simulating the impact of small-scale extrinsic disturbances over forest species volumetric light...

Ecological Modelling 182 (2005) 113–129

Simulating the impact of small-scale extrinsic disturbancesover forest species volumetric light environment

P. Dubéa, A. Ménarda, A. Bouchardb, D.J. Marceaua,∗a Geocomputing Laboratory, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Qué., Canada H3C 3J7

b IRBV, Université de Montréal, Jardin botanique de Montréal, Montréal, Qué., Canada

Received 3 April 2003; received in revised form 2 March 2004; accepted 14 April 2004

Abstract

Small-scale disturbances (SSD) creating canopy gaps are fundamental to successional dynamics in temperate forests. Asgap-oriented management becomes very popular, spatial aspects of gap dynamics, especially the detailed impact of disturbanceson the light environment for different species, remain understudied. The aim of this study is to evaluate this effect using theindividual-based model SORTIE. Using different initial conditions, 10 simulated data sets, each representing temperate forests,were artificially disturbed using four disturbance sizes. For each 3D location of the simulation space, light availability wascomputed using the gap light index to create volumetric light data sets. The growth functions of the nine tree species incorporatedin the simulation were mapped to each light data set, generating species-dependent 3D cubes illustrating the effect of small-scaledisturbances over the different species according to their autecologic relationship to light. The general impact of the simulatedSSD was assessed (1) by extracting the 3D boundaries associated to the absolute spatial influence of each replicated SSD and(2) by analyzing the variation of light inside and outside these boundaries, at different height levels. Results were comparedfor each disturbance size. The species response to different disturbance sizes was evaluated globally and also as a function ofheight levels under the canopy. This study revealed that the impact of different SSD schemes is highly variable among replicates.Nonetheless, results revealed that small size disturbances exhibit more heterogeneous impact. A threshold effect was detectedaround a disturbance size of 1000 m2 suggesting a relative SSD impact that decreases for large SSD sizes. It was also found thatspecies relationship is consistent between different disturbance schemes.© 2004 Published by Elsevier B.V.

Keywords:Small-scale disturbance; Individual-based simulation; Forest management; Light environment; Spatial structure; Species expandedgap

1. Introduction

Most ecologists now recognize that local small-scaledisturbances (SSD) are an important driving force offorest community change in many ecosystems of theglobe (Bormann and Likens, 1979; Lorimer, 1980,

∗ Corresponding author. Tel.:+1 514 343 8067;fax: +1 514 343 8008.

E-mail address:[email protected] (D.J. Marceau).

1984, 1989; Pickett and White, 1985; Withmore,1989; Payette et al., 1990; Runkle and Yetter, 1987;Runkle, 1990, 1991; Belsky and Canham, 1994).Canopy openings are mainly created by natural deathof trees (Barden, 1989) but may also originate fromextrinsic factors such as windstorm and thunderstormlight burst. These different processes are responsiblefor a spectrum of SSD, varying in terms of size, shapeand composition (Lorimer et al., 1988). In temperateecosystems, depending on the source and the intensity

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114 P. Dube et al. / Ecological Modelling 182 (2005) 113–129

of the underlying process that creates them, naturalSSD sizes will range from<50 to 2000 m2 (Runkle,1982; Coates and Burton, 1997).

By increasing local light resources, appearanceof small-scale disturbances is often associated to animportant reconfiguration of tree light habitat withsignificant impacts on tree resource allocation, treeinteractions, and ultimately successional processes.Natural SSD are necessary for almost all tree speciesto attain canopy status (Canham, 1988, 1989; Pous-lon and Platt, 1989) through recurrent suppressionand release episodes, and species-dependent resourceintegration strategies. Adaptive strategies range fromthe capacity to capture and convert sudden local lightincrease in terms of radial growth more efficiently(Wright et al., 2000) to the ability to survive long pe-riods of light suppression and dramatically decreasethe probability of mortality after only a slight increaseof solar radiation (Kobe and Coates, 1997). Gaps playa major role in species coexistence by creating localecological niches for particular species (Denslow,1980; Brokaw and Schneider, 1989; Sipe and Bazzaz,1994; Gray and Spies, 1996; Kupfer et al., 1997) orsimply by adding some noise to the ecosystem dy-namics (Brokaw and Busing, 2000). They constitutean important source of entry sites of new genotypes(Silvertown and Smith, 1988), and may enhance theresistance of some species to herbivory (Coley, 1993).

1.1. The expanded impact of SSD

Over the last two decades, knowledge about SSDpatterns and processes has been significantly im-proved, due to several key pioneer field studies em-phasizing discrete canopy gaps, at the disturbancelevel (Runkle, 1982, 1985; Brokaw, 1985; Canham,1989, 1990; Payette et al., 1990). These studies playeda major role in the characterization of many phe-nomena such as canopy gap replacement, gap closureprocesses and light resource distribution followingthe creation of canopy gaps (Runkle, 1991).

Traditionally, gaps were defined by the verticalprojection of the canopy opening and were sometimesextended to the basis of the first-order neighbour-ing trees (Runkle, 1982). This discrete gap/non-gapparadigm has been highly criticized by some re-searchers (Canham, 1989, 1990; Lieberman et al.,1989) who proposed to reformulate the concept of

SSD in terms of canopy closure continuum with anemphasis on the study of light “as it extends into pro-gressively shadier conditions well beyond the absenceof any recognizable opening in the forest” (Liebermanet al., 1989). The concept of expanded SSD explicitlyrises the following question: what is the impact of adisturbance of a given size and shape inside and out-side its discrete boundaries and how does it changethrough 3D space?

In the context of forest ecology, the impact ofsmall-scale disturbances can be defined and measuredeither by focusing on the individual tree response toa canopy opening (Ménard et al., 2002a) or througha direct analysis of the light increase patterns gener-ated by the disturbance. The first method representsthe only way to assess the real immediate effect of acanopy opening on a specific individual, to investigatethe effect of neighbouring trees and to relate individ-ual response to other variables such as age classes,mortality probability, etc. On the other hand, a directfocus on light distribution allows one to assess theparticular contribution of the impact generated by asingle SSD to any specific spatial 3D location underthe canopy, even when the impact is too small to besensed by individual trees over geographic space.

The impact of a small-scale disturbance is highlydependent on the relative spatial position of the treesin a site, individual DBH, and species foliage opacityamong other factors. For canopy disturbances smallerthan around 300 m2, Canham et al. (1990)demon-strated that the impact was also highly heterogeneousand strongly dependent on site latitude and site topog-raphy. They also showed that light distribution waschanging inside and outside the gaps as a function ofheight under the canopy. SSD impacts also have differ-ent meanings for different species. To illustrate this sit-uation, one may look at the spatial distribution of lightover a simulated, deciduous forest stand. Light usu-ally decreases irregularly from the center of an SSD.Two hypothetical species having a different sensitivityto light will be associated to two distinct SSD impact.

1.2. The role of modelling

In the field of SSD studies, spatially explicitcell-based and individual-based models (Judson,1994) have been considered by many as an interestingcomplement to field surveys. Over the last decade,

P. Dube et al. / Ecological Modelling 182 (2005) 113–129 115

many scientists believed in the potential of such mod-els to predict with accuracy real stand parametersat the patch mosaic level (Shugart and West, 1977;Kercher and Axelrod, 1984; Leemans and Prentice,1989; Luan et al., 1996; Pacala et al., 1996; Liu andAshton, 1998; He et al., 1999; Gustafson et al., 2000).The outcome of such studies, however, has been oftencriticized by field ecologists. Among other issues, theconfrontation with real world data was pointed outas the most important and unresolved challenge ofsimulation models (Hill, 1995; Murdoch et al., 1992;Oreskes et al., 1994; Rykiel, 1996).

While this debate is still active in ecology, anew kind of modelling tradition is also emerging inthe community and derived from the framework ofpost-normal science (Kay et al., 1999; Tognetti, 1999).In this new paradigm, models are mostly used to ver-ify hypotheses only partially tested in the field due tothe small number of samples than can be realisticallyacquired in real ecosystems. Post-normal scienceaims to stimulate the emergence of new hypothesesthat could eventually be tested by field ecologists.

The use of models such as SORTIE (Pacala et al.,1993, 1996) in the context of post-normal science gen-erated many new insights about small-scale distur-bances.Deutschman et al. (1997, 2000)studied therole of visualisation for interpreting the influence ofspatial tree structure on SSD dynamics at the patchmosaic level. Also using SORTIE,Dubé et al. (2001)assessed the stability of self-organised expanded dis-turbance patterns, revealing a coherent SSD dynam-ics between different initial conditions.Ménard et al.(2002b)also found a very similar spatial structure be-tween initial conditions after 300 years of simulation.A significant advantage of using dynamical modelslike SORTIE for SSD studies is the possibility to gobeyond our discrete perception of gaps, and to quan-tify the expanded impact of individual small-scale dis-turbances over tree species.

1.3. Objectives of the study

Our attempt is to evaluate the impact of artificiallycreated SSD over light resources spatial distribution.Using the individual-based model SORTIE, we eval-uate the 3D impact of different SSD as a function oftheir size. Our second objective is to characterize the3D SSD impact in terms of potential space where sup-

pression and release events are possible for the indi-vidual species incorporated in the SORTIE model.

2. Methodology

The general experimental setup of the study is pre-sented inFig. 1First, 10 different forest replicates hav-ing the same general demographic parameters weregenerated, using the SORTIE model. Second, distur-bances of four different sizes were introduced in thesimulated data set and the volumetric-associated lightstructure was extracted. Finally, the SSD impact wasanalyzed as a function of the disturbance size andthe different species incorporated into the model. Themethodological approach is detailed in the followingsections.

2.1. Simulating forest dynamics using the SORTIEmodel

The data set used in this study results from a set ofsimulations performed using the SORTIE-GMF model(Pacala et al., 1993, 1996).

The general structure of SORTIE allows the track-ing of every individual tree over a user-definedsimulated area. As opposed to other distributed mod-els such as cellular automata (Cosalanti and Grime,1993; Wissel, 1994; Botkin et al., 1972; Lett, 1999)and gap models (Green, 1992, 1994; Coquillard andHill, 1997; Shugart and West, 1977; Kercher andAxelrod, 1984; Leemans and Prentice, 1989; Urban,1990, 1991; Acevedo et al., 1995), SORTIE is anobject-oriented, individual-based model that allowsthe positioning of every individual tree over a con-tinuous geographical space, and the explicit con-sideration of the local spatial interactions betweenindividuals.

Globally, the model aims to reproduce temperateforest dynamics by simulating the life cycle of everyindividual tree, based on its autecologic characteris-tics and its spatial interactions with its neighbours.Notwithstanding the diversity of processes involved intemperate forests succession, light is usually seen byresearchers as a key limiting factor (Pacala et al., 1994;Ribbens et al., 1994; Canham et al., 1994; Kobe et al.,1995). Consequently, spatial interactions between in-dividuals in the core module of SORTIE are essentially


Fig. 1. Overall experimental design.

defined by an approximation of the shading effect ofeach individual’s neighbours.

Shading is modeled by computing the incident ra-diation that reaches the top of the center of the crownof each individual seedling, sapling, and adult tree inthe modeled stand. Incident radiation is approximatedusing the gap light index (Canham et al., 1990). Thismeasure takes values from 0 to 100 that represent theproportion of incident photosynthetically active radia-tion (PAR) transmitted through the canopy to any hor-izontal and vertical spatial location in the understoryover the period of the growing season. The gap lightindex (GLI) is formalised byCanham et al. (1990)as

GLI = [TdPd + TbPb] × 100 (1)

wherePd and Pb represent the proportion of diffuseand beam radiation that reaches the top of the canopyover the course of the growing season, and whereTdandTb represent the proportion of diffuse and beamradiation that are transmitted through the canopy to apoint in the understory. The GLI index also takes intoaccount the variation of solar radiation as a function

of season and day time as well as light interceptionby the foliage of surrounding trees, represented in themodel by vertical cylinders whose opacity and size aredefined by species parameters. A value of GLI near0 suggests the absence of any clear, detectable gap inthe canopy while a value of 100 reveals the presenceof a fully open site. It must be mentioned that theshading computation does not take into account lightinterception by tree boles. This situation may lead toa slight overestimation of the understory GLI valuesin SORTIE.

Nevertheless, in a recent study confronting SOR-TIE to field observations, the light model has provento provide reasonable predictions of spatial patternsin understory light levels (Beaudet et al., 2002). Suchpredictions were observed mostly when the type oflight variation was associated to low-density under-story and was resulting from variation in tree sizes andspacing, and was of relatively large magnitude suchafter partial cuts.

In SORTIE, tree interactions and light availabilityinfluence the expression of individual parameters such


as individual growth, dispersal and mortality whichrepresent the last three core modules of the model.Saplings and juveniles radial growths are computed asa function of crown radius and available light. Adulttrees, on the other hand, increase in size on the basisof a constant annual increment. Dispersal is modeledby decreasing the seedling density around each parenttree exponentially as a function of radial distance. Fi-nally, the last module of SORTIE computes individualmortality probability as a function of recent individualgrowth history.

From a complex systems perspective, SORTIEis fairly well balanced between deterministic andstochastic processes. Light calculation represents animportant deterministic aspect of the model. On theother hand, pseudo-randomness is incorporated at thevery beginning of the simulation process when defin-ing initial conditions. A random probability functionis also used to estimate mortality of each individualaccording to its inverse growth rate. The incorporationof stochastic processes in SORTIE is very importantsince it introduces some noise in the dynamics of themodel, thus avoiding the system to be caught in localminima associated to deterministic attractors, as it isoften the case with conventional cellular automata(seeWolfram, 1984).

In this study, simulations are conducted using thenine species already incorporated into the model.These species areTsuga canadensis(TSCA), Fagusgrandifolia (FAGR), Betula alleghaniensis(BEAL),Pinus strobus (PIST), Acer saccharum(ACSA),Prunus serotina(PRSE), Quercus rubra (QURU),Acer rubrum (ACRU), and Fraxinus americana(FRAM). A description of the ecology of these speciesand the experimental stand conditions associated withSORTIE can be found inPacala et al. (1993). Simula-tions were performed using a toroidal lattice of 500 m× 500 m over 300 years, with a time step of 5 years.

A set of 10 experimental scenarios represented bydifferent initial conditions were defined by varyingthe initial seedling spatial configuration using a uni-formly distributed pseudo-random number generator.This operation is important to obtain statistical inter-vals describing the dynamical trajectories the modelcan take no matter its deterministic/stochastic nature.This allows the assessment of the model sensitivity, thedetection of dynamical attractors (i.e. quasi-periodicoscillations of biomass at the climax state of a forest),

the characterization of transient phases, and the identi-fication of the extent of the attraction basin (the num-ber of initial configurations leading to an attractor).

Dynamical sensitivity analysis of SORTIE have al-ready been performed at various levels observation:using demographic descriptors (Pacala et al., 1993;Deutschman et al., 1997, 1999)as well as spatialdescriptors of forest dynamics (Dubé et al., 2001;Ménard et al., 2002b). These studies have highlightedthe presence of important variations of the model be-haviour after small changes in initial conditions orafter a slight modulation of the internal parameters.Despite these fluctuations, the model has been provento exhibit a fairly cohesive behaviour in terms of globalemergent succession dynamics, thus justifying its usein the context of post-normal science (Kay et al., 1999;Tognetti, 1999). In this study, we generated 10 dif-ferent dynamical trajectories to assess the variabilityof the SSD impacts for a same scenario of distur-bance.

After 350 years of simulation, we introduced foursmall-scale disturbances of circular shape of differentsizes of 500, 1000, 1500 and 2000 m2, respectively.

2.2. Extracting forest light structure

Just after the introduction of a disturbance, lightavailability was determined at each 3D location of ev-ery simulated replicate. A gap light index value wascomputed at a horizontal resolution of 1 m2. The ver-tical dimension was also sampled at an increment of1 m from the understory level to the canopy level. Theresulting data set was a GLI cube as illustrated inFig. 2. This representation reveals the highly hetero-geneous structure of light distribution over a simulatedforest.

The first image (Fig. 2A) illustrates the light struc-ture in the forest, without the introduction of anyartificial SSD. For representation purposes, the lightvolume was sliced at different locations in order to re-veal the internal light structure under the canopy. Thecolor associated to each voxel represents a particu-lar GLI value (percentage of incident light). A valuenear 0 suggests the absence of any clear, detectablegap in the canopy. Dark cylinders (1) represent indi-vidual tree crowns into which a variable fraction ofthe incident light is absorbed. A value of 100 indi-cates the presence of a fully open site. Red voxels


Fig. 2. 3D light structure (A) before and (B) after the introductionof a disturbance of 1000 m2. The color palette represents lightavailability from 1 to 100% through the computation of the gaplight index (GLI).

are associated to the highest GLI values at the topof the canopy or inside individual gaps of varyingsizes.

The second image (Fig. 2B) represents the samedata set after the introduction of an artificial SSD of1000 m2. The increase of light generated by the distur-bance is illustrated by an important augmentation ofred voxels inside the geometric discrete boundaries ofthe gap (1); its influence is going far beyond this ex-tent (2). The light cube also reveals the penetration ofa light beam in the lower levels of the forest throughthe base of a tree crown (3).

2.3. Defining the general influence of the small-scaledisturbances

Using the volumetric light data sets previouslydescribed, the spatial influence of each small-scaledisturbance was defined by identifying every 3D loca-tion associated to a measurable increase of light rightafter the introduction of an SSD. This operation wasconducted by: (1) subtracting the light volume gen-erated after the disturbance of the volume producedbeforehand, and (2) extracting every location wherethe difference is positive. To measure the quantitativemagnitude of the SSD impact, the amount of GLI in-crease was recorded for each 3D location in the GLIcube by computing a simple ratio of the GLI indexbefore and after the disturbance event (light increaseratio, LIR). General volumetric measures were thencomputed inside and outside the geometrical limits ofthe disturbance, for each disturbance size. Lateral spa-tial extent of the SSD impact, frequency distributionsand statistical moments for raw GLI values and LIRvalues were also extracted and analyzed as a functionof height levels. SSD volumetric impact was finallyassessed by computing a cumulative pixel frequencydistribution representing the total surface affected byvarying LIR values at three different heights underthe canopy level.

This operation provided a first general apprecia-tion of the influence of the SSD across horizontal andvertical space. However, it does not provide any spe-cific information about the way a particular species“perceives” or benefits from the concentration of lightresources associated to a newly formed SSD. As dif-ferent species are expected to “sense” the influence ofthe disturbance at various distances out of the discreteboundaries of the SSD, a characterization of this na-ture is then essential to really appreciate the impact ofan SSD.

2.4. Defining species-dependent SSD impact

One may argue that it is possible to qualitativelypredict species responses to disturbances using speciesgrowth relationships alone, without any explicit refer-ence to space. One would then postulate that specieshaving similar growth and/or mortality response tolight are likely to experience similar SSD impactsin 3D space. However, while such an assumption


Fig. 3. (A) Comparison of the growth functions of four speciesincluded into SORTIE (Pacala et al., 1993, 1996). (B) First-orderderivatives of the four growth functions.

remains valid when looking at the general aspect ofthe curves, its overuse is likely to hide the influence ofsubtle local differences in species growth functions.In some cases, these differences may lead to a signif-icantly different SSD impact when transposed into aparticular geographical space. This phenomenon willbe particularly important for the geographical areaswhere the GLI values are associated to an importantchange in the shape of the growth function of differentspecies.

Fig. 3 illustrates this situation. From a set of ninegrowth functions associated to the species incorpo-rated in SORTIE (Fig. 3A), we selected two pairsof functions respectively represented by solid dark

Table 1Example of differential effect of light variation over two speciesexhibiting differences in their relationship to light resources, asillustrated inFig. 3

GLI beforedisturbance(%)

GLI afterdisturbance(%)

Species in release?

Fraxinus americana Prunus serotina

1.2 4.7 Yes No0.2 2.0 Yes Yes

17.0 40.0 No No

lines (Betula alleghaniensis–Fagus grandifolia) anddark lines with dots (Fraxinus americana–Prunusserotina). Fig. 3B represents the first-order derivativeof these growth functions. An evaluation of these twographs reveals two scenarios of species-dependentresponse to light variation. When considering thegroup Betula alleghaniensis–Fagus grandifolia, weclearly observe that the growth derivatives are verysimilar for every GLI values. This suggests that thesetwo species will benefit from a similar impact asso-ciated to an increase of light of any magnitude overgeographical space. Conversely, the groupFraxinusamericana–Prunus serotinais represented by twoderivatives functions that change from being dis-similar to being similar around a GLI value of 7%.Hypothesizing an average GLI increment of one unitafter the creation of an SSD, the two species willlikely experience the effect of a given disturbancein a very different way, depending on the frequencydistribution of the GLI values associated to the targetspace before the disturbance. As different disturbancesizes induce different patterns of light increase, itmight occur that the relative impact of a disturbanceover two species will be similar at a given disturbancesize and very dissimilar for another size.Table 1gives a concrete example of this situation. From thereal growth functions of the two species, three differ-ent scenarios of light increase can lead to a similaror antagonist impact on the two species, dependingon the original GLI values and the amount of GLIincrease.

On the basis of these ecological considerations, wedefined an index of light resources using the conceptof species expanded gap (SEG) formulated byDubéet al. (2001)to best account for this inter-specificvariability. Globally, SEG analysis emphasizes thespecies response to local light structure by explicitly


relating the spatial distribution of light resources torelevant autecologic parameters, i.e. mortality rate forthe study of seedling response to light environment.For the purpose of this study, we transformed the GLIvalues into potential radial growth increment valuesusing the growth function of each species in the model.Fig. 4A and Billustrates the growth function ofAcerrubrumapplied to the GLI values before and after theoccurrence of an SSD. This mapping operation gener-ates nine volumes representing the species-dependentspatial structure of light environment for each GLIdata set (extracted for each initial condition and dis-turbance size), enabling qualitative and quantitativecomparisons between species before and after anSSD.

Following this operation, we assessed the qualityof these species-dependent light environment corre-sponding to SSD impacts by classifying the variationof growth values using the suppression-release con-cept (Canham, 1985; Payette et al., 1990). Specifically,we used this concept to identify which tree specieswere likely to benefit the most from the increase oflight generated by the artificial opening of a partic-ular size, inside and outside the geometrical projec-tion of the gap. By reducing the dimensionality ofthe growth values to a single spatial descriptor thatembeds quantitative information about GLI augmen-tation, this approach also facilitates the extraction ofspecies having a similar or antagonist response to lo-cal light resources availability. According to the liter-ature, we selected an increase of 2.5 times the growthrate as a “release” threshold (Henry and Swan, 1974;Payette et al., 1990). The use of this threshold allowedthe identification and the analysis of the spatial loca-tions where it is reasonable to expect a positive im-pact of the SSD on individual trees belonging to aparticular species (Fig. 4C). To ensure the validity ofthe comparative analysis between species, each growthfunction was normalized according to its maximalvalue.

The impact of each SSD was measured in twoways. First, the portion of space corresponding toa “release” state was extracted from the light cubeand the associated volume was computed. Second,a measure of the release surface was extracted andplotted as a function of height. This analysis wasperformed for each scenario and for each disturbancesize.

Fig. 4. Conversion of GLI to growth value forAcer rubrum(A) before the introduction of a disturbance and (B) after theintroduction of a disturbance. (C) Thresholding of the growthvalues representing the proportion of the total extended impact(gray) of the disturbance associated to a release (white) forAcerrubrum.


3. Results and discussion

3.1. Characterizing the absolute impact of an SSD

Fig. 5 illustrates mean GLI value relationship ver-sus height, as observed following a SSD episode insideand outside the projected boundaries of the distur-bance (values are averaged for all replicates). Visualassessment of the first graph reveals, as could be ex-pected, a linear increase of light as a function of heightunder the canopy, for every SSD area considered. In-

Fig. 5. Averaged mean GLI values inside (A) and outside (B) thegeometrical projection of the SSD.

side the SSD limits, a clear differentiation is identi-fiable between 500 and 1000 m2 and between 1000and 1500 m2. This pattern remains consistent at dif-ferent height levels. There appears to be no clear dis-tinction between mean GLI value generated by 1500and 2000 m2. Outside the SSD limits, the GLI valuesalso increases as a function of height. However, themean values are very small and there is no clear signof differentiation between the four SSD sizes. Thisphenomenon can be explained by the large amount ofspace outside the SSD limits undergoing an increaseof light after the disturbance event but still having verysmall GLI values.

Fig. 6 enables a more detailed appreciation ofthe spatial extent associated to light increase afterthe creation of a particular disturbance. We first ob-serve a linear decrease of SSD expanded impact asa function of height for each of the four disturbancesizes, followed by a subsequent increase for height>11 m. This phenomenon can be directly related tothe heterogeneity of the 3D spatial structure of treescomposing individual replicates. While the distancebetween the four curves appears to be relatively con-sistent according to height, it also appears that the dif-ference between the expanded SSD impact associatedto a disturbance size of 500 and 1000 m2 is greater

Fig. 6. Surface associated with an increase of GLI values after theintroduction of a disturbance plotted against height levels underthe canopy.


Fig. 7. Averaged cumulative frequency of LIR values inside thegeometric projection of the SSD. (A, B) Raw and normalized ratiovalues inside the geometrical projection of the SSD at 3, 9 and17 m above ground, respectively.

than between every other combination of disturbancesize.

Figs. 7 and 8summarize the differential SSD impactbetween the four SSD sizes as the amount of spaceexperiencing the same amount of light increase (beingmeasured by the light increase ratio or LIR) at differ-

ent heights under the canopy level.Fig. 7 emphasizeslight increase ratio (LIR) inside of the SSD boundarieswhile Fig. 8 presents the results of the same analysisoutside the vertical projection of the SSD.

An examination ofFig. 7Ashows the amount of sur-face (cumulative number of pixels) experiencing LIRof specific magnitudes. While this impact is clearlydistinct between SSD sizes for LIR of 1–6x, it appearsthat SSD of different sizes are likely to produce highbursts of light (7x..+) over similar areas, especially atlower heights. This observation supports the view thateven close to the understory level, small SSD can in-duce LIR of magnitudes comparable to large size SSD.Moreover, we note that within a single SSD size cat-egory, it also appears that LIR of high magnitude arelikely to occur over larger areas in the upper heightsthan it is the case for lower heights. This relationship,however, appears to be reversed when focusing on LIRof lower magnitude (1x..+ to 6x..+) that occurs overlarger areas in lower heights.

Normalizing the LIR profiles according to SSD sizegives another set of interesting insights (Fig. 7B). Nomatter the SSD size, at least 70% of area coveredby the vertical projection of the SSD is experiencingtwice the radiation level that was available before thedisturbance. At another level, we note that the shapeof the profile and the extent of the standard deviationassociated to SSD size of 500 m2 is clearly distinc-tive compared to the other SSD sizes, which indicatesa more heterogeneous and variable light increase pat-tern than observable for larger SSD. This observationcould suggest that, from a light resource perspective,small size SSD could induce less predictable light en-vironment, which could offer adaptive opportunitiesto higher number of species with broader autecology.As pointed out byCanham et al. (1990)“As indi-viduals reach sapling sizes, their canopies will beginto integrate over some of this heterogeneity and indi-vidual plants may effectively forage for areas of highlight through differential growth and shedding of lat-eral branches”.

Fig. 8A illustrates the cumulative LIR surface out-side the geometrical projection of the SSD, allowingto appreciate the differential impact of the four SSDschemes beyond the gap itself. A first observation isthat the major part of the surface experiencing an in-crease of light resources outside the SSD is coveredby very minor light increase values. Besides, we also


Fig. 8. Averaged cumulative frequency of LIR values outside the geometric projection of the SSD. (A, B) Raw and normalized ratio valuesinside the geometrical projection of the SSD at 3, 9 and 17 m above ground, respectively.


observe that, for all SSD sizes, the external impact isalways greater in lower heights under the canopy. Wealso observe that the differential impact between SSDsizes tend to fade out as a function of height under thecanopy level. According to the results, it appears thatat 3 m, SSD of 1500 and 2000 m2 exhibit a fairly sim-ilar impact that, moreover, appears to be quite distinctcompared to the increase of light resources generatedby the other scenarios (SSD size and height levels).In a same way, it also appears that the impact gener-ated by an SSD of 1000 m2 at 3 m is very similar tothe impact generated by SSD of 1500 and 2000 m2 ata height of 9 m while still at 3 m, an SSD of 500 m2

generates an increase of light resources pattern that iscomparable to what is induced at 17 m by SSD greaterthat 1000 m2, etc. This demonstrates the intricate linkbetween light heterogeneity and 3D tree spatial distri-bution.

Normalizing the cumulative surface values ac-cording to respective SSD size (Fig. 8B) allows toobserve that between approximately 0.2 and 2 timesthe geometrical surface of the SSD can be expectedto experience an increase of light resources that isat least twice the amount of solar radiation availablebefore the introduction of the disturbance. SSD of1500 m2 appears to generate the greater relative im-pact, at every height considered. SSD of 2000 m2

appears to generate a relative impact of less mag-nitude, especially at 17 m, where the mean relativeimpact is below the impact generated by an SSD of500 m2. Therefore, at that height, one could expectthat the surface of impact of four SSD of 500 m2 be-comes more important than a single gap of 2000 m2.We must note however that the impacts generated atthat height are less distinctive than what is observedat 3 m for instance, suggesting that the impact maybe proportional to the logging effort as we increasein height. At 3 m, we note that SSD of 500 m2 pro-duces impacts of less magnitude that other SSD sizes.At another level, we observe, as for the internal im-pact, that the standard deviation associated to theprofiles describing the impact of SSD of 500 m2 isimportant. This fact reveals an impact that is highlyvariable and that can offer many stochastic adap-tive opportunities to multiple species, therefore sup-porting the fundamental role of small sizes SSD innatural ecosystems, from a complex system perspec-tive.

Trying to characterize the relative impact of dif-ferent SSD scenarios using light values alone isnon-trivial because such an impact appears to varydepending on which LIR classes we are interested in.This situation underlines the need to measure this phe-nomenon according to species-specific parameters.

3.2. Characterizing the species-specific impact of anSSD

Fig. 9 illustrates the variation of the thresholdedspecies-specific release environment as a function ofheight for every SSD size. As one would expect, therelease surface of every species increases with distur-bance size while decreases as a function of height.When compared to each other, species tend to exhibita relationship that appears to be fairly consistent, withthe normalized difference between each curve remain-ing approximately the same from one disturbance sizeto another. This consistency is also observed as a func-tion of height under the canopy. Such observationshave very important implications since it may suggest,from a 3D spatial perspective, that species seem toget similar relative opportunities from SSD of varyingsize and that these opportunities are not significantlyaffected by the variability of environmental conditionsgenerated by the stochastic processes incorporated inSORTIE, i.e. the influence of bordering trees on lightpenetration through the canopy.

When looking at the absolute release surface valuesof each species inFig. 9, one observes a broad spec-trum of possible expanded SSD impact, starting fromapproximately the size of the original discrete gap atthe understory level. At the same height, simultane-ous examination of the graphs allows the identifica-tion of a consistent cluster of species having a muchhigher expanded impact of approximately twice thesize of the simulated discrete disturbance. This impactreaches a peak for SSD of 1000 and 1500 m2 support-ing the view that an optimal gain of expanded SSDinfluence seems to occur for a disturbance regime ofthat order of magnitude. Conversely, there are a fewcases where a species only benefits from the open-ing in the interior limits of the discrete SSD. Sucha situation usually occurs for the release thresholdscorresponding toBetula alleghaniensisandAcer sac-charumat heights levels >10 m, for every disturbancesize.


Fig. 9. Averaged variation of the species-dependent light environment volume represented as the proportion of the general SSD impactassociated to a “release” state after a suppression-release thresholding of the species growth values.

4. Conclusion

This study constitutes one of the few attempts touse a simulation model to quantify the 3D foreststructure using a more ecological definition of distur-bance. While some efforts have been done to char-acterize light regimes inside and outside the discreteboundaries of gaps in the field, our main contribu-tion has been to characterize the volumetric lightstructures variability induced by sampling the same

forest at different locations using gaps of differentsizes.

Our exploratory analysis suggested a number ofdifferences in light resource environments generatedby SSD of various sizes. Such differences were moreimportant among SSD of small sizes than betweenlarge size SSD. From this study, it appears that theinfluence of a small-scale disturbance in terms ofgeneral and species-dependent expanded impact isoptimized when dealing with moderate sizes (up


to 1000–1500 m2). Small gaps, however, appears tooffer light resource environments that covers lightincrease magnitudes that may be similar to large gapsbut with more heterogeneity and more variability,as suggested byCanham et al. (1990). As gaps ofsmall sizes are highly dominant in natural forests,such situation could be consistent with the view thatstochastic events are, more than expected, implicatedin the process of maintaining tree species richnessvia gap dynamics by slowing competitive exclusionand maintaining tree diversity (Brokaw and Busing,2000). Such results could ultimately have implica-tions in the definition of more efficient logging ormanagement designs, where the manager aims topreserve particular ecological characteristics to thestand.

Generalizing from any simulated data set, however,must be done with some circumspection. For instance,SORTIE uses growth curves that are fitted on empiricalfield data. The fitting process may be prone to some er-rors and may be biased by the mathematical model se-lected. While the level of generalization of these func-tions may influence greatly the structure and the extentof specific light environment defined in this study, ouranalyses must be considered as SSD impact indicatorsonly. Nonetheless, the proposed method enables thestudy of ecological patterns, such as light resourcesspatial distribution under the canopy in a new way thatis fundamental to the understanding of resource en-vironments into which species interact together. Thisstudy reinforces the view that individual-based simu-lation constitutes a very original and informative wayto look at ecological patterns, such as light distributionacross horizontal and vertical geographical space.

4.1. Where do we go from here?

Future research focusing on light structure analysisat the disturbance level should consider three majorissues.

Research would first benefit from an emphasis onthe study of light structure variation through the tran-sient period following the increase of light resourcesgenerated by a small-scale disturbance. Relating suchanalysis to gap invasion by individual trees would pro-vide new complementary insights to field studies doc-umenting gap-filling patterns by individual trees. Aspointed out byDahir and Lorimer (1996), research

should also focus on the overall gap dynamics acrossa broad range of developmental stages in temperatehardwood forests.

Second, it would be interesting to evaluate the spe-cific expanded impact of small-scale disturbances us-ing new descriptors – i.e. shape variations – that arecomplementary to disturbance size. The analysis of theexpanded impact itself would also benefit from the useof other descriptors such as fuzzy “release thresholds”that could integrate growth response variability amonga single species and an analysis of the spatial structureassociated to the specific light environment.

Finally, while the impact of large human distur-bances on forest dynamics may be addressed by solelyanalyzing the regeneration processes occurring withinand around the discrete disturbance limits, our studysuggests that the same question applied to smaller,natural disturbances should involve a deeper under-standing of the interaction between neighbouring dis-turbance units. Therefore, we propose that an explicitintegration of local light structure at the patch mosaiclevel – i.e. the level of organisation at which individualSSD entities interact together to form a regional land-scape of light resources influencing species dynamics– and the understanding of hierarchical, nested lightstructure is likely to provide scientists new insightsto understand population dynamics over larger geo-graphical areas. Mapping expanded SSD impact overspecific areas could help precise the conditions underwhich individuals reach the canopy level after experi-encing the influence of many SSD over their lifecycle.Such conditions could range from individuals experi-encing a few release episodes following an importantincrease of radiation over short distances to individu-als taking advantage of distant gaps generating moresubtle but more frequent light resources increase. Insome specific cases, space could also have a regulatoryeffect by favouring species that “sense” SSD impactsover larger distances even when having less-efficientresource integration strategies.

These perspectives are presented in the hope ofstimulating new testable hypotheses to improve ourunderstanding of how SSD frequency and intensityis related to light resources heterogeneity. We be-lieve that when combined to species sensitivity andresources integration strategies, these parameters willallow for a thorough understanding of species dynam-ics at multiple levels of organisation.


Acknowledgements

The authors would like to thank Dr. Charles Canhamfor stimulating discussion about suppression-releaseparadigm. This research has been funded by a FCAR(Fonds pour la formation de chercheurs et l’aide àla recherche) and a GREFI (Groupe de recherche enécologie forestière universitaire) scholarships awardedto Patrick Dubé, and by a grant awarded to Danielle J.Marceau from the Natural Sciences and EngineeringResearch Council of Canada.

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