Interactions between forest heterogeneity and surface fire regimes in ...

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Interactions between forest heterogeneity and surface fire regimes in the southern Sierra Nevada Carol Miller and Dean L. Urban

Abstract: Fire is a major agent of spatial pattern formation in forests, as it creates a mosaic of burned and unburned patches. While most research has focused on landscape-level patterns created by crown fires, millions of hectares of forests in North America are subject to surface fire regimes. A spatially explicit forest gap model developed for the Sierra Nevada was used to evaluate the influence of surface fire regimes on the heterogeneity of forest structure and composition within forest stands. Forest pattern was evaluated for a wide range of topographic positions in Sequoia National Park, California, to determine if repeated surface fires amplify existing spatial patterns. The spatial heterogeneity of some forest characteristics increased under a simulated fire regime relative to scenarios without fire. Although a distinct and regular fire-generated spatial pattern was not detected with an analysis of spatial autocorrelation, simulated surface fires did alter the spatial heterogeneity within a forest stand, primarily by degrading a regular structure that is imposed by competition for light in the absence of fire. The interaction between surface fires and forest pattern may be qualitatively different from that which occurs in forests subject to crown fires. As such, what has been learned about forests dominated by crown fires may not apply to forests subject to surface fire regimes. Résumé : Parce qu’il crée une mosaïque de zones brûlées et non brûlées, le feu joue un rôle majeur dans les patrons d’organisation spatiale de la forêt. Alors que la plupart des travaux de recherche ont mis l’accent sur la création de patrons à l’échelle du paysage par les feux de cime, des millions d’hectares de forêt en Amérique du Nord sont sujets à des régimes de feux de surface. Un modèle spatialement explicite de trouées en forêt, développé pour la Sierra Nevada, a été utilisé pour évaluer l’influence des régimes de feux de surface sur l’hétérogénéité de la structure et de la composition de la forêt dans les peuplements forestiers. La configuration de la forêt a été évaluée pour une large gamme de situations topographiques dans le parc national Sequoia, en Californie, pour déterminer si des feux de surface répétés amplifient les patrons spatiaux existants. L’hétérogénéité spatiale de certaines caractéristiques de la forêt augmente avec un régime de feu simulé comparativement à des scénarios où le feu est absent. Même si l’analyse d’autocorrélation spatiale n’a pas permis de mettre en évidence un patron spatial distinct et régulier généré par le feu, les feux de surface simulés ont modifié l’hétérogénéité spatiale dans un peuplement forestier, particulièrement en dégradant la structure régulière imposée par la compétition pour la lumière en l’absence de feu. L’interaction entre les feux de surface et la configuration de la forêt peut être qualitativement différente de celle qui survient dans les forêts sujettes à des feux de cime. Comme tel, ce qui a été appris au sujet des forêts dominées par des feux de cime pourrait ne pas s’appliquer aux forêts sujettes à des régimes de feux de surface. [Traduit par la rédaction]

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Disturbances create landscape pattern, and fire is one of the most widespread and studied disturbances that generates forest pattern. The vegetation mosaics generated after the 1988 Yellowstone wildfires are perhaps the most recent and striking example in North America of how fires can leave a legacy in the form of spatial pattern on the landscape Received May 7, 1998. Accepted November 18, 1998. C. Miller.1 Graduate Degree Program in Ecology, Colorado State University, Fort Collins, CO 80523, U.S.A. D.L. Urban. Nicholas School of the Environment, Duke University, Durham, NC 27708, U.S.A. 1

Author to whom all correspondence should be addressed. Present address: University of Montana and the U.S. Forest Service, Aldo Leopold Wilderness Research Institute, Missoula, MT 59807, U.S.A. e-mail: cmiller/[email protected]

Can. J. For. Res. 29: 202–212 (1999)

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(Christensen et al.1989; Turner et al. 1994, 1997a, 1997b). Fires create pattern on the landscape, and the resulting pattern influences the behavior of subsequent fires. Fire is potentially a self-organizing process, and the interaction between forest pattern and fire may result in the amplification of spatial pattern (Holling et al. 1996). Despite many examples of disturbance caused pattern and despite an improved ability to predict disturbance spread through spatially heterogeneous landscapes (e.g., Turner et al. 1989; Finney 1994), we still know very little about how disturbances and landscape pattern interact over the long term (Turner et al. 1997a). Simulation modeling has been very useful in demonstrating complex interactions between landscape pattern and disturbance regimes. Probabilistic models of fire spread based on percolation theory have shown that critical thresholds in landscape pattern may exist and that slight changes in pattern could produce abrupt shifts in disturbance phenomena (Turner et al. 1989; Gardner and O’Neill 1990). Turner and Romme (1994) suggested how a © 1999 NRC Canada


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probabilistic model might be used to examine the range of weather conditions under which the spatial arrangement of fuels affects fire spread. Other simulation models demonstrated that the mean size of disturbances affects the texture of landscape pattern. Smaller fires create more numerous, smaller patches that are closer together and have more edge (i.e., a fine-grained texture), while larger fires create less numerous, larger patches that result in a coarse texture (Baker 1995). Results from these and other models (Green 1989; Davis and Burrows 1994; Mladenoff et al. 1996; Ratz 1995; Roberts 1996a, 1996b) have enhanced our understanding of the complex interactions between disturbance and landscape pattern. All of these models use stand age or time since the last fire to approximate fuel loads and assume that fuel loads and fire severity are homogeneous within a forest stand. This assumption may be reasonable when simulating crown fires that destroy entire forest stands. However, not all forests are subject to such dramatic stand-destroying events. Ponderosa pine (Pinus ponderosa Dougl. ex Laws.) forests cover 13 × 106 ha in the western United States (USDA 1981) and are just one example of a forest type that experiences frequent, low-intensity surface fires. For our purposes, we define surface fires as fires that primarily spread along the forest floor and through the understory. Surface fires reduce surface fuels and kill off recently established saplings but leave the majority of overstory trees intact. By contrast, crown fires spread through the forest canopy and kill the majority of overstory trees. Do repeated occurrences of the more subtle surface fire events enhance the spatial patterns of forest and fuel conditions within forest stands? The forests of the Sierra Nevada in California experience surface fire regimes, and some evidence indicates that fires do indeed affect the texture of the pattern of vegetation and fuels (Bonnicksen and Stone 1982; Demetry and Duriscoe 1996). High fire frequency periods probably had small patchy fires and resulted in a fine-grained pattern in vegetation and fuels, while low fire frequency periods had wider spreading fires that created a coarser grained pattern on the landscape (Swetnam 1993). During the past century, most fires in the Sierra Nevada have been suppressed, allowing dead fuel to accumulate and understory tree density to increase in many forests (Vankat and Major 1978). Fire suppression likely has created more homogeneous forests that now may be more susceptible to catastrophic wildfires and could lead to a qualitatively different fire regime and ecosystem response. We developed a version of a spatially explicit forest gap model for the Sierra Nevada to study the interaction among surface fires, forest dynamics and climate (Miller 1994; Miller and Urban 1999). The model was designed to generate spatially heterogeneous forest conditions and surface fires that respond to this heterogeneity. We used this model to evaluate the influence of surface fire regimes on the spatial pattern of forest structure and composition within forest stands. Because climatic and forest stand conditions change considerably across the steep elevation gradient of the Sierra Nevada, we also evaluated the relationship between surface fire regimes and forest pattern for a wide range of topographic positions. We were interested in two aspects of the spatial pattern in these forests: the amount of heterogeneity and the spatial structure of that heterogeneity. We expected

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that simulated surface fires would increase the structural heterogeneity within forest stands and that the structure of this spatial pattern would be related to the size of the average fire.

Model description The forest gap model ZELIG (Smith and Urban 1988; Urban et al. 1991) has been applied to Sierra Nevada forests (Miller 1994; Miller and Urban 1999). The model simulates a forest stand as a grid of 15 × 15 m forest plots. In this paper, we used a 20 × 20 grid to simulate a 9-ha forest stand (Fig. 1), which is sufficiently large to generate statistically stable stand-level estimates of forest variables. The model grid is defined by elevation, slope, and aspect. Elevation and topographic position are used internally by the model to adjust temperature and precipitation according to lapse rates (Running et al. 1987) and to adjust radiation (Nikolov and Zeller 1992).

The light regime ZELIG uses allometric equations (Waring et al. 1982; Waring and Schlesinger 1985; S. Garman, Oregon State University, unpublished data) to estimate total leaf area for each tree on each plot and distributes this leaf area uniformly along each tree’s live crown (after Leemans and Prentice 1987). The leaf-area profile is used to estimate available light for each position (grid row, column, and height) within the model stand. ZELIG partitions light into directbeam and diffuse-sky components and samples the forest canopy to estimate each component (Urban et al. 1991; Urban and Shugart 1992). This approach allows a tree’s influence to extend beyond a single grid cell; a small tree’s influence is local to a single cell, but a tall tree may shade smaller trees several cells away. The available light and species shade tolerance are used to constrain seedling establishment and tree growth and to prune the lower canopy (Urban et al. 1991).

The soil moisture regime Each grid cell may have its own soil type defined by a soil texture and number of soil layers. Each soil layer has a depth and water holding capacity. Litter and duff, the partially decomposed portion of foliage litter, together act as the top layer (layer 0) in the soil water routine, with mineral soil layers below. The simulations we present later use a 1 m soil with 10 mineral soil layers of 10 cm thickness each. The soil water balance uses a tipping bucket algorithm. The model operates on a monthly time step in that it uses monthly climate data. Precipitation events, however, are simulated on a daily basis, with event probabilities generated from local weather data. Water falls as rain or snow, a portion is intercepted and throughfall plus any snowmelt infiltrates the top soil layer. A fast-flow (macropore) percolation fraction runs through and is immediately lost to runoff. The remainder, the slow percolation fraction, enters the top layer. The model uses a Priestley–Taylor estimate of potential evapotranspiration (PET) (Bonan 1989) and uses leaf area and this PET to partition actual evapotranspiration (AET) between surface evaporation and transpiration. Evaporative demand affects only the duff layer and top mineral soil layer (layers 0 and 1). Surface evaporation is drawn off the duff layer (layer 0) and any unmet evaporative demand is carried over to the top mineral soil layer (layer 1); residual demand after layer 1 remains unmet. Transpirational demand may affect all layers and is drawn from the top of the soil profile downward, beginning with the duff layer (layer 0). Unmet transpirational demand is carried to the next lower layer. The soil water balance is sensitive to the temperature and precipitation gradients that exist with elevation (Fig. 2). Furthermore, because © 1999 NRC Canada



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Fig. 1. Spatial representation of the model, illustrating the degree of spatial heterogeneity generated by tree-level processes. Each grid cell represents a 15 × 15 m plot within a 9-ha forest stand.

Live woody biomass (kg · ha-1, ×103) 600

transpirational demand is a function of plot leaf area, it is quite responsive to canopy development, and the soil water balance will vary for each grid cell according to local canopy conditions. From the soil water content, the model computes two droughtday indices (Pastor and Post 1986). One index is computed over the top 20 cm of the soil profile and is used to regulate seedling establishment. A second index is integrated over the fine-root depth distribution over the entire soil profile and is used to modify growth of established trees. The drought-day indices are used along with the maximum number of drought-days that each species can tolerate (MDRT; Table 1) to determine relative species drought response.

Tree demographics As in other forest gap models, the model simulates seedling establishment, annual diameter growth, and mortality for individual trees on each grid cell. Each of these demographic processes is specified as a maximum potential that can be achieved under optimal conditions. These potentials are then reduced to reflect suboptimal environmental conditions (e.g., low light or drought) on each simulated plot. Not only are trees affected by their environment, but each tree exerts an influence on its environment (e.g., through shading and transpirational demand). The number of growing degree-days available for a site also constrains tree growth and sorts out species abundance along temperature gradients with latitude or elevation. The degree-day curves improve upon the degree-day parabolas used in previous gap models (e.g., Botkin et al. 1972). The curves used here are one 2

sided; only minimum growing degree-days (DDMIN; Table 1) are used to restrict growth. In other words, the assumption is that trees may be sensitive to temperatures that are too cold, but at Sierra Nevada latitudes they are not sensitive to temperatures that are too warm in a physiological sense. Rather, other factors, especially low soil water, will restrict tree growth in warmer environments (Urban et al., in preparation2). The species parameters for temperature and moisture limits (DDMIN and MDRT, respectively) were calibrated to data collected in Sequoia National Park (Stephenson 1988; Graber et al. 1993). The relative growth rate (G), was calibrated to diameter increment data from tree ring samples (D.L. Urban, unpublished data), site index data (Dunning and Reineke 1933), and species distributions in the Park (Stephenson 1988; Graber et al. 1993). Species parameters are listed in Table 1.

The fire model Fuels accumulate as a function of site environment and forest conditions. Each year during a simulation, a fraction of each tree’s foliage and branchwood are added to the fuel bed according to species-specific allometries (Miller 1994; Miller and Urban 1999). In addition, biomass from dead trees is gradually added to the fuel bed. Only “dead and down” fuels are treated in this model (but see Herbaceous fuels below), and these are classified by size using the conventions of fire behavior and fire danger models (Deeming et al. 1972). Each fuel class decays according to a constant rate, which is modified by an abiotic decay multiplier that describes the temperature and moisture environment of the site.

Urban, D.L., Miller, C., Halpin, P., and Stephenson, N.L. Forest gradient response in Sierran landscapes: the physical template. © 1999 NRC Canada



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Table 1. Selected species parameters. Species

Ga

DDMINb

DDMAXc

MDRTd

SBULKe

White fir (Abies concolor [Gord. and Glend.] Lindl. ex Hildebr.) Red fir (Abies magnifica A. Murr.) Incense cedar (Calocedrus decurrens [Torr.] Floren) Lodgepole pine (Pinus contorta Dougl. ssp. murryana Grev. & Balf.) Jeffrey pine (Pinus jeffreyi Grev. & Balf.) Sugar pine (Pinus lambertiana Dougl.) Western white pine (Pinus monticola Dougl.) Ponderosa pine (Pinus ponderosa Laws.) California black oak (Quercus kelloggii Newb.)

1550 1050 2650 2150 2150 2350 1250 2050 1250

265 50 555 0 145 430 0 950 590

2200 1030 2445 600 1815 2305 940 2600 2775

175 150 200 150 185 165 135 200 200

24.83 35.73 20.83 33.00 21.15 28.36 27.40 23.55 12.82

a

G, relative growth response. DDMIN, minimum temperature limit (degree-days). DDMAX, maximum temperature (degree-days). d MDRT, maximum drought-days tolerated. e SBULK, fuel bed bulk density (kg·m–3). b c

Fig. 2. The soil water balance simulated by the model. Simulations were run at randomly selected combinations of slope, aspect, elevation, and soil depth. Each point represents output from a single simulation.

Because the model is implemented as a grid of forest plots, it can describe the spatial heterogeneity of forest structure and composition that exists within a stand. Fuel inputs, and therefore fuel bed conditions, vary temporally and spatially throughout a stand according to the number, size, and species of trees that are present. In addition, the fuel moisture varies both temporally and spatially with the local site water balance. Fuel moisture is derived for each grid cell from the duff moisture content, calculated monthly in the model’s soil water routine, with the duff layer treated as the top soil layer (layer 0). Thus, as the model generates spatial heterogeneity in forest structure and condition resulting from tree-level processes (Fig. 1), this leads to heterogeneity in fuel bed conditions, thereby generating spatial pattern in fire intensity and effects. Both fire frequency and magnitude (i.e., area burned) are generated internally by the model and are influenced by site conditions. Fire events are simulated as a function of three factors: probability of fire, fuel load, and fuel moisture. The mean ignition interval, in years, for the model grid is specified at run time. Uniform-random numbers are drawn to generate stochastic ignition events around this mean interval. A maximum of one ignition event may occur in any year. For fire to occur from an ignition, low fuel moisture and sufficient fuel loadings must also exist in addition to the stochastic ignition event. Because the soil water balance, and thus fuel moisture, varies with elevation, the model generates a decreasing fire frequency with elevation; the simulated pattern agrees well with independent data (Miller and Urban 1999). When an ignition occurs, the fireline intensity is computed for each of the forest plots from the accumulated fuels and fuel moisture conditions following equations for surface fire behavior (Rothermel 1972; Albini 1976). Only plots with intensities greater than 45 MW·m–1 (13 BTU·ft–1·s–1) are considered to be burnable. Fires may spread to all cells within the model grid, but they are restricted to those plots that are burnable and that are also spatially contiguous to a randomly located ignition point on the grid. Thus, fires are restricted to a contagious cluster of burnable plots, and on average, fires tend to burn the largest cluster of burnable plots. Although this does not realistically simulate the complex nature of fire spread, the model successfully reproduces empirical relationships between area burned and fire frequency (Miller and Urban 1999). Fire effects are calculated for each plot that burns. Fuels are reduced as a function of prefire fuel load (Brown et al. 1985), scorch height is calculated as a function of mean daytime temperature and fireline intensity (Van Wagner 1973), and fire mortality is computed. The probability of mortality due to fire for six of the nine species is calculated using regression equations developed during a fire mortality study in Sequoia National Park (Stephens 1995). © 1999 NRC Canada



206 Fig. 3. Probability of mortality as a function of the volume of a tree scorched in a fire. Equations for white fir (abco), incense cedar (cade), Jeffrey pine (Pinus jeffreyi Grev.& Balf; pije), sugar pine (Pinus lambertiana Dougl.; pila), and ponderosa pine (pipo) are from Stephens (1995) and were adjusted as described in the text. Equations for lodgepole pine (pico), western white pine (pimo), and California black oak (quke) are from Ryan and Reinhardt (1988). Red fir’s (abma) response to fire is assumed to be identical to white fir.

Unfortunately, the most severely scorched trees in the data set were omitted from the regression analysis, and therefore, these equations underestimate fire mortality for wildfire situations (S. Stephens, California Polytechnic State University, San Luis Obispo, personal communication). We adjusted these equations to more accurately estimate fire mortality by tuning the first coefficient to a separate but smaller data set of fire effects (Mutch and Parsons 1998). Equations from Ryan and Reinhardt (1988) were used for lodgepole pine, western white pine (Pinus monticola Dougl.), and California black oak (Quercus kelloggii Newb.). Probability of mortality as a function of crown volume scorched is shown for 30 cm DBH trees in Fig. 3.

Can. J. For. Res. Vol. 29, 1999 Fig. 4. Distribution of herbaceous fuels. (a) Grass simulated by the model and (b) herbaceous cover observed in Sequoia National Park. Model output is from 500-year simulations without fire; each point represents a single simulation.

density. Typically, the net effect of these influences is to increase fireline intensity.

Fuel bed bulk density Herbaceous fuels Fine herbaceous fuels can be an important factor in Sierra Nevada fire regimes, particularly at lower elevations where open ponderosa pine woodlands can occur. To include this additional source of fine fuels at these sites, we simulate grass production in this version of the model as a function of precipitation (Sala et al. 1988), temperature, shade from overstory trees, and forest floor depth (duff layer). Annual decomposition rates were estimated from data in the literature (Bartolome 1986; Jackson et al. 1990). For the purpose of calculating fire intensity, the grass biomass simulated by the model was calibrated using fuel loads described in the short grass fuel model, NFFL (Northern Forest Fire Laboratory) fuel model 1 (Andrews 1986). The distribution of grass simulated by the model varies across the elevation gradient and is displayed with independent data from Sequoia National Park (Graber et al. 1993) in Fig. 4. The model overestimated grass biomass at elevations between 1000 and 1500 m, but given the variability in the data, it was adequate for our purposes. Grass is treated as part of the fuel bed, which also contains the woody fuels and forest litter. The grass component of the fuel bed has a moisture of extinction, surface to volume ratio, and fuel bed bulk density derived from NFFL fuel model 1 (Andrews 1986). A fuel bed with a large grass component may burn quite differently than a fuel bed without grass because of its lower moisture of extinction, higher surface to volume ratio and lower fuel bed bulk

Fireline intensity can be strongly influenced by the bulk density of the fuel bed. For example, the loosely packed litter of longneedled ponderosa pine forests burns more readily than a more tightly packed white fir forest floor. Bulk density of forest fuels is calculated as a weighted average of the species-specific bulk densities (SBULK; Table 1) and species composition on each model plot (van Wagtendonk et al. 1998). The bulk density of forest fuels is then adjusted for the grass component:

[1]

BULKfuelbed = FBAF × BULKforest × (1 − FFR) + BULKgrass × FFR

where FFR is the ratio of grass to total fine fuels, BULKgrass is the bulk density of grassy fuels (0.54 kg·m–3 = 0.034 lb·ft–3), BULKforest is the bulk density of forest fuels, and FBAF is an adjustment factor for forest fuels. This adjustment factor is necessary because the bulk densities measured by van Wagtendonk et al. (1998) are much higher than those assumed in NFFL fuel models for timber situations (Andrews 1986). As a result, packing ratios estimated by this model are generally too high and fire intensities are too low. Bulk density is not explicitly described in NFFL fuel models (Andrews 1986), but they are implicit in the value used for fuel bed depth in these fuel models, and practitioners often tune the fuel bed depth in these fuel models to obtain reasonable estimates of fire intensity (Burgan and Rothermel 1984). Similar to adjusting fuel bed © 1999 NRC Canada



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Fig. 5. Fuel bed bulk density simulated by the model. Each point represents the output from a single simulation run for 500 years without fire.

depth, we tuned fuel bed bulk density using a constant adjustment factor (FBAF = 0.7). Fuel bed bulk density increases with elevation as species composition shifts from pine to fir and as grass production declines (Fig. 5).

Simulations We conducted 300 simulations each for a “fire” and “no fire” scenario. For the simulations with fire, we initially ran the model for 200 years without fire to allow successional trends and fuel bed bulk density to stabilize. Following this initial period, we simulated 300 years of forest growth under a frequent fire regime. We chose 300 years to allow enough time for forest conditions to equilibrate to the fire regime. These simulations were then repeated for scenarios without fire. All simulations were initiated from bare ground, and it was assumed that all species were available for establishment at all sites. This simplifying assumption focuses the analysis on fire. All simulations were for Sequoia National Park (36.6°N, 118.6°W), and we selected sites representative of the topographic range in the Park. We used a Gaussian distribution to randomly select elevation and slope angle and randomly selected aspect from a uniform random distribution. These distributions were estimated empirically from digital terrain data from the Park. We used a uniform soil type for all stands to emphasize the spatial pattern created by internal forest dynamics and fire and to minimize the confounding effects of topographic variation in other variables such as soil depth and texture. Thus, the simulations are designed to represent the range of topographic conditions within the Park, but other variables are controlled in the model experiments, allowing us to focus our interpretations on the spatial pattern generated by fire. As such, we are not attempting to reproduce current conditions in the Park and there are no independent data against which to directly test these simulation results.

Analysis We chose to examine total basal area and species composition as important attributes of these forests. The variation in the mean value of a variable in space is used here to estimate the amount of heterogeneity present in a simulated forest. We computed the variation in basal area as the coefficient of variation (standard deviation/mean) of basal area within a forest stand. The variation in species composition is computed in the model as the average Euclidean distance between each plot and the stand average. Euclidean distance, ED, is calculated for each plot as

[2]

ED =

∑ [RBA(k, i) − XRBA(k)]2 k

where RBA(k,i) is relative basal area of species k = 1, 9 species on plot i for each plot and XRBA(k) is relative basal areas for the stand (i.e., averaged over all plots within the stand). ED is then averaged over all plots within the stand and thus describes the mean internal variability of species composition in the stand. We compared the coefficient of variation of basal area and the Euclidean distance that resulted from simulations without fire and from simulations with fire. To examine the amount of heterogeneity of basal area among the 15 × 15 m plots within the simulated forest stands, we averaged the coefficient of variation of basal area over the last 100 years of each simulation. We averaged over 100 years to describe the steady-state condition while avoiding the confounding effects from year-to-year fluctuations in basal area caused by the stochastic mortality of single large trees. The ED was also averaged over the last 100 years of each simulation. Analysis of the spatial correlation structure can reveal the spatial dependence in a variable. We calculated the spatial autocorrelation of basal area within the simulated forest stands. A variable is spatially autocorrelated when the value of this variable at some point in space can be predicted from the known values at other sampling points. Positive autocorrelation indicates aggregation, and negative autocorrelation indicates segregation. The degree of autocorrelation between points differs with the distance between points. In natural systems, autocorrelation typically is positive for short distances and negative for longer distances. The distance at which a significant value of autocorrelation is found may indicate the scale at which a pattern occurs. We calculated the autocorrelation coefficient Moran’s I (Moran 1950) to detect spatial autocorrelation in the simulation output. Moran’s I may take on values between –1 and 1. A value of 1 indicates perfect positive autocorrelation, 0 indicates no autocorrelation, and –1 indicates perfect negative autocorrelation. We calculated Moran’s I from maps of total basal area generated in the final simulation year for simulations with and without fire. Preliminary inspection suggested that the average autocorrelation for a large stand did not vary appreciably from year to year. Values were computed for the first 10 distance classes and then plotted as a spatial correlogram.

Spatial heterogeneity For the elevation range we simulated, coefficients of variation of basal area were close to 1 for the simulations without fire (Fig. 6a). In the set of simulations with a natural fire regime, the variability of basal area dramatically increased for several of the sites below 1750 m elevation, with values ranging up to 20 (Fig. 6b). For the simulations without fire (Fig. 7a), ED was greatest at elevations below 2000 m and ranged to values over 60. Below 2000 m, the distributions of three important species (incense cedar, Calocedrus decurrens (Torr.) Floren; ponderosa pine; and white fir, Abies concolor (Gord & Glend.) Lindl. ex Hildebr.) overlapped significantly (Fig. 8) creating highly mixed stands and high values of Euclidean distance. Above 2000 m, distributions of the two most dominant species (white fir and red fir, Abies magnifica A. Murray) overlapped much less (Fig. 8), resulting in less diverse stands and lower values of Euclidean distance. Simulated fires increased the variability of species composition (Fig. 7b) by providing suitable conditions for shadeintolerant and fire-tolerant species. © 1999 NRC Canada



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Fig. 6. The variability of basal area within simulated forest stands. Variability is displayed as the coefficient of variation (standard deviation/mean) among individual 15 × 15 m plots averaged over the last 100 years of simulations (a) without fire and (b) with fire. Each point represents a single simulation.

Fig. 7. The variability of species composition within simulated forest stands. Variability is displayed as the average Euclidean distance (ED) between species composition on individual plots and the stand mean for simulations (a) without fire and (b) with fire. Values shown are the average of the last 100 years of each simulation; each point represents a single simulation.

Spatial structure Typical correlograms are shown in Fig. 9 for simulations with and without fire. Values outside of the 95% confidence band represent significant spatial autocorrelation at the associated lag distance class. As portrayed in these correlograms, significant negative autocorrelation was usually detected only at the first lag distance class, and more often in simulations without fire. To see how spatial autocorrelation varies with the elevation gradient, we displayed the value of Moran’s I for the first lag distance class against elevation (Fig. 10). For the simulations without fire, significant negative spatial autocorrelation was detected for most sites above 1750 m (Fig. 10a). Fires apparently degraded this spatial structure and the result is nonsignificant values of Moran’s I in the simulations with fire (Fig. 10b).

increases when frequent fires are simulated. The increase in Euclidean distance reflects the ability of shade-intolerant species such as ponderosa pine to establish in the comparatively open canopy conditions after fire and the pine’s ability to survive fires. The result is a more diverse forest. A similar result was found by Roberts (1996a), who simulated 500 years of the interaction between vegetation dynamics and fire regimes on synthetic landscapes comprised of southwestern U.S. mixed conifer forest stands. He computed gamma diversity, a statistic that measured the diversity of 15 vegetation community types on the synthetic landscapes, during simulations with fire and without fire. Gamma diversity was higher in simulations with fire because post-fire conditions allowed reproduction of shade-intolerant species. Although we cannot directly compare Roberts’ (1996a) gamma diversity to the ED we calculated, diversity increases from the same mechanism in both studies. The influence of a natural fire regime on the variability of total basal area is less conclusive. For most of the simulated sites, the coefficient of variation of basal area does not differ between the natural fire regime scenario and the scenario without fire. The exceptions are several sites below 1750 m elevation that experience a positive feedback that exists in the model between fire and grass. Without fire, these sites can support mature trees, but frequent fires (every 2–3 years) remove almost all the trees and convert most of the model grid to grass. Once the overstory is removed, grass provides sufficient fuel for frequent fires that can maintain

Forest structure and composition Spatial heterogeneity influences the spread of fires, and fires may create new spatial pattern (Romme 1982; Turner 1987; Turner and Romme 1994; Turner et al. 1994, 1997a, 1997b). Whether fires increase or decrease spatial heterogeneity is not well understood. From our simulation results, surface fires appear to increase the amount of heterogeneity of certain characteristics within a forest stand. The variability of species composition, measured by Euclidean distance,

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Miller and Urban Fig. 8. Simulated distributions of the four major species. Results are from the simulations without fire; each point in a panel represents a single simulation.

Fig. 9. Typical correlograms describing the spatial autocorrelation structure of basal area for simulations with and without fire.

the dominance of grass. These fuels can develop on an annual basis because grass production is a function of annual precipitation. Although basal area is zero across the majority of the model grid, it may still be high on one or two plots

209 Fig. 10. Spatial autocorrelation of basal area for simulations across the elevation gradient. Moran’s I was computed for distance class 1 on maps of total basal area in the final year of simulations (a) without fire and (b) with fire. Each point represents a single simulation.

within the grid, reflecting a tree – no tree stand structure and resulting in a high value for coefficient of variation. Spatial structure Fire may also alter the spatial structure of the heterogeneity in a forest. Roberts (1996b) compared spatial statistics for synthetic landscapes that were subjected to fire regimes of different fire return intervals. Two of these statistics, fragmentation and patch diversity, described different aspects of the spatial structure of heterogeneity on a landscape. Roberts (1996b) found that both fragmentation and patch diversity were higher in simulations with long fire return intervals relative to short fire return intervals. Long fire return intervals allowed the underlying spatial structure of the simulated landscapes to be expressed while short fire return intervals attenuated this effect, homogenizing the landscapes (Roberts 1996b). We found similar trends in our simulation results. In the absence of fire, the light regime generated a spatial pattern. Tall trees on one plot cast shade on neighboring plots, restricting the basal area accumulation in the neighboring plots. The pattern was fairly regular, and thus, we found significant negative spatial autocorrelation at short distances in the simulations without fire. In the simulations with fire, this pattern was broken up; fires tended to disrupt the neighborhood effects on the light environment within a stand. While © 1999 NRC Canada



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the simulated fires may have generated spatial heterogeneity, they did not generate a regular pattern and therefore, the pattern did not show up in measures of spatial autocorrelation. Other analyses of spatial structure may better reveal the effect of surface fire on spatial pattern. Fire is generally viewed as a self-organizing process, that is, fire creates pattern and that pattern will influence the spread of future fire. The self-organizing influence of fire should be strongly expressed when flammability increases gradually with time since the last fire (Holling et al. 1996). As time-since-fire increases, fuels slowly accumulate to a critical, or burnable, level, and the patch that was created in the last fire becomes burnable only after sufficient time has passed. In this way, fires can amplify spatial pattern. However, we did not find a strong self-organizing influence of fire in the simulations of Sierra Nevada forests. Time since the last fire is not a very important variable in Sierran forests because these forests are extremely productive and rates of decomposition are relatively slow. Fuels in mixed conifer forests rapidly accumulate to pre-fire conditions within 10 years (Parsons 1978), and ponderosa pine forests may accumulate highly flammable fuels every year (van Wagtendonk 1985). Surface fires may clear the forest floor of fuels, but the source of future fuel inputs typically remains on site in the form of overstory trees. This minimizes the recovery time of fuel loads. Thus, although this model is similar to crown fire models in that it shares a criticality assumption (i.e., fuels accumulate over time to a critical level), this criticality is trivial. Model uncertainties Validating the spatial heterogeneity generated by the model is problematic because environmental conditions within real forests can be highly variable. For example, soil depth was measured every 2.5 m within 1- to 2.5-ha forest stands in Sequoia National Park (Halpin 1995). Not only was soil depth highly variable at this fine scale, but forest pattern was spatially correlated with this highly variable factor. It is unlikely that soil depth will ever be measured at this scale for enough sites to adequately test the spatial heterogeneity generated by the model. Instead, our approach with the model has been to assume homogeneous soils so that we could focus on the heterogeneity that may result from internal forest dynamics and fire. Using a heterogeneous soil map in the simulations would likely weaken the spatial autocorrelation structure that develops as a result of the light regime during the runs without fire. In addition, plots simulated with extremely shallow soils may support only grass, increasing the coefficient of variation for basal area. As discussed in the Results, we saw the existence of a positive feedback in the model between fire and grass that resulted in the conversion of low-elevation forests to largely grass-dominated systems. In reality, this conversion seems unlikely because ponderosa pines in these low-elevation woodlands are usually resistant to grass-fueled surface fires. We suspect that two limitations of the model are acting in concert and resulting in this unlikely conversion. First, the model may overestimate fire intensity of grass-fueled fires, thus overestimating tree mortality. Second, the model generates weather that is unstructured through time; it may not generate enough multiyear occurrences of high rainfall dur-


ing which fire would be absent and trees could grow large enough to withstand a grass fire. Fires tend to spread in characteristic patterns across landscapes, and therefore, the probability of fire varies because of factors such as slope position and proximity to highly flammable vegetation. The model cannot account for the influence of fire spread within this explicit landscape context. Therefore, the model will either over- or under-predict fire frequency at sites where landscape context strongly affects the probability of fire occurrence. There are other uncertainties in the model. Fire spread in the model is simplified and does not account for the variability in weather conditions that may occur during a single fire. Thus, the model will not reproduce spatial patterns of fire spread that may result from a short weather event. Also, the model does not simulate crowning behavior that may occur in severe fires. While these limitations may restrict the level of realism simulated by the model, they allow us to focus on the interaction between fires and internally generated forest pattern.

In many ecosystems dominated by surface fire, vegetation has changed in response to several decades of fire suppression, and land managers are seeking ways to restore the presuppression vegetation pattern. We know very little about the heterogeneity that was once present on the landscape before fire suppression. Before establishing targets for restoration, we need to better understand how fire affects spatial heterogeneity. From our results, we suggest that fire can increase heterogeneity in some forest characteristics. We also found that fire can significantly alter the structure of spatial heterogeneity, but we detected no regular patterns created by the simulated fires. Surface fires obviously have different effects on vegetation and fuels than do crown fires. As such, surface fire regimes may have their own set of rules when it comes to the interaction of fire and spatial pattern. Most researchers who have studied the interaction between landscape pattern and disturbance have focused on crown fire systems. What we have learned from their work may not apply to the many ecosystems subject to surface fire regimes.

Funding for this research was provided by the United States Geological Service, Biological Resources Division’s Sierra Nevada Global Change Research Program under contract CA8800-1-9004. Comments from two anonymous reviewers improved the manuscript. This work was completed as part of a doctoral degree at Colorado State University by Carol Miller.

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