Contagious Disturbance, Ecological Memory, and the Emergence of Landscape Pattern

Contagious Disturbance, EcologicalMemory, and the Emergence of

Landscape Pattern

Garry D. Peterson

Center for Limnology, University of Wisconsin, Madison, Wisconsin, 53706, USA

ABSTRACTLandscapes are strongly shaped by the degree ofinteraction between pattern and process. This paperexamines how ecological memory, the degree towhich an ecological process is shaped by its pastmodifications of a landscape, influences landscapedynamics. I use a simulation model to examine howecological memory shapes the landscape dynamicsproduced by the interaction of vegetative regrowthand fire. The model illustrated that increased eco-logical memory increased the strength and spatialextent of landscape pattern. The extent of thesechanges depended upon the relative rates of vege-tative recovery and fire initiation. When ecologicalmemory is strong, landscape pattern is persistent;

pattern tends to be maintained rather than de-stroyed by fire. The generality of the simulationmodel suggests that these results may also apply todisturbance processes other than fire. The existenceof ecological memory in ecosystems may allow pro-cesses to produce ecological pattern that can entrainother ecosystem variables. The methods presentedin this paper to analyze pattern in model ecosys-tems could be used to detect such pattern in actualecosystems.

Key words: landscape ecology; self-organization;spatial dynamics; patch dynamics; keystone pro-cesses; scale; autocorrelation.

INTRODUCTION

Landscape pattern is a key attribute of ecosystems,organizing and regulating the flow of ecologicalgoods and services (Ludwig and others 2000).Landscape pattern is itself shaped by ecological pro-cesses. The extent of the interaction between land-scape pattern and the processes that shape it has afundamental influence on landscape dynamics.Does a process impose a pattern upon a landscapeunilaterally, or is there a two-way dynamic inter-action between pattern and process? The degree towhich an ecological process is shaped by its historycan be thought of as the strength of the ecologicalmemory of that process. For example, if the loca-tion of tree-fall gaps is influenced by where pasttree falls occurred or if fire spread is influenced by

previous fires, then memory is shaping their dy-namics. The presence of memory allows ecologicalprocesses to interact with one another; its absencemeans that pattern is generated by a single processimposing some type of template of organization ona system. However, in most ecological systems, eco-logical processes cannot be neatly divided betweenthose that exhibit memory and those that do not.Even apparently one-way relationships, such as theeffects of climate on vegetation, contain interac-tions (for example, the effects of vegetation uponhumidity). How much does memory influencelandscape dynamics? In this paper, I use a simula-tion model of fire and vegetation dynamics to ex-amine the role of ecological memory in producinglandscape pattern. Specifically, I examine how eco-logical memory influences the landscape patternthat is produced by the interaction between firefrequency and vegetative regrowth.

Fire is a key structuring processes in many eco-Received 14 November 2000; accepted 21 September 2001.e-mail: [email protected]

Ecosystems (2002) 5: 329–338DOI: 10.1007/s10021-001-0077-1 ECOSYSTEMS

© 2002 Springer-Verlag

329

systems (Bond and van Wilgen 1996). Although theduration of a fire is much shorter than the life spanof the vegetation it consumes, fire produces land-scape patterns that persist for long periods (Baker1993). At small spatial scales, fire homogenizes thelandscape by killing aboveground growth of trees,producing patches of even-aged vegetation. Atlarger spatial scales, fires produce heterogeneity bycreating a mosaic of burned and unburned patches.Although fire produces landscape pattern, land-scape pattern (for example, the presence of firebreaks) can also influence fire dynamics (Baker1995). Researchers working in different locationshave variously proposed that the probability of firespread is either independent of time since fire(Bessie and Johnson 1995), or that it increases withtime since fire (Minnich 1983). These differencessuggest that some forests have little ecologicalmemory, whereas others have a significantamount.

Fire is representative of a larger group of conta-gious disturbance processes. Contagious distur-bance processes—which include fires, insect out-breaks, and grazing herbivores—spread themselvesacross a landscape. Unlike noncontagious distur-bances, such as ice storms, hurricanes, or clear-cutting, the extent and duration of a contagiousdisturbance event are dynamically determined bythe interaction of the disturbance with a landscape.The size of a contagious disturbance depends, atleast partially, on the spatial configuration of land-scape being disturbed. Changes in landscape patternwill alter the nature of a contagious disturbanceregime, but will not alter a noncontagious distur-bance regime. For example, fragmentation of a for-est by roads will impede the spread of a wildfire, butnot determine the path of a hurricane. A conse-quence of this interactivity is that the same drivingforces will produce different contagious disturbancebehaviors in landscapes with different spatial pat-terns.

I used a simulation model to investigate thisquestion because of the difficulty of taking an em-pirical approach. Disentangling the cross-scale in-teractions in heterogeneous real ecosystems is adifficult task that is compounded by the fact thatspatially explicit data that could be used to assessecological pattern have only recently become avail-able. Assessing the dynamics of landscape patternrequires spatially explicit data that span at leastseveral cycles of structuring ecological processes.Fire return times, as well as return times of othercontagious disturbance processes such as insect out-breaks, usually range from decades to centuries.Long-term, spatially explicit records that span hun-

dreds of years do not, to the best of my knowledge,currently exist. A modeling approach allows eco-logical memory to be analyzed in the absence ofconfounding factors. Although such analyses can-not reveal what happens in real ecosystems, theycan suggest where and when theory predicts eventsshould be observable and unobservable in real eco-systems. It is in this sprit that I use simulationmodels to identify ecological situations in whichecological memory can be expected to have a largeeffect.

FOREST FIRE MODEL

Ecologists have developed a variety of models offorest fire dynamics. These models range from firerisk assessment models that predict the detaileddynamics of fire intensity and spread (Andrews1986; Finney 1998) to spatially implicit models ofthe interaction between fire frequency and vegeta-tion dynamics (Casagrandi and Rinaldi 1999). De-tailed spatial models such as the EMBYR model ofYellowstone (Hargrove and others 2000) includedetails of vegetation type, wind, and long-distancefire dispersal via spotting. Spatial models that do notmodel fire spread explicitly have also been used toexamine the distribution of forest age classes (Boy-chuk and others 1997).

Because I am interested in understanding howecological memory shapes landscape pattern, I cre-ated a simple spatial model, based on a minimalmodel of forest fire dynamics developed and ana-lyzed in statistical physics literature (Clar and others1996; Drossel and Schwabl 1992). This model rep-resents a forest as a rectangular matrix of sites. Eachsite is either empty, occupied by trees, or occupiedby burning trees. In this model, a forest fire regimeis defined by three rates: the rate at which treesregrow into empty sites, the rate at which burningtrees ignite neighboring nonburning trees, and therate/area at which fires are ignited across the land-scape. To produce a fire regime in which fire dis-turbs rather than interacts with forest regrowth,these rates must operate at different scales (Drossel1997).

I developed a modified version of this model thatallowed me to examine the effect of ecologicalmemory. My model assumes that a site does notalways burn when fire burns neighboring sites;rather, each site has a probability of burning thatdepends on the time since the site was last burned.This assumption supposes that after a fire there is aprocess of fuel accumulation at a site. For example,if fuel accumulates slowly, then a fire will be un-

330 G. D. Peterson

likely to spread into recently burned sites due to theabsence of fuel.

In my model, a fire regime is defined by the rateof fire ignition, the rate of vegetation recovery fol-lowing a fire, and the rate of fire spread. Theserelationships can be thought of as the interactionsof different scale processes, such as climate andvegetation growth, interacting to define a fire re-gime. Ecological memory is captured in the rela-tionship between vegetation recovery and the prob-ability of fire spread. Rather than explicitlyrepresenting the speed of fire spread, my modelassumes that fire spreads much faster than vegeta-tion recovers from fire. Drossel (1997) has shownthat in the statistical physics forest fire model, if firespreads much faster than a forest recovers from fire,the average fire size is proportional to the rate ofrecovery divided by the rate of ignition. This rela-tionship means that as fire ignition events becomeless frequent relative to the rate of recovery, fireswill tend to become larger and vice versa. Climateand topographic variation influence the probabilityof fire spread across time and space. Because thisinvestigation focuses upon the relationship be-tween regeneration and fire, I hold climate andtopography constant.

Model Structure

My model is spatially explicit. The basic functioningof the model is illustrated in Figure 1. The modeldivides a landscape into a matrix of sites. The be-

havior produced by this model is general; its appli-cability to a specific type of disturbance depends onthe degree to which the grain and extent of thatdisturbance can be captured by this model. Themodeled landscape is 440 � 440 sites. The model isroughly parameterized so that each site in the ma-trix represents an area of vegetation 50 m on edge(0.25 ha). Each site is described by the time sincethat site was last burned, which affects the proba-bility of fire spread.

The dynamics of the model consist of a within-year process of fire initiation and spread, and suc-cession. The entire process of fire initiation andspread occurs within a simulated year. Randomlyselected sites in the landscape are ignited by fires atthe fixed rate. I used three fire initiation rates: 1fire/100 cells/y, 4 fires/100 cells/y, and 16 fires/100cells/y. The probability of fire spreading from aburning site into a neighboring nonburning site ismodeled as a monotonically increasing function ofthe nonburning site’s time since fire (TSF). A firemay spread from a site to any of its eight adjacentsites, provided they have not already burned thatyear. A burning site has only one chance to igniteeach of its neighboring sites. A fire will continue tospread across the landscape until it fails to spread toany unburned cells. Following the extinction of ayear’s fires, vegetation regrows at sites across thelandscape. The combination of fire and vegetationregrowth produces a landscape composed of a mo-saic of differently aged patches (Figure 2).

Figure 1. An illustration ofthe functioning of the firemodel. During each year, anumber of fires are initiatedat random locations. After afire is initiated at a site, itcan spread to any of its eightneighboring sites. Fire spreadinto a site is a probabilisticfunction of the time since asite last burned. Fire spreadsuntil there are no burningsites. When a fire is extin-guished, either another fire isinitiated or the landscapeages a year and anotherround of fires are initiated.

Disturbance, Landscape Pattern, and Memory 331

To simplify the comparison of systems exhibitingdifferent amounts of ecological memory, I assumedthat the probability of fire spread plateaus at a highvalue (Pmax) following a maximum time since fire(TPmax). To allow the strength of ecological memoryto be varied using a single parameter (�), I designeda mathematical function:

Pr�FireSpread�TSF� � �1 � Pmax��TSF

TPmax��

� 1, TSF

� TPmax

Pr�FireSpread�TSF� � Pmax ,TSF � TPmax

(1)

The ecological memory parameter, �, varies theshape of the relationship between time since fireand the probability of fire spread. I found that vari-ation in ecological memory, ranging from no mem-ory to strong memory, was well captured by using �values of 1/100, 1/4, 1/2, 1, 4, 100.

The relationships between time since fire of a siteand the probability of fire spreading into such a siteare shown in Figure 3. The figure illustrates thatwhen � � 1/100, fire spread is independent of timesince fire; as � increases, the effect of fire becomesmore pronounced. When � � 1, there is an approx-imately linear relationship between time since fireand the probability of fire spread; when � � 100,there is approximately a step function between notburning and Pmax when the time since fire equalsTPmax.

The time period over which vegetation reachesmaximum ability to carry fire (TPmax) varies greatlyin different ecosystems. Because my model works ata yearly time step, I had to choose a value of TPmax

that permitted significant differences between thefire spread functions produced by different values of�. I examine fire recovery periods (TPmax) of 12, 25,and 50 years. These values span a reasonable eco-

logical range, yet are brief enough in duration toallow the tractable analysis of multiple fire periods.

The maximum probability of fire spreading intoan unburned neighboring site is Pmax. I choose avalue of Pmax located in the center of the percola-tion transition in this model. The percolationthreshold is the value of the probability of firespread at which a fire will percolate (Stauffer andAharony 1994); that is, fire will be able to spreadfrom one side of an arbitrarily large landscape toanother. A fire that percolates across a landscapewill not burn the entire landscape; some patcheswill escape fire. In this model, percolation dependson the details of how fire spreads (Stauffer andAharony 1994). Fire can spread to any of the eightneighbors of a burning site, provided they have notpreviously burned. I calculated the probability ofpercolation, in homogenous landscapes of Pmax, fordifferent values of Pmax. I chose Pmax � 0.24, a valueat which fire will frequently, but not always, per-colate across the landscape. This value is ecologi-cally reasonable because it probabilistically allows

Figure 2. A pattern of fire-generated patches emergesfrom a random landscapeafter a history of fires. (A)Forest after 1 year of fires.(B) Forest after 300 years offires.

Figure 3. Relationships between time since fire and theprobability of fire spread from Eq. (1). Vegetation’s mem-ory of past fires is controlled by �. If � is low, the vege-tation has no memory of past fires, and fire spreadsindependently of vegetation structure. At high values of�, vegetation has a strong influence on fire spread, andfire spread becomes dependent on vegetative pattern.

332 G. D. Peterson

some fires to spread far while limiting the spread ofothers. Higher or lower values would assume thatfire behavior tends to be exclusively either largerapidly spreading fires or small gradually spreadingfires, respectively. Similar values of Pmax (0.22–0.25)do not change the general behavior of the model.

METHODS

To assess the relationship between contagious dis-turbance and ecological memory, I conducted mul-tiple runs of the forest fire model for each of a rangeof different amounts of ecological memory (�), dif-ferent rates of recovery following fire (TPmax), anddifferent fire frequencies. For each set of modelruns, I compared the cross-scale vegetation patternusing correlograms.

Correlograms measure autocorrelation amongpoints on a landscape by calculating correlationbetween pairs of points that are separated by differ-ent lags (Legendre and Fortin 1989; Radeloff andothers 2000; Rossi and others 1992). Specifically,correlograms measure the autocorrelation betweentwo points separated by a lag for a series of n points.Correlograms are similar to semivariograms, butthey are more robust to local changes in the meansand variances across a data set. I used a two-dimen-sional version of the correlogram to measure auto-correlation across both space and time.

I did this by sampling 6000 randomly selectedpoints (the 0.25-ha sites) that are separated by acombination of temporal lags ranging from 0 to 84years and spatial lags ranging from 0 to 200 cells.These dimensions were chosen to include severalfire cycles while still remaining analytically tracta-ble. In this case lag (h) is a vector that has both aspatial and temporal component. Lag autocorrela-tion is estimated by:

p̂�h� �1

N�h�

�i�1

N�h�

�� z� xi� � m�h� � z� xi � h� � m�h�

S�hS�h

(2)

where p̂(h) is an estimate of the autocorrelation atlag h. z (xi) and z (xi � h) are two data points sep-arated by the lag h. N(h) is the number of datapoints that are separated by lag h. Data point z (xi) isthe tail and z (xi � h) is the head of a vector, andm�h and m�h correspond to the mean values of thepoints at the head and tail end of all the vectors oflag h. s�h and s�h represent the standard deviationsof the tail and head values of the vectors at lag h.

Plotting lag autocorrelation against lag (h) producesa correlogram.

Correlograms were constructed from the dynam-ics of a landscape 20 km on edge over 180 years.The dimensions of this cube of data are such thatthe maximum lags in space and time were less thanhalf the span of the landscape and less than half theduration period during which landscapes were re-corded.

No external disturbance enters the simulatedlandscape from beyond the model’s edges, and firecannot spread beyond the edges of the simulatedarea. These constraints produce an edge effect,which results in the cells near the edges of thesimulated area burning less frequently than thecells near the center of the matrix. The extent of thearea experiencing edge effects depends on the rel-ative size of the simulated fires compared to thetotal extent of the simulated area. The strength ofedge effects is inversely proportional to the amountof memory in the model; however, edge effects aretypically limited to 10–20 cells. Consequently, cor-relograms were only calculated between points thatwere at least 20 cells from the edge of the modeledarea.

In the temporal equivalent of an edge effect, ini-tial landscape conditions influence landscape pat-tern for some period, but their influence declinesover time. To remove the effects of initial condi-tions, data for the correlograms were only collectedafter allowing the landscape to organize for 600years (at least 12 fire cycles). Based on test modelruns, this duration was roughly twice as long asneeded for a dynamic equilibrium to be reached.

I analyzed my model with different amounts ofecological memory (� � 1/100, 1/4, 1, 4, and 100),with different rates of vegetation recovery follow-ing fire (TPmax � 12, 25, and 50 years) and differentfire frequencies (1 fire/100 cells/y, 4 fires/100cells/y, and 16 fires/100 cells/y). For each set ofmodel parameters, the model was run for each �value 26 times. The average autocorrelation at eachlag distance and time was calculated. Because thestandard error around a mean is a function of thesquare root of the number of samples taken, thebenefit of increasing the number of model runsdiminishes rapidly as the number of samples in-creases. From these multiple model runs, standarddeviations of the average autocorrelation were es-timated, and a two-tailed t-test was used to deter-mine whether the autocorrelation at each lag wassignificantly different from zero with a P � 0.01(Zar 1984). Autocorrelations at a lag that are notsignificantly different from zero are plotted as zero.From these calculations, autocorrelation surfaces


were constructed. These surfaces show the autocor-relation of vegetation pattern (represented as timesince fire) at different spatial and temporal lags.These figures show positive autocorrelation (that is,sites are similar) at some temporal and spatial lagsand negative autocorrelation (that is, sites are con-sistently dissimilar) at other temporal and spatiallags. The figures illustrate the spatial and temporallags at which pattern exists from the viewpoint of amodel cell.

RESULTS

The sets of correlograms produced by the modelsare shown in Figures 4 and 5. In each figure, mem-ory increases from left to right. Autocorrelation in-dicates that pattern exists at a given lag. Positiveautocorrelation indicates that sites at a given lag aresimilar; negative autocorrelation indicates that sitesat a given lag are paired with sites that are different(for example, young sites are paired with older sites

and vice versa). Figure 4 compares landscape pat-tern produced by models experiencing different firefrequencies. Figure 5 compares landscape patternproduced by models with different vegetation re-covery periods. As suggested by the inverse rela-tionship between forest recovery and fire initiation(Drossel 1997), the patterns produced by changes infire frequency and forest recovery period are simi-lar. Decreases in fire frequency have an effect sim-ilar, but not identical, to increases in the period offorest recovery.

When there is no ecological memory (� �1/100), spatial pattern is produced by fire, but thatpattern does not persist over time. There is a signif-icant change in spatial and temporal pattern withthe transition from no memory to memory (� �1/100 to � � 1/4). Spatial pattern spans less areaand persists longer. As ecological memory increases,pattern begins to emerge at longer temporal lags,which match the vegetation recovery period(TPmax). When memory is strong, positive autocor-

Figure 4. Covariance at spatial and temporal lags for � � 1/100, 1/4, 1, 4, and 100 at fire frequencies of 1, 4, and 16fires/100 cells/y. Horizontal and vertical scales are log axes. Plus signs indicate positive autocorrelation; negative signsindicate negative zones of autocorrelation. At long temporal lags and high values of �, there are many cycles of positiveand negative autocorrelation, which are unlabeled.

334 G. D. Peterson

relation appears at multiples of the vegetation re-covery period. This increase in temporal structure isalso matched by an increase in spatial extent andstrength of spatial structure.

As ecological memory (�) increases, the spatialand temporal organization of the landscapechanges. At all values of �, the landscape is highlycorrelated at short distances and over brief periods.As � increases, spatial correlation increases, and thiscorrelation decreases faster over time. Along withthis pattern, negative autocorrelation emerges atintermediate temporal lags and positive autocorre-lation at a frequency about that of the recoveryrate. With further increases of �, the strength ofautocorrelation increases and extends across agreater range of spatial lags. Additionally, the tem-poral lag over which there is correlation declines.Furthermore, as � increases, discrete ranges of neg-ative and positive correlation emerge at temporallags related to TPmax at short spatial lags. At veryhigh values of �, weak autocorrelation emerges at

intermediate frequencies at very large spatial lags.This pattern is repeated at different fire frequenciesand values of TPmax; however, variation in fire fre-quency and TPmax changes the spatial and temporallags at which these zones of autocorrelation appear.

As frequency of fire decreases, the scale of spatialcorrelation increases, and correlation over time in-creases. For example, at an intermediate value of �(� � 1), there is minimal organization at larger andlonger lags at a higher fire frequency (16 fires/100cells/y); but as fire frequency decreases, the rangeof spatial lags at which the landscape is correlatedand the intensity of correlation increases. Further-more, at a lower fire frequency (1 fire/100 cells/y),a new weak negative correlation emerges at about a40-year lag.

At low �, there is no difference between thescales of correlation for different values of TPmax;however, as � increases, differences emerge. Theclearest change is that the temporal lags at whichpositive and negative autocorrelation occur track

Figure 5. Covariance at spatial and temporal lags for � � 1/100, 1/4, 1, 4, and 100 at vegetation recovery times (TPmax)of 12, 25, and 50 years. Horizontal and vertical scales are log axes. Plus signs indicate positive autocorrelation; negativesigns indicate zones of negative autocorrelation. At long temporal lags and high values of �, there are many cycles ofpositive and negative autocorrelation, which are unlabeled.


the changes in TPmax. When recovery time is brief(12 years), autocorrelation decays quickly and thenreemerges rapidly; whereas if recovery is longer,autocorrelation decreases gradually with temporallag and a new zone of autocorrelation emerges atlonger periods. As recovery time increases, the spa-tial scale over which autocorrelation occurs de-creases and the strength of autocorrelation also de-creases. This pattern is similar to what is observed asfire frequency decreases.

DISCUSSION

The correlograms reveal that fires generate spatialpattern and that the strength and spatial span of thispattern depend on fire frequency and rates of veg-etation recovery. They also reveal that the persis-tence of the patterns depends on ecological memo-ry—the degree to which previous fires influencethe spread of fire. The amount of memory (�) nec-essary to produce landscape pattern depends on therate of vegetation recovery and the frequency of fireinitiation. As fire initiation rates decrease, or theperiod of vegetation recovery decreases, theamount of memory necessary to produce persistentlandscape pattern also decreases.

Ecological memory produces persistent patternbecause it establishes a feedback loop between firespread and landscape pattern. This feedback loopallows ecological pattern and ecological process toregulate one another (Watt 1947). In the absence ofmemory, there is a one-way relationship betweenfire and landscape pattern. Fire shapes landscapepattern but is not shaped by it. Memory causeslandscape pattern to influence fire spread and viceversa. Mutual influence between fire patterns andlandscape patterns encourages the formation ofmutually reinforcing patterns.

The feedback between fire spread and forest pat-tern produces a patch mosaic on the landscape.Relatively homogenous patches of forest are pro-duced due to the spatially contagious nature of firespread. Sites within these patches have the sameprobability of fire spread, because they were previ-ously burned at the same time. This homogeneitymeans that fires ignited within these patches willtend to either fail to spread or spread across theentire patch. Fire spread tends to stop at the edge ofpatches. Patches neighboring a burning patch aremore likely to have a lower probability of firespread, because patches with a higher probability offire spread are unlikely to have remained un-burned. The mosaic of patches with different prob-abilities of fire spread reduces the ability of fire tospread across the entire landscape. As memory in-

creases, these tendencies are strengthened, increas-ing the spatial extent of autocorrelation and thepersistence of spatial pattern over time.

The memory of past fires is the degree to which alandscape’s vegetative pattern influences the spreadof fire. The memory of past fires fades over time,because differences in the probability of fire spreadthat were produced by different fire histories dimin-ish as the time since fire increases. For example,when there is ecological memory, the probability offire spread varies between different-aged sites ifthose sites are younger than the vegetation recov-ery period (TPmax), whereas there is no differencebetween the probability of fire spread into siteswhose age is greater than TPmax. When forest pat-tern strongly influences the spread of fires (for ex-ample, when � is greater than 1), forest pattern willtend to be renewed by fire. When memory is weak(for example, when � is less than 1), future fireswill produce a new pattern that erases past patterns.

Implications of Ecological Memory

The consequences of manipulating landscape pat-tern or the processes that control the fire regimewill be more complex when an ecosystem hasmemory than when it does not. Ecological memoryis encoded in the pattern of vegetation across thelandscape. This pattern constrains and channels thespread of fire. Consequently, changes in vegetativepattern, via abiotic, biotic, or anthropogenic pro-cesses, have the potential to alter a fire regime, evenif the drivers of that disturbance regime, such as theclimate and vegetation of the region, remain con-stant. Homogenizing the landscape may removebarriers to fire spread, leading to a period of largefires. Alternatively, fragmenting the landscape willlead to a period of smaller fires. Despite these gen-eralities, the degree to which a fire regime changesin response to landscape modification will dependon the specific details of landscape pattern and howit is changed.

Similarly, due to the constraining effects of land-scape pattern, shifts in either vegetation regrowthor climate can also alter a fire regime in complexways. For example, a change in climate could in-crease fire frequency, which would produce smallerand more frequent fires. Alternatively, a region in-vaded by pyrogenic grass will more rapidly becomecombustible following a fire, decreasing the vegeta-tion recovery time (D’Antonio and Vitousek 1992).The behavior of ecosystems with little memory willsimply track changes in vegetation recovery and firefrequency. However, ecosystems with strong mem-ory can be expected to respond to changes in driv-ing processes in complex ways. Strong memory

336 G. D. Peterson

should initially inhibit ecological response tochange. However, if change is rapid and intense,extreme transient behavior can be expected. Forexample, if fire frequency decreases, the existinglandscape pattern will constrain fires, but eventu-ally the lack of maintenance of this pattern, due tothe reduced fire frequency, will result in very largefires, before a new landscape structure is estab-lished. This suggests that ecosystems with largeamounts of memory will respond to changes indisturbance regimes in more complicated ways thanecosystems with little memory of the past.

Ecological Memory in Ecosystems

The general nature of the fire model suggests thatthe interaction of ecological memory and conta-gious disturbances may influence landscape dy-namics in a number of situations. In Californiachaparral, fire intensity depends on vegetation den-sity over small spatial scales (approximately 1 m),while regeneration occurs primarily in areas thatexperience less intense fire (Odion and Davis 2000).In this ecosystem, the connection between vegeta-tion pattern and fire introduces the memory of pastdisturbances into the system and thus produces per-sistent spatial pattern. Ecosystems that are domi-nated by externally driven fluctuations in climate,water levels, or biota are unlikely to be shaped bythe memory of past disturbances. For example, firein the western boreal forest of North America ap-pears to be driven by climate variation (Johnson1992), which suggests that ecological memory doesnot influence the fire regime.

Animal behavior, like fire, has the potential toencode memory into landscape pattern. Selectivegrazing by herbivores produces disturbance pat-terns that are determined by existing landscape pat-tern. If the vegetative response to disturbance in-fluences future grazing decisions by herbivores,then the ecosystem exhibits memory and the inter-action of selective herbivores can produce persistentspatial pattern. For example, in the boreal forest ofeastern North America, moose selectively consumeearly successional deciduous tree species. Thisbrowsing facilitates the replacement of deciduousspecies by coniferous species, producing a change invegetation pattern that alters future browsing deci-sions. This foraging behavior, in conjunction withother contagious disturbance processes, producespersistent spatial pattern in the forest (Pastor andothers 1998, 1999). In general, I expect that eco-logical memory is likely to arise in ecosystems inwhich biotic variation has a strong influence onecological dynamics.

Extended Keystone Hypothesis

The results of my fire model show that ecologicalmemory encourages the emergence of persistentspatial pattern, which provides some support forthe extended keystone hypothesis (Holling 1992)and also suggests some limits. Holling (1992) pro-posed that landscape pattern is generated by theinteraction of a few “keystone” processes that op-erate at separate and distinct spatial and temporalscales. He argues that these keystone processes en-train other ecological processes and variables to thecharacteristic frequencies of these processes; conse-quently, the properties of ecosystems should exhibitdiscrete rather than continuous structure. AlthoughHolling (1992) and others (Allen and others 1999;Havlicek and Carpenter 2001; Manly 1996; Raffaelliand others 2000) have examined the question ofwhether ecosystem attributes exhibit a discontinu-ous structure, there has been little consideration ofhow feasible it is for the interactions of keystoneecological processes to produce discrete ecologicalpattern.

Holling and others (1996) suggested that conta-gious disturbance processes, such as fire, are exam-ples of keystone processes. My results show thatmodels of fire have the potential to produce discretelandscape pattern, thus supporting the idea that fireis indeed a keystone process. Persistent patternsoccur at temporal frequencies related to the recov-ery time of the vegetation from fire (that is, at 12-,25-, and 50-year frequencies in the model). How-ever, my model suggests that such patterns do notemerge in the absence of ecological memory. Theseresults suggest that the extended keystone hypoth-esis is most likely to be demonstrated in ecosystemsthat exhibit strong ecological memory—ecosystemsin which the spread of a key disturbance process isstrongly influenced by the legacies of past distur-bance.

The spatial and temporal correlograms that I usedto search for persistent pattern could also be used totest the extended keystone hypothesis in actualecosystems. It is difficult to find data that span atime period several times the frequency of a distur-bance over a spatial scale several times the extent ofthe disturbance. However, historical and paleoeco-logical research is making such data sets increas-ingly available (Niklasson and Granstrom 2000).

CONCLUSIONS

Ecological memory shapes landscape pattern by in-creasing the strength of the interaction betweenecological processes and landscape pattern. When


ecological memory is strong, landscape pattern ispersistent; pattern tends to be maintained ratherthan destroyed by fire. The existence of ecologicalmemory in ecosystems may allow processes to pro-duce ecological pattern that can entrain other eco-system variables. Changes in landscape pattern orkey process drivers, such as fire frequency or veg-etation recovery rates following disturbance, aremore likely to have nonlinear and surprising effectsin ecosystems with strong memory. There is someevidence that ecological memory exists in real eco-systems. The methods presented in this paper toanalyze pattern in model ecosystems could be usedto detect evidence of persistent landscape pattern inactual ecosystems.

ACKNOWLEDGMENTS

A part of this work was conducted while I was apostdoctoral fellow at the National Center for Eco-logical Analysis and Synthesis at the University ofCalifornia Santa Barbara. It uses models that I de-veloped during my doctoral research, which wasfunded by a NASA Earth Science Fellowship. Thepaper benefited from conversations with BruceMilne, and comments from Craig Allen, Elena Ben-nett, Lisa Dent, Tim Essington, and two anonymousreviewers.

REFERENCES

Allen CR, Forys EA, Holling CS. 1999. Body mass patterns pre-dict invasions and extinctions in transforming landscapes. Eco-systems 2:114–121.

Andrews PL. 1986. Behave: fire behavior prediction and fuelmodeling system—burn subsystem, part 1 Report INT-194. USForest Service.

Baker WL. 1995. Long-term response of disturbance landscapesto human intervention and global change. Landscape Ecol10:143–159.

Baker WL. 1993. Spatially heterogeneous multiscale response oflandscapes to fire suppression. Oikos 66:66–71.

Bessie WC, Johnson EA. 1995. The relative importance of fuelsand weather on fire behavior in subalpine forests. Ecology76:747–762.

Bond WJ, van Wilgen BW. 1996. Fire and plants. London:Chapman & Hall.

Boychuk D, Perera AH, TerMikaelian MT, Martell DL, Li C. 1997.Modelling the effect of spatial scale and correlated fire distur-bances on forest age distribution. Ecol Model 95:145–164.

Casagrandi R, Rinaldi S. 1999. A minimal model for forest fireregimes. Am Nat 153:527–539.

Clar S, Drossel B, Schwabl F. 1996. Forest fires and other exam-ples of self-organized criticality. J Physics-Condensed Matter8:6803–6824.

D’Antonio CM, Vitousek PM. 1992. Biological invasions by ex-otic grasses, the grass/fire cycle and global change. Annu RevEcol Syst 23:63–87.

Drossel B. 1997. Self-organized criticality due to a separation ofenergy scales. Physica A 236:309–320.

Drossel B, Schwabl F. 1992. Self-organized critical forest-firemodel. Phys Rev Lett 69:1629–1632.

Finney MA. 1998. FARSITE: fire area simulator—model devel-opment and evaluation. no. 4. USDA Forest Service, RockyMountain Forest and Range Experiment Station Research.

Hargrove WW, Gardner RH, Turner MG, Romme WH, DespainDG. 2000. Simulating fire patterns in heterogeneous land-scapes. Ecol Model 135:243–263.

Havlicek TD, Carpenter SR. 2001. Pelagic species size distribu-tions in lakes: are they discontinuous? Limnol Oceanogr 46:1021–1033.

Holling CS. 1992. Cross-scale morphology, geometry and dy-namics of ecosystems. Ecol Monogr 62:447–502.

Holling CS, Peterson G, Marples P, Sendzimir J, Redford K,Gunderson L, Lambert D. 1996. Self-organization in ecosys-tems: lumpy geometries, periodicities, and morphologies. In:Walker BH, Steffen WL, editors. Global change and terrestrialecosystems. Cambridge (England): Cambridge UniversityPress. p 346–384.

Johnson EA. 1992. Fire and vegetation dynamics: studies fromthe North American boreal forest. Cambridge (England): Cam-bridge University Press.

Legendre P, Fortin M-J. 1989. Spatial pattern and ecologicalanalysis. Vegetatio 80:107–138.

Ludwig JA, Wiens JA, Tongway DJ. 2000. A scaling rule forlandscape patches and how it applies to conserving soil re-sources in savannas. Ecosystems 3:84–97.

Manly BFJ. 1996. Are there clumps in body-size distributions?Ecology 77:81–86.

Minnich RA. 1983. Fire mosaics in Southern-California andNorthern Baja California. Science 219:1287–1294.

Niklasson M, Granstrom A. 2000. Numbers and sizes of fires:long-term spatially explicit fire history in a Swedish boreallandscape. Ecology 81:1484–1499.

Odion DC, Davis FW. 2000. Fire, soil heating, and the formationof vegetation patterns in chaparral. Ecol Monogr 70:149–169.

Pastor J, Cohen Y, Moen R. 1999. Generation of spatial patternsin boreal forest landscapes. Ecosystems 2:439–450.

Pastor J, Dewey B, Moen R, Mladenoff DJ, White M, Cohen Y.1998. Spatial patterns in the moose-forest-soil ecosystem onIsle Royale, Michigan, USA. Ecol Appl 8:411–424.

Radeloff VC, Miller TF, He HS, Mladenoff DJ. 2000. Periodicity inspatial data and geostatistical models: autocorrelation betweenpatches. Ecography 23:81–91.

Raffaelli D, Hall S, Emes C, Manly B. 2000. Constraints on bodysize distributions: an experimental approach using a small-scale system. Oecologia 122:389–398.

Rossi RE, Mulla DJ, Journel AG, Franz EH. 1992. Geostatisticaltools for modeling and interpreting ecological spatial depen-dence. Ecol Monogr 62:277–314.

Stauffer D, Aharony A. 1994. Introduction to percolation theory.Bristol (PA): Taylor & Francis.

Watt AS. 1947. Pattern and process in the plant community. JEcol 35:1–22.

Zar JH. 1984. Biostatistical analysis. Englewood Cliff (NJ): Simon& Schuster.

338 G. D. Peterson

Contagious Disturbance, Ecological Memory, and the Emergence of Landscape Pattern

Documents