Development of the gap model ZELIG-CFS to predict the dynamics of North American mixed forest types with complex structures

Ecological Modelling 222 (2011) 2570–2583 Contents lists available at ScienceDirect Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel Development of the gap model ZELIG-CFS to predict the dynamics of North American mixed forest types with complex structures Guy R. Larocque ∗ , Louis Archambault, Claude Delisle Natural Resources Canada, Canadian Forest Service, Laurentian Forestry Centre, 1055 du P.E.P.S., P.O. Box 10380, Stn. Ste-Foy, Quebec, QC G1V 4C7, Canada a r t i c l e i n f o Article history: Available online 6 October 2010 Keywords: Forest dynamics Succession Historical data Gap models Survival rate Individual-based models (IBM’s) a b s t r a c t When the development of gap models began about three decades ago, they became a new category of forest productivity models. Compared with traditional growth and yield models, which aim at deriving empirical relationships that best fit data, gap models use semi-theoretical relationships to simulate biotic and abiotic processes in forest stands, including the effects of photosynthetic active radiation interception, site fertility, temperature and soil moisture on tree growth and seedling establishment. While growth and yield models are appropriate to predict short-term stemwood production, gap models may be used to predict the natural course of species replacement for several generations. Because of the poor availability of historical data and knowledge on species-specific allometric relationships, species replacement and death rate, it has seldom been possible to develop and evaluate the most representative algorithms to predict growth and mortality with a high degree of accuracy. For this reason, the developers of gap models focused more on developing simulation tools to improve the understanding of forest succession than predicting growth and yield accurately. In a previous study, the predictions of simulations in two southeastern Canadian mixed ecosystem types using the ZELIG gap model were compared with long-term historical data. This exercise highlighted model components that needed modifications to improve the predictive capacity of ZELIG. The updated version of the model, ZELIG-CFS, includes modifications in the modelling of crown interaction effects, survival rate and regeneration. Different algorithms representing crown interactive effects between crowns were evaluated and species-specific model components that compute individual-tree mortality probability rate were derived. The results of the simulations were compared using long-term remeasurement data obtained from sample plots located in La Mauricie National Park of Canada in Quebec. In the present study, three forest types were studied: (1) red spruce-balsam fir-yellow birch, (2) yellow birch-sugar maplebalsam fir, and (3) red spruce-balsam fir-white birch mixed ecosystems. Among the seven algorithms that represented individual crown interactions, two better predicted the changes in basal area and individualtree growth: (1) the mean available light growing factor (ALGF), which is computed from the proportion of light intercepted at different levels of individual crowns adjusted by the species-specific shade tolerance index, and (2) the ratio of mean ALGF to crown width. The long-term predicted patterns of change in basal area were consistent with the life history of the different species. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. 1. Introduction Much effort has been devoted to developing forest gap models in the last few decades. Researchers and forest managers have used this class of individual-tree models to examine different forest successional pathways and evaluate the effects of different types of disturbances (Keane et al., 2001; Pabst et al., 2008). These efforts were partially justified by the increasing importance given to the maintenance of ecological sustainability of forest ecosystems or the application of the basic principles of forest ecosystem manage- ∗ Corresponding author. Tel.: +1 418 648 5791; fax: +1 418 648 5849. E-mail address: Guy.Larocque@NRCan.gc.ca (G.R. Larocque). ment (see Landsberg, 2003; Canham et al., 2004; Pabst et al., 2008; Taylor et al., 2009). In particular, Taylor et al. (2009) mentioned that sound management planning should consider the impacts of different practices on forest dynamics for periods as long as 200 years. Until recently, forest managers relied nearly exclusively on traditional growth and yield models to fulfill their growth prediction needs. These models can be as simple as traditional growth and yield tables or as complex as the Forest Vegetation Simulator (FVS) (see Lacerte et al., 2006; Havis and Crookston, 2008). However, growth and yield models generally focus on the prediction of the dominant commercial tree species of merchantable size within forest stands. The majority of them were developed for evenaged pure stands and they are less flexible to predict the growth of uneven-aged mixed stands with different age cohorts or com- 0304-3800/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2010.08.035 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 plex stand structures (Canham et al., 2004; Larocque, 2008; Pabst et al., 2008). Also, the level of confidence in their predictions is limited to the range of the data used for their derivation (Yaussy, 2000; Porté and Bartelink, 2002). In particular, they assume that environmental conditions, such as climate or soil fertility, will not change in the future (Johnsen et al., 2001; Canham et al., 2004; Peng and Wen, 2006). As it is likely that environmental conditions will change and more emphasis will be put on the management of complex stands, models that include representations of tree and stand growth mechanisms will have more flexibility to deal with these issues. In this regard, gap models, which can be considered semimechanistic, have the potential to deal with complex stands. Also, the majority of gap models were designed to facilitate their calibration for different forest types in various site conditions (Bartelink, 2000; Bugmann, 2001; Keane et al., 2001) and predict the dynamics and succession of stands with complex structures, as they simulate tree mortality, treefall gaps and regeneration establishment (Botkin, 1993; Peng and Wen, 2006; Pabst et al., 2008). Among the different gap models that have been developed in the last two decades, the ZELIG model (Urban, 1990, 2000; Urban et al., 1991) has been used to simulate the dynamics or successional pathways of several forest ecosystem types. Recent examples can be found in Jiang et al. (1999), Yaussy (2000), Seagle and Liang (2001), Robinson and Monserud (2003), Song and Woodcock (2003), Larocque et al. (2006) and Pabst et al. (2008). ZELIG is a descendant of the JABOWA (Botkin et al., 1972) and FORET (Shugart and West, 1977) gap models, but several modifications were made, particularly to the structure. For instance, relative to JABOWA and FORET, the stratification of the species-specific shade tolerance classes was increased from two to five. Other models were derived from ZELIG. Sirois et al. (1992) used ZELIG as a template to develop FOREST-TUNDRA to simulate the dynamics of the transition from forest to tundra in northeastern Canada. Despite the fact that ZELIG has been recognized for making realistic predictions, several studies concluded that improvements were desirable for some components, such as mortality rate and regeneration establishment (Larocque et al., 2006; Pabst et al., 2008) or crown interactions (Larocque et al., 2006). This conclusion is in agreement with the long-recognized observation that few studies have been conducted to test the algorithms used in gap models (see Keane et al., 2001). The main reason that may explain this situation is the lack of long-term historical data to evaluate the performance of gap models. This has been recognized for several years (e.g., Botkin et al., 1972; Wein et al., 1989; Shugart and Smith, 1996; Lindner et al., 1997) and remains a correct assessment of the situation (Didion et al., 2009). For this reason, there are very few studies that utilized long-term data to compare gap model predictions with observations, such as those by Lindner et al. (1997), Yaussy (2000), Badeck et al. (2001), Risch et al. (2005), Larocque et al. (2006), Pabst et al. (2008) or Didion et al. (2009). However, the lack of historical data has also been an issue for the development of algorithms. In particular, the modelling of mortality has suffered from the lack of appropriate data in comparison with the availability of growth data, which is critical for the modelling of community dynamics (Keane et al., 2001). As a consequence, several model components were developed on the basis of realistic assumptions applicable to many species (Pacala et al., 1993; Shugart, 1998), but not necessarily accurate. The crown interaction model components used in several gap models are among the algorithms that have seldom been tested. According to Purves et al. (2007), the approaches used in gap models are relatively simple and do not integrate sufficient plasticity, which may lead to representation of canopy interactions incompatible with observations. For instance, in ZELIG, a grid square network conceptually defines the potential area occupied by each dominant tree within a forest (Urban et al., 1991; Coffin and Urban, 1993). 2571 This potential area, considered as a zone of influence, represents the typical gap size that a tree creates when it dies (Urban and Shugart, 1992). Using this system, there is no direct interaction among individual trees: each tree affects the environment within its zone of influence and the aggregation of the zones of influence become the constraints that define the competitive environment. Thus, the size of the zones of influence or gaps have an effect on stemwood production and demographics (e.g., Urban et al., 1991; Coffin and Urban, 1993; Larocque et al., 2006). In particular, Larocque et al. (2006) observed that the optimal size of the zones of influence differed among species. The first objective of the present study was to introduce a modified version of ZELIG, ZELIG-CFS, which was developed using different algorithms for crown interaction effects and prediction of mortality rate and regeneration. In particular, the original crown interaction algorithm of ZELIG was compared with new algorithms. The second objective was to evaluate how well the predictions from ZELIG-CFS agreed with long-term observations in three forest ecosystem types of southeastern Canada that included yellow birch (Betula alleghaniensis Britton), red spruce (Picea rubens Sarg.), white birch (Betula papyrifera Marsh.), balsam fir (Abies balsamea (L.) Mill.), red maple (Acer rubrum L.), northern white-cedar (Thuja occidentalis L.), sugar maple (Acer saccharum Marsh.) and beech (Fagus grandifolia Ehrh.) in the dominant cohort. 2. Materials and methods 2.1. Description of ZELIG-CFS ZELIG-CFS is a modified version of the original ZELIG model, the development of which was derived by retaining the core structure of JABOWA and FORET (Urban, 1990, 2000; Urban et al., 1991). This type of gap model simulates, on an annual time step, inter-tree competition, single-tree mortality and the effects of light interception, site fertility, temperature and precipitation on tree growth and seedling establishment. As these models include representations of species-specific ecological characteristics and of basic forest ecosystem processes, they are well suited to simulate the dynamics and succession of mixed uneven-aged forest ecosystems with complex structures (Larocque, 2008). Despite several modifications, ZELIG-CFS retains the same basic framework as ZELIG with respect to most of the basic fundamental relationships and the computational order of variation in climatic conditions, mortality, tree growth, regeneration and update of the main state variables. For instance, the predicted dbh tree growth rate relationship, based on species-specific potential growth rate reduced by limiting site factors, was kept in ZELIG-CFS. The potential growth rate represents the maximum dbh growth rate that a species can achieve under optimal conditions. Limiting site factors are modelled using dimensionless multiplicative functions ranging between 0 and 1. Ecological differences among species are represented by tolerance classes: 5 for shade tolerance (tolerant to intolerant), 3 for soil fertility (responsive to stress tolerance) and 5 for soil moisture (drought tolerant to intolerant). For each species, the temperature effect on growth rate is modelled using a parabolic equation constrained by its minimum and maximum growing degree-days within its area of distribution. Thus, the effect of local temperature on growth is computed by scaling the site-specific growing degree-days relative to minimum and maximum growing degree-days. Species differentiation with respect to potential growth rate, degree-days and limiting site factors are provided as input using the values in Table 1. ZELIG-CFS is characterized by a complex structure with many model sub-components, but a simple conceptual diagram can be used to illustrate its main features (Fig. 1). In the initialization component, physical site data, monthly temperature and precipitation 2572 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 Table 1 Allometric and ecological parameters provided to ZELIG-CFS for tree species included in the three forest types located in southeastern Canada. Species Maximum age (year) Red spruce Yellow birch Balsam fir White birch Red maple Sugar maple American beech Northern white-cedar 400 250 200 140 150 300 366 400 Maximum dbh (cm) 100.0 150.0 65.0 70.0 80.0 110.0 100.0 100.0 Maximum height (m) 35 45 30 30 30 44 37 29 Growth rate scaling coefficient 100 100 69 160 176 89 72 55 Growing degree-days Minimum Maximum 500 1420 250 700 1260 1204 1327 1000 2580 3084 2404 2500 6601 3200 5556 2188 Shadea tolerance class Maximumb drought tolerance Fertilityc class 1 3 1 4 2 1 1 2 2 2 1 3 3 2 2 4 3 2 3 3 3 2 2 3 Adapted from http://ecobas.org/www-server/rem/mdb/zelig.html and Botkin et al. (1972). a Rank: 1 = very shade-tolerant; 5 = very intolerant. b Rank: 1 = very drought intolerant; 5 = very drought tolerant. c Rank: 1 = nutrient stress intolerant; 3 = nutrient stress tolerant. values, species-specific ecological characteristics and individualtree dbh data are read to initialize the simulations. Then, the annual changes are computed in the following order: (1) generation of random fluctuations in monthly climatic conditions, (2) prediction of individual-tree dynamics (mortality and growth), (3) prediction of seedling establishment and sapling development, (4) update of forest characteristics, such as leaf area index or basal area, and (5) recording of the main state variables. These repetitive computations are conducted for the number of annual cycles requested. Among the modifications in ZELIG-CFS, two were related to the modelling of available light growing factor (ALGF) and crown recession rate on dbh growth, which are essential components for the computation of limiting factors. In the original version of ZELIG, it was assumed that leaf area was distributed equally with canopy depth. In ZELIG-CFS, the variation in leaf area distribution with canopy depth is computed using a sigmoidal cumulative leaf area distribution function, an approach compatible with the findings of Yang et al. (1993, 1999), Baldwin et al. (1997) and Larocque (2002). The modelling of realistic representation of foliage distribution was Fig. 1. Basic conceptual diagram of the ZELIG-CFS gap model. important to improve the prediction of light variation with crown depth, which is essential for the evaluation of crown recession rate. When crown recession takes place due to reduction in understory light, the subsequent change in crown width is adjusted by considering species-specific crown shape functions: (1) a parabolic function for red spruce, red maple and northern white-cedar, (2) an ellipsoid function for yellow and white birches, sugar maple and beech, and (3) a conical function for balsam fir. The ALGF expresses the effect of light extinction on tree growth and is computed from the top to the bottom of individual-tree crowns. It is a function of the amount of available light in a given crown section adjusted by the species-specific shade tolerance class. For any crown section, ALGF is computed using a negative exponential model based on the Beer-Lambert Law, but with coefficients that take into account the species-specific shade tolerance class in the computation of light extinction. Thus, for any available light intensity, ALGF increases from very intolerant to very tolerant species, but differences among shade tolerance classes increase with decrease in available light. In ZELIG, ALGF is computed at 1 m height intervals (which is also the interval for the computation of both leaf area and available-light profiles), summed and divided by (crown length + 1). In ZELIG-CFS, leaf area, available-light profiles and ALGF were computed at 0.5 m height intervals and different algorithms for the computation of the ALGF effect on tree growth were tested: Mean(ALGF) (1) Mean(ALGF) crown length (2) Mean(ALGF) crown projection (3) Mean(ALGF) crown width (4) Mean(ALGF) leaf area (5) Sum(ALGF) crown length (6) Sum(ALGF) leaf area (7) Mean(ALGF) and Sum(ALGF) are the average and sum of the ALGF values, respectively, computed from the different crown sections at 0.5 m height intervals. Algorithms 2 and 6 adjust the ALGF values relative to the vertical space occupied by the crowns. For algorithms 3 and 4, the adjustment is expressed relative to the horizontal space occupied by the crowns. Algorithms 5 and 7 may be considered as specific values that summarize the ALGF values per unit of leaf area. G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 2573 Table 2 Basic statistics of the data used to compute survival rates for each species in the forest ecosystems under study. The new dataset developed was used to derive the parameters of the survival rate models as a function of dbh and dbh growth rate. Range of variation Species Dbh (cm) Dbh growth rate (cm) Survival rate modelsa Red spruce (10.0–55.0) (0–0.7) SR = 1.0042 − Yellow birch (10.0–80.0) (0–1.2) SR = 0.9959 − Balsam fir (10.0–40.0) (0–1.1) SR = 0.9858 − White birch (10.0–55.0) (0–1.2) SR = 0.9991 − Red maple (10.0–55.0) (0–1.4) SR = 0.9955 − Sugar maple (10.0–65.0) (0–1.4) SR = 0.9954 − American beech (10.0–50.0) (0–1.1) SR = 1.0089 − Northern white-cedar (10.0–80.0) (0–1.5) SR = 0.9968 − a SR: Survival rate; dbh: diameter at breast height; dgr: dbh growth rate (mm year−1 ). Simulations were conducted using algorithms 1–7. The predictions of change in basal area over time and individual-tree growth rate using the different algorithms were compared with observed data described below. The mortality model component was also considerably modified. In ZELIG, mortality may be natural or result from stress due to site factors or suppression. In both cases, it is modelled as a stochastic event. For natural mortality, ZELIG assumes that only 1% of trees reach maturity. Also, its rate remains constant with age. Thus, natural mortality is adjusted by the maximum age of each species. Mortality caused by stress concerns the trees with a diameter growth rate that is below 10% of their potential growth rate or less than 1 mm for 2 or more consecutive years. Even though this approach may appear biologically realistic, it is not necessarily the most accurate approach for the prediction of demographics, which is an issue previously identified (Larocque et al., 2006). Also, a problem with this approach is that it does not consider differences among species in the degree of tolerance to slow growth rate before triggering mortality (Wyckoff and Clark, 2002). For these reasons, an approach based on the derivation of species-specific singletree survival rate using historical data was used in ZELIG-CFS. The dataset, maintained by the ministère des Ressources naturelles et de la Faune du Québec, consisted of 54,818 individual trees from 1036 remeasured permanent sample plots located in large forest regions (Table 2). The methodology proposed by Buchman (1983, 1985) and Buchman et al. (1983) was used to compute survival rate. Data for each species were partitioned into classes of 5 cm in dbh and 1 mm year−1 in dbh growth rate. Once the matrix was established, the survival rate of each combination of dbh and dbh growth rate classes was computed using the formula:   Xi SURV =  i i Ni  N i i ⁄  i i•Ni (8) where SURV is the annual survival rate, Ni and Xi the number of trees alive at the beginning and the end of the time interval between two measurements, respectively, and i the interval length between two measurements. The derivation of species-specific survival rate models as a function of dbh and dbh growth rate resulted in model forms similar to those derived by Buchman (1983, 1985) and Buchman et al. (1983) (Table 2). All the models derived were      1+exp2.2534+0.5329 √ dgr+0.0768dbh   1 2 −4 1+exp2.8399+1.0438dgr+2.21×10 (dbh−1) 1 1+exp2.8570+0.5820dgr−6.70×10 −4 (dbh−1)2 1 2 −4 1+exp3.1495+0.7697dgr+3.51×10 (dbh−1) 1 1+exp2.0642+0.7878dgr+0.0306dbh   1 1     2.3021+19.6667(dgr/dhp)+0.0685dbh−9.5×10−3 dhp2 1+exp 1 2 1+exp3.6398+0.9899(dgr/dhp)  1 1+exp2.5219+1.3306dgr+0.0386dbh   based on the sigmoidal function, but the order of the independent variables changed a little among species to ensure that the speciesspecific patterns of change in survival rate would be adequately represented. The other major modifications were related to the zone of influence and regeneration establishment. In ZELIG, a zone of influence is assigned to every tree. This zone is a conceptual representation of the space where trees uptake and compete for site resources. Its area, which is the same for all the species, can be as small as a typical forest gap or as large as a plot and affects seedling establishement and mortality (Larocque et al., 2006). In ZELIG-CFS, trees grow within a forest community that may be variable in area. This area must be provided as input and may coincide with the size of a sample plot. For regeneration, ZELIG-CFS computes a potential number of seedlings that can germinate under the prevalent site conditions, including understory light, but adjusted by a stocking factor. The stocking factor is an estimate of the proportion of the area that the seedlings of a species may occupy and must be provided as input. It is highly variable among species within a forest community. This modification is in agreement with Price et al. (2001) who mentioned that the assumption of uniformity in regeneration niches in gap models was not realistic for many species in temperate forests. They suggested that gap models should better represent spatial heterogeneity in this respect. 2.2. Study area and forest types Historical data of forest ecosystems located in the Lake Edward Experimental Forest (LEEF) were used for the present study to compare predictions from ZELIG-CFS with observations (Table 3). This experimental forest is located within the limits of La Mauricie National Park (46◦ 45′ N, 72◦ 56′ W), a national park maintained by the Government of Canada. The landscape includes different configurations that vary between moderate hills and mountains as high as 431 m. According to Rowe (1972), the park is within the Great Lakes-St. Lawrence forest region. The climate type is continental. Winter conditions occur between November and April and are characterized by temperature conditions below 0 ◦ C and regular snowfalls. During the summer, air temperature is generally above 20 ◦ C. The growing season lasts between 160 and 170 days with growing degree-days that vary between 2000 and 2600. Total 2574 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 Table 3 Summary of ecological characteristics and tree statistics for the dominant species of the three forest types under study. Forest type RSYB (O–Co) (n = 15) SMYB (Vi–O) (n = 5) RSWB (Co) (n = 13) Main species Red spruce (Picea rubens Sarg.) Balsam fir (Abies balsamea (L.) Mill.) Yellow birch (Betula alleghaniensis Britton) White birch (Betula papyrifera Marsh.) Yellow birch Sugar maple Balsam fir Red spruce Red spruce Balsam fir White birch Associated species Red maple (Acer rubrum L.) Sugar maple (Acer saccharum Marsh.) American beech (Fagus grandifolia Ehrh.) Eastern hemlock (Tsuga canadensis (L.) Carr.) Northern white-cedar (Thuja occidentalis L.) Mountain maple (Acer spicatum Lamb.) White birch Mountain maple Red maple American beech Northern white-cedar Yellow birch Red maple Sugar maple Northern white-cedar Deposit Humus types Humus thickness (cm) Common soil texture (B horizon) Undifferentiated till Mor, moder 9.0 ± 0.4 Loamy sand Undifferentiated till Mor, moder 12 ± 1.5 Loamy sand, sandy loam Undifferentiated till Mor, moder 7 ± 0.5 Loamy sand, sandy loam Dbh range (cm) Balsam fir Red spruce Yellow birch Sugar maple White birch (2.5–37.7)a (2.5–48.4) (2.5–53.3) (2.5–36.2) (2.5–43.1) (2.5–33.0) (2.5–43.2) (2.5–76.9) (2.5–44.7) (5.1–30.8) (0.5–34.0) (0.5–53.6) (0.7–76.2) – (0.7–38.1) a Minimum and maximum values observed between the first and most recent measurements. annual precipitation ranges between 900 and 1000 mm (Robitaille and Saucier, 1998). The LEEF has a long history of implementation and repeated measurements. It is one of the unique historical datasets in Canada. The first sample plots were established by the Canadian Government in 1918 to monitor growth, regeneration following harvesting and mortality (Hatcher, 1959; Archambault et al., 2003). Different problems were identified within the limits of the LEEF: insufficient softwood regeneration, increase in hardwood regeneration and competition from mountain maple (Acer spicatum Lamb.) and other non-commercial hardwoods. Additional sample plots of 404 m2 were established in 1936 in forest types that were representative of the regional forests. The grid network that was implemented contained 343 sample plots that were separated by a distance of about 200 m. Successive measurements were completed in 1936, 1946, 1956, 1967, 1994 to 1996, 2001–2007 and 2009. However, since 1994, approximately half of the original sample plots have been remeasured. Three forest types were examined for the present study: red spruce-balsam fir-yellow birch (RSYB), yellow birchsugar maple-balsam fir (SMYB) and red spruce-balsam fir-white birch (RSWB) (Table 3). Before 1994, all the trees larger than 1.3 cm in dbh within sample plots were simply tallied by 2.54 cm (1 in.) dbh classes. When the plots were reactivated in 1994, individual trees were tagged to ensure that repeated measurements could be retrieved at the individual-tree level. Even though the above dataset contains rich information, its use for comparing predictions and observations was limited to stand statistics per species, such as basal area, of the following species: yellow birch, red spruce, white birch, balsam fir, red maple, northern white-cedar, sugar maple and beech. An additional dataset was used to compare individual-tree dbh growth rate predicted by ZELIG-CFS with observations. This dataset, developed at the Faculté de foresterie, de géographie et de géomatique of Université Laval and at the ministère des Ressources naturelles et de la Faune du Québec, Direction de la recherche forestière,1 consisted of ring width data obtained from boring cores sampled at breast 1 The development of this dataset was conducted by Dr. Jean Bégin, professor at Université Laval, and Dr. Mathieu Fortin, forest researcher at the Direction de la recherche forestière, ministère des Ressources naturelles et de la Faune du Québec. height in trees growing in sample plots within the SMYB forest type (Table 4). To initialize the simulations, ZELIG-CFS requires individual-tree dbh data. Thus, the dbh data at the first measurement (1936 or 1946) of the permanent sample plots described in Table 3 were used to initialize the simulations for 200 years using a 1-year time step. The predictions of basal area for each forest type were compared with observations by plotting the changes over time from the simulations of individual permanent sample plots (see Table 3) (means and standard errors). Observed and predicted individualtree dbh growth rates for the SMYB forest type were plotted by 1 cm dbh classes. For dbh distribution, stand densities were computed by 10 cm dbh classes. For the 5 cm dbh class, the smallest dbh was 2.5 cm. Then, bar charts were drawn for each corresponding year of observed data. 3. Results 3.1. Comparing predicted and observed basal areas Among the seven crown interaction algorithms that were tested, Mean(ALGF) was among the algorithms that showed fairly low average differences between observed and predicted basal areas for the greatest number of species within the three forest types (Table 5). For the other algorithms, the amplitudes of differences were similar or greater, but there was substantial variation among Table 4 Basic statistics of the ring width data measured from boring cores sampled in the yellow birch-sugar maple-balsam fir forest type that were used to evaluate how well ZELIG-CFS predicted individual-tree dbh growth rate. Species Dbh range (cm) Dbh growth rate range (mm year−1 ) Red spruce Yellow birch Balsam fir White birch Red maple Sugar maple Northern white-cedar (2.4–48.2)a (2.4–43.2) (2.4–38.54) (2.4–27.8) (2.4–32.3) (2.4–20.5) (2.4–30.9) (0.04–5.7) (0.1–4.9) (0.04–6.8) (0.1–6.7) (0.1–5.9) (0.1–5.9) (0.1–3.7) a Minimum and maximum. n 7037 1326 5501 3199 2359 464 675 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 2575 Table 5 Average differences (m2 ha−1 ) between observed and predicted basal area for the seven crown interaction algorithms that were tested and each species in the three forest types. Species Mean (ALGF) Red spruce-balsam fir-yellow birch (RSYB) Yellow birch 0.1 Red spruce 1.2 White birch 2.2 Balsam fir 0.9 Red maple 0.7 Northern white-cedar 0.6 Yellow birch-sugar maple-balsam fir (SMYB) 1.7 Yellow birch Red spruce 3.0 1.7 White birch Balsam fir 0.7 Sugar maple 2.9 2.7 Beech Red spruce-balsam fir-white birch (RSWB) 0.5 Yellow birch Red spruce 3.0 1.1 White birch 0.1 Balsam fir 0.4 Red maple Northern white-cedar 2.1 Mean(ALGF)/ CRLEN Mean(ALGF)/ CRPROJ Mean(ALGF)/ CRWID Mean(ALGF)/ leaf area Sum(ALGF)/ CRLEN Sum(ALGF)/ leaf area 1.8 9.9 0.7 5.6 0.8 2.2 2.0 4.8 0.8 2.2 0.7 1.3 1.6 3.1 0.2 1.4 1.0 1.5 1.5 6.0 0.3 2.2 1.0 1.6 0.1 7.2 6.2 1.0 0.6 0.5 1.2 0.5 0.5 7.0 0.5 0.8 3.0 23.6 0.3 3.7 3.5 1.6 1.2 0.4 0.3 0.1 3.6 2.9 0.3 0.0 0.1 0.5 3.2 2.3 0.4 0.4 0.2 0.8 3.5 2.9 2.7 5.2 5.6 1.8 1.3 2.6 0.1 1.2 0.4 1.3 2.5 2.4 0.5 8.9 0.1 1.0 0.5 1.8 0.1 10.7 0.2 0.7 0.5 1.8 0.7 7.1 0.3 0.5 0.5 1.8 0.7 12.6 0.1 1.0 0.5 2.0 0.4 14.8 4.5 0.1 0.0 1.1 0.6 4.6 0.1 5.9 0.0 1.8 ALGF: Available light growing factor; CRLEN: crown length; CRPROJ: crown projection: CRWID: crown width. species and forest types. For instance, using the ratio of Mean(ALGF) to crown projection, relatively small differences were obtained for some species, but differences were more pronounced for other species, such as red spruce in RSYB and RSWB and sugar maple in SMYB. Three of the algorithms showed relatively close differences between predictions and observations for several species: the ratios of Mean(ALGF) to crown width, Mean(ALGF) to leaf area and Sum(ALGF) to leaf area. The ratio of Mean(ALGF) to crown length was characterized by relatively high differences between predictions and observations for red spruce in the three forest types and balsam fir in RSYB and SMYB. For conciseness, the long-term comparisons between observations and predictions at different ages are shown for only three algorithms (Figs. 2–4). Mean(ALGF) and the ratio of Mean(ALGF) to crown width were selected because they had fairly small average differences between observations and predictions for most species. For comparison purposes, the ratio of Sum(ALGF) to crown length was included because it is identical to the original algorithm in ZELIG. In the long-term simulations, the algorithm Mean(ALGF) indicated good agreement between observations and predictions for yellow birch, red spruce and balsam fir in RSYB and RSWB (Figs. 2 and 4) and for balsam fir in SMYB, respectively (Fig. 3). A nearly perfect agreement was obtained for yellow birch in RSYB and red spruce and balsam fir in RSYB and RSWB, indicating that the long-term simulations were very consistent with observations. Basal area first declined and then increased for yellow birch in RSYB, steadily increased over time for red spruce, and regularly decreased over time for balsam fir. For yellow birch and balsam fir in SMYB (Fig. 3), mean differences between predictions and observations were more pronounced than in the other two forest types, but the large overlap between standard errors indicated that high proportions of observed and predicted basal areas at the plot level were very close, and the long-term pattern of change for predicted basal area was consistent with observations for both species. Relatively more pronounced differences were obtained for the other species with the algorithm Mean(ALGF). For sugar maple in SMYB, observations indicated a gradual increase in basal area (Fig. 3). Predicted basal area remained relatively constant during the entire simulations, but the high standard errors indicated a large overlap with observations. There was relatively good agreement between observed and predicted basal areas for red maple for the first 30 and 21 years in the simulations in RSYB and RSWB, respectively (Figs. 2 and 4). Then, ZELIG-CFS predicted a sharp decline in RSYB and its disappearance in RSWB. Observed basal area for northern white-cedar did not change very much in RSYB, but increased in RSWB (Figs. 2 and 4). There was a large degree of overlap between the standard errors for predictions and observations, which indicated close agreement between several observed and predicted basal areas at the plot level. The predicted long-term pattern of change in RSYB was consistent: ZELIG-CFS predicted more or less stable basal area during the first 67 years, consistent with observations, followed by a small decline. On the other hand, despite the relatively large degree of overlap between observations and predictions in RSWB, the patterns of change in the predictions diverged completely from the trends shown by the observations. There were relatively large differences between predictions and observations for white birch and beech (Figs. 2–4). For both species, the degree of overlap between their standard errors was generally small. Except for white birch in RSWB, the patterns of change for observed and predicted basal areas diverged over time. The results of the simulations using the algorithm based on the ratio of Mean(ALGF) to crown width indicated a significant improvement for white birch in the three forest types relative to the Mean(ALGF) algorithm (Figs. 2–4). There was a large degree of overlap between the standard errors of the predictions and observations and the patterns of change over time were consistent. There was also an improvement for red spruce in SMYB, but it was marginal for the first 21 years relative to the Mean(ALGF) algorithm (Fig. 3). For all the other species, differences between predictions and observations were generally greater than those obtained using the Mean(ALGF) algorithm, and the degrees of overlap between the standard errors were also generally smaller. Compared with the other two algorithms, the ratio of Sum(ALGF) to crown length did not perform as well in the prediction of basal area, except for northern white-cedar (Figs. 2 and 4). For both RSYB and RSWB, there was a large degree of overlap between the standard errors for northern white-cedar. While observations appeared to indicate relatively stable values for 67 2576 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 Fig. 2. Mean predicted and observed basal area (m2 ha−1 ) for species in the red spruce-balsam fir-yellow birch forest type (RSYB) using crown interaction algorithms based on mean available light growing factor, the ratio of mean available light growing factor to crown width and the ratio of the summation of available light growing factor to crown length. Error bars represent standard deviations. years, the predictions also suggested this trend, despite the small decline between years 50 and 100 in the simulations. On the other hand, the trend simulated in RSWB was not consistent with the observations, as ZELIG-CFS predicted its disappearance before year 100. 3.2. Predicted and observed dbh growth rates at the tree level For the comparison of observed and predicted individual-tree dbh growth rates, the algorithm based on Mean(ALGF) was used for yellow birch, red spruce, balsam fir, red maple, northern whitecedar and sugar maple, while the algorithm based on the ratio of Mean(ALGF) to crown width was used for white birch. The values for both observed and predicted dbh growth rates were averaged by 1 cm dbh classes. In general, there was a good agreement between observed and predicted dbh growth rates for most species (Fig. 5). On average the difference in absolute value between predictions and observations was 0.5 mm year−1 for yellow birch. Differences greater than 1 mm year−1 were found only in the 10.5, 11.5, 12.5, and 17.5 cm dbh classes. For red spruce, there was a very good agreement between observations and predictions between the 2.5 and 19.5 cm dbh classes, with an average difference of 0.24 mm year−1 . For the dbh classes greater than 19.5 cm, differences between predictions and observations increased gradually, despite fluctuations, and reached about 2 mm year−1 for the two greatest dbh classes. However, the large overlap between the standard errors for several dbh classes indicated that a good proportion of observed and predicted dbh growth rates at the tree level were relatively close. The majority of the differences between observed and predicted dbh growth rates for white birch were smaller than 1 mm year−1 (average = 0.5 mm year−1 ). It is only in the 24.5 and 25.5 cm dbh classes that differences were about 1 mm. For balsam fir, the majority of the absolute differences between observed and predicted dbh growth rates were smaller than 1 mm year−1 . Large discrepancies were obtained only for the dbh classes between 26.5 and 29.5 cm. For most of the dbh classes, predictions and observations differed by less than 1 mm year−1 for red maple. It is only for the three greatest dbh classes that substantial differences were observed. For northern white-cedar, very close agreement between observations and predictions was obtained between the 8.5 and 11.5 cm dbh classes. Differences of about 1 mm year−1 were obtained for the 3.5, 16.5 and 17.5 cm dbh classes. Compared G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 2577 Fig. 3. Mean predicted and observed basal area (m2 ha−1 ) for species in the yellow birch-sugar maple-balsam fir forest type (SMYB) using crown interaction algorithms based on mean available light growing factor, the ratio of mean available light growing factor to crown width and the ratio of the summation of available light growing factor to crown length. Error bars represent standard deviations. with the other species, relatively large differences between predictions and observations were observed for sugar maple, averaging 0.85 mm year−1 . The two largest dbh classes had the greatest differences between observations and predictions. 3.3. Comparing observed and predicted stand densities For conciseness, the comparisons of observed and predicted stand densities are illustrated using only the results of the simulations based on the Mean(ALGF) algorithm (Fig. 6). For the three forest types, there was generally good agreement between observed and predicted mean stand densities for the dbh classes greater than 5 cm. The relatively large standard errors indicated that relatively close values between observations and predictions were obtained for several sample plots. For the 5 cm dbh class, good agreement between predicted and observed stand densities was obtained only in the first year of the simulation in the three forest types and in year 67 for RSYB. In general, differences between predicted and observed densities increased with time. A closer look at individual species changes in density indicated that the pronounced differences in the 5 cm dbh class were caused mainly by one species in each forest type. In RSYB, substantial differences were caused by balsam fir. Predicted densities were about 4, 10, and 9 times greater than observed densities at years 10, 31 and 67 in the simulations, respectively. Sugar maple was the cause of the substantial differences in SMYB. Relative to observed densities, predicted densities were about 7 times greater at years 10 and 21 in the simulations, but 59 times greater at year 67. In RSWB, the substantial differences were caused by red spruce. Predicted densities were about 3, 4, and 15 times greater than observed densities at years 21, 56 and 63 in the simulations, respectively. 4. Discussion The newly developed algorithms based on different formulations of ALGF improved the predictive capacity of ZELIG-CFS for most species, particularly the algorithm based on average ALGF for the dominant species, compared with the original algorithm used in ZELIG (the ratio of Sum(ALGF) to crown length). For some species, the simulations conducted using a particular algorithm appeared unrealistic. For instance, the use of the ratio of Sum(ALGF) to crown length predicted basal area as high as 100 m2 ha−1 for 2578 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 Fig. 4. Mean predicted and observed basal area (m2 ha−1 ) for species in the red spruce-balsam fir-white birch forest type (RSWB) using crown interaction algorithms based on mean available light growing factor, the ratio of mean available light growing factor to crown width and the ratio of the summation of available light growing factor to crown length. Error bars represent standard deviations. red spruce in RSYB and RSWB. This was the case also for white birch in SMYB using the same algorithm. The results of the present study also suggest that the coding development process must be flexible enough to take into account the fact that the most appropriate algorithm may vary among species. While the algorithm based on Mean(ALGF) was among the most appropriate ones for yellow birch, red spruce, balsam fir and red maple, the algorithm based on the ratio of Mean(ALGF) to crown width was more appropriate for white birch. For northern white-cedar and sugar maple, the Mean(ALGF) and Sum(ALGF)/crown length algorithms had about the same performance in terms of differences between predictions and observations. The fact that the algorithm based on the ratio of Mean(ALGF) to crown width performed very well for white birch can be explained by the high degree of shade intolerance of this species. Crown width in the ratio reflects the fact that the lateral crown development of this species is highly sensitive to reduction in light conditions and crowding, as is the case for any shade intolerant species. As previously mentioned, the mean(ALGF) algorithm was very efficient for red spruce and balsam fir for the forest types that were studied. There was nearly a perfect agreement between observations and predictions for both species in RSYB and RSWB (Figs. 2 and 4), while poorer agreement was obtained at year 58 for red spruce and at years 10 and 58 for balsam fir in SMYB (Fig. 3). The fact that poorer agreement was obtained for some simulated years in one forest type does not invalidate the Mean(ALGF) algorithm as an efficient algorithm, even though the ratio of Mean(ALGF) to crown width algorithm appeared to perform better (Fig. 3). The relatively poor agreement in only one forest type can probably be explained by other factors not captured by ZELIG-CFS and unnoticed in the observations. For instance, a possible factor may be unusual mortality of healthy trees due to windthrow. This type of unusual event may go unnoticed when there is a long period between successive measurements. In several gap models, the representation of variation in crown structure was greatly simplified (Shao et al., 2001; Didion et al., 2009). For instance, some gap models assume that the bulk of the foliage is concentrated in a ring at the top of the stems. ZELIG assumes that leaf area density is the same at all levels of the crowns. It is likely that the increase in the complexity of the representation of variation in the crown structure in ZELIG-CFS contributed to improving its predictive capacity. This observation is supported by the fact that two new algorithms (Mean(ALGF) and Mean(ALGF)/crown width) performed better than the origi- G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 2579 Fig. 5. Mean observed and predicted dbh growth rate for species in the red spruce-balsam fir-yellow birch forest type using a crown interaction algorithm based on mean available light growing factor for yellow birch, red spruce, balsam fir, red maple, northern white-cedar and sugar maple and the ratio of mean available light growing factor to crown width for white birch. nal algorithm of ZELIG (Sum(ALGF)/crown length) to predict basal area for several species. Also, these two algorithms predicted individual-tree dbh growth rate fairly accurately (Fig. 5). This type of modification, which introduces more species-specific differentiation, is supported by other studies that observed strong linkages between tree growth, shade tolerance and crown morphology (Chen et al., 1996; Wright et al., 1998; Claveau et al., 2002). In particular, the modifications in crown representation conducted by Didion et al. (2009) with the ForClim model, which were similar to the modifications in ZELIG-CFS, also contributed to improving accuracy in the predictions. However, a weakness in their approach is that the use of empirical relationships to represent the effect of crown recession on diameter increment limited the range of applicability for different forest site conditions. In general, the simulated long-term patterns of change in basal area of the different species are consistent with their biology. Red spruce, a shade-tolerant species that can live as long as 400 years (Blum, 1990), is an important species in the three forest types under study (Hatcher, 1954, 1959; Ménard, 1999; Archambault et al., 2003). Several studies concluded that it has an essential role in the maintenance of long-term stability when growing with other species, such as balsam fir (e.g., Ray, 1956; Busing and Wu, 1990; Amos-Binks et al., 2010), which may explain its regular increase in basal area. For balsam fir, ZELIG-CFS predicted a decline in the three forest types over the long term. This may appear surprising because it is considered a shade-tolerant species with a good seedling establishment rate (Tubbs and Houston, 1990) and as a climax species in these forest types. On the other hand, compared with red spruce, it has a slower growth rate and its maximum age is about half that of red spruce. Thus, as the life expectancy of balsam fir is much shorter than that of red spruce, it is more likely to have a higher mortality rate caused by natural senescence. These 2580 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 reasons may explain why red spruce in these mixed stands tends to increase its presence more than balsam fir. The predicted pattern is compatible with the observations of Amos-Binks et al. (2010) who observed the same long-term dynamics of both species in mixed stands. They suggested that forest stands with a large presence of balsam fir could, in fact, be in temporary transition. The results of the simulations for red spruce and balsam fir in the present study are consistent with those of El-Bayoumi et al. (1984) and Wein et al. (1989) obtained with the SMAFS gap model in similar forest types in eastern Canada. Their model also predicted the dominance of red spruce and a decline of balsam fir. They also explained this pattern by the long-lived nature of red spruce and concluded that balsam fir becomes a dominated species in the presence of red spruce. Regarding white birch, two algorithms predicted an increase in basal area over time, while the algorithm based on the ratio of average ALGF to crown width predicted a decrease early in the sim- Fig. 6. Comparison of observed (black) and predicted (gray) dbh distributions in the red spruce-balsam fir-yellow birch (RSYB) (a), yellow birch-sugar maple-balsam fir (SMYB) (b) and red spruce-balsam fir-white birch (RSWB) (c) forest types at different projection years. The numbers of trees per ha for dbh size classes greater than 15 cm are also plotted in smaller bar charts to facilitate visualization. Error bars represent standard deviations. G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 2581 Fig. 6. (Continued). ulations, followed by a stabilization. The pattern predicted using the ratio of Mean(ALGF) to crown width was more consistent with its life history. Compared with species such as red spruce or balsam fir, white birch is a short-lived intolerant transitional species (Safford et al., 1990). This implies that it may occupy a site for a certain period, particularly early in the succession, but gradually declines or even disappears to be replaced by more tolerant species. Except for the algorithm based on Mean(ALGF), the decline and disappearance of yellow birch were predicted by ZELIG-CFS. While its predicted decline was very fast in SMYB and RSWB, it was more gradual in RSYB. These patterns can be associated with the poor regeneration rates predicted by ZELIG-CFS over the long-term period (data not shown). Dominant yellow birch trees that lived for a long time were not replaced by other yellow birch trees in the subdominant cohorts. These results agree with previous observations made on yellow birch regeneration, which is characterized by both the difficulty of its seeds to germinate and of young seedlings to grow beyond the first few years (e.g., Bellefleur and Larocque, 1983; Houle and Payette, 1990; Roberts and Dong, 1993; Hewitt and Kellman, 2004). Red maple, northern white-cedar, sugar maple and beech were comparatively less present. The predicted decline and disappearance of red maple in both RSYB and RSWB is consistent with the observations of Smallidge and Leopold (1994), who concluded that it can disappear in forest ecosystems where red spruce is present. Predicted basal area for northern white-cedar either indicated a decline or remained stable. The fact that ZELIG-CFS predicted a gradual decline or a more or less stable presence is consistent with its life history. Northern white-cedar may be considered as a pioneer species that may occupy a site for a long time, but needs disturbances to join the overstory; their seedlings or saplings may survive long periods of suppression and grow rapidly when there is a disturbance (Heitzman et al., 1997). All the stands used in the present study were not disturbed much for 70 years. Two spruce budworm (Choristoneura fumiferana (Clem.)) infestations took place in the area, but had very small effects on tree mortality (Archambault et al., 2003). In the absence of disturbances, the main reason that may explain a more or less stable presence is the poor viability of its seeds, which are poorly disseminated by wind and may not survive for very long on the forest floor (Johnston, 1990). Sugar maple and beech were the only two species that showed an inconsistency with their life history. Observed basal area indicated an increase in the presence of the two species, while the results of the simulations indicated a decline or a more or less stable presence. On the other hand, both species are shade tolerant with good seedling establishment rate (Godman et al., 1990; Tubbs and Houston, 1990). It has long been recognized that the modelling of mortality in gap models has not received as much attention as the modelling of other processes (see Battaglia and Sands, 1998; Keane et al., 2001; Pabst et al., 2008). This situation is mainly due to the scarcity of data and lack of knowledge on tree death. For this reason, the model components on tree mortality in gap models were kept simple and general (Shugart, 1998; Hawkes, 2000). As the prediction of mortality in gap models is critical for the simulation of the dynamics of different cohorts within forest communities characterized by complex structures (Keane et al., 1990; Lexer and Hönninger, 1998), it is important to examine different modelling options, as performed in the present study. The most logical approach may be to develop model components that better integrate the complexity of the mechanisms that trigger tree mortality. Even though chance may play a role, which explains the use of probability estimates in existing models, abiotic and biotic factors, including age, physiology, successional stage or pest infestation, also affect tree mortality (Franklin et al., 1987; Harcombe, 1987). It is not obvious to identify a specific cause when tree mortality is observed because the effects of different factors may vary in intensity or have additive or multiplicative effects (see Keane et al., 2001). In reality, complex interactions are involved (Franklin et al., 1987). For instance, it may be argued that the net carbon balance (photosynthate production − carbon loss through respiration) would be a good indicator of tree mortality. However, a poor balance in a given year does not necessarily result in mortality because trees can acclimate to reduce respiration, change carbon allocation pattern to survive or 2582 G.R. Larocque et al. / Ecological Modelling 222 (2011) 2570–2583 use carbohydrate reserves (Keane et al., 2001). For these reasons, Keane et al. (2001) mentioned that mechanistic models to predict mortality were beyond reach, and this assessment still remains true today. An alternative option is to consider empirical formulations that better represent species-specific differences, which may contribute to improving the accuracy of the predictions associated with changes in basal area and dbh distributions. This is in agreement with Buchman (1983), Kobe et al. (1995), Wyckoff and Clark (2000) and Yaussy (2000) who mentioned that the integration of empirical data in a process-based model may prove useful, particularly if the relationships derived are biologically consistent. The survival models in ZELIG-CFS were derived by using empirical data and included only dbh and dbh growth rate, which both integrated tree vigour. They are similar in concept to models derived for other species (e.g., Buchman, 1983, 1985; Hamilton, 1990; Wyckoff and Clark, 2002). The general form of the relationships is biologically consistent: (1) tree survival probability increases with increase in dbh and dbh growth rate; (2) a large tree may see its survival probability decrease appreciably if its dbh growth rate is reduced, which occurs in old trees close to senescence. This approach has the advantage of integrating life history differences among species. While some species cannot survive a long time under stressful conditions, other species can grow very slowly for a long period. This is the case for balsam fir. When compared with observed stand densities, the mortality models in ZELIG-CFS made consistent predictions. Differences between observed and predicted average number of trees per ha may appear important for some dbh classes in the three forest types, but the high standard deviations for both observed and predicted stand densities indicated overlap for several sample plots. The pronounced differences between observations and predictions occurred mostly in the 5 cm dbh class. In a way, the large amplitude of difference is not surprising in this dbh class. Seedling regeneration varies considerably from year to year. As a consequence, it is not evident to capture the amplitude of annual variation. A good example can be seen for RSYB (Fig. 6a). The difference between observed and predicted stand densities is much less pronounced at age 67 in the 5-cm dbh class than for the same dbh class in the last simulation year in the other two forest types. However, a regeneration survey conducted the previous year in RSYB indicated a much lower number of seedlings. Nevertheless, despite the fact that ZELIG-CFS over-predicted seedling regeneration, the mortality functions worked reasonably well to adjust tree density in the higher dbh classes in the simulations. 5. Conclusion Long-term historical datasets are valuable for evaluating the performance of forest productivity models, such as gap models, that simulate the long-term dynamics of forest ecosystems. When the dataset used contains repeated measurements over long periods, as in the present study, the evaluation exercise gains in credibility because the comparison of the uncertainties in the predictions using different algorithms is conducted for one of the most critical experimental conditions for forest ecosystems, that is, the time factor. For instance, the comparison of different crown interaction algorithms allowed us to modify ZELIG by integrating two new algorithms that better predicted tree and stand growth than the original algorithm. The fact that these two algorithms performed better over a long observation period gave more credibility to the modifications that were implemented in ZELIG-CFS. Acknowledgements Sincere thanks are extended to the staff of La Mauricie National Park, Parks Canada, for providing facilities and information to access the sample plots that compose the experimental site of the Lake Edward Experimental Forest. We greatly appreciated the support of Dr. Jean Bégin, professor at Université Laval, and Dr. Mathieu Fortin, researcher at Direction de la recherche forestière, ministère des Ressources naturelles et de la Faune du Québec, who provided the boring core data used in the present study. The contributions of several students, interns or technicians to the field work were greatly appreciated: Maxime Camiré, Marie Bélanger, Marie-Claude Laflamme-Bérubé, Geneviève Gagnon-Bhérer, Richard Michaud, Jean-Pierre Cabaret, Laurent Jardin, and Luc St-Antoine. We greatly appreciated the support of the Forest Inventory Service of the ministère des Ressources naturelles et de la Faune du Québec for granting us access to their forest inventory dataset. References Amos-Binks, L.J., MacLean, D.A., Wilson, J.S., Wagner, R.G., 2010. Temporal changes in species composition of mixedwood stands in northwest New Brunswick: 1946–2008. Can. J. For. Res. 40, 1–12. 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