Distance-independent Competition Indices Research Articles

Individual tree mortality: Risks of climate change in the eastern Brazilian Amazon region

The mortality of trees in humid tropical forests plays a fundamental role in understanding forest development, particularly after disturbances such as those caused by logging and extreme weather events. The aim of this study was to evaluate estimates of individual tree mortality following Reduced Impact Logging (RIL) in the Eastern Brazilian Amazon at biennial intervals from 2005 to 2012. RIL is based on operations planning, personnel training, and investments in forest management, and harvesting through RIL must: (a) minimize environmental damage, (b) diminish operation cost by increasing work efficiency, and (c) reduce operational waste. A mortality model was constructed based on the estimation of three distance-independent competition-indices (DII) and five models for predicting the probability of individual tree mortality. The Kolmogorov-Smirnov statistical test was used to determine the most representative model, from which a Neural Network Autoregressive (NNAR) model was constructed to forecast mortality after RIL. Mortality data was correlated with the El Niño–Southern Oscillation (ENSO) and climate (Rainfall, Maximum, Minimum, and Average air temperature). The tested models showed similar and accurate estimates with R2 exceeding 0.90, although underestimation and overestimation trends were observed. The NNAR satisfactorily represented species mortality over the simulated years. The period from 2012 to 2014 was characterized by a Neutral and Weak El Niño event, and exhibited the highest mortality value for a 25 cm DBH (diameter at breast height), the smallest DBH class measured in this study. In the correlation matrix analysis, maximum air temperature showed the highest positive correlation with trees mortality. Despite the challenges in estimating individual tree mortality in tropical forests after selective logging, accurate estimates were achieved using traditional regression techniques and NNAR. These results can support technical and silvicultural decisions regarding forest management in the Eastern Amazon region of Brazil.

Select or Not? Comparing the Impact of Selective and Schematic Thinning on Scots Pine Tree Growth and Stand Structure

The first commercial thinning usually entails a high cost in harvest operations and a low resulting income. From a practical forestry perspective, a schematic spatial selection might be more efficient than a selective approach. Therefore, this study aimed to compare basal area, total and standing volumes, and periodic annual increment (PAI), as well as stand structure, between different thinning designs (selective and schematic thinning) and strategies (thinning once or more than once) over a long-term monitoring period of Scots pine (Pinus sylvestris) plantations in Sweden. We also evaluated the relevancy of distance-dependent competition indices (CIs) in individual tree growth models by comparing growth model predictions with the use of distance-dependent and distance-independent CIs. Despite higher heterogeneity in schematically thinned stands, there were no significant differences in standing and total volumes (m3·ha−1) among treatments in the short or long term. Although the inclusion of a distance-dependent CI improved the model slightly, distance-independent models predicted diameter growth just as effectively. Schematic thinning could be a viable option for a first commercial thinning or one-time thinning if, at least, one more thinning is included in the management plan, or if the motivating interest is mainly volume.

Do Distance-Dependent Competition Indices Contribute to Improve Diameter and Total Height Tree Growth Prediction in Juvenile Cork Oak Plantations?

Competition indices may improve tree growth modelling in high-density stands, found often in new cork oak plantations. Distance-dependent competition indices have hardly been considered for juvenile cork oak plantations since existing models were developed for low-density mature stands. This study aims at inspecting the potential of including distance-dependent competition indices into diameter at breast height (d) and total height (h) growth models for Quercus suber L., comparing several distance-dependent and distance-independent competition indices. Annual d and h growth were modelled with linear and non-linear growth functions, formulated as difference equations. Base models were initially fitted considering parameter estimates depending only on site index (S) and/or stand density (N). They were refitted, testing the significance of adding each competition index to the model parameters. Selected models included the best-performing distance-dependent or -independent competition indices as additional predictors. Best base d and h growth models showed a modelling efficiency (ef) of ef = 0.9833 and ef = 0.9900, respectively. Adding a distance-dependent competition index slightly improved growth models, to an ef = 0.9851 for d and ef = 0.9902 for h. Best distance-dependent competition indices slightly overperformed distance-independent ones in diameter growth models. Neither S nor N were included on best fitted models. If inter-tree competition is present in juvenile undebarked cork oak plantations, it does not yet strongly impact individual tree growth, which may diminish the importance of using, at this stage, more complex spatially explicit competition indices on predicting individual tree growth.

Effects of a selective thinning on wind loading in a naturally regenerated balsam fir stand

Recent trends in forest management promote the development of stands with a complex structure involving the use of partial cuts of various types. Partial cuts can increase the risk of wind damage but prior research on wind damage has largely focused on simple stand types and new modeling approaches are needed for these more complex stands. The present study looked at how the wind loading distribution in a naturally regenerated balsam fir (Abies balsamea (L.) Mill.) stand is modified by a local selective thinning. Two anemometers placed at canopy height and 2/3 canopy height, and strain gauges attached to the trunks of balsam fir trees allowed us to measure the wind-induced turning moments experienced by a sample of trees. A localized thinning was implemented around 2/3 of the sample trees in the second year of the experiment. Competing trees were removed within a 3.5 m radius of residual trees. Results show a dominant effect of the selective thinning at the tree scale but with an additional effect at the stand scale. The stand scale effect is likely linked to a change in wind profile within the canopy. A distance-independent competition index was useful in explaining the wind load distribution within the stand. Trees experiencing more competition were exposed to the largest increase of turning moment after the selective thinning. This study confirms the potential of competition indices for wind damage modeling in heterogeneous stands.

Variable selection for estimating individual tree height using genetic algorithm and random forest

Tree height is an important trait in forest science and is highly associated with the site quality from which the trees are measured. However, other factors, such as competition and species interaction, may yield better estimates for individual tree height when taken into account, but these variables have so far been challenging in model fitting. We propose a hybrid approach using genetic algorithms for variables selection and a machine learning algorithm (random forest) for fitting models of individual tree heights. We compare our proposed hybrid method with a mixed-effects model and random forest model using a dataset of 5,608 trees and 189 environmental variables (forest inventory-based variables, soil, topographic, climate, spectral, and geographic) from sites in southeastern Brazil. The tree height models were evaluated using the coefficient of determination, absolute bias, and root means square error (RMSE) based on the validation of dataset performance. The optimal set of variables of the proposed method include the ratio of diameter at breast height to quadratic mean diameter, distance independent competition index, dominant height, the soil silt and boron content. Our findings showed that the proposed hybrid method achieved an accuracy comparable with other methodologies in estimating the total height of the individual trees, and such a modelling approach could have broader applications in forestry and ecological science where a studied response trait has a large number of potential explanatory variables.

Competition Effects on Growth and Crown Dimensions of Shortleaf and Loblolly Pine in Mature, Natural-Origin, Pine–Hardwood Mixtures of the Upper West Gulf Coastal Plain of Arkansas, USA: A Neighborhood Analysis

The need for a comprehensive and mechanistic understanding of competition has never been more important as plants adapt to a changing environment and as forest management evolves to focus on maintaining and enhancing complexity. With the recent decline in shortleaf pine (Pinus echinata Mill.) land area, it is critical to determine the effects of competition on shortleaf pine and its performance against loblolly pine (Pinus taeda L.), the preferred planted replacement. We evaluate differences in shortleaf and loblolly pine 10 year mean basal area increment (BAI) and crown dimensions across a gradient of neighborhoods. Linear mixed-effects regression models were developed using BAI and several crown metrics as responses and crowding, competitor species abundance and identity, and initial size and species identity of focal tree as predictors. Crowding of focal trees negatively impacted BAI and crown size (p < 0.001, respectively). Although loblolly pine had three times higher BAI as compared to shortleaf pine within similar neighborhoods, BAI was variable, and the crowding effect did not differ between shortleaf and loblolly pine (p ranged from 0.51–0.99). Competitive impacts on focal trees did not differ by competitor identity (p ranged from 0.07–0.70). Distance-independent competition indices better explained the variation in BAI and horizontal crown metrics, while distance-dependent size ratios were more effective at evaluating vertical crown metrics. These findings highlight shortleaf pine competitive potential in mature, natural-origin stands and provide support for the restoration of pine–hardwood and hardwood–pine stratified mixtures as well as management of shortleaf pine at long rotations.

Influencing plantation stand structure through close-to-nature silviculture

New silvicultural practices to meet the requirements of ecosystem-based forest management are being adopted operationally, even if the long-term outcomes remain unknown. In eastern Quebec, Canada, the conversion of plantations from even-aged to irregular or uneven-aged stands is being carried out in 10% of commercial thinning operations. Existing growth and yield simulators cannot be used to forecast stand development. Here we apply a novel individual tree-level simulator to plantations characterized by high levels of natural regeneration ingrowth, such as those observed in Quebec. The simulator user can either choose distance-dependent or distance-independent competition indices, depending on user preference or simulation needs. Calibration statistics and validation results indicate that both versions perform very well. When applied to operational silvicultural scenarios, the simulator shows that thinning does not influence total stand yield; however, tree spatial aggregation does change. Moreover, the variability among the different simulation runs is greater for spatial statistics than for stand yield. Overall, thinning from below has the greatest effect on stand structure, whereas the smallest is from early crop tree release, used as the initial conversion step. This pattern implies that the first and second thinnings of the conversion process towards irregular or uneven-aged stands may not have a major effect on stand structure. In the case of the conversion process, the consequences for stand structure must thus be viewed as a longer-term issue. More importantly, the conversion process does not reduce stand yield, thereby reducing one of the key concerns of forest managers.

Effects of manual brushing on 10-year survival and growth of Douglas-fir in the mixed broadleaf – shrub complex of southern interior British Columbia

Manual brushing is used to minimize the competitive effects of paper birch (Betula papyrifera Marsh) and associated broadleaved trees on young Douglas-fir (Pseudotsuga menziesii var. glauca) in southern interior British Columbia. Effects of brushing broadleaved trees, predominantly birch, on interior Douglas-fir survival and growth were studied on four sites. Treatments were applied when plantations were five to nine years old. Through 10 years post treatment, brushing did not affect Douglas-fir survival, but increase height by 22 % and stem diameter by 31 % and the differences were greater than seen at five years. After 10 years, linear models described a declining Douglas-fir height or diameter with increasing broadleaved tree density. Boundary line analysis was used to describe maximum treatment response to broadleaved density and two distance independent competition indices for birch and broadleaves, combining either cover or density with relative heights (CRH, DRH, respectively). A negative exponential relationship was fit to 10-year Douglas-fir heights and diameters with increasing values CRH or DRH. Competition thresholds for density, CRH and DRH were not apparent. The quantile regression results indicated the 10-year response of young Douglas-fir diameter to brushing occurred primarily with the largest 55 % to 85 % of the population, CRH and DRH respectively.

Evaluation of Individual Distance-Independent Diameter Growth Models for Japanese Cedar (Cryptomeria japonica) Trees under Multiple Thinning Treatments

Understanding the tree growth process is essential for sustainable forest management. Future yields are affected by various forest management regimes such as thinning; therefore, accurate predictions of tree growth are needed under various thinning intensities. This study compared the accuracy of individual-level distance-independent diameter growth models constructed for different thinning intensities (thinning intensity-dependent multiple models: TDM model) against the model designed to include all thinning intensities (thinning intensity-independent single model: TIS model) to understand how model accuracy is affected by thinning intensity. We used long-term permanent plot data of Japanese cedar (Cryptomeria japonica) stands in Japan, which was gathered from four plots where thinning was conducted at different thinning intensities: (1) intensive (41% and 38% of trees removed at 25 and 37 years old, respectively), (2) moderate (38% and 34%), (3) light (32% and 34%), and (4) no thinning. First, we specified high interpretability distance-independent competition indices, and we compared the model accuracy both in TDM and TIS models. The results show that the relative spacing index was the best competition index both in TDM and TIS models across all thinning intensities, and the differences in the RMSE (Root mean square error) and rRMSE (relative RMSE) in both TDM and TIS models were 0.001–0.01 cm and 0.2–2%, respectively. In the TIS model, rRMSE varied with thinning intensity; the rRMSE was the lowest for moderate thinning intensity (45.8%) and the highest for no thinning (59.4%). In addition, bias values were negative for the TIS model for all thinning intensities. These results suggest that the TIS model could express diameter growth regardless of thinning intensities. However, the rRMSE had varied with thinning intensity and bias had negative values in the TIS model. Therefore, more model improvements are required for accurate predictions of long-term growth of actual Japanese cedar stands.

Competition and water stress indices as predictors of Pinus halepensis Mill. radial growth under drought

The frequency, duration, and severity of drought events are expected to increase in the Mediterranean area as a result of climate change, with strong impacts on forest ecosystems and in particular individual tree growth. Tree growth response to drought is strongly influenced by local site and stand characteristics that can be quantified using competition indices (CIs) and water stress indices (WSIs). These indices have been widely used to predict tree growth; however, they are numerous, and few studies have investigated them jointly. In this context, we investigated the potential of using CIs and WSIs to investigate tree behaviour under drought. The main objective of this study was to quantify P. halepensis Mill. annual radial growth using tree size from the previous year, CIs and WSIs.We studied twelve 50-year-old Pinus halepensis plots located in the South-East of France distributed in different density treatments (light, medium and dense). At each plot, all trees were measured (height, circumference), spatialized and the ring-widths were measured for ~15 trees. We also developed a two-strata (over- and understorey) forest water balance model to simulate soil water content at a daily resolution based on stand characteristics (LAI values in particular) and soil properties. A mixed modelling approach was eventually used to investigate the drivers of P. halepensis annual radial growth and to test the performance of five CIs and four WSIs.The best growth model included tree size, the sum of Basal Area of Larger trees in a 5 m-radius (BAL; as CI), and the number of days that trees experienced water stress in a year (as WSI) as predictors. This model explained up to 56% of the variance in observed pine tree growth, which increased up to 77% when the individual tree was included as a random effect on the intercept. We found that distance-independent CIs can perform as well as distance-dependent CIs in our study site. The duration of drought alone appeared to better predict tree growth than drought intensity and duration, or drought timing. The selected model led us to reaffirm the positive effect of thinning on tree secondary growth when facing long and intense drought.

Evaluation of distance-independent competition indices in predicting tree survival and diameter growth

Competition indices play a significant role in modeling individual-tree growth and survival. In this study, six distance-independent competition indices were evaluated using 200 permanent plots of loblolly pine (Pinus taeda L.). The competition indices were classified into three families: (1) size ratios, which include diameter ratio and basal area ratio; (2) relative position indices, which include basal area of larger trees (BAL) and tree relative position based on the cumulative distribution function (CDF); and (3) partitioned stand density index and relative density. Results indicated that different families of competition indices were suitable for different tree survival or diameter growth prediction tasks. The diameter ratio was superior for predicting tree survival, whereas the relative position indices (BAL and CDF) performed best for predicting tree diameter growth, with CDF receiving the highest rank.

Contributions of competition and climate on radial growth of Pinus massoniana in subtropics of China

It is critical to investigate the effects of competition and climate on forest growth as they are main forces affecting forest dynamics. However, in subtropics of China such a study has never been conducted. Here we conducted a pioneer study to evaluate the effects of competition and climate on growth of Chinese red pine (Pinus massoniana) in mixed forests of subtropical China along a broad latitudinal gradient (23°N∼32°N). Twenty-three plots (20m × 20m) were randomly selected from 11 sites and competition and tree radial growth data were collected. Principal component analysis (PCA) was used to detect the potential spatial pattern in site-specific standard tree-ring chronologies during the common period (1990-2015). The linear mixed-effect models (LMMs) were employed to quantify the relationships between cumulated basal area increment (5, 10, 15, 20 and 25 years) of subject trees and six distance-independent competition indices. The relationships between tree radial growth and climate were evaluated by response analyses. Finally the best predicted competition index and climate factor were employed in a full model and their relative importance were calculated. The PCA results allowed classifying the mixed forests into southeastern and northern groups along the Nanling Mountains and Wuyi Mountains. LMMs results revealed that competition pressures mainly come from density and size of larger individuals. Response coefficients demonstrated that precipitation in September and sunshine duration in October influenced trees radial growth of southeastern group and northern group respectively. Our results clearly showed that effects of competition on tree radial growth decreased from southeast to north while effects of climates increasing over this large spatial scale. This is the first attempt to clarify the effects of competition, and further quantify the contributions of competition and climate on tree radial growth in China subtropics. Our finds will certainly contribute to a better policy-making for sustainable forest management.

Competition Indexes to Evaluate Tree Growth in a Semi-Deciduous Seasonal Forest

ABSTRACT Most of the studies that analyze the behavior of tree competition approach even-aged plantations. Therefore, it is possible to notice a lack of this kind of information regarding natural forests with high biodiversity. The objective of this study was to evaluate the competition in a fragment of Semi-Deciduous Seasonal Forest, according to the ecologic group, light depending and non-depending groups for all species sampled in the fragment. The Distance Independent Competition Index and Semi-Distance Independent Competition Index were applied in this study. The basal area in larger trees index, without the radius of influence, was the most efficient to analyze how the competition affects the growth of the specimens in the studied fragment. It was stated that evaluating the competition per ecologic group is more efficient. The results confirm that the forest competition cannot be determined by considering only a fixed radius of influence that embraces the neighbors and the subject tree.

COMPETIÇÃO <i>VERSUS</i> CRESCIMENTO DE ÁRVORES EM FLORESTA OMBRÓFILA DENSA NO ESTADO DO AMAPÁ - BRASIL

O objetivo deste trabalho é o de avaliar, comparativamente, diferentes índices de competição independentes da distância (IID) em três dimensões de parcelas, e identificar aqueles que mais se correlacionam com o incremento diamétrico (IPA DAP), indicando o que melhor explica a competição entre as árvores do estrato arbóreo em uma Floresta Ombrófila Densa. Este estudo foi conduzido com dados do Projeto Bom Manejo (Embrapa/CIFOR/ITTO) – Manejo sustentável de florestas de produção em escala comercial na Amazônia brasileira, desenvolvido pela Embrapa Amazônia Oriental, em área da Jari Florestal S.A., município de Vitória do Jari, Estado do Amapá. Foram empregadas três parcelas permanentes de um hectare cada uma (100 m x 100 m), nas quais foram medidos todos os indivíduos arbóreos com DAP ≥ 20 cm. Foram comparados os seguintes IID: G (área basal/ha), BAL (Basal Area of Larger Trees), Glover e Hool e Stage. Os índices de competição foram avaliados a partir de análise dos coeficientes de correlação lineares entre cada índice e a variável IPA DAP (cm ano-1). A significância dos coeficientes de correlação foi avaliada pelo p valor (α = 0,05). Todas as variações de índices testadas resultaram em correlações de até 20%, consideradas muito fracas. Isto indica que os IID conseguem representar apenas parcialmente a competição em florestas naturais tropicais. No entanto, entre os índices, o índice BAL é o IID que apresentou a maior correlação com o IPA DAP (r=-0,212 e p = 0,000) em parcelas de 50 m x 50 m e, portanto, mesmo apresentando uma correlação baixa, é o mais indicado para estudos de competição no crescimento diamétrico em florestas tropicais naturais. Foi detectada uma relação espacial dos IID, em que a correlação diminui com o aumento do tamanho da parcela. Recomendam-se pesquisas adicionais para avaliar os efeitos da competição sobre o crescimento das árvores, bem como o aumento do entendimento de competição intraespecífica e interespecífica, a fim de melhorar a compreensão da dinâmica da competição em florestas tropicais.

A novel approach to selecting a competition index: the effect of competition on individual-tree diameter growth of Calabrian pine

In this study, we evaluated the performance of 18 competition indices composed of nine distance-dependent and nine distance-independent indices in explaining the variation in individual-tree diameter growth of Calabrian pine (Pinus brutia Ten.) in the central Mediterranean region of Turkey. The data were obtained from 432 sample plots with varying stand age, site index, and stand density. To evaluate the performance of each competition index, the mean square error reduction approach was used relative to the noncompetition. Also, this study compared fixed and mixed effects models to analyze diameter growth. Statistical analyses showed that the best distance-independent competition indices performed as well as the best distance-dependent competition indices. The distance-independent competition index of Schröder and Gadow (1999; Can. J. For. Res. 29(2): 280–283, doi: 10.1139/x98-199) performed best and is recommended for use in future growth and yield models to be used in the central Mediterranean region of Turkey. Also, the best selection of competitive neighbors was achieved using the area of influence overlap method, whereas the fixed-radius and angle count sampling methods had no significant improvement in quantifying the competition effects. On the other hand, all mixed effects models provided much better fits than their fixed model counterparts.

Competition Indices and Their Relationship With Basal Area Increment of Araucaria

Models that report the effect of competition are important for forest management since forests with higher levels of competition have lower increment rates, and their use is necessary to plan forest interventions. Thus, this study aimed to assess the effect of competition in the basal area increment of individual trees of Araucaria angustifolia (Bertol.) Kuntze in a natural forest. A total of 397 subject trees were measured, covering the diametric range. The dendrometric and morphometric characteristics of subject trees and their competitors were obtained, and 22 distance-dependent and distance-independent competition indices were calculated, in addition to increment cores extracted radially from the trunk at diameter at breast height. The relationship between models of periodic annual increment in basal area based on competition indices has allowed to obtain R2 values of 0.425 and Syx% ≥ 50.2. The multivariate technique of principal component analysis has shown that three principal components explain 78.43% of total variation. The first component was responsible for explaining 52.95%, with similar eigenvector for 11 competition indices, evidencing that these models can be used to describe especies competition, although they show different variables and mathematical equations in calculations. Results show the importance of competition to predict increment of Araucaria in individual trees.

Influencia de la competencia en el crecimiento diamétrico de Pinus durangensis Martínez en Durango, México

En esta investigación se analizó la influencia de la competencia sobre el crecimiento en diámetro normal en árboles de Pinus durangensis en bosques mixtos e irregulares del estado de Durango. Se utilizaron datos de dos inventarios realizados en 2009 y 2014, en 16 Sitios Permanentes de Investigación Forestal y de Suelos (SPIFyS) de 2 500 m2, dentro de los cuales, Pinus durangensis fue la especie dominante del estrato arbóreo, con 39.44 % del valor de importancia, y crece de manera mezclada con otras 18 especies arbóreas. El efecto de la competencia fue analizado mediante 14 índices de competencia independientes de la distancia y 11 dependientes de la distancia; para ello, se evaluaron 11 criterios de selección de árboles competidores. Los índices independientes de la distancia explicaron ligeramente mejor que los índices dependientes de la distancia el crecimiento en diámetro normal de la especie estudiada. El índice de competencia independiente de la distancia que se deriva de la razón entre el área basal del árbol objetivo y el área basal por hectárea describió mejor el efecto deseado, por lo que se recomienda para su posible inclusión en futuros modelos de crecimiento en diámetro normal desarrollados para P. durangensis.

Effect of climate and competition on radial growth of Pinus massoniana and Schima superba in China’s subtropical monsoon mixed forest

Tree growth is affected by many exogenous and endogenous factors, especially climate and competition. To address the issue of how these factors influence tree growth under global warming, dendroclimatology combined with competition analysis was used to examine the radial growth response of two major species – Pinus massoniana and Schima superba in subtropical monsoon mixed forests in southern China. For growth-climate relationship analysis, residual and ARSTAN chronologies of these two species were compared for the response function analysis over the past several decades. In terms of competition analysis, annual basal area increment (BAI) over several time intervals was calculated and linear mixed model techniques were employed. Several distance-independent competition indices were measured, including density (N), basal area (BA), and sum of diameter at breast height (SDBH). For competition trees with greater diameter (GR) than the subject tree, NGR, BAGR, SDBHGR were also calculated. Growth-climate relationship analysis suggested that tree growth varied in response to climate and was mostly correlated with minimum, mean and maximum air temperature as indicated by the adjusted R2 value. Summer and winter temperatures had a negative effect on tree growth, while early spring temperature showed positive effects. Competition analysis suggested that subtropical trees had been affected by competition in varying degrees. Trees in the oldest forest had the most competition stress, while trees in younger forests were less affected by competition according to the adjusted R2 value. Given that subtropical forests in China have been found to have more smaller trees with recent warming, it is expected that these forests will experience a decreasing effect of competition in near future. This can have profound effects on forest productivity and carbon sequestration potentials in Chinese subtropical forests.

Allometric modelling of crown width for white spruce by fixed- and mixed-effects models

Crown width is an important predictor for tree growth, crown surface area, forest canopy cover, tree-crown profiles and wildlife habitat indices. This paper developed crown width models for white spruce (Picea glauca (Moench) Voss) in Alberta using allometric fixed and mixed models with varying degrees of model complexity. Diameter at breast height was the most important predictor and was used in the base model. Crown ratio, height-diameter ratio and two competition indices (CIs) were additional predictors added to the base model to form four expanded models. At each level of complexity, a fixed model and a mixed model were fitted. Improved fits were achieved for both model types as model complexity increased, and all mixed models provided much better fits than their fixed model counterparts. Population-averaged (PA) predictions by fixed models, and typical mean (TM), PA and plot-specific (PS) predictions by mixed models were compared on both model fitting and validation data. TM and PA predictions by each mixed model were almost identical, and they were less accurate than PA predictions by the fixed model counterpart, especially for simpler models. Much better PS predictions by mixed models were observed on both datasets. Although the distancedependent CI was slightly better than the distance-independent CI, both were not recommended due to their marginal contributions to crown width predictions.

Evaluating a single tree-based growth model for even-aged stands against the maximum size–density relationship: Some insights from balsam fir stands in Quebec, Canada

In this study, we addressed the issue of model evaluation when long-term monitoring data are unavailable or inappropriate. More specifically, we fitted a single tree-based growth model for pure even-aged balsam fir stands and we compared stochastic predictions with an existing maximum size–density relationship (MSDR). Growth trajectories for plots of different initial densities and diameter distributions were simulated over a 70-year period using 500 realizations for each combination of initial density-diameter distribution. Long-term predictions were consistent with the existing MSDR. The model properly reproduced the senescence phase in which the trajectories diverge from the MSDR. This phase was initiated when the average tree volume reached 0.2-0.3 m3 per tree, which roughly corresponded to a DBH (diameter at breast height, 1.3 m from the ground) between 19 and 23 cm. Although it cannot be generalized, our case study shows that a simple single tree-based growth model with a distance-independent competition index and no stand density index can reproduce an existing MSDR. The match between long-term predictions and an existing MSDR strengthens the confidence in the biological behaviour of the model.