Individual-tree Mortality Models Research Articles

Predicting Individual Tree Mortality of Larix gmelinii var. Principis-rupprechtii in Temperate Forests Using Machine Learning Methods

Accurate prediction of individual tree mortality is essential for informed decision making in forestry. In this study, we proposed machine learning models to forecast individual tree mortality within the temperate Larix gmelinii var. principis-rupprechtii forests in Northern China. Eight distinct machine learning techniques including random forest, logistic regression, artificial neural network, generalized additive model, support vector machine, gradient boosting machine, k-nearest neighbors, and naive Bayes models were employed, to construct an ensemble learning model based on comprehensive dataset from this specific ecosystem. The random forest model emerged as the most accurate, demonstrating 92.9% accuracy and 92.8% sensitivity, making it the best model among those tested. We identified key variables impacting tree mortality, and the results showed that a basal area larger than the target trees (BAL), a diameter at 130 cm (DBH), a basal area (BA), an elevation, a slope, NH4-N, soil moisture, crown density, and the soil’s available phosphorus are important variables in the Larix Principis-rupprechtii individual mortality model. The variable importance calculation results showed that BAL is the most important variable with an importance value of 1.0 in a random forest individual tree mortality model. By analyzing the complex relationships of individual tree factors, stand factors, environmental, and soil factors, our model aids in decision making for temperate Larix gmelinii var. principis-rupprechtii forest conservation.

Can a multistage approach improve individual tree mortality predictions across the complex mixed-species and managed forests of eastern North America?

Tree mortality plays a fundamental role in the dynamics of forest ecosystems, yet it is one of the most difficult phenomena to accurately predict. Various modeling strategies have been developed to improve individual tree mortality predictions. One less explored strategy is the use of a multistage modeling approach. Potential improvements from this approach have remained largely unknown. In this study, we developed a novel multistage approach and compared its performance in individual tree mortality predictions with a more conventional approach using an identical individual tree mortality model formulation. Extensive permanent plot data (n ​= ​9442) covering the Acadian Region of North America and over multiple decades (1965–2014) were used in this study. Our results indicated that the model behavior with the multistage approach better depicted the observed mortality and showed a notable improvement over the conventional approach. The difference between the observed and predicted numbers of dead trees using the multistage approach was much smaller when compared with the conventional approach. In addition, tree survival probabilities predicted by the multistage approach generally were not significantly different from the observations, whereas the conventional approach consistently underestimated mortality across species and overestimated tree survival probabilities over the large range of DBH in the data. The new multistage approach also predictions of zero mortality in individual plots, a result not possible in conventional models. Finally, the new approach was more tolerant of modeling errors because it based estimates on ranked tree mortality rather than error-prone predicted values. Overall, this new multistage approach deserves to be considered and tested in future studies.

Stand-Age Derived Competition Indices Influence Individual Tree Mortality Model Prediction for Naturally Occurring Even-Aged Shortleaf Pine Stands

To understand the influence of competition indices and post-thinning effects in predicting individual tree mortality, we developed two models, one without the effect of thinning and another, with the effect of thinning for naturally occurring even-aged natural shortleaf pine (Pinus echinata Mill.) stands in the Ozark and Ouachita National Forests in Oklahoma and Arkansas, USA. Over the period of 25 years, six re-measurements of an individual tree from each plot were collected between 1985 and 2014. The logistic function was used to model the probability of mortality for which the binary response variable was, ‘0’ for living and ‘1’ for dead trees, using iteratively weighted regression and mixed-effects model. Stand-age derived competition indices such as, the ratio of stand basal area to stand age (SBAG), ratio of individual diameter to stand age (DAG), and the quadratic mean diameter (QMD), were found significant in predicting the probability of mortality. These variables were also found to be effective in the thinning effect model. However, excluding the thinning variable resulted in better performance with the chi-square test based on mortality within mid-diameter classes. Thus, the mortality model suggests that over time, individual tree mortality is influenced more greatly by competition modified by stand age rather than by a post-thinning effect in even-aged naturally occurring shortleaf pine trees.

A two-step approach for modeling tree mortality in Larix olgensis plantation based on effects of thinning

Ten permanent plots of Larix olgensis plantation were established in 1972 and 1974 at Jiangshanjiao and Mengjiagang forest farms in Heilongjiang Province, respectively. The plots including 8 thinning plots and 2 control plots were measured annually. The effects of thinning on the probability of plot mortality and individual tree mortality were analyzed. Based on the binary logistic regression, two-step models of the probability of mortality were developed. The approach consisted of estimating the probability of mortality after thinning on a sample plot (1) and the mortality of individual tree within mortality plots (2). The generalized estimating equations (GEE) method was adopted to estimate the parameters of models. An optimal cutpoint was determined for each model by plotting the sensitivity curve and the specificity curve and choosing the cutpoint at which the specificity and sensitivity curves cross. The results showed that four models (models 1-4) were developed based on the data of plots which was divided into 4 groups by thinning times, respectively. The significant explicatory variables of model 1 were site index, the logarithm of stand age, thinning age and thinning intensity. Principal component analysis was used to develop models 2-4. The primal variables of the principal components were stand age, tree numbers per hectare, mean square diameter at breast height and thinning factors. This showed that thinning significantly affected the probability of plot mortality. The effect of thinning was not significant for the pro-bability of individual tree mortality. The significant variables of the individual tree mortality model were planting density, age, the inverse of diameter at breast height and the basal area of all trees larger than the subject tree. Hosmer and Lemeshow goodness of fit tests were not significant for the mortality models of plots and individual trees (P＞0.05). The areas under the receiver operating characteristic curve (AUC) of the models were all greater than 0.91, the accuracies were all above 80%, suggesting the fitting results of the models performed very well.

Climatic information improves statistical individual-tree mortality models for three key species of Sichuan Province, China

Climate variables improve individual-tree mortality models for fir, oak and birch. Climate is considered as an important driver of tree mortality, but few studies have included climate factors in models to explore their importance for modelling individual-tree mortality. To measure the performance of climate-based models, we built individual-tree mortality models using individual, stand, and climate variables for fir (Abies faxoniana Rehd. et Wils.), oak (Quercus aquifolioides Rehd. et Wils.), and birch (Betula albo-sinensis Burk.) in Southwest China, and explored the corresponding effects on tree death. We developed tree mortality models based on 287 permanent plots from the Sichuan Forest Inventory data, and compared the models based on variables of individual (I), stand (S), and climate (C) levels, and different combinations (I + S, I + C, S + C, I + S + C) among these groups to improve model performance. We employed relative Akaike information criterion (AIC), area under receiver operating characteristic curve (AUC), and Hosmer-Lemeshow’s goodness-of-fit statistic for model evaluation and validation. We found that tree mortalities of the three species could be better predicted (AUC > 0.8) by carefully selecting variables at three ecological scales (individual, stand, and regional climate). Our results suggest that the higher mortality of the object trees occurs when they endure lower radial growth of the previous years, more intensive competition, and moderate canopy cover (for birch), while lower mortality was seen in an appropriate range of climate conditions and at higher stand canopy cover (for fir and oak). The results have significance for incorporating the effects of a changing climate into mortality models.

Resource communication. Individual-tree growth model for radiata pine plantations in northwestern Spain

Individual-tree basal area and height increment models were developed with data from 130 permanent plots of Pinus radiata D. Don located in Galicia (northwestern Spain). Mixed-models techniques were used for model fitting. Covariates acting at tree and stand level were included as fixed effects. Estimated values of stand variables obtained from aggregation of individual-tree predictions were used in model evaluation. The developed models accounted for 54% of the variability in basal area increment and 36% of the variability in height increment, with mean errors of 16 cm2 and 0.36 m, respectively. These models, along with an existing individual-tree mortality model, constitute a whole individual-tree growth model that can be used to simulate forest management alternatives, helping in forest managers’ decision making.

Individual Tree Mortality Model for Slash Pine in Florida: A Mixed Modeling Approach

Tree mortality is an important biological process and should be incorporated in forest growth simulation models to improve their accuracy and biological authenticity. We developed individual tree mortality models for slash pine using data from north central Florida. We first fit mortality models with only fixed effects using a logistic model and then added a random effect to account for the multilevel nature of the data. We used a generalized linear mixed modeling (GLMM) framework to compare the outcomes of the two fitting processes. Predictions from both models were evaluated using receiver operating characteristics (ROC) curves. Area under the ROC curve was higher for predictions from the GLMM compared with the fixed effects logistic model. Subject-specific responses (including plot-level random effects in the model of individual trees) from the GLMM were better at predicting mortality. Similar results were obtained after performing a cross-validation of the models. Although the fixed effects accounted for regular mortality because of suppression and competition for resources, the plot-level random effect accounted for the effects of other unmeasured plot-level variables. In our models, dbh, height, competition, site index, and basal area per hectare were significant predictors.

Evaluation of mixed-effects models for predicting Douglas-fir mortality

We examined the performance of several generalized linear fixed- and mixed-effects individual-tree mortality models for Douglas-fir stands in the Pacific Northwest. The mixed-effects models accounted for sampling and study design overdispersion. Inclusion of a random intercept term reduced model bias by 88% relative to the fixed-effects model; however, model discrimination did not substantially differ. An uninformed version of the mixed model that used only its fixed effects parameters produced predicted mortality values that exceeded the fixed-effects model bias by 31%. Overall, we did not find compelling evidence to suggest that the mixed models fit our data better than the fixed-effects model. In particular, the mixed models produced fixed-effects parameter estimates that predicted unreasonably high mortality rates for trees approaching 1m in diameter at breast height.

Modeling non-catastrophic individual-tree mortality for Pinus radiata plantations in northwestern Spain

An individual-tree mortality model for radiata pine ( Pinus radiata D. Don) plantations in northwestern Spain was developed. The model relies on data from three inventories of a network of 130 permanent plots. The equation that predicts the probability of complete survival is a logistic function, which depends on tree size and competition (diameter, mean-squared diameter, stand basal area, dominant height and BALMOD competition index). Several methods of implementing the mortality model were tested (deterministic versus stochastic threshold selection and the use of expansion factors). The best results were obtained when using a fixed cut-off value to decide which trees would survive to the next growing period. When a cut-off value of 0.55 was applied, the model correctly classified 99% of the live trees and 25% of the dead trees. A cut-off of 0.71 provided an estimated mortality rate that was closest to the observed rate. With this cut-off value, the model correctly classified 95% of the live trees and 47% of the dead trees. This cut-off value is recommended when using the model to predict radiata pine individual-tree mortality in the study area.

An Individual-Tree Mortality Model for Complex Stands of Southeastern British Columbia

Abstract An individual-tree mortality model was developed for major tree species in complex stands (multi-cohort, multiaged, and mixed species) of southeastern British Columbia (BC), Canada. Data for 29,773 trees were obtained from permanent sample plots established in BC. Average annual diameter increment and mortality rates ranged from 0.08 to 0.17 cm/year and from 0.3 to 2.6%, respectively. Approximately 70% of the trees were used for model development and 30% for model evaluation. After evaluating the model, all 29,773 trees were used to fit the final model. A generalized logistic model was used to relate mortality to tree size, competition, and relative position of trees in a stand. The evaluation test demonstrated that the model appears to be well behaved and robust for the tree species considered in this study. For the eight tree species, the average deviation between observed and predicted annual mortality rates varied from −0.5 to 0.7% in the test data. West. J. Appl. For. 20(2):101–109.

Are Self-Thinning Constraints Needed in a Tree-Specific Mortality Model?

Abstract Can a tree-specific mortality model elicit expected forest stand density dynamics without imposing stand-level constraints such as Reineke's maximum stand density index (SDImax) or the −3/2 power law of self-thinning? We examine this emergent properties question using the Austrian stand simulator PROGNAUS. This simulator was chosen specifically because it does not use stand density constraints to determine individual tree mortality rates. In addition, it is based on a probability sample of the population that includes the span of the data being used to test the hypothesis. Initial conditions were obtained from 27 permanent research plots that were established in young pure stands of Norway spruce (Picea abies L. Karst.) and Scots pine (Pinus sylvestris L.) in Austria. A growth period of 250 years was simulated. We conduct our test in two parts. First, we compare our simulated results to Reineke's theory of maximum density and stand density index by examining the self-thinning relationship between stem number per hectare and quadratic mean diameter (log-log scale). Second, we compare our results to Sterba's full competition density rule, which incorporates dominant height along with stem number and quadratic mean diameter. From the results for Norway spruce, we conclude that stand-level density constraints are not necessary to obtain Reineke's maximum size-density relations. Norway spruce results confirm that the maximum size-density relationship reflects reasonable and stable stand dynamics and conforms to that expected by Reineke's theory. Results from simulation of Scots pine also display reasonable and stable stand dynamics, except that they greatly exceed Reineke's maximum stand density index determined empirically from the literature. This Scots pine result argues for stand-level constraints (such as specifying SDImax) to ensure that the appropriate intercept for the maximum density line is used. Our second test revealed that the estimated maximum stand density index according to Sterba's theory was too high for both species, but that the relative rankings across plots were correct. Thus, we are left with ambiguous results. First, that a density-dependent individual-tree mortality model, developed on an adequate data set, is sufficient for the desired stand-level behavior of Reineke to emerge. Second, that stand-level constraints on SDImax need to be imposed if the underlying mortality modeling database is not adequate. FOR. SCI. 50(6):848–858.

Bedrock type significantly affects individual tree mortality for various conifers in the inland Northwest, U.S.A.

Individual tree mortality models for western white pine (Pinus monticola Dougl. ex D. Don), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), grand fir (Abies grandis (Dougl. ex D. Don) Lindl.), western redcedar (Thuja plicata Donn ex. D. Don), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western larch (Larix occidentalis Nutt.) were developed using data from permanent research plots located throughout the inland Northwest. The proposed linear logistic models included the following independent variables: diameter at breast height, basal area in larger trees, basal area per hectare, individual tree diameter increment, and a set of dummy variables for the six bedrock types, which were granite, basalt, metasedimentary, sedimentary, mixed – glacial till, and deep deposit. The results show that rock type significantly affects individual tree mortality for western white pine, Douglas-fir, and western redcedar, while grand fir, western hemlock, and western larch were not affected. Western white pine and Douglas-fir growing on meta sedimentary rocks exhibited greater mortality probabilities than on other rocks. Mortality probabilities for western hemlock were low across all rock types, including "nutrient-poor" rocks like metasedimentary types.

Modeling individual tree mortality for white spruce in Alberta

An individual tree mortality model, based on the provincial PSP data, was developed for white spruce ( Picea glauca (Moench) Voss), an important tree species in Alberta, Canada. Annual probability of survival was modeled by a generalized logistic function with the measurement interval length as a predictor variable to overcome the problem of unequal measurement intervals. Potential predictor variables were selected based on their ecological importance to tree mortality and unknown parameters were estimated using the maximum likelihood method. A U-shaped mortality trend was captured by diameter and diameter squared. Annual diameter increment was used to indicate tree vigor. Basal area of larger trees and a ratio of basal area of larger broadleaf trees to stand total basal area were both used to capture competition from neighboring trees. The newly developed mortality function outperformed the old one previously used in the Mixedwood Growth Model (MGM) based on both goodness-of-fit and prediction statistics.

The Effect of Nitrogen Fertilization, Rock Type, and Habitat Type on Individual Tree Mortality

Abstract An individual tree mortality model for nitrogen fertilized Douglas-fir (Pseudotsuga menziesii var. glauca [Beissn.] Franco) stands was developed using data from permanent research plots located throughout the inland Northwest. The proposed linear logistic model included the following independent variables: a dummy variable for the two habitat types, a set of dummy variables for the five rock types, a set of dummy variables for the three N fertilizer treatments, diameter at breast height, crown ratio, and crown competition factor. The results show that N fertilization, rock type, and habitat type significantly affect individual tree mortality. The probabilities of tree mortality on fertilized plots were greater than those on control plots and increased with increasing N fertilizer application rates. Trees growing on granitic and metasedimentary rocks had lower foliar potassium concentration and exhibited greater probabilities of mortality than did those growing on other rocks. The probabilities of mortality for trees growing on sedimentary rocks were very low. Moist sites had lower soil fertility and produced higher mortality rates than dry sites. Furthermore, the N fertilization response ratio, defined as the annual mortality probability of a fertilized tree over the annual mortality probability of a unfertilized tree with identical tree and stand characteristics, was estimated based on the mortality model. The response ratios were nearly constant (about 1.4) across a range of tree diameters for all rock types with the 224 kg N treatment. The response ratios were also nearly constant (about 2.1) across a range of tree diameters for all rock types with the 448 kg N treatment. Finally, the mortality prediction model passed a validation test on independent data not used in model development. For. Sci. 47(2):203–213.

Modeling individual tree mortality for Austrian forest species

Individual tree mortality models were developed for the six major forest species of Austria: Norway spruce ( Picea abies), white fir ( Abies alba), European larch ( Larix decidua), Scots pine ( Pinus sylvestris), European beech ( Fagus silvatica), and oak ( Quercus spp.); a joint model for the remaining broadleaf species was also developed. Data came from 5-year remeasurements of the permanent plot network of the Austrian National Forest Inventory. Parameters of the logistic equation were estimated using maximum likelihood methods. For all species, we found the hyperbolic transformation of diameter ( D −1 ) to be highly significant in predicting the high mortality rates for small diameter trees and decreasing mortality rates for larger diameters. For spruce, a quadratic transformation in D was needed to accurately model the increase in mortality observed for large, low-vigor trees with diameter >70 cm, which resulted in a U-shaped distribution. Crown ratio was also consistently significant, except for oak. We likewise found basal-area-in-larger-trees ( BAL) to be a highly significant predictor of mortality rate for all species except fir and oak. Predicted mortality rate increases as the basal area in larger trees increases and as crown ratio decreases. The resulting logistic mortality model had the same general form for all species, with the signs of all parameters conforming to expectations. In general, chi-square statistics indicate that the most important variable is D −1, the second most important is crown ratio, and the third most important predictor is BAL. The relative importance of crown ratio appears to be greater for shade tolerant species (fir, beech, spruce) than for shade intolerant species (larch, Scots pine, oak). Examination of graphs of observed vs. predicted mortality rates reveals that the species-specific mortality models are all well behaved, and match the observed mortality rates quite well. The D −1 transformation is flexible, as can be seen by comparing the rather different mortality rates of larch and Scots pine. Predicted and observed mortality rates with respect to crown ratio are quite close to the observed mortality rates for all but the smallest crown ratios ( CR<20%), a class with very few observations. Finally, the logistic mortality models passed a validation test on independent data not used in parameter estimation. The key ingredient for obtaining a good mortality model is a data set that is both large and representative of the population under study, and the Austrian National Forest Inventory data satisfy both requirements.

Extending the range of applicability of an individual tree mortality model

Limits are frequently encountered in the range of values of independent variables included in data sets used to develop individual tree mortality models. If the resulting model is to be utilized, its ability to extrapolate to conditions outside these limits must be evaluated. This paper describes the development and evaluation of six assumptions required to extend the range of applicability of an individual tree mortality model previously described. The assumptions deal with mortality in very dense stands, mortality for very small trees, mortality on habitat types and regions poorly represented in the data, and mortality for species poorly represented in the data.

A Signal Detection Framework to Evaluate Models of Tree Mortality Following Fire Damage

Abstract Signal detection theory provides an appropriate framework to evaluate the performance of various individual tree mortality models. Receiver operating characteristic (ROC) curves show the tradeoffs that are possible by varying the decision criteria, show predictive performance with respect to chance, and show the difference between various models. Two ROC curves were generated to predict ponderosa pine mortality following fall prescribed fires in northern Idaho. One ROC curve was developed from rules of thumb using percent crown scorch. A second ROC curve was developed from a logistic mortality model using diameter at breast height and scorch height. Overall, percent crown scorch is a better predictor of mortality than scorch height, and thus should be used to plan and conduct salvage operations in ponderosa pine following a fire. Because of the difficulties involved in predicting percent crown scorch before a fire, the logistic model based on scorch height can be used to plan understory prescribed fires. For. Sci. 36(1):66-76.