Forest age structure as indicator of boreal forest

e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Forest age structure as indicator of boreal forest
sustainability under alternative management and fire
regimes: A landscape level sensitivity analysis
M. Didion ∗,1 , M.-J. Fortin 1,2 , A. Fall 1
School of Resource and Environmental Management, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
a r t i c l e
i n f o
a b s t r a c t
Article history:
Effective forest ecosystem-based management requires a thorough understanding of the
Received 10 August 2005
interactions between anthropogenic and natural disturbance processes over larger spatial
Received in revised form 4 July 2006
and temporal scales than stands and rotation ages. Because harvesting does not preclude
Accepted 5 July 2006
fire, it is important to evaluate the combined effects of harvesting and fire on forest age
Published on line 22 August 2006
structure, a coarse indicator of forest ecosystem state. We performed a sensitivity analysis
of landscape scale effects of forest management (strategy, harvest rate and access cost) and
Keywords:
fire regime (fire return interval and extent) in terms of combined impacts on forest stand
Ecosystem-based forest
age-class structure on a study area of 3.5 million hectares of boreal forest of Québec. A
management
series of scenarios were simulated over 500 years and replicated 30 times using a previously
Fire
reported spatially explicit landscape model. Within the parameter space of our sensitivity
Forest harvesting
analysis, we found that harvest rate, fire return interval and management strategy were
Spatially-explicit modelling
the most significant parameters affecting stand age-class distribution across the landscape.
Stand age-class distribution
The former are not so surprising, given that they combine to produce an overall disturbance
rate, but the latter shows that the resulting impact on age-class structure can be influenced
to some degree through management objectives. A harvesting strategy of clearcutting for
sustained timber supply, using a harvest rotation based on minimum merchantable age
(approximately 100 years in this analysis), creates a trend for the stand age-class distribution
away from the expected range of natural variation for the study area. Within the scope of our
simulations, alternative management strategies with extended harvest rotation age proved
the most robust forest management practice to absorb variations in fire regime.
© 2006 Elsevier B.V. All rights reserved.
1.
Introduction
For much of the past century, natural forests have been
increasingly converted to managed forests, and this has had
a wide range of impacts such as forest fragmentation, loss of
∗
old-growth and a decline in biodiversity (Hansen et al., 1991;
Spies et al., 1994; Wallin et al., 1994, 1996). Increasing concerns
about maintaining the ecological integrity of forest ecosystems (i.e., resilience and ability to withstand stresses such
as disturbances) and preserving biodiversity as well as other
Corresponding author. Present address: Forest Ecology, Swiss Federal Institute of Technology, Department of Environmental Science,
ETH-Zentrum, CHN Universitaetstr. 22, CH-8092 Zurich, Switzerland. Tel.: +41 44 632 5629; fax: +41 44 632 1358.
E-mail addresses: [email protected] (M. Didion), [email protected] (M.-J. Fortin), [email protected] (A. Fall).
1
Tel.: +1 604 291 5971; fax: +1 604 291 4659.
2
Present address: Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, Ont., Canada M5S 3G5. Tel.: +1 416
946 7886; fax: +1 416 978 8532.
0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2006.07.011
46
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
ecosystem services have led to ongoing research by scientists and resource managers about how to balance ecological
and socio-economic values (Coates and Burton, 1997; Cissel et
al., 1999; Messier and Kneeshaw, 1999; Carey, 2000; Kneeshaw
et al., 2000). Emerging knowledge suggests that management
practices emulating aspects of natural ecosystem variability
and dynamics may help maintain or restore forest functions
(Grumbine, 1994; Rogers, 1996; Landres et al., 1999). To explore
the potential of emulating the effects of natural disturbances
over large management areas and long periods of time, spatially explicit models have been used (Mladenoff and Baker,
1999; Canham et al., 2003; Messier et al., 2003; Mladenoff, 2004;
Pennanen et al., 2004).
Most landscape level modelling studies examined either
the impact of human induced changes in landscape structure (e.g., Franklin and Forman, 1987; Mladenoff et al., 1993;
Gustafson and Crow, 1994; Wallin et al., 1994; Gustafson and
Crow, 1996) or those of natural disturbance (e.g., Turner et
al., 1989; Gauthier et al., 1996; He and Mladenoff, 1999); few
studied anthropogenic and natural disturbance effects simultaneously (e.g., Gustafson et al., 2000; Fall et al., 2004). Because
complete suppression of natural disturbance events such as
wildfire, windthrow and insect outbreaks is not realistic (Van
Wagner, 1983), forest management strategies should be adaptive to accommodate uncertainty associated with such events.
To compare alternative forest management practices combined with changes in fire regime, stand age-class distribution
was used as a coarse filter indicator of the forest state at the
landscape scale (Kneeshaw et al., 2000; Fall et al., 2004). Indeed,
stand age is a surrogate for structural condition, and productivity and habitat are functions of different stand seral stages
(Bergeron et al., 1999; Franklin et al., 2002; Lindenmayer and
Franklin, 2002). Although spatial pattern of stand age may be
important in certain circumstances, the amount of area in
various age classes is likely a stronger driver of forest state
(Hunter, 1990; Kneeshaw et al., 2000). Also, because stand
age-class structure is modified by both disturbance processes
(Franklin et al., 2002), it can be used as a currency to compare the combined effects of natural processes and human
activities at the landscape scale over long time periods. The
effects of fire and harvesting on biodiversity, however, differ: fire creates a heterogeneous forest structure (Bergeron
and Dansereau, 1993; Bergeron et al., 1998) with a mix of
younger and older stands critical for maintaining biodiversity (Bergeron et al., 2002), whereas logging activities tend
to homogenize and simplify forest structure due to evenaged timber management with predominantly younger stands
(Franklin and Forman, 1987; Mladenoff et al., 1993; Spies et al.,
1994; Gustafson and Crow, 1996; Coates and Burton, 1997; Crow
and Gustafson, 1997; Bergeron et al., 1998) leading to a reduction in biodiversity (Bergeron et al., 2002).
In the spirit of the ecosystem management paradigm, we
are interested in assessing the long-term sustainability of the
forest over a large territory. For example, Fall et al. (2004) investigated how alternative harvesting strategies, such as those
proposed by Bergeron et al. (1999) and Burton et al. (1999), compared with conventional management in terms of impact on
age-class structure and timber production. Here, we extend
the work of Fall et al. (2004) with a goal of improving the
understanding of interactions between anthropogenic distur-
bance of forest harvesting and natural disturbance dynamics
at the landscape scale and their effects on boreal forest ecosystem sustainability. Using a simulation modelling approach we
also aim to contribute to the discussion of the relevance of
computer models for simulating long-term forest dynamics
(Sturtevant et al., 2004).
To do so, we carried out a sensitivity analysis using a spatially explicit landscape-scale disturbance model (Fall et al.,
2004) to assess the combined effects of these disturbances on
stand age-class structure relative to current conditions in a
boreal forest study area of south central Québec, Canada. Since
we have control over harvest rate, we investigated the effect
of changes of this parameter in a more detailed analysis that
attempted to minimise the confounding effects of parameters
we cannot control as easily such as stochastic fire ignition and
fire regime changes. Our specific objectives were:
• to conduct an extensive sensitivity analysis of key parameters describing the fire and management regimes;
• to compare alternative forest management strategies for
planning and conservation purposes, in particular strategies that target a specified age-class distribution as proposed in Burton et al. (1999);
• to examine how stand age-class targets are applied as harvesting constraints (explained in more detail in Section 2),
in particular whether areas of forest required to meet the
constraint are reserved from harvesting (hard constraint
where age-class target takes precedent so that if an ageclass is short, then no harvesting of forest in that age-class
can occur) or can be accessed with low preference in situations when the targeted yield cannot be achieved, e.g., due
to losses to forest fires (soft constraint where harvest target
takes precedence-logging will avoid cutting in age-classes
that do not meet the age-class target, but if there is timber
shortage cutting can/will occur there).
Particularly, this research aims to provide information at
the landscape-scale on the range and combination of parameters that move boreal forest stand age-class structure out of
the range of variability produced by the historical disturbance
regime alone. The details of this research will also allow an
investigation of the implications of current and alternative forest management strategies considering the potential effects
of climate change on fire disturbance impacts. For illustration
and comparison purposes, boreal forest data from Québec will
be used.
2.
Methods
2.1.
Study area
The study area is in the upper Mauricie region of southcentral Québec (47◦ 57 N, 74◦ 52 W to 49◦ 08 N, 73◦ 45 W) (Fig. 1).
The landscape matrix consists of boreal forest dominated by
conifer stands of black spruce (Picea mariana) and to a lesser
extent jack pine (Pinus banksiana) and balsam fir (Abies balsamea) interspersed with lakes, wetlands and bogs. Mixed
stands of softwood and hardwood species, and pure deciduous
stands with trembling aspen (Populus tremuloides) and white
birch (Betula papyrifera) are also found.
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
47
Fig. 1 – Study area—Mauricie region in south-central Québec, Canada (47◦ 57 N, 74◦ 52 W to 49◦ 08 N, 73◦ 45 W).
Stand replacing fire with a mean return interval of around
150–160 years is the main natural disturbance agent based on
fire history information for the study area (Lefort et al., 2000).
Processes that often confound historical fire cycle estimation
(Lertzman et al., 1998) are not very important in the study area
(i.e., fire suppression efforts have been low and are likely to
have been ineffective particularly for large fires; Lefort et al.,
2000). Natural disturbance and, more recently, forest harvesting in the southern part of the region have created a forest
ecosystem dominated by immature and mature stands of less
than 150 years with some remnant stands of older mature and
old-growth forest between 150 and 300 years (Fig. 1) (Bergeron
et al., 2001).
Data on initial forest conditions (species and forest
age) were obtained from a 1980’s digitized forest inventory database from Québec’s Ministry of Natural Resources
(SIFORTMRN-DCF, SOPFEU; Fortin et al., 2002). The goal of
this forest inventory database is to update forest composition and age each decade over the entire province of Québec
using a systematic sampling grid (Ministère des Ressource
naturelles et Faune Québec, 2003). While the resolution of
14 ha (375 m × 375 m) for a study area extent of 3.5 million
hectares (721 × 360 grid cells) is somewhat coarse, it served
our purpose of comparing forest management alternatives
at a strategic level over a large spatial area and a long-term
planning horizon. Soil moisture was estimated from a digital
topography map of the same area (Fall et al., 2004).
2.2.
Landscape level forest disturbance model
We used an existing spatially explicit forest dynamics landscape model, the Mauricie Model (Fall et al., 2004), with
which key parameters regarding management planning
(strategy, harvest rate and access cost) and fire regime (fire
return interval and extent) that affect stand age could be
combined in a series of scenarios (Fig. 2). The Mauricie Model
was implemented in the spatially explicit landscape event
simulator (SELES) spatio-temporal modelling tool (Fall and
Fall, 2001), and includes sub-models that describe processes
of succession, fire and harvesting. This model shares some
commonality with the LANDIS landscape model (Sturtevant
et al., 2004), such as iterative processing of process submodels during fixed time steps (we used 10-year steps,
which is fairly common for long-term simulations). The
Fig. 2 – Conceptual representation of the Mauricie Landscape Model. The fire return interval parameter is in years, and fire
extent is in hectares. Harvest rate is the proportion of forest to harvest per year, and block size is a uniform distribution
(minimum and maximum size in hectares). Management strategy specifies the type (Status Quo, ecosystem management),
and constraints include the age-class target (if used) and minimum harvest age. Access cost is a spatial input layer. There
are three process sub-models, for fire, species aging and succession, and timber harvesting. The main portion of the
dynamic landscape state and output includes stand age (in years) and species type.
48
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
Mauricie Model was originally derived from a version of
LANDIS implemented in SELES and applied in the Abitibi
region of Québec (unpublished). However, in the spirit of
parsimony, our model differs from LANDIS fundamentally in
how the forest is represented: rather than representing presence/absence of 10-year cohorts for each species, we chose
to represent the forest using age and species of the dominant
tree species or species mix in order to match the input data
available from inventory. This simpler forest representation
was adequate for our purposes here, which focus primarily on
age-class structure (and rely less on changes due to species
succession).
2.2.1.
Succession sub-model
We limited the effect of succession to stand aging (i.e., time
since last stand replacing disturbance). Because stand type is
not a significant factor for fire intensity in the boreal forest
(Johnson et al., 1998), and silvicultural prescriptions in Québec
require planting of a similar species mix as prior to harvesting
(Bergeron et al., 1998), this assumption allows our model to be
relatively simple while retaining the main driving forces.
2.2.2.
fire size emerges as an output due to the interaction between
exogenous (number of fires and burn duration) and endogenous conditions (fuel). Variability of the fire regime in Québec
(Bergeron et al., 1998; Bergeron et al., 2001) was also partly captured by stochastically selecting fire duration from a negative
exponential distribution, and hence the fire return interval is
an outcome for each run. This bottom-up fire model provides
an approximation of historical conditions because it captures
more realistically the fairly well-developed knowledge of fire
dynamics in the boreal forest of Québec. The drawback is that
it is more difficult to control as an experimental factor so we
used it only to investigate the effects of potential fire regime
changes due to climate changes.
Fire sub-models
We used two fire sub-models to examine different kinds of
interactions with the management regime. The first (hereafter referred to as the top-down fire model, and the one
presented in Fall et al. (2004)) is an empirical model driven by
parameters that specify the fire return interval and mean fire
size, whereby the mean annual number of fires is defined as
landscape size/(fire return interval × mean fire size). Fire ignition
locations are assigned randomly while fire size is selected a
priori from a negative exponential distribution. Fires spread
to neighbouring cells until this selected extent is reached (Fall
et al., 2004). The advantage of this top-down model is that the
fire regime can be controlled allowing a comprehensive sensitivity analysis of fire regime and forest management options
(harvesting strategy, harvesting rate, access cost) simultaneously.
The second fire model (hereafter referred to as the bottomup fire model) was designed to represent the fire regime more
realistically, and to allow an investigation of the effect of
changes in harvest rate with corresponding response of the
fire regime since fire size is partly a function of the landscape conditions. It is similar to the first except that, based
on methods by Pennanen (2002), fire duration rather than size
is selected beforehand for each fire to represent variable burn
rates resulting from different fuel estimates. The number of
fires per year was selected as in the top-down fire model. Relative burn rate, as a function of fuel type and loading, is estimated based on stand type (deciduous, coniferous or mixed),
age and landform. More specifically, this fire model assumed
that stands younger than 30 years have less fuel (20%) than
older stands; that deciduous stands have less flammable fuel
types (20%) than coniferous stands; and that fuel flammability decreased with soil moisture (by a factor of 25% between
the drier and more mesic sites). These factors were derived
using fire history information and expert opinion, and are
combined multiplicatively to give a burn rate between 0 (stop
burning) and 1 (fastest relative rate). Fires spread to neighbouring cells until the selected time duration passes. Hence,
2.2.3.
Harvesting sub-model
The harvesting sub-model allows simulation of different harvest strategies (minimum harvest age and various harvesting
constraints, e.g., road access limitations, forest cover limits,
harvest rate and relative access costs (cf. Fall et al., 2004). Harvesting was spatially restricted to harvest units that varied
in size from 60 to 250 ha according to typical harvest block
sizes in the region by uniform random selection. Three management strategies were simulated. The “Status Quo” strategy
was designed to be consistent with current maximum sustained yield management practices in this region with the
exception that our model is driven by an area-based harvest
target and not volume. Forest is harvested through clearcutting at a constant annual rate (e.g., 1%) of the forest area.
Although annual harvest targets are often volume based, we
used constant annual area to keep interpretation of results
clear, and hence volume harvested may vary over time. The
constant area-based harvest target facilitates comparisons
between the effects of fire and harvesting. Based on information from the Québec Ministry of Natural Resources (Pothier
and Savard, 1998), the minimum age at which harvest can
economically occur depends on site and species, and varies
in the boreal forest of Québec from 30 to 145 years. To simplify
interpretation and maintain generality of our analysis, we
applied a single minimum harvest age of 100 years for all stand
types.
To incorporate options for ecosystem management, the
harvest regime can include a specified age-class target for
stands across the landscape. We developed two alternative
management strategies to apply such a target as either a
strict constraint or as an objective, which represent different policies concerning the relative priorities of ecological and
economic objectives. The hard strategy reserves forest from
harvest in order to maintain the targeted age-class structure (i.e., achieving the targeted stand age-class structure
becomes a constraint). The soft strategy adjusts harvest preferences to reduce the likelihood of harvest in age-classes below
the target, and hence maintaining older forest types is secondary to achieving timber yield, (i.e., achieving the targeted
stand age-class structure becomes a guideline). The difference relates primarily to what happens when the harvest
target and age-class target conflict. Using the hard strategy,
the harvest target may not be achieved if all forest older than
minimum harvest age is required to meet the age-class target. Conversely, using the soft strategy, the deviations away
from the age-class target may occur if all forest all forest older
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
49
(i.e., harvest units expand from the start location to include
adjacent available stands).
2.3.
Fig. 3 – Percentage targeted distribution for remaining
forest per age-class (2) in the Burton management strategy.
than minimum harvest age is within age-classes at or below
target levels. See Fall et al. (2004) for more details of these
strategies.
Based on the proposal by Burton et al. (1999) and the estimated fire return time of 150–160 years for the region, an
ecologically based harvest rotation should maintain a heterogeneous age-class structure with 35% of the forest older than
the minimum harvest age of 100 years (Fig. 3). This 35% is harvested spatially at a range of extended rotations in order to
maintain a linearly declining stand age-class structure broadly
resembling a negative exponential distribution expected to be
created by fire under natural conditions (Van Wagner, 1978;
Johnson and Van Wagner, 1985), and sets a target to maintain
some forest stands up to just older than 200 years (Fig. 3; cf.
Burton et al., 1999; Fall et al., 2004). We designed two management regimes to apply this age-class target as a hard or
soft constraint, which we call respectively “Burton hard” and
“Burton soft”.
Two relative access cost surfaces were used to explore the
general effect of different access costs on spatial and temporal
harvest patterns (not to estimate real management costs; (Fall
et al., 2004)). The “linear” cost surface assigns values to each
cell according to the distance to the southeast corner of the
study area, closest to the nearest mill, to capture access costs
due to time, gas, road maintenance, etc., which increase proportional to distance. A 10-fold increase was applied across
water and bogs to capture the additional road construction
and maintenance costs associated with accessing islands in
lakes and “tree islands” surrounded by bog (cf. Fall et al.,
2004). For contrast, we applied an “exponential” cost surface to
capture the effects of assuming rapidly increasing cost at distances beyond 100 km from the southeast corner. After 100 km,
cost values of the “linear” cost surface were multiplied by
a factor starting with 1.3 and increasing by 0.1 every 15 km.
We used this to examine the effect of a steeper access cost
gradient that might occur as a result of difficult terrain or
higher roading and transport costs and time to access remote
areas. Unless otherwise stated, we applied the linear cost
surface.
Selection of starting locations for harvest units was based
on a probabilistic “oldest-first” rule, with relative cell preference positively correlated with stand age (harvest preference
increases with the square of stand age) and negatively correlated with access cost (i.e., harvest preference decreases exponentially with the access cost surface). Block shape emerges
based on a target size selected from a uniform distribution,
and landscape pattern surrounding the cutblock start location
Sensitivity analysis
We performed two sensitivity analyses to investigate the effect
of different parameters on stand age-class structure: (1) a twofactor analysis to investigate the effect of changes in harvest
rate in combination with management strategy in two sets
of simulations, with and without the bottom-up fire model;
and (2) a five-factor analysis to investigate the effect of combinations of management strategy, harvest rate, access cost,
fire return interval and fire extent. All simulations were run
for 500 years (i.e., 5 rotations of 100 years) and replicated 30
times.
In the two-factor analysis, we focus on the sensitivity of
results to harvest rate because it is more directly controllable by managers than natural disturbance parameters that
influence the fire regime. For each of the three management
strategies, we simulated no harvesting (0%) to represent natural conditions in addition to a range of 8 harvest rates starting
with 0.65% to the maximum potential rate of 1% (assuming a
minimum harvest age of 100 years) with increments of 0.05%.
Harvest rate simply defines the portion of the forest area that
can be harvested each year. Because this analysis focused on
the effect of harvest rate, we used the bottom-up fire model
based on the current fire regime estimated for the region to
provide a better match with historical fire variation and pattern. To reduce complexity in this analysis, we used the linear
access cost.
In the five-factor analysis, we aimed to address uncertainty
associated with fire return interval and fire extent (Gauthier et
al., 1996; Bergeron et al., 1998) to analyze more specifically the
combined effects of changes in fire regime and management
factors. We simulated three management strategies for 0%,
0.65% and 1% annual harvesting, two access cost surfaces (linear and exponential), and six fire regimes. Fire regimes were a
combination of 50, 150 and 250 year fire return intervals and
1500 and 6500 ha mean fire extents. Because we wanted precise control over the fire return interval and extents, we used
the top-down fire model.
2.4.
Statistical analysis
Stand ages were categorized into four classes based on model
assumptions about reproductive age and harvest rotation, and
adapted from classification schemes used in the literature
(e.g., Frazer et al., 2000): early-seral (0–40 years); immature
(41–100 years); mature (101–200 years); old (201 years and
more). To evaluate the combined effects of the disturbance
parameters, we graphed the results and used standard deviations between runs and analyses of variance (ANOVAs) (Proc
GLM; SAS Institute, 1999) at 50-year intervals to assess the
significance of differences. To perform ANOVA the data must
follow a normal distribution. The data on age-class frequency
distribution obtained from the model simulations were significantly skewed (Kolmogorov–Smirnoff test: p < 0.0001). We
applied a natural log transformation and a constant to normalize the data and eliminate the skewness (Legendre and
Legendre, 1998). In some cases the transformation did not
50
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
achieve a normal distribution. A visual examination of the
frequency distribution and residuals in those cases indicated
that the use of ANOVA was acceptable given that ANOVAs are
robust to some departure from normality and the independence assumption (Kenny and Judd, 1986). The concerns are
also addressed by choosing a low significance level of 0.0001.
3.
Results
One result common to all analyses was that the stand ageclass distribution experienced large changes from initial
conditions, although trends to reach steady state dynamics
differed according to the combination of harvesting and fire
parameters. In most cases, large-scale fluctuations stabilized
between 100 and 150 years (Fig. 4). The age-class structure
in natural forests that are dominated by extensive standreplacing fires, such as the boreal forest, can be approximated
by a negative exponential distribution over large areas (Van
Wagner, 1978; Johnson and Van Wagner, 1985). Fig. 5 shows
the emerging age-class structure in the case of the Burton
hard and Status Quo strategies in the presence of fire for
a moderate annual harvest rate of 0.75% after 300 years of
simulations, i.e., after the system stabilized and legacies disappeared. For comparison, Fig. 5 also shows initial conditions
and conditions after 300 years in the case of fire only, which
represents natural conditions. The difference between the
initial and subsequent stand age-class distributions becomes
larger over time until a quasi steady state for natural conditions establishes after 250–300 years. The steady-state in fire
only scenarios appears later than in scenarios with harvesting and fire and the fluctuations before the steady-state is
reached are shallower (cf. Fig. 4) because the system slowly
approaches the negative exponential distribution, as imposed
by the modelled fire regime.
Compared to initial conditions, the area of early-seral forest increases significantly in all cases with harvesting (Fig. 6).
However, in the case of the Status Quo and Burton soft strategies, as a consequence of this increase there is a similar
decrease in area of mature and old forest. The expansion of
the area of early-seral forest in the case of the Burton hard
strategy is compensated for by a decrease of immature forest
between 41 and 100 years while the area of mature and old
forest also expands.
3.1.
Two-factor analysis: harvest rate levels
This analysis addressed the effect of harvest rate on age-class
distribution and the performance of alternatives to Status
Quo management. The overall mean fire return interval that
emerged from the bottom-up fire model was 162 years, with
a minimum of 128 years and a maximum of 214 years, which
was consistent with the estimated historical fire return interval of 150–160 years (Lefort et al., 2000).
To examine the hypothesis that alternative ecosystembased management strategies produce a different stand ageclass structure than Status Quo management, we graphed
mean area of early-seral, immature, mature and old forest for
the three simulated management strategies for the minimum
(0.65%) and maximum (1%) annual harvest rates in presence
and absence of fire (Fig. 6). The standard deviations in Fig. 6
support the ANOVA results that the effects of harvest rate and
management strategy on stand age-class structure are significant for early-seral, immature, mature, and old forest (Table 1).
The graphs distinguish further that the effect of Status Quo
and Burton soft on forest stand age-class structure was not
significantly different. However, a highly significant difference
in the effect of these two strategies and the Burton hard strategy existed (Fig. 6).
Fig. 4 – Mean area age-class distribution (20 year intervals are represented by alternating pattern; early-seral forest is
dotted; immature forest is striped lines; mature forest is dashed stripes, old forest is white) for 30 replicates starting with
the youngest age-class at the bottom for (a) Burton hard; (b) Burton soft; (c) Burton hard and fire; and (d) Burton soft and fire.
Harvest rate was 1% and fire was at historical levels.
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
51
Fig. 5 – Age-class frequency distributions for (a) initial conditions; (b) conditions after 300 years in the presence of fire
without harvesting; (c) conditions after 300 years in the case of the Burton hard strategy in the presence of fire and a 0.75%
harvest rate; and (d) conditions after 300 years in the case of the Status Quo strategy in the presence of fire and a 0.75%
harvest rate over 30 replicates. Fire was simulated using the bottom-up fire model.
The standard deviations for the data presented in Fig. 6
indicate that in the case without fire different harvest rates
result in a significantly different stand age-class distribution
over 500 years of simulation. In presence of fire, annual harvest
rates higher than 0.8% do not produce significantly different
results. As can be expected, standard deviations of forest area
are higher in the presence of fire than in simulations without
fire due to the additional stochasticity from the fire behaviour
(Fig. 6). In fact, in the absence of fire the effect of evenaged management practices, as is the case in the Status Quo
management and management without age-class restriction,
results in no variance in the area of early-seral and immature
forest after initial adjustments of the system due to legacies
after approximately 50 years (Fig. 6).
One goal of our research was to examine the hypothesis
of compensatory effects where harvesting replaces mortality from natural disturbance in conjunction with suppression
(MacLean, 1990; Carleton and MacLellan, 1994; Bergeron et al.,
1998; Aber et al., 2000; Harvey et al., 2002). Fig. 7 contrasts the
Table 1 – Fixed effects ANOVA for the effect of harvest
rate and management strategy on age-class distribution
over 500 years of simulation and 30 Monte Carlo runs
Stand age-class
Early-seral
Immature
Mature
Old
Harvest rate
Management strategy
F-value
p-value
F-value
p-value
186.23
240.14
101.40
552.32
< 0.0001
< 0.0001
< 0.0001
< 0.0001
4034.03
5180.60
1091.97
4795.68
< 0.0001
< 0.0001
< 0.0001
< 0.0001
effects of harvesting in the presence and absence of natural
disturbance for four of the eight harvest rates simulated in the
case of the Status Quo strategy. The interaction of harvesting
and fire leads to significant changes in age structure relative
to initial conditions (Figs. 4–7). In particular, the cumulative
effect of harvesting and fire results in significant changes to
the area of mature and old forest (Figs. 4–7).
The detailed analysis of the effect of harvest rate allowed a
fine discrimination of the implication of small changes of this
parameter. Harvest rates can be expressed in terms of the area
of forest that is targeted for harvest. For an annual harvest
rate of 1%, an area the size of the entire forested landscape
under management is expected to be harvested over a 100year period. Table 2 shows the mean total area harvested after
500 years and the mean annual area harvested in the presence
of fire for each of the eight harvest rates, and the respective
total and annual harvest targets for the Status Quo and Burton
soft strategies. Area harvested for rates between 0.8% and 1%
are similar because fire limits the harvestable area causing
increasing differences between the target and actual harvest
with increasing harvest rate.
3.2.
Five-factor analysis
The effect of fire return interval on stand age-class structure
is statistically significant overall for mature forest (i.e., the
age classes between 100 and 200 years) in the case of the
Status Quo (F = 414.60; p < 0.0001) and Burton soft (F = 233.04;
p < 0.0001) strategies (see Fig. 8 for a graph for the Burton soft
strategy). However, fire return time is not statistically significant for mature forest in the case of the Burton hard strategy
(F = 0.94; p = 0.6782). This management strategy is able to main-
52
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
Fig. 6 – Mean area of early-seral, immature, mature and old forest for three management strategies and two harvest rates in
presence (linemarkers ‘x’) and absence (no linemarkers) of fire. Whiskers represent 1 S.D. (a) Burton hard: harvest rate
0.65%; (b) Burton soft: harvest rate 0.65%; (c) Status Quo: harvest rate 0.65%; (d) Burton hard: harvest rate 1%; (e) Burton soft:
harvest rate 1%; and (f) Status Quo: harvest rate 1%.
tain similar areas of mature and old forest regardless of fire
frequency (Fig. 8). The Status Quo and the Burton soft strategies could not maintain an age-class distribution within the
bounds of the simulated natural range. The Burton hard strat-
egy performed well and, with the exception of a very short
fire return interval of 50 years, sustained a forest age structure within its historical range (Fig. 8). It did so, however at
the cost of timber yield.
Table 2 – Mean total harvested area after 500 years and mean annual harvested area for 30 replicates in the presence of
fire
Harvest
rate (%)
Mean total harvested area after
500 years (thousands of hectares)
Burton soft
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
7585
8109
8428
8619
8656
8688
8766
8781
Total targeted yield
(thousands of hectares)
Status Quo
7586
8086
8396
8567
8644
8733
8761
8819
Mean annual harvested
area (±1 S.D.) (hectares)
Burton soft
7588
8169
8750
9331
9919
10500
11081
11669
15170 (±679)
16218 (±757)
16855 (±1275)
17238 (±1994)
17313 (±3049)
17376 (±3780)
17532 (±4144)
17562 (±4640)
Annual targeted
yield (hectares)
Status Quo
15173 (±678)
16171 (±796)
16791 (±1400)
17133 (±2123)
17287 (±2989)
17466 (±3729)
17522 (±4081)
17637 (±4489)
15176
16338
17500
18662
19838
21000
22162
23338
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
53
Fig. 7 – Mean percentage forest area age-class distribution over 30 replicates in the case of the Status Quo strategy in the
absence of fire for age classes (a) early-seral forest 0–40 years; (b) immature forest 41–100 years; (c) mature forest 101–200
years; (d) old forest 201+ years; and in the presence of fire for age classes, (e) early-seral forest 0–40 years with fire; (f)
immature forest 41–100 years with fire; (g) mature forest 101–200 years with fire; (h) old forest 201+ years with fire. The
greyed-out area in each graph represents the range between minimum and maximum area per age-class obtained through
simulating fire with no harvesting.
54
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
Fig. 8 – The effect of fire return interval in the case of the Burton hard (no linemarkers) and the Burton soft (linemarkers ‘x’)
strategies on mean percentage forest area age-class distribution over 30 replicates for a harvest rate of 0.65% for age classes
(a) early-seral forest 0–40 years; (b) immature forest 41–100 years; (c) mature forest 101–200 years; (d) old forest 201+ years;
and for a harvest rate of 1% for age classes (e) early-seral forest 0–40 years; (f) immature forest 41–100 years; (g) mature
forest 101–200 years; (h) old forest 201+ years. Whiskers represent 1 S.D.
As can be expected, at higher fire frequency (shorter fire
return interval) the disturbance effect increases (Fig. 8). Status
Quo and Burton soft maintain a forest age structure similar to
natural conditions and a constant timber yield (in terms of
area harvested) only at long fire return intervals of 250 years
and a harvesting rate of 0.65%. An increase in fire frequency
leads to a decrease in mature and old forest in favour of earlyseral forest and to a decrease in timber yield. At a harvesting
rate of 0.65%, a change in fire return interval mainly affects the
area of early-seral, mature and old forest whereas immature
forest between 41 and 100 years is less affected (Fig. 8). This is
due to an interaction between harvesting and fire: increased
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
fire disturbance leads to an increase in early seral, and therefore age classes entering the immature age class, as well as
an increase in amount of immature disturbed by fire; since
harvesting does not occur in immature forest and increased
fire disturbance leads to reduced harvest rates, the balance
between increased younger forest and decreased older forest
resulting from increases in the combined disturbance effect of
fire and harvest pivots on the immature age-class (until the fire
return interval becomes very short). The forest ecosystem’s
ability to recover from the combined effects of harvesting and
fire is maintained at this relatively low harvest rate of 0.65%.
However, at a harvest rate of 1% the area of early-seral forest
and forest between 41 and 100 years increases at the expense
of forest older than 101 years, which is virtually eliminated
in the case of Burton soft and Status Quo (see Fig. 8 for the
Burton soft strategy). As fire frequency increases, the area per
age-class experiences non-linear changes suggesting a depensatory effect of fire and harvesting.
In this analysis, a change in mean fire extent results in statistically significant effects in a few cases only. Map outputs
(not shown) suggest that changes in fire extent will, however,
result in important changes in the spatial distribution of forest
stands of different age classes in the landscape.
The effect of a change in relative access cost is not very
marked. Statistically significant changes were caused in a few
cases only. However, simulation results suggest that a change
from the linear to the exponential cost function will lead to a
concentration of harvest units at closer proximity to the mill,
while forest beyond a threshold distance will experience primarily natural disturbance effects (Didion, 2002).
4.
Discussion
Natural disturbance processes are inherent to forest ecosystems and will persist despite fire suppression efforts. Within
the scope of our simulations, this research shows that the
combined effects of harvesting in the presence of wildfire disturbance are different from the sum of the individual effects.
That is, not only do fires and harvesting produce dramatically
different effects on the age-class structure of a landscape,
their effects combine to accelerate loss of late seral stands,
and fire exacerbates the effect of harvesting even at fire cycles
substantially longer than historic levels. This held whether fire
was modelled as a top-down or bottom-up process. Hence, in
order to maintain the forest ecosystem within its historical
range of variability requires a change in management practices away from traditional sustained yield, even-aged systems (Kneeshaw et al., 2000) to approaches based on natural
dynamics (Attiwill, 1994; Lieffers et al., 1996; Bergeron et al.,
1999) such as the strategies examined in this research, and to
plan at a management scale that is commensurate with natural disturbance scales.
Strong agreement exists that by emulating natural forest
disturbance biological and ecological functions of forests can
be maintained (Attiwill, 1994; Lieffers et al., 1996; Bergeron et
al., 1999). Sustainable forest management should thus strive
to maintain an age structure within the historic range of the
forest (Hansen et al., 1991; Landres et al., 1999). Applying constraints on harvesting of old forest presented the most sig-
55
nificant difference in the simulated alternative management
strategies. In general, only the Burton hard strategy maintained a significant amount of stands older than the minimum harvest age because it was designed to do so with
an explicit management constraint. The Burton soft strategy, which applied the age-class target as an objective not a
constraint, produced an age-class structure similar to the Status Quo strategy because when old forest was limited due to
interactions between management and fire, it was harvested
to achieve timber yield targets. The Status Quo and Burton
soft strategies produced a more uniform age-class distribution typical for industrial forestry defined by harvest rotation
length. Only at harvest rates lower than 0.75% did these strategies maintain significant amounts of forest older than the
minimum harvest age. This implies that achieving a target
age-class distribution likely requires precedence over meeting the harvest target, emphasising the need for strong forest
policies if ecological values are to be maintained. That is,
setting an explicit constraint for the age-class structure can
be a key component of ecosystem-based management, as it
would ensure the maintenance of mature and old forest that
is important for biodiversity (Burton et al., 1999; Carey, 2000).
It is worth noting that our use of an area-based harvest level
masks a positive feedback that a volume-based harvest target
would create, aggravating the effects we have identified. This
effect is due to the interaction between decreasing volume per
hectare as mean stand age decreases and increasing areas that
would need to be harvested to meet an even flow of timber. We
also assumed a constant minimum harvest age of 100 years
for all stands, while in reality this may vary across a landscape. Application of variable minimum harvest ages would
result in changes to the specific quantities reported, but would
not change the overall findings as long as the mean minimum
harvest age remained at the same. Since results depend on
the ratio of fire cycle/mean minimum harvest age, a different
mean minimum harvest age would affect results proportional
to changes in this ratio (e.g., if the mean minimum harvest age
was doubled, the relative effect would be similar to results for
a 100 year minimum harvest age and a fire cycle half as long),
but clearly with other interactions with the applied age-class
target.
The Burton hard strategy performed well in maintaining
the targeted age-class distribution. Note, however, that forest older than the maximum reserved age of 220 years was
available to harvest in the strategy as modelled (i.e., the late
seral target can be rotated). It is therefore important to be clear
about the targeted age-class range in a management approach
with a hard constraint, and whether the oldest stands are
open for lengthened rotations or for preservation. Ecosystembased forest management must examine the significance of
the entire possible age-class range for the forest community.
Because using a hard constraint implies potentially
reduced timber targets, effective implementation of such a
measure requires a shift in forest management from a constant yield policy to a more flexible approach. Our results
showed that in the presence of a fire regime with a 150-year
cycle, with no age-class constraint, the actual area harvested
for annual rates of 0.8–1% of the theoretical maximum (based
on minimum harvest age) are similar. Thus, attempting to
harvest at the maximum harvest rate produces little eco-
56
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
nomic gain (i.e., competition with fire for forests means that
the effective maximum harvest rate is significantly less than
1/minimum harvest age). Lower harvest levels permit persistence of older age classes. Managers should therefore set
harvest rates that take into account natural disturbances and
to create flexibility in the system in order to meet the goals
of ecosystem-based management and resiliency to unforeseen natural disturbance events. Another alternative may be
to stratify the area under management by having intensively
managed zones and other zones with limited or no forestry
(Hunter and Calhoun, 1996). This would result in reduced operational costs as the majority of harvesting could be carried out
in closer proximity to a mill and intensive fire suppression
could be focused in this area. Accessing a smaller area with
higher intensity would also reduce the ecological damage of
forestry operations such as fragmentation, and spread of disease and other negative effects associated with roads (Aber et
al., 2000).
5.
Conclusion
We used simulation modelling to explore the combined effects
of forest management and fire. Because a model cannot represent the complexity inherent to natural processes, our results
must be interpreted in the context of the model assumptions.
This study provided an estimation of the magnitude of the
synergic effect of forest harvesting and fire, and it demonstrated the temporal trend of stand age-class development
across the landscape as a result of harvesting and fire. This
information is important for sustainable forest management
in that it shows that the combined effects of harvesting and
fire are more complex than the sum of the individual effects,
and that age-class legacies persist from forest management.
The study also showed that implementing a goal of maintaining forest older than rotation age using a hard harvest
constraint is the most effective option to offset the typical
effect of industrial management to produce a homogeneous
stand age-class structure.
Although models are simplified representations of real systems and reflect our limited knowledge of a system, we can
use them to increase our understanding and to evaluate the
implications of our assumptions (Botkin, 1977). Strengths of
spatially explicit models are that processes can be modelled
more realistically, and the results can be examined with spatial analysis statistics to identify spatio-temporal changes in
landscape patterns that can be used to improve management
practices, e.g., aggregation of harvesting units to reduce fragmentation. Spatial analysis of our simulation results is the
next step offering a spatial assessment of stand age-class
structure (James et al. in preparation).
Acknowledgements
We thank Ken Lertzman for his valuable comments. This
research is funded through a grant by the Sustainable Forest Management Network (Québec Integration Project) to Drs.
M.-J. Fortin, A. Fall and others, and a NSERC grant to Dr. MarieJosée Fortin. We thank SIFORTMRN-DCF, SOPFEU, SOPFIM for allow-
ing us to use their data set as the initial conditions for this
research.
references
Aber, J., Christensen, N., Fernandez, I., Franklin, J., Hidinger, L.,
Hunter, M., MacMahon, J., Mladenoff, D., Pastor, J., Perry, D.,
Slangen, R., van Miegroet, H., 2000. Applying Ecological
Principles to Management of the U. S. National Forests. Issues
in Ecology No 6. Ecological Society of America, Washington,
DC, pp. 1–20.
Attiwill, P.M., 1994. The disturbance of forest ecosystems: the
ecological basis for conservative management. For. Ecol.
Manage. 63, 247–300.
Bergeron, Y., Dansereau, P.-R., 1993. Predicting the composition of
Canadian southern boreal forest in different fire cycles. J. Veg.
Sci. 4, 827–832.
Bergeron, Y., Gauthier, S., Kafka, V., Lefort, P., Lesieur, D., 2001.
Natural fire frequency for the eastern Canadian boreal forest:
consequences for sustainable forestry. Can. J. For. Res. 31,
384–391.
Bergeron, Y., Harvey, B.D., Leduc, A., Gauthier, S., 1999. Forest
management guidelines based on natural disturbance
dynamics: stand- and forest-level considerations. For. Chron.
75, 49–54.
Bergeron, Y., Leduc, A., Harvey, B.D., Gauthier, S., 2002. Natural
fire regime: a guide for sustainable forest management of the
Canadian boreal forest. Silva Fenn. 36, 81–95.
Bergeron, Y., Richard, P.J.H., Carcaillet, C., Gauthier, S., Flannigan,
M., Prairie, Y.T., 1998. Variability in fire frequency and forest
composition in Canada’s southeastern boreal forest: A
challenge for sustainable forest management. Conserv. Ecol. 2
(2), 6 (online) URL: http://www.consecol.org/vol2/iss2/art6.
Botkin, D.B., 1977. Life and death in a forest community: the
computer as an aid to understanding. In: Hall, C., Day, J. (Eds.),
Models as Ecological Tools: Theory and Case Histories. Wiley,
New York, pp. 213–234.
Burton, P.J., Kneeshaw, D.D., Coates, K.D., 1999. Managing forest
harvesting to maintain old-growth in boreal and sub-boreal
forests. For. Chron. 75, 623–631.
Canham, C.D., Cole, J.J., Lauenroth, W.K. (Eds.), 2003. Models in
Ecosystem Science. Princeton University Press, Princeton, NJ,
p. 476.
Carey, A.B., 2000. Effects of new forest management strategies on
squirrel populations. Ecol. Appl. 10, 248–257.
Carleton, T.J., MacLellan, P., 1994. Woody vegetation responses to
fire versus clear-cutting logging: a comparative survey in the
central Canadian boreal forest. EcoScience 1, 141–152.
Cissel, J.H., Swanson, F.J., Weisberg, P.J., 1999. Landscape
management using historical fire regimes: Blue River, Oregon.
Ecol. Appl. 9, 1217–1231.
Coates, K.D., Burton, P.J., 1997. A gap-based approach for
development of silvicultural systems to address ecosystem
management objectives. For. Ecol. Manage. 99, 337–354.
Crow, T.R., Gustafson, E.J., 1997. Ecosystem management:
managing natural resources in time and space. In: Kohm,
K.A., Franklin, J.F. (Eds.), Creating a Forestry for the 21st
Century. Island Press, Washington, DC, pp. 215–228.
Didion, M., 2002. Improving Forest Management Decisions by
Modeling Landscape Disturbance Impacts on Forest Age
Structure Dynamics. M.R.M., Simon Fraser University,
Burnaby, BC.
Fall, A., Fall, J., 2001. A domain-specific language for models of
landscape dynamics. Ecol. Model. 137, 1–21.
Fall, A., Fortin, M.-J., Kneeshaw, D.D., Yamasaki, S.H., Messier, C.,
Bouthillier, L., Smyth, C., 2004. Consequences of various
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
landscape-scale ecosystem management strategies and fire
cycles on age-class structure and harvest in boreal forests.
Can. J. For. Res. 34, 310–322.
Fortin, M.-J., Fall, A., Didion, M., 2002. Intégration de la
problématique des feux dans la planification forestière. In:
Chabot, M., Gauthier, S. (Eds.), Actes de colloque. Ministère
des ressources naturelles du Québec, Chicoutimi (Québec), pp.
73–75.
Franklin, J.F., Forman, R.T.T., 1987. Creating landscape patterns by
forest cutting: ecological consequences and principles.
Landscape Ecol. 1, 5–18.
Franklin, J.F., Spies, T.A., Pelt, R.V., Carey, A.B., Thornburgh, D.A.,
Berg, D.R., Lindenmayer, D.B., Harmon, M.E., Keeton, W.S.,
Shaw, D.C., Bible, K., Chen, J., 2002. Disturbances and
structural development of natural forest ecosystems with
silvicultural implications, using Douglas-fir forests as an
example. For. Ecol. Manage. 155, 399–423.
Frazer, G.W., Trofymow, J.A., Lertzman, K.P., 2000. Canopy
openness and leaf area in chronosequences of coastal
temperate rainforests. Can. J. For. Res. 30, 239–256.
Gauthier, S., Leduc, A., Bergeron, Y., 1996. Forest dynamics
modelling under natural fire cycles: a tool to define natural
mosaic diversity for forest management. Environ. Monit.
Assess. 39, 417–434.
Grumbine, R.E., 1994. What is ecosystem management? Conserv.
Biol. 8, 27–38.
Gustafson, E.J., Crow, T.R., 1994. Modeling the effect of forest
harvesting on landscape structure and the spatial distribution
of cowbird brood parasitism. Landscape Ecol. 9,
237–248.
Gustafson, E.J., Crow, T.R., 1996. Simulating the effects of
alternative forest management strategies on landscape
structure. J. Environ. Manage. 46, 77–94.
Gustafson, E.J., Shifley, S.R., Mladenoff, D.J., Nimerfro, K.K., He,
H.S., 2000. Spatial simulation of forest succession and timber
harvesting using LANDIS. Can. J. For. Res. 30,
32–43.
Hansen, Spies, Swanson, Ohlmann, 1991. Conserving biodiversity
in managed forests. BioScience 41, 382–392.
Harvey, B.D., Leduc, A., Gauthier, S., Bergeron, Y., 2002.
Stand-landscape integration in natural disturbance-based
management of the southern boreal forest. For. Ecol. Manage.
155, 369–385.
He, H.S., Mladenoff, D.J., 1999. Spatially explicit and stochastic
simulation of forest-landscape fire disturbance and
succession. Ecology 80, 81–99.
Hunter Jr., M.L., 1990. Wildlife, Forests, and Forestry: Principles of
Managing Forests for Biological Diversity. Prentice Hall,
Englewood Cliffs, NJ, USA, 370 pp.
Hunter Jr., M.L., Calhoun, A., 1996. A triad approach to land-use
allocation. In: Szaro, R.C., Johnston, D.W. (Eds.), Biodiversity in
Managed Landscapes: Theory and Practice. Oxford University
Press, New York, pp. 477–491.
Johnson, E.A., Miyanishi, K., Weir, J.M.H., 1998. Wildfires in the
western Canadian boreal forest: landscape patterns and
ecosystem management. J. Veg. Sci. 9, 603–610.
Johnson, E.A., Van Wagner, C.E., 1985. The theory and use of two
fire history models. Can. J. For. Res. 15, 214–220.
Kenny, D.A., Judd, C.W., 1986. Consequences of violating the
independence assumption in analysis of variance. Psychol.
Bull. 99, 422–431.
Kneeshaw, D.D., Leduc, A., Drapeau, P., Gauthier, S., Paré, D.,
Carignan, R., Doucet, R., Bouthillier, L., Messier, C., 2000.
Development of integrated and ecological standards of
sustainable forest management at an operational scale. For.
Chron. 76, 481–493.
Landres, P.B., Morgan, P., Swanson, F.J., 1999. Overview of the use
of natural variability concepts in managing ecological
systems. Ecol. Appl. 9, 1179–1188.
57
Lefort, P., Gauthier, S., Leduc, A., Bergeron, Y., Grondin, P., Fortin,
M.-J., 2000. Étude de l’impact des facteurs physiographiques
sur les feux de forêt en milieu boréal et analyse spatiale de
l’homogénéité du régime de feux, MRNQ, Direction de la
forêt.
Legendre, P., Legendre, L., 1998. Numerical Ecology. Elsevier
Science BV, Amsterdam, 853 pp.
Lertzman, K., Fall, J., Dorner, B., 1998. Three kinds of
heterogeneity in fire regimes: at the crossroads of fire history
and landscape ecology. Northwest Sci. 72, 4–23.
Lieffers, V.J., Macmillan, R.B., MacPherson, D., Branter, K., Stewart,
J.D., 1996. Semi-natural and intensive silvicultural systems for
the boreal mixedwood forest. For. Chron. 72, 286–292.
Lindenmayer, D.B., Franklin, J.F., 2002. Conserving Forest
Biodiversity. A Comprehensive Multiscaled Approach. Island
Press, Washington, DC, 351 pp.
MacLean, D.A., 1990. Impact of forest pests and fire on stand
growth and timber yield: implications for forest management
planning. Can. J. For. Res. 20, 391–404.
Messier, C., Fortin, M.-J., Schmiegelow, F., Doyon, F., Cumming,
S.G., Kimmins, J.P., Seely, B., Welham, C., Nelson, J., 2003.
Modelling tools to assess the sustainability of forest
management scenarios. In: Burton, P.J., Messier, C., Smith,
D.W., Adamowicz, W.L. (Eds.), Towards Sustainable
Management of the Boreal Forest. NRC Research Press,
Ottawa, Canada, pp. 531–580.
Messier, C., Kneeshaw, D.D., 1999. Thinking and acting differently
for sustainable management of the boreal forest. For. Chron.
75, 929–938.
Ministère des Ressource naturelles et Faune
Québec, 2003. De l’information forestière à grande échelle. URL:
http://www.mrnfp.gouv.qc.ca/forets/fimaq/information/fimaqinformation.jsp (accessed June
2005).
Mladenoff, D.J., 2004. LANDIS and forest landscape models. Ecol.
Model. 180, 7–19.
Mladenoff, D.J., Baker, W.L. (Eds.), 1999. Spatial Modeling of Forest
Landscape Change: Approaches and Applications. Cambridge
University Press, Cambridge, U.K., p. 352.
Mladenoff, D.J., White, M.A., Pastor, J., Crow, T.R., 1993. Comparing
spatial pattern in unaltered old-growth and disturbed forest
landscapes. Ecol. Appl. 3, 294–306.
Pennanen, J., 2002. Forest age distribution under mixed-severity
fire regimes—a simulation-based analysis for middle boreal
Fennoscandia. Silva Fenn. 36, 213–231.
Pennanen, J., Greene, D.F., Fortin, M.-J., Messier, C., 2004. Spatially
explicit simulation of long-term boreal forest landscape
dynamics: incorporating quantitative stand attributes. Ecol.
Model. 180, 195–209.
Pothier, D., Savard, F., 1998. Actualisation des tables de production
pour les principales espèces forestières du Québec. Ministère
des ressources naturelles, Forêt Québec, Québec City,
184 pp.
Rogers, P., 1996. Disturbance ecology and forest management: a
review of the literature. General Technical Report No.
INT-GTR-336, USDA Forest Service, 16 pp.
SAS Institute, 1999. SAS Procedures Guide, Version 8, SAS
Institute, Inc., Cary, NC.
Spies, T.A., Ripple, W.J., Bradshaw, G.A., 1994. Dynamics and
pattern of a managed coniferous forest landscape in Oregon.
Ecol. Appl. 4, 555–568.
Sturtevant, B.R., Gustafson, E.J., He, H.S., 2004. Modelling
disturbance and succession in forest landscapes using
LANDIS: introduction. Ecol. Model. 180, 1–5.
Turner, M.G., Gardner, R.H., Dale, V.H., O’Neill, R.V., 1989.
Predicting the spread of disturbance across heterogeneous
landscapes. Oikos 55, 121–129.
Van Wagner, C.E., 1978. Age-class distribution and the forest fire
cycle. Can. J. For. Res. 8, 220–227.
58
e c o l o g i c a l m o d e l l i n g 2 0 0 ( 2 0 0 7 ) 45–58
Van Wagner, C.E., 1983. Simulating the effect of forest fire on
long-term annual timber supply. Can. J. For. Res. 13, 451–457.
Wallin, D.O., Swanson, F.J., Marks, B., 1994. Landscape pattern
response to changes in pattern generation rules: land-use
legacies in forestry. Ecol. Appl. 4, 569–580.
Wallin, D.O., Swanson, F.J., Marks, B., Kertis, J., Cissel, J., 1996.
Comparison of managed and pre-settlement landscape
dynamics in forests of the Pacific Northwest, U.S.A. For. Ecol.
Manage. 85, 291–310.