Forest Age Distribution under Mixed-Severity Fire Regimes – a Simulation-Based Analysis for Middle Boreal Fennoscandia

A simulation model was used to study the age structure of unmanaged forest landscapes under different fi re regimes. Stand age was defi ned as the age of the oldest tree cohort in a stand. When most fi res are not stand-replacing, the theoretical equilibrium stand age distribution is either bell-shaped or bimodal and dominated by old age-classes. Old-growth forests (oldest cohort > 150 y) dominate the landscape unless fi res are both frequent and severe. Simulation results and analytical calculations show that if a regime of frequent fi res (about every 50 y) maintains landscapes dominated by old-growth forests, then old-growth dominance persists when the number of fi res is decreased, despite the associated increase in fi re severity. Simulation results were applied to Pinus sylvestrisdominated landscapes of middle boreal Fennoscandia, which according to empirical results were dominated by old-growth forests when fi res were frequent during the 19th century. Since the changes in the fi re regime can be plausibly explained by changes in the number of human-caused ignitions, old-growth forests have evidently also dominated the landscapes earlier when fi res were less frequent. The simulation model is used to produce plausible age distributions of middle boreal Fennoscandian forest landscapes under different historical fi re regimes. In summary, the frequency of large-scale disturbance alone predicts forest landscape dynamics poorly, and the roles played by fi re severity and residual stands need to be considered carefully. Maintaining and restoring oldgrowth structures is essential to regaining the natural variability of Fennoscandian forest landscapes.


Introduction
Maintaining or restoring the natural range of variability in boreal forest ecosystems is a widely approved approach to protecting biodiversity and other nontimber values (Haila et al. 1994, Angelstam and Pettersson 1997, Fries 1997, Landres et al. 1999, Niemelä 1999, Bergeron et al. 2002, Kuuluvainen 2002).A specifi c application of the natural variability concept is to manage for landscape-level forest age-class distributions that occur in natural, fi re-controlled forests (Bergeron et al. 1999, 2002, Niku et al. 2000).A prominent issue related to forest age structure is the maintenance of old-growth forests and structures.Oldgrowth structures, as used here, are old and large living, dying, and dead trees.Old-growth forests are broadly understood as stands in which these structures are present, whether or not the majority of the trees are old.
Designing management based on natural variability requires information on the historical age structure of unmanaged landscapes, but reconstructing past landscape structure and dynamics is never straightforward (Swetnam et al. 1999).Field studies, inventory data, and dendroecological methods can only be used to study landscape structures that prevailed in relatively recent times.These patterns have been shaped by disturbance regimes that may be different from the regimes of the more remote past.Finding unmanaged landscapes for empirical studies in Northern Europe is diffi cult, and thus there is little empirical data on their age structure.
Past landscape patterns may be estimated using knowledge of past fi re regimes.Forest age-class distributions have commonly been considered in terms of time-since-fi re distributions, using several theoretical approaches (Van Wagner 1978, Johnson and Van Wagner 1985, Boychuk et al. 1997, McCarthy et al. 2001).Simple analytical models of equilibrium dynamics yield exponential or Weibull distributions of fi re interval length, from which the corresponding time-since-fi re distributions are easily derived (Johnson and Van Wagner 1985).More or less erratic age-class distributions produced by random fi res, which may be large in relation to landscape size, have also been simulated (Boychuk andPerera 1997, Boychuk et al. 1997).
Several studies have shown that in the 19th century middle boreal Fennoscandian landscapes displayed a regime of frequent fi res, with mean intervals of about 50 y (Lehtonen 1997, Pitkänen and Huttunen 1999, Niklasson and Granström 2000, Lehtonen and Kolström 2001).Fire intervals were longer in the more remote past.Niklasson and Granström (2000) demonstrated by dendroecological means a gradual increase of fi re frequency in northern Sweden from the 17th century onward.Fire frequencies peaked in the 19th century prior to a rapid onset of the current regime of very infrequent fi res.Niklasson and Granström (2000) also argue that the increase in fi res between the 17th and 19th centuries was primarily caused by a growing number of humancaused ignitions.In eastern Finland a similar trend of gradually increasing fi res appears to have prevailed for the last 2000 y, according to estimates based on peat and sediment stratigraphies (Pitkänen 1999, 2000, Pitkänen and Huttunen 1999, Pitkänen and Grönlund 2001).The estimated fi re frequencies for the past few centuries are very similar in the two areas of Finland and Sweden.Studies suggest fi re intervals of 40-70 y in the 1800s, about 130 y in the 1600s and about 200 y around 1700 y BP, but it is not clear over what regions such fi gures could be extrapolated (Pitkänen and Huttunen 1999, Niklasson and Granström 2000, Pitkänen and Grönlund 2001).The longest fi re intervals have been observed on spruce swamps (Hörnberg et al. 1995), in northern high-elevation forests (Steijlen andZackrisson 1987, Hyvärinen andSepponen 1988), and in European Russia outside Fennoscandia (Syrjänen et al. 1994, Wallenius 2002).
Using theoretical time-since-fi re distributions to model landscape age structure would result in the conclusion that old-growth forests do not persist under regimes of frequent fi res.For example, in the exponential model with a mean fi re interval of 50 y the proportion of forests older than 150 y is exp(-150/50) ≈ 0.05.In contrast, frequently burning middle boreal Fennoscandian landscapes were dominated by multiaged, old-growth pine forests (Linder and Östlund 1992, 1998, Östlund et al. 1997, Axelsson and Östlund 2000, Lehtonen and Kolström 2001, Karjalainen and Kuuluvainen 2002, Kuuluvainen et al. 2002).The obvious explanation is that fi re severity has been low.Accordingly, it appears that stand-replacing fi res have been rare in Fennoscandia (Saari 1923, Zackrisson 1977, Zackrisson and Östlund 1991, Engelmark et al. 1994), and development of frequently burning stands may resemble gap dynamics (Kuuluvainen 1994).In many other ecosystems throughout the world low-severity fi res are also common or prevalent (Agee 1998), and fi res usually leave living trees even in systems that are considered crown fi re-dominated (Bergeron et al. 2002).
The existence of frequently burning old-growth pine forests shows that models of forest age structure and old-growth forest occurrence should take account of fi re severity, in addition to fi re frequency.A distinction should be made between time-since-fi re and stand age.Using time-sincefi re distributions in timing terminal cuttings to mimic natural disturbance patterns (e.g.Niku et al. 2000) may result in landscape structures that are far outside the natural range of variability.
In the present study, computer simulations and analytical arguments are used to explore landscape age structure, in terms of actual tree or cohort age, in response to variation in the fi re regime.The ecosystems targeted are Scots pine (Pinus sylvestris L.)-dominated forests of the middle boreal zone (Ahti et al. 1968) of Fennoscandia.
The theoretical research question is how the shape of stand age distribution and the abundance of old-growth forests are determined under mixed-severity fi re regimes.The more practical problem is what can be inferred about the forest age structure of natural Fennoscandian landscapes.The main diffi culty in estimating the structure of past landscapes is the lack of direct data on the severity of past fi res.However, empirical studies suggest that frequent fi res have maintained old-growth-dominated landscapes.This information can be used as a constraint when choosing simulation scenarios that are consistent with empirical data.One specifi c question considers, whether old-growth forests were also dominant when fi re frequency was lower.The answer is not obvious, because longer fi re intervals increase the mean time-since-fi re, which may increase the severity of fi res.

Modeling Approach
Simulations were conducted using FIN-LANDIS, which is a spatially explicit, grid-based model of forest landscape dynamics, tailored for Fennoscandian conditions.The model simulates landscape change in 10-y time steps, and operates on raster maps derived through GIS.Stand development is driven by seed availability based on spatially explicit seed dispersal, competition between cohorts, and fi re events.Ignition and spread of forest fi res are simulated dynamically during each time step.The model is based on the LANDIS model (Mladenoff et al. 1996, He and Mladenoff 1999, He et al. 1999).FIN-LANDIS has been described in detail and tested elsewhere (Pennanen and Kuuluvainen 2002).In this section, we describe the most relevant aspects of model structure, and the assumptions incorporated in these parameter values that were common to all simulations conducted in this study.
In the simulations, the landscape is a collection of stands represented by grid cells.Stands contain cohorts of different species and age.A stand may accommodate several tree species, and several cohorts of the same species but different ages.Tree cohorts have no quantitative attributes apart from age, but are divided into thin and dense cohorts.
The modeling approach is rule-based rather than quantitative, meaning that the dynamics is mostly based on defi ning conditions under which transitions of state occur instead of equations determining change in state variables (Pennanen and Kuuluvainen 2002).For instance, new cohorts are established if requirements related to shading, seeding, and seedbed are met.The processes involved are the establishment of new cohorts and the death of cohorts.In addition, cohorts may be converted from dense to thin cohorts, but not the other way around, and the cohort age increases by 10 y in each iteration.
The tree species explicitly considered in this study are Scots pine and Norway spruce (Picea abies Karst.).In forests on mineral soil, with abundant seeds present, regeneration occurs as follows: pine always regenerate in dense cohorts, but only immediately after fi res, and if there are no dense cohorts of any species already present.Spruce also regenerate after fi res, but are indifferent to the presence of other cohorts.After 10 y since last fi re, spruce establishment probability drops to a lower value (0.25 per cell and iteration).Spruce cohorts may be thin from the beginning, but this has no feedback on model behavior, since regeneration of species other than spruce is not considered in the late-successional stands.The decrease in establishment probabilities with increasing time-since-fi re, which is especially clear for pine, has been confi rmed empirically (Sirén 1955, Agee 1998).
Dense tree cohorts will eventually disintegrate due to senescence.After tree cohorts attain half the maximum longevity of their species, they begin turning into thin cohorts with increasing probability (Fig. 1).Cohorts above 80% of the maximum age begin to die entirely with increasing probability (Fig. 1).The longevity of individual cohorts is assumed to be approximately normally distributed, which holds if the deaths of individual trees are not too correlated.A maximum age of 400 y was used for pine and 350 y for spruce.At these ages the contribution of the cohort to the stand volume would be negligible (Norokorpi 1979, Nikolov and Helmisaari 1992, Kuuluvainen et al. 2002).
Fire severity is defi ned through tree mortality and is represented by positive integer values.Spruce cohorts are killed in any fi re, while the mortality of pine cohorts is dependent on cohort age.The susceptibility of pine cohorts changes at age thresholds of 24, 56, 120, and 200 y, which give the maximum ages of cohorts that are killed by fi res of severity classes 1-4 respectively.Fires of class 5 or higher kill all cohorts.Dense cohorts in the 2 highest susceptibility classes that survive a fi re become thin cohorts, e.g. a class 1 fi re thins pine cohorts up to 120 y of age.

Simulation Runs
Simulations were divided into 4 simulation sets.Differences between simulation sets are summarized in Table 1.Sets I and II explored the shape of stand age distributions under varying fi re regimes, using simple assumptions.Simulation set III investigated the average amount of old-growth forests in the landscape under varying fi re regimes.Simulation set IV attempted to reproduce realistic dynamics of middle boreal forest landscapes under different fi re frequencies, consistent with the empirical knowledge of historical Fennoscandian forest structure.
Theoretical exploration of landscape dynamics is simpler when not considering spatially explicit dynamics.Therefore, simulations of the fi rst 3 simulation sets were conducted as effectively nonspatial simulations, in which the size of fi res was limited to one cell, tree seeds were assumed to be always present, and all cells represented similar forest sites on mineral soil.Such schemes simulate collections of identical independently evolving stands whose attributes are aggregated in the model output.These nonspatial model runs were conducted on a 'landscape' of 86 056 cells.Nonspatial simulations ignore several aspects of actual landscape dynamics, such as sitedependent spatial variation in fi re frequency and behavior (Engelmark 1987).Limited seed dispersal could also affect the stand age distribution.The last simulation set IV was conducted in a spatially explicit manner, using explicit seed dispersal of tree species and fi res that spread according to a spatially explicit algorithm.
In simulation sets III and IV it was assumed that fi re severity increases with time-since-fi re and that most fi res are stand-replacing if time since the previous fi re is long enough.Such assumption is reasonable (Schimmel and Granström 1996), but the detailed form of the relationship is not known.The assumption was made to investigate whether it is possible that decrease in the number of fi res could lead to decrease in the abundance of old-growth forests.This would be possible if the lengthened mean time-since-fi re would increase fi re severity strongly.If fi re severity and fi re frequency were independent, the amount of oldgrowth forests and fi re frequency would obviously be negatively correlated.
Output from each simulation was recorded after running the model for at least 100 iterations (1000 y).It was separately assessed that the simulations were lengthy enough to eliminate the effect of initial conditions.The results thus rep-resent theoretical steady state landscape structures.
When interpreting the simulation results, stand age means the age of the oldest tree cohort, which is a suitable indicator for describing the structural diversity of the stand when the focus is on the occurrence of old-growth structures.Stand age distribution means the frequency distribution of stand ages in the landscape.

Simulation Set I
Simulation set I examined the effect of fi re severity on stand age distribution in 4 scenarios.In the fi rst simulation run fi re severity was always 5, in the second run fi re severity was a random number between 1 and 5, and in the third a random number between 1 and 3.The last scenario assumed that fi res always thin pine cohorts but never kill them completely.The probability of burning was 0.1 per site and decade, corresponding to a mean fi re interval of 95 y.To keep the assumptions and the interpretation of results simple, fi res occurred randomly, and the probability of burning and fi re severity were independent of time-since-fi re and stand structure.

Simulation Set II
Simulation set II examined the effect of mean fi re interval on stand age distribution under a moderate-severity fi re regime.The mean fi re intervals in the 4 simulation runs were 40, 50, 70, and in a realistic landscape fi re severity distribution 150 y.In all runs, the severity of each fi re was a random number between 1 and 3. Fire occurrence and severity were independent of time-since-fi re and stand structure.

Simulation Set III
Simulation set III examined the combined effect of fi re frequency and fi re severity on the abundance of old-growth forests and on the frequency of stand-replacing fi res.Experimenting with 5 values of mean fi re interval and 7 fi re severity scenarios yielded 5 × 7 = 35 simulations.The phrase 'severity scenario' is used because fi re severity and fi re frequency were not independent, since fi re severity was assumed to increase with time since previous fi re in the stand.Each scenario corresponds to a specifi c form of the relationship between fi re severity and time since last fi re.The severity scenarios were labeled with numbers from 1 to 9, giving the maximum fi re severity that could be attained under any conditions.The potential fi re severity increased linearly with time-since-fi re, so that it reached the maximum at a time-since-fi re of 90 y and remained constant after that.The actual severity of each fi re was randomly chosen from the integers between 0 and the potential severity determined by the severity scenario and the time-since-fi re.Severity class 0 corresponded to a failed ignition.The stochastic component in the determination of fi re severity corresponds to variations in weather conditions, which infl uence fi re behavior (Bessie andJohnson 1995, Schimmel andGranström 1996).Empirical evidence shows that fi re severity (Schimmel and Granström 1996) and the probability of burning (Lehtonen 1997, Niklasson 2000) increase with time-since-fi re.Fire probability also increases in the simulations with time-since-fi re, since the occurrence of discarded 'fi res' of severity class 0 decreases when potential fi re severity grows.

Simulation Set IV
For spatially explicit simulation set IV, most tree life history attributes were chosen as in Pennanen and Kuuluvainen (2002).The landscape used in the simulations was an actual eastern Finnish landscape, and was represented by a site-type map with the following site-type distribution: 30% dryish sites, 30% mesic sites, 10% spruce swamps, and 30% pine bogs, open mires, and waters.This distribution is similar to the average vegetation of the Eastern middle boreal Finland (Salminen and Salminen 1998).
On mesic and dryish sites, pine and spruce regenerated as described in section 2.1.In spruce swamps establishment probabilities for pine and spruce were 1.0 and 0.5 immediately after fi res and 0 and 1.0 later, respectively.In pine bogs the respective probabilities were 1.0 and 0 after fi res, and 0.5 and 0 later.The fl ammability of swamp and bog forests was assumed to be 10 times lower, and the fl ammability of mesic sites 2 times lower than the fl ammability of dryish sites (Engelmark 1987, Hörnberg et al. 1995).Flammability corresponds to the probability of a site being burnable during a fi re (Pennanen and Kuuluvainen 2002).
Fire spread is determined in FIN-LANDIS by setting the mean fi re duration and defi ning the rate-of-spread in relation to fi re severity (Pennanen and Kuuluvainen 2002).The rate of spread was of the form c • 2 I , where I is fi re severity class.Potential fi re severity was set to increase with time-since-fi re (until time-since-fi re of 100 y) and with the age of the oldest spruce cohort present (until age of 175 y), spruce age having twice as strong an effect as time-since-fi re.
The goal of simulation set IV was to reproduce realistic dynamics of middle boreal forest landscapes under different fi re frequencies.Consistency with empirical studies required that, when the mean fi re intervals were 50-70 y, the majority of the forests were old-growth pine forests (Zackrisson 1977, Zackrisson and Östlund 1991, Östlund et al. 1997, Axelsson and Östlund 2000, Lehtonen and Kolström 2001, Kuuluvainen et al. 2002).Therefore, the parameters determining fi re severity were adjusted until simulations yielded old-growth-dominated landscapes under mean fi re intervals of 50-70 y.Simulation parameters were such that when time-since-fi re was high, fi res were severe and frequently standreplacing.
The simulation set consisted of 10 simulations.The only parameter varying between the simulations was the number of ignition attempts, which was doubled between each simulation.Thus the frequency and severity of fi res were not determined externally as in the nonspatial simulations.It was therefore possible to investigate the relationship between the number of ignitions and the fi re regime.

Stand Age Distributions in Relation to Fire
Different fi re severity scenarios with a mean fi re interval of 95 y gave rise to strongly varying age-class distributions (simulation set I, Fig. 2).
Stand-replacing fi res produced an approximately exponential age distribution with a cutoff due to the limited longevity of trees (Fig. 2a).Under a low-severity fi re regime the stand age distribution was bell-shaped, with the mode near the maximum longevity of pine (Fig. 2d).The distributions were in all cases unimodal with the mode either at the youngest or near the oldest age-classes.Age distributions based on spruce cohorts were approximately exponential in all cases because of the assumed zero tolerance to fi res (Fig. 2).The smooth shape of the age distributions demonstrates that the number of stands used in the nonspatial simulations was high enough to eliminate the effect of stochastic variation in the aggregated output.
Age distributions dominated by old age-classes (Fig. 2c-d) represent landscapes with multi-layered pine stands.These arise when fi res are not stand-replacing, but thin stands and facilitate regeneration of new cohorts.When the oldest cohort dies of old age, younger cohorts are released under them, and stand age remains high.
When fi re frequency was changed in the moderate-severity fi re scenario, only the occurrence of the youngest age-classes was notably affected (simulation set II, Fig. 3).Shortened fi re rotation increased the abundance of young stands, resulting in bimodal stand age distributions under high-frequency fi re regimes.
In simulation sets I and II, both the probability of burning and the fi re severity were independent of time since previous fi re.In reality, both appear to be lower at the early stages of succession (Schimmel andGranström 1996, Niklasson andGranström 2000).This may increase the occurrence of young age-classes in the simulations, because the high occurrence and severity of fi res during early succession make it less likely that young stands survive to old age and become less susceptible to fi res.

Occurrence of Old-Growth Forests
The results of simulation set III were summarized by plotting the occurrence of old-growth forests and the frequency of stand-replacing fi res against mean fi re interval and the fi re severity scenario (Fig. 4).Old-growth forests were defi ned as stands that are at least 150 y of age.'Standreplacing fi res' are fi res that actually destroy all existing cohorts, so whether a fi re is stand-replacing, is dependent not only on fi re severity but also on the stand structure prior to the fi re.Old-growth forests were primarily defi ned based on the age of the oldest cohort in a stand (Fig. 4a), but also based separately on the age of the oldest pine cohorts (Fig. 4c) and the oldest spruce cohorts (Fig. 4d).The occurrence of old-growth forests is high except when fi res are frequent in the highseverity fi re scenarios (Fig. 4a), which alone supports a high stand-replacement rate (Fig. 4b).
In the scenarios where frequent fi res maintain old-growth-dominated landscapes, the proportion of old-growth forests decreases slightly when mean fi re rotation increases from 50 to 200 y (scenarios 1-5 of Fig. 4a).However, old-growth dominance still persists under all fi re rotations in these scenarios.The reason for decreased oldgrowth occurrence is the increased fi re severity caused by longer mean time-since-fi re.
The occurrence of old-growth pine forests peaks at the combination of low severity and high frequency of fi res (Fig. 4c).As fi re interval increases, the old-growth pine forests are gradually replaced by old-growth spruce forests (Figs.4c,d).Since fi res were assumed to be always lethal to spruce, the mean fi re severity does not infl uence the pattern of old-growth spruce (Fig. 4d).

Spatially Explicit Simulations
The spatially explicit simulations (simulation set IV) produced results similar to severity scenario 5 of simulations set III, with regard to the relationship between fi re frequency and occurrence of old-growth forests (Fig. 5).In both scenarios the proportion of old-growth forests is high regardless of mean fi re frequency.The spatially explicit simulations produced slightly bimodal age distributions that were quite fl at for moderate or low fi re frequencies (Fig. 6).
The bimodality of stand age distributions based on spruce age (Figs.6a,b) is related to spatial variation in fi re frequency.The peak at high cohort age consists of climax-type old-growth spruce forests that occur on rarely burning spruce swamps or on sites that are isolated by mires.Such old-growth spruce forests are important in actual landscapes with intermediate fi re frequencies (Zackrisson and Östlund 1991, Hörnberg et al. 1995, Esseen et al. 1997).
The spatial simulations also demonstrate how increased number of ignitions and increased fi re frequency decrease fi re severity.The area burned increases with the number of ignitions, but not proportionally (Fig. 7a), and the mean fi re severity decreases (Fig. 7b).Changing the area burned 3-fold, from 0.5%/y to 1.5%/y, requires a 16-fold increase in the number of ignitions (Fig. 7a).As an example of the simulation fi re regime, in a simulation with an annual burn rate of 0.7%, the mean fi re size was 0.5% of the burnable landscape area.Most of the burned area was due to fi res larger than 2% of the area, while the largest fi re covered 43% of the landscape.

Pennanen
Forest Age Distribution under Mixed-Severity Fire Regimes -a Simulation-Based Analysis …

Shape of Age Distributions
The simulations demonstrated that when fi res are not always stand-replacing, stand age distributions differ considerably from time-since-fi re distributions.Theoretical time-since-fi re distributions of equilibrium landscapes (exponential, Weibull, or any other) are always monotonously decreasing and dominated by stands that are young in relation to mean disturbance interval (McCarthy et al. 2001).However, stand age distributions based on actual tree age may be dominated by old stands and be unimodal or bimodal, regardless of the fi re interval (Figs.2-3).
A simple conceptual model clarifi es how the age-class distributions observed in the simulations (Figs.2-3) arise (Fig. 8).Stands can be divided into those in which the oldest cohort was established after a stand-replacing disturbance and those in which the currently oldest cohort was released when an earlier cohort died of senescence.The shape of the age distribution of those stands established after stand-replacing fi res (Fig. 8) arises because cohorts are most susceptible to fi res at young age.On the other hand, the age distribution of the stands dominated by released cohorts is concentrated at the high end of the age scale (Fig. 8), because when an old cohort dies, the next oldest cohort is formed of trees that regenerated under the dying cohort, when it 'thinned' in a low-severity fi re or due to old age.The frequency of stand-replacing disturbances determines the relative importance of the 2 types of stand, producing different unimodal and bimodal age distributions.

Old-Growth Forests under Mixed-Severity Fires
The results of simulation run III demonstrate a relationship between the fi re regime and the mean occurrence of old-growth forests in a forest landscape.Old-growth forests are rare when fi res are frequent in the high-severity scenarios, but otherwise they dominate the landscape (Fig. 4a).
The simulations show that under some circumstances it is possible that decreased fi re frequency leads to a decrease in the abundance of old-growth forests, when longer time-since-fi re leads to higher fi re severity.However, this decrease in old-growth abundance was only slight even though a strong positive relationship between time-since-fi re and fi re severity was assumed.Simulation set IV gave a similar outcome, demonstrating that the result is not peculiar to a nonspatial model.In summary, the simulations suggest that if old-growth forests dominate landscapes under frequent fi res, old-growth dominance persists under all fi re rotations.The simulations assumed that the relationship between time-sincefi re and fi re severity remains the same when fi re frequency changes.This requires that both the climate and the successional pathway that stands follow remain constant.
The simulations assumed that the increase in potential fi re severity occurs gradually during the stand succession after a fi re.However, it is conceivable that the nonlinear dynamics of fi re propagation could produce 'catastrophic' changes in fi re behavior in response to change in parameters such as stand structure (Hesseln et al. 1998), e.g. at the point where the spruce canopy becomes developed enough to support crown fi res.Such system behavior could make fi re severity even more sensitive to mean fi re intervals than was assumed, increasing the stand-replacement rate and decreasing the occurrence of old-growth forests at intermediate fi re frequencies.Therefore it should be determined if the results are very sensitive to detailed assumptions of the temporal pattern of fi re severity.
Let us consider the hypothetical case that is most favorable to the occurrence of old-growth forests at high fi re frequencies and least favorable at intermediate fi re frequencies.Assume that there is a sharp threshold at a certain time-since-fi re, separating the young stands that do not sustain standreplacing fi res from older stands that do support them.Using some simplifying assumptions it is possible to calculate analytically the occurrence of old-growth forests in this extreme scenario (Appendix 1).It appears that as long as old-growth forests clearly dominate at short fi re intervals (50 y) the old-growth stands cover the majority of forests at any fi re frequency (Fig. 9).We conclude that the pattern of Fig. 4a appears robust even under extreme assumptions of fi re behavior.
In fact, there is no necessary clear successional trend in crown fi re behavior (Bessie and Johnson 1995).Therefore, it is possible that the relationship between fi re frequency and fi re severity in simulation sets III and IV was unrealistically strong.If the relationship between fi re frequency and mean fi re severity were weaker, the general pattern of Fig. 4a would remain the same, but the decrease in old-growth forest abundance at intermediate fi re frequencies would be shallower.
The nonspatial simulations assumed a uniform 'landscape' of forest stands with identical mean fi re intervals.In an actual landscape the susceptibility of different sites to fi res varies (Engelmark 1987).Given a certain mean fi re interval for a landscape, the age distribution of the entire landscape would be the sum of the age distributions at each site.This would decrease further the sensitivity of the landscape age distribution to the mean fi re interval.

Historical Fennoscandian Landscapes
Empirical knowledge can be used to link the previous theoretical picture with the actual historical dynamics of middle boreal Fennoscandian forest landscapes.The main diffi culty is that there is no direct evidence for the severity of fi res at those times.However, several studies have shown that when fi re intervals have been short (about 50-70 y), landscapes have been dominated by multi-aged old-growth pine forests (Zackrisson 1977, Zackrisson and Östlund 1991, Östlund et al. 1997, Axelsson and Östlund 2000, Lehtonen and Kolström 2001, Kuuluvainen et al. 2002).This implies, according to the previous discussion, that old-growth forests have also dominated landscapes when fi re intervals were longer, if the climate and the succession of vegetation after fi res have been relatively constant.
The conclusion on landscapes constantly dominated by old-growth forests would be in question if the climate was much more favorable to severe fi res prior to the 19th century.However, Niklasson and Granström (2000) found no correlation between climate proxies and the fi re regime.The drop in mean fi re size between the 17th and 19th centuries (Niklasson and Granström 2000) could indicate a change in climatic conditions, but the spatially explicit simulations (set IV) show that decreased fuel loads resulting from more frequent fi res can well explain the change in fi re size.The reason is that the increasing area burned decreases the mean time-since-fi re in the landscape.This decreases the mean fi re severity (Fig. 7b), leading to lower rates of fi re spread and consequently to smaller fi re size.This relationship between number and size of fi res was earlier suggested by Niklasson and Granström (2000).
Fire frequencies appear to have increased steadily for the last 2000 y until they peaked in the 19th century (Pitkänen and Huttunen 1999).This does not suggest that forests have been signifi cantly more fi re-prone in older times.In summary, it seems plausible that the trend in fi re frequency has followed the number of human-caused ignitions and the unmanaged middle boreal Fennoscandian forest landscapes have been constantly dominated by old-growth forests.Wimberly et al. (2000) have previously used a simulation model incorporating non-stand-replacing fi res and multicohort stands to investigate the historical amount of old-growth forests and its temporal variability.They had an empirical estimate of fi re severity available, but due to lack of data they had to assume that fi re intervals and fi re severity were independent.For the present study, no direct data on fi re severity were available, but empirical data on the structure of frequently burning landscapes could be used instead to infer realistic fi re intensity scenarios.

Limitations of the Modeling Approach
The basic limitation of the modeling approach is the assumption of equilibrium dynamics.In real landscapes fi res that are large in relation to landscape size may be common, producing irregular and erratic time-since-fi re distributions (Baker 1989, Cumming et al. 1996, Boychuk et al. 1997).Therefore the simulation results must be interpreted as theoretical mean age distributions.
Non-stand-replacing fi res have been typical under Fennoscandian conditions, and large fi res are spatially heterogeneous, with fi re severity varying inside each burned area.Therefore the effect of spatially correlated disturbance on the stand age distribution is lower than on the time-since-fi re distribution.Furthermore, since the old-growth forests include a wide range of age-classes, their occurrence is considerably less sensitive to the infl uence of nonequilibrium dynamics than the exact shape of the age distribution.However, Wimberley et al. (2000) showed that variability in the amount of old-growth forests may be very high, even on landscape level.Even under nonequilibrium dynamics, the previous conclusion could be rephrased that unmanaged landscapes have most of the time, and on a regional scale perhaps constantly, been dominated by old-growth stands.
The shape of the age-class distribution produced by a simulation model is dependent on the model structure and the chosen parameter values; thus it is useful to consider how sensitive the results are to changes in the assumptions incorporated.Moderate changes in the assumptions governing the establishment, thinning, and death of cohorts would only affect the width and exact location of the peak in age distributions (Fig 8).The results regarding old-growth occurrence are therefore also insensitive to these parameters, as long as the maximum age of the species is considerably higher than the old-growth threshold of 150 y.Regarding the effect of fi res on age distribution, the assumption that mortality decreases with cohort age is realistic (Ryan andReinhardt 1988, Kolström andKellomäki 1993).
The assumption that cohorts in the 2 lowest fi re tolerance classes above the survival threshold will be thinned by a fi re is more arbitrary.This assumption affects the regeneration of understory cohorts and, therefore, infl uences indirectly the mean age of cohorts released when the oldest cohort dies.Altering the assumption would change the exact shape of the peak in the age distribution under low fi re severities, but would not change the general pattern.
Relating the simulation results to quantitative forest data would require defi ning the size of grid cells and setting up quantitative thresholds defi ning 'thin' and 'dense' cohorts.Such thresholds would obviously be specifi c to species, cohort age, and site type.However, in the present study such quantitative comparisons are not made, and the actual values of the thresholds are not relevant to the conclusions, as long as the rules defi ning model behavior are qualitatively correct.
The inferred domination of old-growth stands under all fi re frequencies is specifi c to landscapes

Pennanen
Forest Age Distribution under Mixed-Severity Fire Regimes -a Simulation-Based Analysis … in which the fi re-resistant Scots pine is abundant and to the conditions of middle boreal Fennoscandia.However, the theoretical conclusions may generalize to other regions where mixedseverity fi re regimes prevail.

Conclusions and Management Implications
The main results of this study are the following: 1) When not all fi res are stand-replacing, theoretical stand age distributions of forest landscapes may be roughly bell-shaped or bimodal and qualitatively different from the time-since-fi re distributions.Actual forest landscapes may follow such equilibrium distributions when averaged over suffi ciently wide areas or suffi ciently long times.2) If old-growth forests dominate landscapes when fi res are frequent, old-growth dominance persists when the number of fi res is decreased, even if longer fi re intervals increase the severity of fi res. 3) Assuming, in accordance with empirical studies, that frequent fi res maintained landscapes dominated by old-growth pine forests and that historical trends in fi re frequency were due to human-caused ignitions, middle boreal Fennoscandian forest landscapes have been consistently dominated by old-growth forests and stand-replacing fi res have been rare.4) Fig. 6 shows plausible age distributions of historical Fennoscandian forest landscapes under varying fi re frequencies corresponding to empirical observations (Pitkänen and Huttunen 1999, Niklasson and Granström 2000, Pitkänen and Grönlund 2001).Changes in fi re frequency have mostly infl uenced the abundance of old-growth spruce stands.
Old-growth forests, defi ned as here, based on the age of the oldest tree cohorts, include a wide range of forest structures, varying in species composition, density, and spatial pattern.The simple defi nition used emphasizes the most obvious difference between unmanaged and uniformly managed production landscapes.Late-successional forests that have escaped logging are rare in the managed landscape today, and the open, recently disturbed old-growth stages maintained by fi re are even more exceptional (Linder et al. 1997(Linder et al. , Östlund et al. 1997)).
The observed structure of unmanaged forests may be misleading, when determining the natural range of variability in the forest landscape.Fire regimes have varied fundamentally during the history of Fennoscandian forests.Therefore, current late-successional forests are denser than the open stands maintained by frequent fi res of the 19th century.On the other hand, the conversion to late-successional spruce forests (Linder et al. 1997) may bring back spruce-dominated stand types that were more common before the 19th century, when fi res were less frequent (Pitkänen andHuttunen 1999, Niklasson andGranström 2000).For the same historical reasons, the present even-aged old-growth spruce stands may not resemble the old-growth spruce forests of historical or 'natural' landscapes, in which more open 'climax' structures are common (Norokorpi 1979, Syrjänen et al. 1994, Kuuluvainen et al. 1998).
The habitat requirements of the species classifi ed as threatened in Finland suggests that, apart from the destruction of certain spatially confi ned habitat types, the most detrimental effects of forest management have been the elimination of old, dying, and dead trees, the critical components of old-growth structure (Esseen et al. 1997, Jonsell et al. 1998, Rassi et al. 2001).Of course, stand-replacing disturbances are not harmful as such.Early-and mid-successional habitats, such as broad-leaved stands often created by standreplacing fi res (Sirén 1955), are an essential part of the natural variability of forest landscapes (Esseen et al. 1997, Martikainen et al. 1998).
The prevalence of old-growth forests in the natural landscape and the importance of such forests to biodiversity suggest that old-growth structures should be maintained and restored.Since late-successional stands are not easily maintained in the context of commercial management, setting aside protected areas is probably the most cost-effective method to protect species that are sensitive to stand-replacing disturbance and do not disperse effectively between isolated or shortlived habitat patches.For the same reason, as long as only a low proportion of forests is reserved primarily for the maintenance of biodiversity, it may be most effi cient to use such areas to accommodate late-successional stands.
A considerable proportion of threatened forest species do not require late-successional stands, however, but prefer open stands with a good supply of dying and dead trees (Jonsell et al. 1998, Martikainen 2001, Rassi et al. 2001).Such conditions may be found in old-growth forests maintained by frequent fi res of moderate severity.Maintaining such open, multiaged old-growth forests could require management through logging, since reintroducing natural fi re regimes on an extensive scale is diffi cult.Restoring oldgrowth structures would require management scenarios that avoid conventional terminal cuttings, such as variable-retention and group selection schemes that leave a considerable proportion of trees permanently unharvested (Seymour and Hunter 1999, Bergeron et al. 2002, Kuuluvainen 2002).

Appendix 1
Assume that fi res occur randomly with time-homogenous Poisson distribution.The mean fi re interval is 1/b, and the probability density function (p.d.f.) for the length of fi re intervals t is e -bt (Van Wagner 1978).Parameter b is approximately the annual probability of burning for a specifi c site.Fire severity is assumed to be determined so that fi res are stand-replacing if time since the previous fi re exceeds a threshold value m, and otherwise they are not.Stand age will be defi ned as the time since last stand-replacing fi re.
Assume that a stand-replacing fi re occurs at time t = 0, and denote the probability that the stand survives until year a (i.e.does not burn in a stand-replacing fi re before that) by F(a).Obviously, F(a) = 1 when a ≤ m.The derivative F'(t) = -f(t), where f(t) is the p.d.f. of the random variable giving the time of the next standreplacing fi re.The fi rst stand-replacing fi re after t = 0 occurs at time a if and only if the stand burns at time a, the stand has not burned in the time interval [a-m, a[, and the stand has not suffered a stand-replacing fi re during the time interval ]0, a-m[.Since fi res occur randomly, these 3 events are mutually independent.The probability that a stand does not burn during a period of m years is e -bm .Combining these facts, we obtain, for a > m, The survival curve F(a) is by defi nition normalized so that F(0) = 1.To obtain the p.d.f. for the equilibrium stand age distribution in the landscape, F(a) must be multiplied by the rate at which stands burn in stand-replacing fi res, i.e. be -bm .Thus stand ages are distributed according to the p.d.f.A(t) = be -bm F(t).Now the proportion of forest stands that are more than a years of age is All the calculations could be repeated and solved numerically using a more realistic assumption that the probability of stand replacement is determined as a continuous function of time since the last fi re.However, the actual tree cohort age structure would still be ignored, which is one of the reasons that a simulation approach was used in this study.

Fig. 1 .
Fig. 1.Mortality and thinning of pine cohorts due to senescence, as assumed in the simulations.Survival curves describe the fate of entire cohorts, not of single trees.Time of 'thinning' or death of cohorts is assumed to approximate a normal distribution.Mortality or thinning rates give the fraction of cohorts thinned or removed per 10-y time step.

Fig. 2 .
Fig. 2. Steady state stand age distribution in response to fi re severity.Stands are classifi ed separately according to age of the oldest spruce cohort and the age of the oldest pine cohort.Mean fi re rotation is 95 y (0.1 fi res/decade at each site).A) Fires are always stand-replacing (severity class 5).B) Any severity from 1 to 5 is equally probable.C) Any severity from 1 to 3 is equally probable.D) Fires always thin pine cohorts but never kill them completely.

Fig. 3 .
Fig. 3. Stand age distribution under a moderate-severity fi re regime in response to mean fi re interval.Fire severity takes values from 1 to 3 with equal probability.Fire severity is assumed to be independent of time-since-fi re.

Fig. 4 .
Fig. 4. Landscape properties under varying fi re severity scenarios (labeled by maximum potential fi re severity) in response to mean fi re interval, based on simulation set III. A) Proportion of old-growth forests (OGF, oldest cohort > 150 y) in the landscape.B) Stand replacement rate (mean yearly proportion of landscape suffering a stand-replacing fi re).C) Proportion of stands with oldest pine cohort > 150 y of age.D) The proportion of stands with oldest spruce cohort > 150 y of age.

Fig. 5 .
Fig. 5. Proportion of old-growth forests (OGF) in the landscape in response to mean fi re interval according to spatially explicit simulation set IV (SP), and to scenarios of nonspatial simulation set III (1-9).

Fig. 6 .
Fig. 6.Stand age distributions in response to fi re frequency according to simulation set IV. Stands are classifi ed separately according to age of the oldest tree cohort, oldest spruce cohort and oldest pine cohort.Mean fi re rotations are 240 (A), 150 (B), and 50 y (C).

Fig. 7 .
Fig. 7. Fire regime in relation to number of ignition events per time step (unit arbitrary) in spatially explicit simulation set IV. A) Annual burn fraction.Area burned is divided according to fi re severity class.B) Proportion of area burned in each fi re severity class.

Fig. 8 .
Fig. 8. Conceptual model of stand age distribution in a Scots pinedominated forest landscape.Stands can be divided into 2 classes:Stands in which the oldest cohort was born after a stand-replacing disturbance, and stands whose oldest cohort was released when an earlier cohort died.It is assumed that cohorts older than 120 y survive fi res.New cohorts are only created after fi res.

Fig. 9 .
Fig. 9. Theoretical proportion of old-growth stands in a landscape.Fire severity is assumed to be determined so that fi res are stand-replacing if time since the previous fi re exceeds the threshold age, and otherwise they are not.Old-growth forests are stands where time since last stand-replacing fi re is at least 150 y. 'Inf' stands for infi nite fi re interval (no fi res).See Appendix 1 for details.
F can now be solved from Equation 2 inductively for any a > 0. The solution is m] means the largest integer less than or equal to a/m.
Fig. 9 shows M b,m (150), i.e. the proportion of stands that are at least 150 y of age, for different values of mean fi re interval 1/b and threshold age m.For a given m, M b,m (a) is minimized by maximizing the stand-replacement rate be -bm through setting b = 1/m, i.e. when the mean fi re interval coincides with the threshold age.This can be confi rmed by evaluating the derivative ∂ ∂ M a b b m , ( ) .

Table 1 .
Summary of differences between simulation sets.