ECOSYSTEMS
Ecosystems (2002) 5: 329 –338 DOI: 10.1007/s10021-001-0077-1
© 2002 Springer-Verlag
Contagious Disturbance, Ecological Memory, and the Emergence of Landscape Pattern Garry D. Peterson Center for Limnology, University of Wisconsin, Madison, Wisconsin, 53706, USA
ABSTRACT Landscapes are strongly shaped by the degree of interaction between pattern and process. This paper examines how ecological memory, the degree to which an ecological process is shaped by its past modifications of a landscape, influences landscape dynamics. I use a simulation model to examine how ecological memory shapes the landscape dynamics produced by the interaction of vegetative regrowth and fire. The model illustrated that increased ecological memory increased the strength and spatial extent of landscape pattern. The extent of these changes depended upon the relative rates of vegetative recovery and fire initiation. When ecological memory is strong, landscape pattern is persistent;
pattern tends to be maintained rather than destroyed by fire. The generality of the simulation model suggests that these results may also apply to disturbance processes other than fire. The existence of ecological memory in ecosystems may allow processes to produce ecological pattern that can entrain other ecosystem variables. The methods presented in this paper to analyze pattern in model ecosystems could be used to detect such pattern in actual ecosystems.
INTRODUCTION
previous fires, then memory is shaping their dynamics. The presence of memory allows ecological processes to interact with one another; its absence means that pattern is generated by a single process imposing some type of template of organization on a system. However, in most ecological systems, ecological processes cannot be neatly divided between those that exhibit memory and those that do not. Even apparently one-way relationships, such as the effects of climate on vegetation, contain interactions (for example, the effects of vegetation upon humidity). How much does memory influence landscape dynamics? In this paper, I use a simulation model of fire and vegetation dynamics to examine the role of ecological memory in producing landscape pattern. Specifically, I examine how ecological memory influences the landscape pattern that is produced by the interaction between fire frequency and vegetative regrowth. Fire is a key structuring processes in many eco-
Key words: landscape ecology; self-organization; spatial dynamics; patch dynamics; keystone processes; scale; autocorrelation.
Landscape pattern is a key attribute of ecosystems, organizing and regulating the flow of ecological goods and services (Ludwig and others 2000). Landscape pattern is itself shaped by ecological processes. The extent of the interaction between landscape pattern and the processes that shape it has a fundamental influence on landscape dynamics. Does a process impose a pattern upon a landscape unilaterally, or is there a two-way dynamic interaction between pattern and process? The degree to which an ecological process is shaped by its history can be thought of as the strength of the ecological memory of that process. For example, if the location of tree-fall gaps is influenced by where past tree falls occurred or if fire spread is influenced by
Received 14 November 2000; accepted 21 September 2001. e-mail:
[email protected]
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systems (Bond and van Wilgen 1996). Although the duration of a fire is much shorter than the life span of the vegetation it consumes, fire produces landscape patterns that persist for long periods (Baker 1993). At small spatial scales, fire homogenizes the landscape by killing aboveground growth of trees, producing patches of even-aged vegetation. At larger spatial scales, fires produce heterogeneity by creating a mosaic of burned and unburned patches. Although fire produces landscape pattern, landscape pattern (for example, the presence of fire breaks) can also influence fire dynamics (Baker 1995). Researchers working in different locations have variously proposed that the probability of fire spread is either independent of time since fire (Bessie and Johnson 1995), or that it increases with time since fire (Minnich 1983). These differences suggest that some forests have little ecological memory, whereas others have a significant amount. Fire is representative of a larger group of contagious disturbance processes. Contagious disturbance processes—which include fires, insect outbreaks, and grazing herbivores—spread themselves across a landscape. Unlike noncontagious disturbances, such as ice storms, hurricanes, or clearcutting, the extent and duration of a contagious disturbance event are dynamically determined by the interaction of the disturbance with a landscape. The size of a contagious disturbance depends, at least partially, on the spatial configuration of landscape being disturbed. Changes in landscape pattern will alter the nature of a contagious disturbance regime, but will not alter a noncontagious disturbance regime. For example, fragmentation of a forest by roads will impede the spread of a wildfire, but not determine the path of a hurricane. A consequence of this interactivity is that the same driving forces will produce different contagious disturbance behaviors in landscapes with different spatial patterns. I used a simulation model to investigate this question because of the difficulty of taking an empirical approach. Disentangling the cross-scale interactions in heterogeneous real ecosystems is a difficult task that is compounded by the fact that spatially explicit data that could be used to assess ecological pattern have only recently become available. Assessing the dynamics of landscape pattern requires spatially explicit data that span at least several cycles of structuring ecological processes. Fire return times, as well as return times of other contagious disturbance processes such as insect outbreaks, 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 ecological memory to be analyzed in the absence of confounding factors. Although such analyses cannot reveal what happens in real ecosystems, they can suggest where and when theory predicts events should be observable and unobservable in real ecosystems. It is in this sprit that I use simulation models to identify ecological situations in which ecological memory can be expected to have a large effect.
FOREST FIRE MODEL Ecologists have developed a variety of models of forest fire dynamics. These models range from fire risk assessment models that predict the detailed dynamics of fire intensity and spread (Andrews 1986; Finney 1998) to spatially implicit models of the interaction between fire frequency and vegetation dynamics (Casagrandi and Rinaldi 1999). Detailed spatial models such as the EMBYR model of Yellowstone (Hargrove and others 2000) include details of vegetation type, wind, and long-distance fire dispersal via spotting. Spatial models that do not model fire spread explicitly have also been used to examine the distribution of forest age classes (Boychuk and others 1997). Because I am interested in understanding how ecological memory shapes landscape pattern, I created a simple spatial model, based on a minimal model of forest fire dynamics developed and analyzed in statistical physics literature (Clar and others 1996; Drossel and Schwabl 1992). This model represents a forest as a rectangular matrix of sites. Each site is either empty, occupied by trees, or occupied by burning trees. In this model, a forest fire regime is defined by three rates: the rate at which trees regrow into empty sites, the rate at which burning trees ignite neighboring nonburning trees, and the rate/area at which fires are ignited across the landscape. To produce a fire regime in which fire disturbs rather than interacts with forest regrowth, these rates must operate at different scales (Drossel 1997). I developed a modified version of this model that allowed me to examine the effect of ecological memory. My model assumes that a site does not always burn when fire burns neighboring sites; rather, each site has a probability of burning that depends on the time since the site was last burned. This assumption supposes that after a fire there is a process of fuel accumulation at a site. For example, if fuel accumulates slowly, then a fire will be un-
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Figure 1. An illustration of the functioning of the fire model. During each year, a number of fires are initiated at random locations. After a fire is initiated at a site, it can spread to any of its eight neighboring sites. Fire spread into a site is a probabilistic function of the time since a site last burned. Fire spreads until there are no burning sites. When a fire is extinguished, either another fire is initiated or the landscape ages a year and another round of fires are initiated.
likely to spread into recently burned sites due to the absence of fuel. In my model, a fire regime is defined by the rate of fire ignition, the rate of vegetation recovery following a fire, and the rate of fire spread. These relationships can be thought of as the interactions of different scale processes, such as climate and vegetation growth, interacting to define a fire regime. Ecological memory is captured in the relationship between vegetation recovery and the probability of fire spread. Rather than explicitly representing the speed of fire spread, my model assumes that fire spreads much faster than vegetation recovers from fire. Drossel (1997) has shown that in the statistical physics forest fire model, if fire spreads much faster than a forest recovers from fire, the average fire size is proportional to the rate of recovery divided by the rate of ignition. This relationship means that as fire ignition events become less frequent relative to the rate of recovery, fires will tend to become larger and vice versa. Climate and topographic variation influence the probability of fire spread across time and space. Because this investigation focuses upon the relationship between regeneration and fire, I hold climate and topography constant.
Model Structure My model is spatially explicit. The basic functioning of the model is illustrated in Figure 1. The model divides a landscape into a matrix of sites. The be-
havior produced by this model is general; its applicability to a specific type of disturbance depends on the degree to which the grain and extent of that disturbance can be captured by this model. The modeled landscape is 440 ⫻ 440 sites. The model is roughly parameterized so that each site in the matrix represents an area of vegetation 50 m on edge (0.25 ha). Each site is described by the time since that site was last burned, which affects the probability of fire spread. The dynamics of the model consist of a withinyear process of fire initiation and spread, and succession. The entire process of fire initiation and spread occurs within a simulated year. Randomly selected sites in the landscape are ignited by fires at the fixed rate. I used three fire initiation rates: 1 fire/100 cells/y, 4 fires/100 cells/y, and 16 fires/100 cells/y. The probability of fire spreading from a burning site into a neighboring nonburning site is modeled as a monotonically increasing function of the nonburning site’s time since fire (TSF). A fire may spread from a site to any of its eight adjacent sites, provided they have not already burned that year. A burning site has only one chance to ignite each of its neighboring sites. A fire will continue to spread across the landscape until it fails to spread to any unburned cells. Following the extinction of a year’s fires, vegetation regrows at sites across the landscape. The combination of fire and vegetation regrowth produces a landscape composed of a mosaic of differently aged patches (Figure 2).
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Figure 2. A pattern of firegenerated patches emerges from a random landscape after a history of fires. (A) Forest after 1 year of fires. (B) Forest after 300 years of fires.
To simplify the comparison of systems exhibiting different amounts of ecological memory, I assumed that the probability of fire spread plateaus at a high value (Pmax) following a maximum time since fire (TPmax). To allow the strength of ecological memory to be varied using a single parameter (␣), I designed a mathematical function: Pr共FireSpread兩TSF兲 ⫽ 共1 ⫹ P max兲 冉TPmax冊 ⫺ 1, TSF TSF
␣
ⱕ TP max Pr共FireSpread兩TSF兲 ⫽ P max
,TSF ⬎ TP max (1)
The ecological memory parameter, ␣, varies the shape of the relationship between time since fire and the probability of fire spread. I found that variation in ecological memory, ranging from no memory 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 site and the probability of fire spreading into such a site are shown in Figure 3. The figure illustrates that when ␣ ⫽ 1/100, fire spread is independent of time since fire; as ␣ increases, the effect of fire becomes more pronounced. When ␣ ⫽ 1, there is an approximately linear relationship between time since fire and the probability of fire spread; when ␣ ⫽ 100, there is approximately a step function between not burning and Pmax when the time since fire equals TPmax. The time period over which vegetation reaches maximum ability to carry fire (TPmax) varies greatly in different ecosystems. Because my model works at a yearly time step, I had to choose a value of TPmax that permitted significant differences between the fire 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-
Figure 3. Relationships between time since fire and the probability of fire spread from Eq. (1). Vegetation’s memory of past fires is controlled by ␣. If ␣ is low, the vegetation has no memory of past fires, and fire spreads independently of vegetation structure. At high values of ␣, vegetation has a strong influence on fire spread, and fire spread becomes dependent on vegetative pattern.
logical range, yet are brief enough in duration to allow the tractable analysis of multiple fire periods. The maximum probability of fire spreading into an unburned neighboring site is Pmax. I choose a value of Pmax located in the center of the percolation transition in this model. The percolation threshold is the value of the probability of fire spread at which a fire will percolate (Stauffer and Aharony 1994); that is, fire will be able to spread from one side of an arbitrarily large landscape to another. A fire that percolates across a landscape will not burn the entire landscape; some patches will escape fire. In this model, percolation depends on the details of how fire spreads (Stauffer and Aharony 1994). Fire can spread to any of the eight neighbors of a burning site, provided they have not previously burned. I calculated the probability of percolation, in homogenous landscapes of Pmax, for different values of Pmax. I chose Pmax ⫽ 0.24, a value at which fire will frequently, but not always, percolate across the landscape. This value is ecologically reasonable because it probabilistically allows
Disturbance, Landscape Pattern, and Memory some fires to spread far while limiting the spread of others. Higher or lower values would assume that fire behavior tends to be exclusively either large rapidly spreading fires or small gradually spreading fires, 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 disturbance and ecological memory, I conducted multiple runs of the forest fire model for each of a range of different amounts of ecological memory (␣), different rates of recovery following fire (TPmax), and different fire frequencies. For each set of model runs, I compared the cross-scale vegetation pattern using correlograms. Correlograms measure autocorrelation among points on a landscape by calculating correlation between pairs of points that are separated by different lags (Legendre and Fortin 1989; Radeloff and others 2000; Rossi and others 1992). Specifically, correlograms measure the autocorrelation between two points separated by a lag for a series of n points. Correlograms are similar to semivariograms, but they are more robust to local changes in the means and variances across a data set. I used a two-dimensional version of the correlogram to measure autocorrelation across both space and time. I did this by sampling 6000 randomly selected points (the 0.25-ha sites) that are separated by a combination of temporal lags ranging from 0 to 84 years and spatial lags ranging from 0 to 200 cells. These dimensions were chosen to include several fire cycles while still remaining analytically tractable. In this case lag (h) is a vector that has both a spatial and temporal component. Lag autocorrelation is estimated by:
冘 关共 z共 x 兲 ⫺ m
N共h兲
i
1 pˆ 共h兲 ⫽ N共h兲
兲 共 z共 x i ⫹ h兲 ⫺ m ⫹h兲兴
⫺h
i⫽1
S ⫺hS ⫹h (2)
where pˆ(h) is an estimate of the autocorrelation at lag h. z (xi) and z (xi ⫹ h) are two data points separated by the lag h. N(h) is the number of data points that are separated by lag h. Data point z (xi) is the tail and z (xi ⫹ h) is the head of a vector, and m⫺h and m⫹h correspond to the mean values of the points at the head and tail end of all the vectors of lag h. s⫺h and s⫹h represent the standard deviations of the tail and head values of the vectors at lag h.
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Plotting lag autocorrelation against lag (h) produces a correlogram. Correlograms were constructed from the dynamics of a landscape 20 km on edge over 180 years. The dimensions of this cube of data are such that the maximum lags in space and time were less than half the span of the landscape and less than half the duration period during which landscapes were recorded. No external disturbance enters the simulated landscape from beyond the model’s edges, and fire cannot spread beyond the edges of the simulated area. These constraints produce an edge effect, which results in the cells near the edges of the simulated area burning less frequently than the cells near the center of the matrix. The extent of the area experiencing edge effects depends on the relative size of the simulated fires compared to the total extent of the simulated area. The strength of edge effects is inversely proportional to the amount of memory in the model; however, edge effects are typically limited to 10 –20 cells. Consequently, correlograms were only calculated between points that were at least 20 cells from the edge of the modeled area. In the temporal equivalent of an edge effect, initial landscape conditions influence landscape pattern for some period, but their influence declines over time. To remove the effects of initial conditions, data for the correlograms were only collected after allowing the landscape to organize for 600 years (at least 12 fire cycles). Based on test model runs, this duration was roughly twice as long as needed for a dynamic equilibrium to be reached. I analyzed my model with different amounts of ecological memory (␣ ⫽ 1/100, 1/4, 1, 4, and 100), with different rates of vegetation recovery following fire (TPmax ⫽ 12, 25, and 50 years) and different fire frequencies (1 fire/100 cells/y, 4 fires/100 cells/y, and 16 fires/100 cells/y). For each set of model parameters, the model was run for each ␣ value 26 times. The average autocorrelation at each lag distance and time was calculated. Because the standard error around a mean is a function of the square root of the number of samples taken, the benefit of increasing the number of model runs diminishes rapidly as the number of samples increases. From these multiple model runs, standard deviations of the average autocorrelation were estimated, and a two-tailed t-test was used to determine whether the autocorrelation at each lag was significantly different from zero with a P ⫽ 0.01 (Zar 1984). Autocorrelations at a lag that are not significantly different from zero are plotted as zero. From these calculations, autocorrelation surfaces
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Figure 4. Covariance at spatial and temporal lags for ␣ ⫽ 1/100, 1/4, 1, 4, and 100 at fire frequencies of 1, 4, and 16 fires/100 cells/y. Horizontal and vertical scales are log axes. Plus signs indicate positive autocorrelation; negative signs indicate negative zones of autocorrelation. At long temporal lags and high values of ␣, there are many cycles of positive and negative autocorrelation, which are unlabeled.
were constructed. These surfaces show the autocorrelation of vegetation pattern (represented as time since fire) at different spatial and temporal lags. These figures show positive autocorrelation (that is, sites are similar) at some temporal and spatial lags and negative autocorrelation (that is, sites are consistently dissimilar) at other temporal and spatial lags. The figures illustrate the spatial and temporal lags at which pattern exists from the viewpoint of a model cell.
RESULTS The sets of correlograms produced by the models are shown in Figures 4 and 5. In each figure, memory increases from left to right. Autocorrelation indicates that pattern exists at a given lag. Positive autocorrelation indicates that sites at a given lag are similar; negative autocorrelation indicates that sites at 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 pattern produced by models experiencing different fire frequencies. Figure 5 compares landscape pattern produced by models with different vegetation recovery periods. As suggested by the inverse relationship between forest recovery and fire initiation (Drossel 1997), the patterns produced by changes in fire frequency and forest recovery period are similar. Decreases in fire frequency have an effect similar, but not identical, to increases in the period of forest recovery. When there is no ecological memory (␣ ⫽ 1/100), spatial pattern is produced by fire, but that pattern does not persist over time. There is a significant change in spatial and temporal pattern with the transition from no memory to memory (␣ ⫽ 1/100 to ␣ ⫽ 1/4). Spatial pattern spans less area and 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-
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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; negative signs indicate zones of negative autocorrelation. At long temporal lags and high values of ␣, there are many cycles of positive and negative autocorrelation, which are unlabeled.
relation appears at multiples of the vegetation recovery period. This increase in temporal structure is also matched by an increase in spatial extent and strength of spatial structure. As ecological memory (␣) increases, the spatial and temporal organization of the landscape changes. At all values of ␣, the landscape is highly correlated at short distances and over brief periods. As ␣ increases, spatial correlation increases, and this correlation decreases faster over time. Along with this pattern, negative autocorrelation emerges at intermediate temporal lags and positive autocorrelation at a frequency about that of the recovery rate. With further increases of ␣, the strength of autocorrelation increases and extends across a greater range of spatial lags. Additionally, the temporal lag over which there is correlation declines. Furthermore, as ␣ increases, discrete ranges of negative and positive correlation emerge at temporal lags related to TPmax at short spatial lags. At very high values of ␣, weak autocorrelation emerges at
intermediate frequencies at very large spatial lags. This pattern is repeated at different fire frequencies and values of TPmax; however, variation in fire frequency and TPmax changes the spatial and temporal lags at which these zones of autocorrelation appear. As frequency of fire decreases, the scale of spatial correlation increases, and correlation over time increases. For example, at an intermediate value of ␣ (␣ ⫽ 1), there is minimal organization at larger and longer lags at a higher fire frequency (16 fires/100 cells/y); but as fire frequency decreases, the range of spatial lags at which the landscape is correlated and the intensity of correlation increases. Furthermore, at a lower fire frequency (1 fire/100 cells/y), a new weak negative correlation emerges at about a 40-year lag. At low ␣, there is no difference between the scales of correlation for different values of TPmax; however, as ␣ increases, differences emerge. The clearest change is that the temporal lags at which positive and negative autocorrelation occur track
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the changes in TPmax. When recovery time is brief (12 years), autocorrelation decays quickly and then reemerges rapidly; whereas if recovery is longer, autocorrelation decreases gradually with temporal lag and a new zone of autocorrelation emerges at longer periods. As recovery time increases, the spatial scale over which autocorrelation occurs decreases and the strength of autocorrelation also decreases. This pattern is similar to what is observed as fire frequency decreases.
DISCUSSION The correlograms reveal that fires generate spatial pattern and that the strength and spatial span of this pattern depend on fire frequency and rates of vegetation recovery. They also reveal that the persistence of the patterns depends on ecological memory—the degree to which previous fires influence the spread of fire. The amount of memory (␣) necessary to produce landscape pattern depends on the rate of vegetation recovery and the frequency of fire initiation. As fire initiation rates decrease, or the period of vegetation recovery decreases, the amount of memory necessary to produce persistent landscape pattern also decreases. Ecological memory produces persistent pattern because it establishes a feedback loop between fire spread and landscape pattern. This feedback loop allows ecological pattern and ecological process to regulate one another (Watt 1947). In the absence of memory, there is a one-way relationship between fire and landscape pattern. Fire shapes landscape pattern but is not shaped by it. Memory causes landscape pattern to influence fire spread and vice versa. Mutual influence between fire patterns and landscape patterns encourages the formation of mutually reinforcing patterns. The feedback between fire spread and forest pattern produces a patch mosaic on the landscape. Relatively homogenous patches of forest are produced due to the spatially contagious nature of fire spread. Sites within these patches have the same probability of fire spread, because they were previously burned at the same time. This homogeneity means that fires ignited within these patches will tend to either fail to spread or spread across the entire patch. Fire spread tends to stop at the edge of patches. Patches neighboring a burning patch are more likely to have a lower probability of fire spread, because patches with a higher probability of fire spread are unlikely to have remained unburned. The mosaic of patches with different probabilities of fire spread reduces the ability of fire to spread across the entire landscape. As memory in-
creases, these tendencies are strengthened, increasing the spatial extent of autocorrelation and the persistence of spatial pattern over time. The memory of past fires is the degree to which a landscape’s vegetative pattern influences the spread of fire. The memory of past fires fades over time, because differences in the probability of fire spread that were produced by different fire histories diminish as the time since fire increases. For example, when there is ecological memory, the probability of fire spread varies between different-aged sites if those sites are younger than the vegetation recovery period (TPmax), whereas there is no difference between the probability of fire spread into sites whose age is greater than TPmax. When forest pattern strongly influences the spread of fires (for example, when ␣ is greater than 1), forest pattern will tend to be renewed by fire. When memory is weak (for example, when ␣ is less than 1), future fires will produce a new pattern that erases past patterns.
Implications of Ecological Memory The consequences of manipulating landscape pattern or the processes that control the fire regime will be more complex when an ecosystem has memory than when it does not. Ecological memory is encoded in the pattern of vegetation across the landscape. This pattern constrains and channels the spread of fire. Consequently, changes in vegetative pattern, via abiotic, biotic, or anthropogenic processes, have the potential to alter a fire regime, even if the drivers of that disturbance regime, such as the climate and vegetation of the region, remain constant. Homogenizing the landscape may remove barriers to fire spread, leading to a period of large fires. Alternatively, fragmenting the landscape will lead to a period of smaller fires. Despite these generalities, the degree to which a fire regime changes in response to landscape modification will depend on the specific details of landscape pattern and how it is changed. Similarly, due to the constraining effects of landscape pattern, shifts in either vegetation regrowth or climate can also alter a fire regime in complex ways. For example, a change in climate could increase fire frequency, which would produce smaller and more frequent fires. Alternatively, a region invaded by pyrogenic grass will more rapidly become combustible following a fire, decreasing the vegetation recovery time (D’Antonio and Vitousek 1992). The behavior of ecosystems with little memory will simply track changes in vegetation recovery and fire frequency. However, ecosystems with strong memory can be expected to respond to changes in driving processes in complex ways. Strong memory
Disturbance, Landscape Pattern, and Memory should initially inhibit ecological response to change. However, if change is rapid and intense, extreme transient behavior can be expected. For example, if fire frequency decreases, the existing landscape pattern will constrain fires, but eventually the lack of maintenance of this pattern, due to the reduced fire frequency, will result in very large fires, before a new landscape structure is established. This suggests that ecosystems with large amounts of memory will respond to changes in disturbance regimes in more complicated ways than ecosystems with little memory of the past.
Ecological Memory in Ecosystems The general nature of the fire model suggests that the interaction of ecological memory and contagious disturbances may influence landscape dynamics in a number of situations. In California chaparral, fire intensity depends on vegetation density over small spatial scales (approximately 1 m), while regeneration occurs primarily in areas that experience less intense fire (Odion and Davis 2000). In this ecosystem, the connection between vegetation pattern and fire introduces the memory of past disturbances into the system and thus produces persistent spatial pattern. Ecosystems that are dominated by externally driven fluctuations in climate, water levels, or biota are unlikely to be shaped by the memory of past disturbances. For example, fire in the western boreal forest of North America appears to be driven by climate variation (Johnson 1992), which suggests that ecological memory does not influence the fire regime. Animal behavior, like fire, has the potential to encode memory into landscape pattern. Selective grazing by herbivores produces disturbance patterns that are determined by existing landscape pattern. If the vegetative response to disturbance influences future grazing decisions by herbivores, then the ecosystem exhibits memory and the interaction of selective herbivores can produce persistent spatial pattern. For example, in the boreal forest of eastern North America, moose selectively consume early successional deciduous tree species. This browsing facilitates the replacement of deciduous species by coniferous species, producing a change in vegetation pattern that alters future browsing decisions. This foraging behavior, in conjunction with other contagious disturbance processes, produces persistent spatial pattern in the forest (Pastor and others 1998, 1999). In general, I expect that ecological memory is likely to arise in ecosystems in which biotic variation has a strong influence on ecological dynamics.
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Extended Keystone Hypothesis The results of my fire model show that ecological memory encourages the emergence of persistent spatial pattern, which provides some support for the extended keystone hypothesis (Holling 1992) and also suggests some limits. Holling (1992) proposed that landscape pattern is generated by the interaction of a few “keystone” processes that operate at separate and distinct spatial and temporal scales. He argues that these keystone processes entrain other ecological processes and variables to the characteristic frequencies of these processes; consequently, the properties of ecosystems should exhibit discrete rather than continuous structure. Although Holling (1992) and others (Allen and others 1999; Havlicek and Carpenter 2001; Manly 1996; Raffaelli and others 2000) have examined the question of whether ecosystem attributes exhibit a discontinuous structure, there has been little consideration of how feasible it is for the interactions of keystone ecological processes to produce discrete ecological pattern. Holling and others (1996) suggested that contagious disturbance processes, such as fire, are examples of keystone processes. My results show that models of fire have the potential to produce discrete landscape pattern, thus supporting the idea that fire is indeed a keystone process. Persistent patterns occur at temporal frequencies related to the recovery time of the vegetation from fire (that is, at 12-, 25-, and 50-year frequencies in the model). However, my model suggests that such patterns do not emerge in the absence of ecological memory. These results suggest that the extended keystone hypothesis is most likely to be demonstrated in ecosystems that exhibit strong ecological memory— ecosystems in which the spread of a key disturbance process is strongly influenced by the legacies of past disturbance. The spatial and temporal correlograms that I used to search for persistent pattern could also be used to test the extended keystone hypothesis in actual ecosystems. It is difficult to find data that span a time period several times the frequency of a disturbance over a spatial scale several times the extent of the disturbance. However, historical and paleoecological research is making such data sets increasingly available (Niklasson and Granstrom 2000).
CONCLUSIONS Ecological memory shapes landscape pattern by increasing the strength of the interaction between ecological processes and landscape pattern. When
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ecological memory is strong, landscape pattern is persistent; pattern tends to be maintained rather than destroyed by fire. The existence of ecological memory in ecosystems may allow processes to produce ecological pattern that can entrain other ecosystem variables. Changes in landscape pattern or key process drivers, such as fire frequency or vegetation recovery rates following disturbance, are more likely to have nonlinear and surprising effects in ecosystems with strong memory. There is some evidence that ecological memory exists in real ecosystems. The methods presented in this paper to analyze pattern in model ecosystems could be used to detect evidence of persistent landscape pattern in actual ecosystems.
ACKNOWLEDGMENTS A part of this work was conducted while I was a postdoctoral fellow at the National Center for Ecological Analysis and Synthesis at the University of California Santa Barbara. It uses models that I developed during my doctoral research, which was funded by a NASA Earth Science Fellowship. The paper benefited from conversations with Bruce Milne, and comments from Craig Allen, Elena Bennett, Lisa Dent, Tim Essington, and two anonymous reviewers.
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