. 2006). InBritish Columbia, for example, the provincial Chief Foresterrecently launched a major initiative to adapt the existing for-est management framework to achieve resilient forest eco-systems (Snetsinger et al. 2006). The success of suchinitiatives will rest upon the ability of forest scientists to de-velop techniques for effectively measuring and monitoringecological resilience.

Resilience refers to the ability of a dynamic system to re-cover from disturbances that profoundly alter its composi-tion and structure. Holling (1973) distinguished betweentwo concepts of resilience. The first or traditional concept,which he termed engineering resilience, emphasizes stabilityof the system near an equilibrium steady state and measuresthe ability or tendency of a system to return to a steady-state

Received 11 January 2007. Accepted 20 May 2007. Publishedon the NRC Research Press Web site at cjfr.nrc.ca on 5 February2008.

E.H. Hamilton.1 BC Ministry of Forests and Range, ResearchBranch, P.O. Box 9519 Stn Prov Gov, Victoria, BC V8W 9C2,Canada.S. Haeussler. The University of British Columbia, 2424 MainMall, Vancouver, BC V6T 1Z4, Canada.

1Corresponding author (e-mail: Evelyn.Hamilton@gov.bc.ca).

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condition following disturbance (Sutherland 1974). Holling(1973) proposed that since real-world ecosystems are almostalways far from equilibrium, resilience is more appropriatelymeasured as the amount of disturbance that a system can ab-sorb before it changes its organizing processes and struc-tures to an alternative state or stability domain. This seconddefinition he termed ecological resilience.

The relationship between these two concepts can be illus-trated by means of the familiar ball and cup heuristic of sys-tem stability (Gunderson 2000; Fig. 1a), in which thevertical axis or depth of the cup indicates the rate at whichthe system returns to a stable state, whereas the horizontalaxis or width of the cup indicates the amount of disturbancethe system can absorb before the ball (representing the cur-rent state of the system) exits the cup for an alternativestability domain. We find the terms engineering resilienceand ecological resilience to be cumbersome and will referhereafter to the vertical (depth) component of the system as‘‘stability’’ (i.e., the tendency for the system to remain at orreturn to an equilibrium state) and the horizontal (width)component as ‘‘resilience’’ (i.e., the amount of disturbancethe system can absorb while still remaining within in its cur-rent stability domain).

Plant ecologists have often measured the stability of for-ests and other long-lived terrestrial plant communities (e.g.,Halpern 1988; Rydgren et al. 2004). However, measurementof resilience, as defined here, is more difficult. The longgeneration times of the dominant tree and shrub species inforest ecosystems preclude direct experimental observationof alternative stable states (Connell and Sousa 1983;Schroder et al. 2005). Therefore, indirect methods for as-sessing resilience in young forest communities must be de-veloped. One approach for addressing this challenge is toestimate differences in resilience among vegetation com-munities across ecological gradients, rather than attemptingto directly measure resilience within a single community. Inthis manuscript, we begin the difficult process of measuringresilience empirically in young postdisturbance foreststhrough a modeling approach that assesses relative ratherthan absolute resilience.

Studies of forest succession after wildfire, clear-cut log-ging, volcanic eruptions, and windstorms have demonstratedthe remarkable ability of plant communities to reassemblefollowing major disturbances (e.g., Zobel and Antos 1997;Turner et al. 1998). Many studies have focused on themechanisms underlying succession after disturbance (e.g.,Chapin et al. 1994). Others have shown the essential roleplayed by biological legacies, such as buried plant propa-gules, residual live patches, and downed woody debris inthe recovery process (Franklin et al. 2000). There has beenless study of how the response of plant communities or eco-systems to catastrophic disturbances varies across geo-graphic and environmental gradients (e.g., Denslow 1980;De Grandpre et al. 2003).

In British Columbia, broadcast burning of clear-cut log-ging slash and residual vegetation (hereafter referred to asslashburning) was widespread during the 1970s and 1980sas a means of fuel hazard reduction and site preparation forplanting. This silvicultural treatment entailed felling all liv-ing and dead trees within a cutblock typically 30–100 ha insize, mechanical removal of all merchantable boles, fol-

lowed by aerial ignition of the residual and resprouting veg-etation and organic debris. The radical nature of this forestdisturbance and lack of a close analogue in nature(Haeussler and Kneeshaw 2003) make slashburning an at-

stability

alternativedomain

resilience

currentstabilitydomain

Fire return intervalshort long

Res

ou

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avai

lab

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high

low

mesic transitionalmesic sub-boreal

dry sub-boreal mesic subalpine

high stability, moderate resiliencemoderate stability, high resilience

moderate stability, low resiliencelow stability, moderate resilience

( )a

( )b

Fig. 1. The ball and cup model of system stability and resilience(modified from Gunderson 2000). (a) The ball represents the cur-rent state of the system; the cup represents its current domain ofattraction. The depth of cup represents stability (persistence close toan equilibrium or steady state), whereas the width of the cup repre-sents resilience (the amount of disturbance the system can absorbwhile remaining within the same domain of attraction). (b) Hypo-thesized stability and resilience for four contrasting forest eco-systems: (i) mesic sub-boreal (high resource availability, short firereturn interval); (ii) dry sub-boreal (low, short); (iii) mesic transi-tional (high, long); and (iv) mesic subalpine (low, long).

Quesnel

Prince George

ClearwaterOS/OF

GL

FL WC

WTGR

MA

CH

HC

IC BM

·

0 100 200

km

Scale

·

·

Fig. 2. Map of study locations in British Columbia. Sites are de-fined in Table 1.

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Table 1. Environmental characteristics of the study areas.

Studysite

Latitude(N)

Longitude(W)

Elevation(m) Plant association*

GDD>5 8C{

Precipitation{

(mm/year) AspectSlope(%) SMR§ SNR||

SI}

(m)FRI**(years)

MA 5585’42@ 122859’7@ 770 Picea glauca � Picea engelmannii –Oplopanax horridus

1174 515 N 40 Moist Rich 21.5 145

CH 54831’13@ 122831’9@ 820 Picea glauca � Picea engelmannii – Spireabetulifolia – Gymnocarpium dryopteris

1132 927 Flat 0 Moist Medium-rich 21.2 227

FL 53844’56@ 122820’52@ 850 Picea glauca � Picea engelmannii – Lonicerainvolucrata – Gymnocarpium dryopteris

1107 713 NE 22 Fresh Medium 19.1 450

BM 53826’ 15@ 121833’39@ 910 Picea glauca � Picea engelmannii –Oplopanax horridus

1057 752 E 31 Fresh Medium 19.7 685

GL 53815’35@ 122822’20@ 920 Picea glauca � Picea engelmannii –Gymnocarpium dryopteris

1049 689 Flat 11 Moist Rich 19.1 476

IC 53826’37@ 121833’3@ 950 Pinus contorta – Vaccinium membranaceum –Vaccinium myrtilloides

1024 751 Flat 0 Dry Poor 15.0 314

HC 53830’27@ 121830’27@ 1020 Picea glauca � Picea engelmannii –Oplopanax horridus

965 810 S 22 Fresh Medium 19.7 900

WC 53854’30@ 120835’45@ 1050 Picea glauca � Picea engelmannii –Oplopanax horridus

940 1058 NE 27 Fresh Medium 19.7 1000

GR 53821’46@ 120841’13@ 1040 Abies lasiocarpa – Gymnocarpium dryopteris –Brachythecium

949 1030 Flat 0 Fresh-wet Medium-poor 15.5 800

WT 53824’58@ 120834’18@ 1400 Abies lasiocarpa – Menziesia ferruginea –Gymnocarpium dryopteris

648 1123 S 33 Fresh Medium 11.7 700

OS/OF 51845’33@ 119812’46@ 1560 Abies lasiocarpa – Oplopanax horridus –Athyrium filix-femina

502 1345 SE 22 Fresh-moist Medium-rich 12.3 950

Note: Site locations are shown in Fig. 2.*Plant associations (called site series) are from www.for.gov.bc.ca/hre/becweb/standards-becdb.html. For scientific authorities of plant names see www.eflora.bc.ca.{Interpolated growing degree-days >5 8C (Wang et al. 2006).{Interpolated annual precipitation (Wang et al. 2006).§Soil moisture regime (Meidinger and Pojar 1991).||Soil nutrient regime (Meidinger and Pojar 1991).}Spruce site index in metres of height at age 50 years, calculated from equations of Klinka et al. (1996) and Wang and Klinka (1996).**Fire return interval from DeLong (1998), modified for local topographic conditions after Rogeau et al. (2001) and Rogeau (M.-P. Rogeau. 2000. Fire regime analysis. Mount Revelstoke National Park.

Contract report available from Parks Canada, Mount Revelstoke National Park, Revelstoke, British Columbia; M.-P. Rogeau. 2001. Fire history study. Mackenzie TSA, British Columbia. Contract reportFRBC00-021-058/1. Available from Abitibi Consolidated Inc., Mackenzie Region, P.O. Box 250, Mackenzie, British Columbia).

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tractive candidate for investigating the phenomenon of eco-system resilience to disturbance.

Patterns of vegetation succession after wildfire and afterprescribed burn of clearcuts have been extensively docu-mented in western coniferous forests (see Brown and Smith2000 and references therein). Many of the early and moregeographically extensive studies assessed succession indi-rectly through a chronosequence approach (e.g., Dix andSwan 1971). Studies that documented succession directly(e.g., Halpern 1988) were typically restricted to a few,nearby study sites. Our study is unique in that repeated sam-pling was done on 12 slashburned sites across a broad cli-matic and geographic gradient, enabling us to model theresponse of vegetation communities to burns of varying se-verity across gradients of resource availability and fire re-turn interval (FRI).

Our objective was to use vegetation dynamics to modelstability and resilience across a range of sub-boreal to sub-alpine forest ecosystems representative of the timber-producing forests of central British Columbia. We hypo-thesized that the most stable forest ecosystems would havehigh resource availability and long FRIs. By contrast, wehypothesized that the most resilient forest ecosystemswould have high resource availability and short FRIs. Inshort, we anticipated that productive forest ecosystemswith recurrent exposure to wildfire would best withstandhigh burn severities without undergoing a shift in vegeta-tion structure and composition to an alternative stabilitydomain. Our hypotheses for the relative stability and resil-ience of four hypothetical central British Columbia eco-systems representing the extremes of a high to lowresource availability gradient and a short to long FRI gra-dient are illustrated in terms of the ball and cup model(Fig. 1b). Ecosystems possessing both necessary attributesfor stability or resilience were rated high for that property,those possessing one attribute were rated moderate, andthose possessing neither attribute were rated low.

Methods

Study area descriptionEleven study areas were situated in plateau and mountain

forests of east-central British Columbia between 51846’Nand 5586’N and 119813’W and 122859’W at elevations rang-ing from 770 to 1560 m (Fig. 2 and Table 1). Seven werelocated in midelevation forests of the Sub-boreal Spruce(SBS) biogeoclimatic zone, two in high-elevation (sub-alpine) forests of the Engelmann Spruce – Subalpine Fir(ESSF) biogeoclimatic zone, and two were transitional be-tween inland mountain rainforests of the InteriorCedar – Hemlock (ICH) biogeoclimatic zone and the SBSand ESSF zones. See Meidinger and Pojar (1991) for a de-scription of this system of ecosystem classification. Withinthe study region, there is a strong northwest to southeastgradient of increasing elevation and decreasing growingdegree-days accompanied by generally increasing precipita-tion and decreasing wildfire frequency from the Interior Pla-teau north of Prince George to the Quesnel Highland andColumbia Mountains physiographic regions northeast ofClearwater (DeLong 1998; Fig. 2).

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old-growth (125- to >300-year-old) forests dominated by whitespruce (Picea glauca (Moench) Voss), Engelmann spruce(Picea engelmannii Parry ex. Engelm.), and their hybrids;subalpine fir (Abies lasiocarpa (Hook.) Nutt.); and lodge-pole pine (Pinus contorta Dougl. ex. Loud var. latifoliaEngelm.) with late seral understory vegetation rangingfrom ericaceous shrubs and feathermosses on well-drained,nutrient-limited sites to devilsclub (Oplopanax horridusMiq.), ferns, and leafy mosses on moist, nutrient-rich sites(Table 1). The forests were clear-cut between 1985 and 1988in the winter when the snow cover was deep enough to pro-tect the vegetation outside of the skid roads from disturb-ance. Thus, minimal difference in pre- and post-loggingunderstory species composition was evident shortly afterlogging (Hamilton and Peterson 2003; E.H. Hamilton, un-published data). Slashburning took place during the firstgrowing season after logging on dates listed in Table 2. TheOtter Creek study area had both a spring burn (OS) and a fallburn (OF) (Hamilton and Peterson 2003). Our study thus in-cluded 12 slashburned sites located within 11 study areas.

Field proceduresFor all sites, Canadian forest fire weather index conditions

(Van Wagner 1987) were recorded, depth-of-burn pins wereinserted, and forest floor depths (L, F, and H layers) andwoody fuel loads were measured along fuel assessment tri-angles (Trowbridge et al. 1987) prior to and immediatelyafter the burn (Table 2). Depth-of-burn pins were also estab-lished in a grid pattern in the vegetation sampling quadrats.Corners of square quadrats and centres of circular quadratswere marked with metal rods.

Vegetation monitoring quadrats, 0.785 m2 (1 m diametercircle), 9 m2 (3 m � 3 m), or 25 m2 (5 m � 5 m) in size,were established either prior to logging (three sites), justafter logging and prior to slashburning (four sites), or shortlyafter slashburning (five sites) (Table 2). An ocular estimateof percent cover and modal height was made for each vege-tation stratum (conifers, tall shrubs, low shrubs, herbs anddwarf woody plants, and mosses), and percent cover was re-corded for each vascular plant species on all sites one, two,three or four, and five growing seasons after slashburningand, for some sites, two (–2) or one (–1) growing seasonsbefore and 10 or 11 years after slashburning (Table 2). Ad-ditional sampling details are found in Hamilton and Peterson(2003, 2006) and Hamilton (2006a, 2006b).

Data analysisWe used stepwise linear and nonlinear least-squares re-

gression to develop models relating three plant communityresponse variables (revegetation, diversity, and composition)to four predictor variables (time since fire, resource avail-ability, FRI, and fire severity) (Table 3). Hamilton andHaeussler2 tested many different indices of plant communityresponse and environmental predictor variables and onlytheir best variables are used in the current study.

Plant community response variablesFor revegetation, which essentially measures how biomass

accumulates after slashburning, the best descriptor was anindex of vegetation volume production (V).

½1� V ¼X5

i¼1

½ð% cover of all species in stratum iÞ

� ðmodal height of stratum iÞ�

For diversity, we used a second-order jack-knife estimator(Hellmann and Fowler 1999) of site-scale vascular plantspecies richness (SJ2) to compensate for differences in quad-rat size and sampling intensity (Table 2) among sites

½2� SJ2 ¼ Sobs þ Q1ð2m� 3Þm

� Q2ðm� 2Þ2mðm� 1Þ

where Sobs is the observed gamma species richness across allquadrats at one site, Q1 is the mean number of species perquadrat, Q2 is the mean number of species in all possiblecombinations of two quadrats, and m is the total number ofquadrats.

For composition, we used a Bray–Curtis (BCt1:t2) distancemeasure (Legendre and Legendre 1998), based on percentcover by species, to calculate the percent similarity betweenpreburn (t1 = –1 or –2 years at site CH) and postburn (t2 =5 or 10 years) plant community composition, only for theseven sites (Table 2) where preburn data were available.

½3� C5 ¼ 1� BC�1:5

½4� C10 ¼ 1� BC�1:10

Environmental predictor variablesTo estimate resource availability, we used the site index

(SI) of white or Engelmann spruce (estimated spruce heightin metres at 50 years). White and Engelmann spruce hybrid-ize extensively within the study region and are commonlytreated as a single species, known as ‘‘interior spruce.’’ Weused BC Ministry of Forests and Range (2005) SI estimatesfor all sub-boreal and transitional site types for which thesite index was based on seven or more samples. For sitetypes with fewer site index samples, we used the best fitequation of Wang and Klinka (1996) for sub-boreal sites,the equation of Klinka et al. (1996) for subalpine sites, andthe mean of the two equations, weighted by elevation, fortransitional sites.

Our estimate of the FRI was a refinement of the work ofDeLong (1998). DeLong’s estimated FRIs for large topo-climatic (landscape) units were adjusted for topographic ef-fects such as valley orientation, elevation, and aspect usingmodels developed by Rogeau3,4 and Rogeau et al. (2001)for areas within and adjacent to the study region.2

Fire severity was estimated by the depth of burn (DOB) in

2 E. Hamilton and S. Haeussler. 2005. Recovery of sub-boreal and subalpine forest plant communities after slashburning. Contract reportavailable from British Columbia Ministry of Forests, Research Branch, Victoria, British Columbia.

3 M.-P. Rogeau. 2000. Fire regime analysis. Mount Revelstoke National Park. Contract report available from Parks Canada, Mount Revel-stoke National Park, Revelstoke, British Columbia.

4 M.-P. Rogeau. 2001. Fire history study. Mackenzie TSA, British Columbia. Contract report FRBC00-021-058/1. Available from AbitibiConsolidated Inc., Mackenzie Region, P.O. Box 250, Mackenzie, British Columbia.

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Table 3. Regression models for plant community response to slashburning. (a) Revegetation response, (b) recovery of diversity, recovery of composition (c) 5 years and (d) 10 yearsafter slashburning.

(a) Revegetation response.

Parameter estimates

Scale n Y X a1 a2 a3 a4 b1 b2 b3 b4 c1 c2 R2 Extra R2 F ratio P value

Best general time-since-fire model (combined exponential and power function)Y = aXbecX Quadrat 1053 V* Year 3.0 — — — 3.2 — — — 0.61 —Linearized form:

LN(Y) = a’ + bLN(X) +c(X), where a’ = ln(a)

Year + 1 1.1 — — — 3.2 — — — –0.5 — 0.34 273 <0.0001

Best multifactor model (combined exponential and power function)Linearized form:

LN(Y) = a1 + a2SI +a3FRI + a4DOB + (b1 +b2SI + b3FRI +b4DOB)LN(X) + (c1 +c2DOB)(X)

Quadrat 1024 V* Year + 1 –2.18 0.14 0.0006 0.22 5.0 –0.046 –0.0004 –0.32 –0.60 0.055 0.43 0.09 84 <0.0001

Rate of increase in vegetation percent cover � heightdY/dX = aXbecX(c + b/X)

(b) Recovery of diversity.

Parameter estimates

Scale n Y X a b1 b2 b3 b4 b5 b6 R2 Extra R2 F ratio P value

Best general time-since-fire model (linear)Y = a + b(X) Site 64 SJ2

{ Year 35.7 2.3 — — — — — 0.30 27 <0.0001

Best multifactor model (linear)Y = a + (b1 + b2SI + b3FRI +

b4SIFRI + b5DOB + b6SIDOB)XSite 64 SJ2

{ Year 35.1 –23.9 1.35 0.02 –0.001 2.69 –0.14 0.65 0.35 18 <0.0001

Rate of increase in vascular plant species richnessdY/dX = b1 + b2SI + b3FRI +

b4SIFRI + b5DOB + b6SIDOB

(c) Recovery of composition 5 years after slashburning.

Parameter estimates

Scale n Y X a1 a2 a3 b1 b2 R2 Extra R2 F ratio P value

Best single factor model (logarithmic)Y = a + bLN(X) Quadrat 134 C5

{ DOB + 1 0.47 — — –0.18 — 0.35 67 <0.0001

Best multifactor model (logarithmic)Y = a1 + a2FRI + a3SIFRI + (b1FRI +

b2SI�FRI)LN(X)Quadrat 129 C5

{ DOB + 1 0.17 0.001 –0.00005 –0.001 0.00006 0.62 0.27 51 <0.0001

(d) Recovery of composition 10 years after slashburning.

Parameter estimates

Scale n Y X a b c1 c2 R2 Extra R2 F ratio P value

Best single factor model (quadratic)Y = a + bX + cX2 Quadrat 110 C10

§ FRI 0.51 –0.0016 1.6�10–6 — 0.43 40 <0.0001

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centimetres of the forest floor LFH layers, derived from themean depth-of-burn pin measurements for each quadrat orsite (Table 2). DOB was the best overall predictor among11 indices of fire severity, including relative and absolutemeasures of forest floor and woody fuel consumption, testedby Hamilton and Haeussler.2

Regression analysesWe first tested for statistical independence of the environ-

mental descriptors, SI, FRI, and DOB, using scatter dia-grams and Pearson’s correlation coefficients (r). For therevegetation and composition regressions, we used quadrat-scale data (n = 1053 for V; 106 < n < 134 for C) that en-abled us to take advantage of the full range of burnseverities across each site. Data from each quadrat wereweighted as the reciprocal of the number of vegetation mon-itoring quadrats per site so that sites with many quadrats didnot unduly influence the regression equations. For diversity(SJ2), we used unweighted site by year data (n = 64) thataveraged burn severity across each site.

For revegetation and diversity regressions, we first devel-oped a general model of the time-since-fire (t) relationship,then added the environmental predictor variables (SI, FRI,and DOB) and their interaction terms in a stepwise fashionto improve the relationship. We then took the first derivative(dV/dt, dSJ2/dt) of the multifactor time-since-fire model toassess the response rate. Time-since-fire was not includedas an independent variable in composition models becauseC5 and C10 already factor in the effects of t. Instead, wefound the best single-factor regression model using SI, FRI,or DOB, then added the remaining variables and interactionterms to that model in a stepwise fashion. The significancelevel for entry into all regression models was � = 0.05. Be-cause each regression observation did not represent a statisti-cally independent combination of SI, FRI, DOB, and t (i.e.,we did not sample 1053 unique slashburns), we addressedconcerns about spatial autocorrelation in the quadrat scalemodels and temporal autocorrelation in the revegetation anddiversity models by ensuring that residuals were reasonablynormally distributed with respect to the y axis and thatDurbin–Watson D statistics were within acceptable limits.

To test hypotheses about relative stability and resilience,we defined the four contrasting ecosystems of Fig. 1b as fol-lows: mesic sub-boreal, SI = 22 m (high), FRI = 200 years(short); dry sub-boreal, SI = 15 m (low), FRI = 300 years(short); mesic transitional, SI = 20 m (high), FRI =800 years (long); and mesic subalpine, SI = 12 m (low),FRI = 1000 years (long). We then plotted dSJ2/dt, C5, andC10 against DOB ranging from 0 to 12 cm for each ofthese four representative ecosystem conditions. BecausedV/dt was not time independent, we defined the maximumamount of revegetation (Vmax) as

½5� Vmax ¼ fV jdV=dt ¼ 0; t � 12 yearsg

and the rate of revegetation (Vrate) as

½6� Vrate ¼ f1=tjdV=dt ¼ 0; t � 12 yearsg

We plotted eqs. 5 and 6 for the four sets of SI and FRI valuesabove and for DOB ranging from 0 to 12 cm. For each eco-system and each response variable (Vmax, Vrate, dSJ2/dt, C5, orT

able

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C10), the y intercept (i.e., the value of the response variableat low burn severity) was interpreted as an estimate of stabi-lity, whereas the x intercept (i.e., the depth of burn atwhich the response variable approaches either 0 or ?)was interpreted as an estimate of resilience.

Results

Environmental gradientsThe three environmental variables were not statistically

independent of one another (r = –0.64 for SI versus FRI;r = 0.20 for SI versus DOB; r = –0.07 for FRI versusDOB; all p < 0.05), because low-elevation ecosystemstended to have high resource availability, short FRIs, anddeeper, more uniform burns, whereas higher elevation eco-systems tended to have low resource availability, longFRIs, and shallow, spotty burns. Our study did, however,include one dry sub-boreal ecosystem with low resourceavailability and short FRIs, and several transitional and hu-mid sub-boreal sites that had relatively high resource avail-ability and long FRIs (Table 1). The 12 study burns includedwithin-site burn severities ranging from 0 to 11.3 cm DOB(Fig. 3) but did not encompass a full array of resourceavailabilities, FRIs, and fire severity extremes.

Model predictions and the ecosystem stability and resil-ience rankings, summarized below, were thus subject to twomain, interacting sources of uncertainty. The first uncer-tainty was related to the number of samples representativeof each of the four contrasting ecosystems, and the range ofDOB of those samples. Dry sub-boreal sites were under-represented in the sample, and sub-boreal sites generallyhad a narrower range of burn depths than transitional andsubalpine sites (Table 4); thus, response behaviour of sub-boreal ecosystems at higher DOBs extrapolates the observedtrend beyond the range of real data. The second source ofuncertainty relates to the sensitivity of the model to differen-ces in the predictor variables. Where the response curves arelocated close together relative to the variability reflected inthe r2 for the relationship, rankings should also be viewedas more uncertain.

RevegetationThe combined volume (V) of woody, herbaceous, and moss

layers developed consistently across sites, rising rapidly inyears 1–3, peaking at 5–6 years after slashburning, and thentapering off. This pattern reflects the dominant influence oftall herbs, notably fireweed (Epilobium angustifolium L.), inthe early postfire vegetation, giving way to shrubs, coniferoustrees, and mosses that have lower cover � height indices thanherbs during the first postfire decade. A combined exponen-tial and power time-since-fire function gave the best fit to thequadrat-scale data (r2 = 0.34; Table 3a). SI, FRI, and DOBall significantly influenced the model parameters, with SIproviding the most additional explanatory power (extra r2 =0.05), and FRI the least (extra r2 = 0.003). Although SI, FRI,and DOB together controlled the rate at which the curve in-creased and decreased (parameters a and b, Table 3a), onlyDOB had a significant effect on the shape of the curve (para-meter c, Table 3a, Fig. 4). The depth of burn at which thecurve changed from concave downward to upward (DOB >10 cm) was independent of SI and FRI. The implication of

this relationship is that for revegetation, SI and FRI influ-enced stability but had no significant effect on resilience.

Plots of Vmax and Vrate versus DOB (Figs. 5a and 5b) illus-trate the predicted differences in revegetation stability and re-silience for the four contrasting ecosystems. Contrary to ourhypotheses, Vmax ranked stability as mesic sub-boreal > mesictransitional > dry sub-boreal > mesic subalpine, because of thedominant influence of SI on this variable. On the other hand,Vrate ranked stability in accordance with our hypothesis(mesic transitional > mesic sub-boreal > mesic subalpine >dry sub-boreal), because it was positively correlated withboth SI and FRI. For both Vmax and Vrate, all four ecosystemswere predicted to have equal resilience and to remain withinthe same domain of attraction at DOB below 10 cm.

DiversityAcross all sites, vascular plant species richness increased

monotonically with time since fire, with the best generaltime-since-fire model being linear (R2 = 0.30; Table 3b). SI,FRI, and DOB all had a significant positive effect on theslope parameter b, but there were significant negative inter-actions between SI and FRI and between SI and DOB (R2 =0.65 for the combined model; Table 3b). Thus, the relation-ship between diversity and burn severity was a complex onethat could be positive at low SI (i.e., deep burns encourage vas-cular species invasion on poor sites), but negative at high SI(i.e., deep burns reduce preburn species survival and retardnew species invasion on rich sites) with the rate of increaseor decrease being influenced by FRI. When the rate of diver-sity increase, dSJ2/dt, was plotted against DOB for the fourcontrasting ecosystems (Fig. 5c), mesic sub-boreal and mesictransitional ecosystems had higher predicted stability andlower predicted resilience (x intercept ‡ 12 cm) than mesic sub-alpine and dry sub-boreal ecosystems on which deep burns werepredicted to increase species richness. Stability rankings fordiversity were mesic sub-boreal > mesic transitional > mesicsubalpine > dry sub-boreal, which is relatively close to ourhypotheses. By contrast, resilience rankings for diversity

0 2 4 6 8 10 12

Depth of burn (cm)

0

10

20

60

70

80

90

0.0

0.1

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No

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30

40

50

Ln(DOB)

30

40

5

No.ofobserv

ations

Fig. 3. Depth of burn (DOB) distribution across the 253 samplequadrats located within the 12 study sites.

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(mesic subalpine > dry sub boreal > mesic transitional >mesic sub boreal) were the reverse of our hypotheses.

CompositionPercent similarity between preburn and 5 year postburn

plant community composition (C5) was correlated with DOBin a negative logarithmic relationship (R2 = 0.35, Table 3),which predicted that quadrats with <1 cm of forest floorreduction would be 40% similar to preburn conditions at5 years, whereas quadrats with 6–8 cm DOB would recoveronly 10% of their preburn composition over the same timeperiod. Adding SI and FRI significantly improved themodel (R2 = 0.62; Table 3c). Longer FRIs raised the inter-cept (i.e., greater stability) and steepened the negativeslope of the line (i.e., lower resilience), but there was asignificant interaction between SI and FRI such that higherSIs reduced the effect of FRI on the intercept and slope.As a result, the plot of C5 versus DOB for the fourcontrasting ecosystems (Fig. 5d) predicts stability rankingsas mesic subalpine > mesic transitional ‡ dry sub-boreal >mesic sub-boreal and resilience rankings as mesictransitional ‡ mesic sub-boreal > dry sub-boreal > mesicsubalpine. Only the mesic subalpine ecosystem was pre-dicted to shift to an alternative stability domain within therange of DOB experienced in our study (at DOB = 6 cm).

Ten years after slashburning, plant communities were, onaverage, 4% more similar to unburned conditions than theyhad been at 5 years. C10 was not as strongly correlated withDOB as C5, but was well correlated with FRI in a concave

upward quadratic relationship (R2 = 0.43; Table 3c). In otherwords, although fire severity strongly influenced early re-covery patterns, the FRI had greater impact on composi-tional changes that affect succession over longer timeframes. Both SI and DOB interacted significantly with FRI toreduce the c parameter of the quadratic equation (R2 = 0.48;Table 3c). Thus, the C10 equation predicts that, at higher SIand DOB, the similarity to preburn conditions will be lower,most notably for ecosystems with long FRI. The graph of C10versus DOB (Fig. 5e) shows that long FRIs were associatedwith stability (mesic subalpine > mesic transitional > mesicsub-boreal > dry sub-boreal), whereas short FRIs were associ-ated with resilience (mesic sub-boreal > dry sub-boreal > mesicsubalpine > mesic transitional).

Discussion

Our premise for this study was that sub-boreal to sub-alpine forest vegetation communities of central British Co-lumbia would differ in their stability and resilience afterslashburning across gradients of resource availability (meas-ured as the spruce SI) and prior exposure to wildfire (meas-ured as the FRI). We hypothesized that ecosystems withabundant resources (high SI) and long FRIs would be themost stable — that is, they would most quickly return totheir original state provided the slashburn was of relativelylow severity (measured as DOB) — and that ecosystemswith abundant resources (high SI) and short FRIs would bethe most resilient — that is, they would absorb the most severe

Table 4. Comparison of ecological and sample size characteristics, hypothesized and observed stability ranks, and hypothesized and ob-served resilience ranks for four representative central British Columbia ecosystems.

Ecosystem

Characteristic Indicator variable AbbreviationDrysub-boreal

Mesicsub-boreal

Mesictransitional

Mesicsubalpine

Productivity Site index (m at 50 years) SI 15 22 20 12Prior exposure to wildfire Fire return interval (years) FRI 300 200 800 1000Sample size No. of burns (observations) on sites

with broadly similar SI and FRIn 1 (15) 4–5 (212–227) 2–3 (784–799) 4 (426)

Burn severity Depth of burn (cm) DOB 0–2 0–5 0–11 0–8

Hypothesized stability — — Low Moderate High ModerateObserved stability rank 1 = lowest; 4 = highest

Revegetation Amount of revegetation Vmax 3 1 2 4Rate of revegetation Vrate 4 2 1 3

Diversity Jack-knifed species richness SJ2 4 1 2 3Composition Percent similarity to unburned at 5 years C5 3 4 2 1

Percent similarity to unburned at 10 years C10 4 3 2 1Three-way stability rank 4 2 1 3Two-way stability rank 4 3 1 2

Hypothesized resilience — — Moderate High Moderate LowObserved resilience rank 1 = lowest; 4 = highest

Revegetation Amount of revegetation Vmax 1 1 1 1Rate of revegetation Vrate 1 1 1 1

Diversity Jack-knifed species richness SJ2 2 4 3 1Composition Percent similarity to unburned at 5 years C5 2 1 1 3

Percent similarity to unburned at 10 years C10 2 1 4 3Three-way resilience rank 1 3 4 2Two-way resilience rank 2 1 4 2

Note: Hypothesized stability and hypothesized resilience are from Fig. 1. Observed stability and resilience ranks are from Fig. 5. The three-way rankassigns equal weight to revegetation, diversity, and composition. The two-way stability rank assigns equal weight to composition-free (Vmax, Vrate, and SJ2)versus composition-based (C5 and C10) indicator variables.

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burns without shifting to an alternative stability domain. Weexpected interactions between SI and FRI but did not developformal hypotheses about which of these two factors was moreimportant and under what circumstances. What we found wasthat, although all of our plant community response variables(Vmax, Vrate, dSJ2/dt, C5, and C10) were significantly correlatedwith SI, FRI, and DOB, the shape of the response surface andthe degree of interaction among the environmental variablesvaried substantially according to the response variable se-lected (Table 4). Consequently, few universal conclusions canbe drawn regarding the relative stability or resilience of theseforest plant communities; their ranking depends to a largedegree on which qualities or characteristics of the vegetationcommunity are deemed to be important for meeting eco-system management goals. As shown by the differences be-tween C5 and C10, the rankings are also time sensitive.

Stability, in agreement with our hypothesis, was positivelyassociated with both SI and FRI. However, revegetation(particularly Vmax) and diversity were more strongly influ-enced by resource availability than by fire history. There-fore, if we disregard taxonomic composition and considerthe most stable ecosystem to be the one that most rapidlyreacquires biomass and species diversity after slashburning,our models predict that a mesic sub-boreal ecosystem(highest SI and shortest FRI) will be more stable than a me-sic transitional or a mesic subalpine ecosystem, both ofwhich have longer FRIs. On the other hand, species compo-sition was more strongly influenced by FRI than by SI.Thus, if we deem taxonomic composition to be important,

we will conclude that mesic subalpine communities (lowestSI but highest FRI) are the most stable, because they remainmost similar to their preburn composition after slashburning.Although model predictions for such ecosystem conditionsare highly uncertain because of the small sample size, oneuniversal prediction is that a dry sub-boreal ecosystem withlow SI and short FRI will have low stability (Table 4). Thesingle study site (IC) that best represented these ecosystemconditions was a gravelly lodgepole pine – blueberry eco-system that had slow rates of revegetation, had relativelylow species richness, and was invaded by short-lived seed-banking herbs and trembling aspen after slashburning.

Resilience is considerably more difficult to assess thanstability, because we have so little concrete evidence, partic-ularly in 5- to 11-year-old forest plant communities, as towhat constitutes a switch to an alternative stability domain(c.f., Bastow-Wilson and Agnew 1992; Schroder et al. 2005).At this stage in our field-based studies, the notion is moreabstract than real, because we have only one decade ofsuccessional data and because our study sites did not in-clude a full suite of exceptionally high severity burns thatwould have definitively exceeded the recovery capacity ofthese ecosystems. We proposed a mathematical criterion, thex intercept, as our estimate of resilience — fully recognizingthat many of our resilience predictions involve extrapolatingbeyond the burn depths that are well represented in ourstudy and may be empirically unrealistic. For example, forC5 and C10, the DOB at which the similarity between pre-and post-burn plant community composition reaches zero

Fire return intervalshort long

Res

ou

rce

avai

lab

ility

high

low

mesic transitional SI = 20 FRI = 800mesic sub-boreal SI = 22 FRI = 200

dry sub-boreal SI = 15 FRI = 300 mesic subalpine SI = 12, FRI = 1000

12

0

DOB (cm)

128

40

48

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DOB (cm)

128

40 4

812

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Time since fire(years)

Perc

entcover

×heig

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Time since fire(years)

Perc

entcover

×heig

ht

Time since fire(years)

Time since fire(years)

Perc

entcover

×heig

ht

Perc

entcover

×heig

ht

Fig. 4. Revegetation response surfaces for the four contrasting ecosystems (equation in Table 3a). The x axis is time since fire (years), the yaxis is depth of burn (cm), and the z axis is vegetation percent cover � height (ht), by layer. In all cases, the response curve switches fromconcave downward to upward at DOB > 10 cm, beyond or near the limit of observed data for similar ecosystems (Table 4).

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was defined as the point at which the community shifts to analternative stable state (Figs. 5d and 5e). A real-world sim-ilarity curve would approach zero asymptotically, and aswitch to an alternative stability domain does not absolutelyrequire that the two alternative states have no plant species incommon. Despite these deficiencies, the x intercept providesa simple and relatively intuitive way to begin quantifying re-silience (i.e., the amount of disturbance absorbed = DOB).We view these models as preliminary and have begun to re-fine them with additional data sets covering a more completerange of ecosystem conditions, a greater range of burn se-verities, and longer time periods.

The revegetation response surfaces (Fig. 4) more clearlyillustrate how our resilience criterion relates to complex sys-tems theory and to the ball and cup diagram in Fig. 1. Incomplex systems theory, a dynamic system fluctuates underthe influence of an attractor, defined as a region in the spaceof possible states that the system can enter but cannot leave.The shift from one stability domain to another occurs whenthe original attractor dissipates — as a result of disturbance,for example — and a new attractor restructures the system

under a different set of dynamic constraints (Drake et al.1999). Our exponential–power function model predicts that,for burns of less than 10 cm depth, the shape of the vegeta-tion cover � height trajectory will remain constrained by thesame attractor — increasing rapidly for the first few yearsthen falling off during the transition from dominantly herb-aceous to dominantly woody vegetation. This trajectory ispresumably driven by the well-known postburn nutrientflush or ‘‘assart’’ effect (Kimmins 1997). At burn depths ex-ceeding 10 cm, the equation predicts that vegetation re-growth will be governed by a different attractor and assumea different trajectory. Because our study included few vege-tation quadrats with DOB > 10 cm, we cannot reliably pre-dict what that trajectory might be. The model alsoinadequately addresses the question of what happens on siteswith a total humus depth of less than 10 cm. Nonetheless,we conclude that burns of similar severity to those in ourstudy within this range of sub-boreal to subalpine eco-systems will not result in a shift of the general revegetationresponse to an alternative state.

The diversity response depicted in Fig. 5c is difficult to

( ) Recovery of composition (C )d 5

0 4 8 120

30

60

90

0 4 8 12Depth of burn (cm)

Max

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perc

entc

over

xhe

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( ) Amount of revegetation ( )a Vmax

stab

ility

0 4 8 12Depth of burn (cm)

0.00

0.05

0.10

0.15

0.20

1/(y

ears

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ach

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( ) Rate of revegetation ( )b Vrate

stab

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resilience

0 4 8 12Depth of burn (cm)

1/(y

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tore

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)

( ) Recovery of diversity (d /d )c S tJ2

resilience

0 4 8 120

5

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New

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0 4 8 12Depth of burn (cm)

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Per

cent

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Depth of burn (cm)Depth of burn (cm)

mesic sub-borealmesic transitionaldry sub-borealmesic subalpine

0

20

40

80

100

Per

cent

sim

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yto

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60

( ) Recovery of composition (C )e 10

resilience

resiliencestab

ility

resiliencestab

ility

resiliencestab

ility

at5

year

sat

10ye

ars

Fig. 5. Predicted effect of burn severity on revegetation, diversity, and species composition for the four contrasting ecosystems using multi-factor models from Table 3. (a) The amount of revegetation, which is the maximum percent cover � height achieved in the first decadeafter burning. (b) The rate of revegetation, which is the reciprocal of the time required to reach the maximum. (c) The rate of increase inspecies richness (second-order jack-knife estimate). (d) and (e) Percent similarity in species composition to unburned condition 5 and10 years after prescribed burning, respectively. As indicated by double-headed arrows, the y intercept for each curve estimates ecosystemstability, whereas the the upper (Fig. 5a) or lower (Figs. 5b–5e) x intercept estimates ecosystem resilience.

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interpret without considering underlying changes in speciescomposition that may occur after slashburning. For thismodeling exercise, we assumed that an increase in vascularspecies richness after slashburning was an indicator of eco-system recovery and that the more rapid the rate of increase,the greater the degree of recovery. Given that all of ourstudy sites experienced monotonic increases in species rich-ness over the first decade after fire, this appears to be a validassumption. However, our models predict that, on resource-rich ecosystems, the rate at which species richness growswill decrease with higher burn severity, whereas the rate willincrease on resource-poor ecosystems. This result is counter-intuitive, because species richness increases with resourceavailability. We believe it reflects competitive exclusion,mainly by Epilobium angustifolium, which is more intenseon resource-rich ecosystems (Huston 1994) and after moresevere fires (Haeussler et al. 1990). On resource-rich eco-systems, deep burns create ideal conditions for rapidEpilobium invasion to the point of excluding other species;on slow-growing, resource-poor ecosystems, deep burnsopen up seedbeds for ongoing species invasion. The ques-tion of whether either of these phenomena represent a tran-sition to an alternative stability domain can best beanswered by comparing pre- and post-burn plant composi-tion by species.

Our study included a good representation of sites (8 or 9of 12) along the gradient from mesic subalpine (low re-source availability and long FRI) to mesic sub-boreal (highresource availability and short FRI). Both the 5 and 10 yearmodels of pre- and post-burn similarity of species composi-tion predict that mesic subalpine ecosystems are less resil-ient than mesic sub-boreal ecosystems (Table 4), althoughthe 5 year model predicts a shift for subalpine ecosystemsto an alternative stability domain at DOBs >6 cm, whereasthe 10 year model suggests a shift closer to 12 cm.

Mesic subalpine ecosystems with plant communities dom-inated by fire-sensitive feathermosses, mycoheterotrophic,and late-seral herbs, ericaceous shrubs such as Vaccinium,Rhododendron, and Menziesia, and coniferous trees have alimited capacity for resprouting after disturbance (Coates etal. 1991). They are likely to be particularly sensitive to dual,short-interval disturbances such as those associated withclear-cutting followed immediately by a broadcast burn. Bycontrast, mesic sub-boreal sites at lower elevations and withmore frequent past exposure to fire possess a greater diver-sity of plant species representing a variety of plant functionalgroups2 with a greater capacity for seed regeneration andmore rapid resprouting and rhizomatous growth. Thus, sub-boreal plant communities are predicted to be relatively in-sensitive to fires of increasing severity. High species richnessand redundancy within functional groups have been demon-strated to be associated with increased resilience in ecologi-cal communities (Tilman et al. 1997; Elmqvist et al. 2003).

In boreal forests of northeastern Canada, De Grandpre etal. (2003) reported a strong shift in the dominance and di-versity of plant functional groups along a gradient fromlong (>250 year) to short (50–100 year) FRI and linkedthese inherent differences to patterns of species persistenceand invasion following logging with low to high severityforest floor disturbance. In these boreal landscapes, a switchfrom a black spruce – ericaceous shrub dominated forest to a

poplar-dominated mixed-species forest with markedly differ-ent understory composition and nutrient cycling processeshas been recorded following disturbances that substantiallyremove the forest floor (Carleton and MacLellan 1994). Incontrast, mixedwood boreal forests with diverse, multi-layered understories do not undergo an observable shift inspecies composition after high-severity logging. We con-clude that the differences in resilience predicted by ourslashburning models for sub-boreal to subalpine ecosystemsare analogous to these observed differences in the borealforest.

AcknowledgementsWe thank H. Karen Yearsley and Robin Munro for their

invaluable help and the many people who assisted in field-work, data collation, analysis, and reviews. Funding wasprovided by the British Columbia Ministry of Forests andRange, the Canada – British Columbia Forest Resource De-velopment Agreement (FRDA), and the Forest InvestmentAccount (FIA) grant to W. Klenner, British Columbia Min-istry of Forests and Range, Kamloops, British Columbia.

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