Distance-dependent Growth Research Articles

Individual-tree distance-dependent growth models for uneven-sized Norway spruce

Abstract Individual tree selection (ITS) is one option to manage uneven-sized forest ecosystems. However, scientifically based field guidelines adapted to ITS and economic profitability are rare, often because there is a lack of suitable tree models to use in growth and treatment simulations. The objective of this study is to develop individual-tree distance-dependent growth models focusing on Norway spruce dominated uneven-sized stands. Three models of different complexity, but with the same structural basis, are presented, followed by some examples of growth patterns for the subject trees. The data include 1456 trees (307 sample trees) collected from five sites in southern Sweden. The basic model (S) depends on subject tree size as the predictor, the second model (SD) adds distance to competitors as a predictor, and the third model (SDC) adds crown ratio as a predictor to the structure. R2Adj increases with number of predictors from 0.48 to 0.58 to 0.62. The levels of RMSE improve accordingly from 5.02 cm2 year−1 (S) to 4.43 cm2 year−1 (SD) and 4.26 cm2 year−1 (SDC). The present calibration range and model structures primarily make the models suitable for management simulation of individual-tree selection of Norway spruce in southern Sweden. The format of the models allows for further extension with additional predictors and calibration data with greater coverage.

Developing distance-dependent growth models from irregularly measured sample plot data – A case for Larix olgensis in Northeast China

The need for distance-dependent individual-tree models for diameter increment and survival is increasing due to the increased use of individual-tree detection in forest inventories based on remote sensing data. Distance-dependent models can be used to analyze alternative thinning schemes, planting patterns and species mixing. The present study developed a methodology to develop distance-dependent models from data where the measurement interval of the sample plots is irregular. The method employs optimization to find the parameters of a simulation software in such a way that the simulated diameter distribution at the end of the measurement interval matches with the measured distribution. The methodology was applied to Larix olgensis A. Henry plantations of the Heilongjiang province of northeastern China. The distance-dependent models were fitted using two alternative competition indices adopted from earlier literature. The optimal way of computing the competition indices was solved simultaneously with the coefficients of model predictors. Distance-independent models were also fitted, and they provided a reference for assessing the performance of the distance-dependent models. The results indicated that the distance-dependent models did not provide better estimates on the periodical change of stand basal area or number of trees per hectare, compared to distance-independent models. However, the distance-dependent models are still useful as they enable model-based analyses of spatial questions.

Relaxation Dynamics of Electronically Coupled Au20(SC8H9)15-n-glyme-Au20(SC8H9)15 Monolayer-Protected Cluster Dimers

The electronic relaxation dynamics of photoexcited Au20(SC8H9)15-n-glyme and Au20(SC8H9)15-n-glyme-Au20(SC8H9)15 (n- = di-, tri-, and tetra-) dimers, where glyme refers to n-ethylene glycol dimethyl ether bridging molecules, were studied using pump–probe femtosecond time-resolved transient absorption spectroscopy (fsTAS). The utilization of n-glyme molecular bridging linkers provided a method to prepare Au20(SC8H9)15-n-glyme-Au20(SC8H9)15 dimers with control over intercluster spatial separation. A dimer-specific electronic absorption resonance was observed at 2.6 eV. Analysis of fsTAS differential spectra for dimer species revealed a pump–probe waiting time-dependent blue shift of the low energy excited-state absorption (ESA) feature, suggesting electronic relaxation into a dimer-specific excited-state. Single probe-energy differential signal amplitude analysis of the ESA feature yielded a distance-dependent growth component for the electronic relaxation dynamics with time constants of 130 ± 20, 60 ± 8, a...

Competition and dominance between angiosperms and Araucaria angustifolia (Bert.) O. Kuntze in the Atlantic Forest in southern Brazil

The dominance relationship between angiosperms and gymnosperms in natural forests has long been widely discussed, with some researchers believing that angiosperms tend to displace conifers due to competitive processes between the two species groups. The Lozenge or “temporal stand replacement” model states that a cohort of conifers is first established after a disturbance, while angiosperms establish themselves under the conifer canopy in a secondary stage that thereafter hinders conifer regeneration. This causes a drastic decline in conifer recruitment, restricting them to filling in gaps opportunistically. The objective of this study was to evaluate the competition for growth and survival between a conifer (Araucaria angustifolia) and two groups of angiosperms (shade-tolerant and light-demanding) in a species-rich forest using a distance-dependent competition index. We also investigated dominance among the three species groups by projecting the aboveground biomass of the groups for 50 years using an individual-tree distance-dependent growth model. We used data collected from 25 1-ha permanent plots located in the National Forest (FLONA) of Irati in southern Brazil, where all trees with more than a 10-cm diameter at breast height were identified for species and tagged, mapped, and measured. These plots have been measured every 3 years since their establishment in 2002. For diameter growth, the results indicated the araucarias were subject to severe intraspecific competition, while the light-demanding species suffered only moderate competition from the araucarias. The shade-tolerant species experienced little competition from any species group. No empirical evidence was found to support the hypothesis that competition estimates improve mortality predictions in a simple model based on stem diameter. Regarding the long-term dominance of the Araucaria, light-demanding, and shade-tolerant groups, the growth model indicated that araucarias will tend to dominate over the two angiosperm groups in aboveground biomass within 50 years, suggesting that this forest type follows the Lozenge model.

A tree distance-dependent growth and yield model for naturally regenerated pure uneven-aged maritime pine stands in central inland of Portugal

Maritime pine (Pinus pinaster Aiton) is one of the most important Portuguese species, growing in pure stands ranging from even-aged to multi-aged structures. Current growth and yield models were developed only for even-aged, managed stands and/or for very specific regions of Portugal. This paper focuses on the validation of the existing size-class model PBRAVO, adapted to even-aged stands, and on the subsequent development of a single tree distance-dependent growth and yield model (PBIRROL), both in distance-independent and distance-dependent versions, for uneven-aged stands. The new model is composed of four modules, each with a set of sub-models for: tree variable prediction, tree volume prediction, future tree list prediction and growth projection. The evaluation of the PBRAVO and PBIRROL models showed that the new model gives more accurate predictions. Moreover, medium-term simulations provided consistent and logical predictions. It was verified that individual tree models are more suited to simulate poorly managed uneven-aged stands than diameter distribution models. No clear superiority of distance-dependent models was found over models using just distance-independent measures of inter-tree competition.

Spatial Tree Mapping Using Photography

Abstract Stem maps describing the spatial location of trees sampled in a forest inventory are used increasingly to model relationships between neighboring trees in distance-dependent growth and yield models, as well as in stand visualization software. Current techniques and equipment available to acquire tree spatial locations prohibit widespread application because they are time-consuming, costly, and prone to measurement error. In this report, we present a technique to derive stem maps from a series of digital photographs processed to form a seamless 360° panorama plot image. Processes are described to derive distance from plot center and azimuth to each plot tree. The technique was tested on 46 field plots (1,398 sample trees) under a range of forest conditions and compared with traditional methods. Average absolute distance error was 0.38 ± 0.44 m, and average absolute azimuth error was 2.3 ± 2.5°. Computed average horizontal accuracy was 0.40 ± 0.42 m, with 85% of measured trees being within 0.5 m of the field-measured tree location.

Scale and spatial structure effects on tree size distributions: implications for growth and yield modelling

Diameter and other size distributions are extensively used in growth modelling. These are usually obtained from sample plot data and assumed to apply both at the stand level, of interest for production planning, and at the forest patch level, the level relevant for tree growth interactions. However, spatial correlation can cause distribution parameters and their estimates to vary with the extent of ground considered. Using mapped tree data from four forest stands in central Canada, it is shown that differences in DBH variance with plot size can be substantial. In addition, size correlations between neighbouring trees were positive, rather than negative as implied by current distance-dependent growth models. Biases in mean DBH are also found. It is proved that plot totals and frequencies are unbiased estimates of stand parameters, but variances and some other statistics are not. The expected variance is expressed in terms of plot size and shape and of second-order stand spatial structure properties. Some possible approaches for reducing bias in stand-level variance estimates are discussed, and the desirability of modelling microsite or genetic spatial correlations in individual-tree simulators is pointed out.

TADAM: A dynamic whole-stand approximation for the TASS growth model

Growth and yield predictions for managed even-aged stands in British Columbia are based on TASS, an individual-tree distance-dependent growth model driven by an unusually detailed description of cr...

TADAM: A dynamic whole-stand approximation for the TASS growth model

Growth and yield predictions for managed even-aged stands in British Columbia are based on TASS, an individual-tree distance-dependent growth model driven by an unusually detailed description of crown development. Because of its complexity, most applications utilize previously generated stand-level yield tables rather than running TASS directly. I have developed a differential equation approximation to the stand-level dynamics predicted by TASS that mimics the aggregate behaviour with sufficient accuracy for many practical purposes. Versions of this model, called TADAM, exist for planted coastal Douglas-fir, lodgepole pine, and white spruce. TADAM can efficiently project stand development starting from any initial conditions, and subject to any combination of thinnings. Its relative simplicity makes it suitable for embedding into landscape-level planning models and other decision support systems. It has been implemented as a C function library, as an interactive simulator running on a PDA, and as an Excel spreadsheet add-in. An example of thinning and planting density optimization is briefly described. Key words: growth and yield, stand dynamics, thinning, optimization, Pinus contorta, Picea glauca

Application of ecological field theory in distance-dependent growth modelling

In this study, we compared the performance of an additive competition index and two new index types derived from ecological field theory. One type of competition index at a time was used as a distance-dependent predictor in a diameter growth model, together with a permanent set of distance-independent predictors. One of the new index types was computed multiplicatively from the relative influences of competitors at the location of the subject tree. This may be called the ecological interference potential of competitors. The other new index was a simple spatial integral of the ecological interference potential around the subject tree. Its value depends on the directional distribution of competitors. The results indicated that, for both Scots pine ( Pinus sylvestris L.) and Norway spruce ( Picea abies (L.) Karst.), the indices based on ecological field theory are better predictors of a growth model than a traditional additive index is. The spatial integral of the interference potential was better than the point value.

Modelling the conversion from even-aged to uneven-aged stands of Norway spruce (Picea abies L. Karst.) with a distance-dependent growth simulator

The paper provides a conversion regime from even-aged to uneven-aged stands of Norway spruce (Picea abies L. Karst.). The conversion regime was tested by the distance-dependent single-tree simulator SILVA 2.1. The initial data for the simulation and the assumed site productivity were deduced using inventory data of the north Black Forest. The conversion regime was compared to a typical future-tree oriented age–class treatment system. Thereby four variants of the conversion regime, differing in the number and diameter of the ‘regeneration-funnels’ (gaps in the canopy of the stand) which were created during the ‘graded-regeneration-phase’, were compared to a basal-area oriented future-tree age–class treatment. A simulation-run of 110 years — divided into 22 periods of five years — was conducted. The analysis of the simulation-run showed that the possibilities to achieve uneven-aged structures in single-layered, even-aged stands through ‘structuring measures’ during thinning or target–diameter harvesting were very limited. The success of the conversion depended mainly on the success of the regeneration during the conversion. The early creation of ‘regeneration-funnels’ was linked to severe losses in increment and standing volume. As well as influences on different stand-parameters (e.g. stem-distribution) changes in structure-parameters caused by the conversion could be assessed. In particular, the modified Shannon-index did react distinctly to the implementation of the natural regeneration in the regeneration-funnels. Indeed, a steady state was only temporarily reached with the variant with the largest gaps. Finally, the results of the conversion experiment were subject to a critical review. Thus, the limits of the model in its current version and further research needs were discussed.

MORPHOMETRIC ANALYSIS OF CC10-hASH1 TRANSGENIC MOUSE LUNG: A Model for Bronchiolization of Alveoli and Neuroendocrine Carcinoma

Constitutive expression of human achaete-scute homolog-1 (hASH1) alone or in combination with Simian virus 40 (SV40) large T antigen (TAg) under the Clara cell 10-kDa secretory protein (CC10) promoter results in bronchiolization of alveoli and enhanced tumorigenesis, respectively. A novel morphometric system composed of series of fixed distance concentric rings originating at the bronchioloalveolar junction was used to determine spatial growth patterns. hASH1 mice exhibited progressive airway epithelial hyperplasia near this junction, and minimal changes further away in the alveolar compartment. TAg animals shared this increase, but exhibited variable distancedependent growth. By 2 months TAg/hASH1 animals showed highly increased growth at all points measured. Remarkably, TAg/hASH1 animals expressed both CC10 and extensive neuroendocrine differentiation in airways and tumors. The results suggest that these transgenic mice provide a useful model with many similarities to human lung carcinogenesis, which originates in airway epithelium, and often reveals neuroendocrine differentiation.

New derivation reduces bias and increases power of Ripley’s L index

The development of distance-dependent growth and survival models depends on an understanding of the spatial distribution of the population in question. Ripley’s L index ( L R) has found wide application for examining the spatial dispersion of plants. L R is calculated as the square root of a weighted sum of the number of observed plant pairs that are less than a certain distance apart. The weighting used by L R inflates the pair count sum to compensate for reduced pair counts for plants near the plot boundary. Using Monte Carlo simulations, we show that the variance in the observed number of tree pairs is not stabilized by the square root transformation at low expected counts. The non-linearity of the square root transformation introduces a consistent bias in both the first and second moments of the tree pair distribution. We present a derived estimator for Ripley’s analytical L index ( L A) that provides a more accurate estimate of variance and mean. This new approach, based on a true Poisson variate, includes a modification of the previous edge correction method that incorporates a global estimate of mean pair density, rather than local values. This reduces variance caused by stochastic placement of point pairs near the boundary. Monte Carlo simulations verified the predictions of this model over a wide range of population sizes (25–1400). Simulation results showed that the L R numerical estimate of the confidence limit was overly conservative by nearly a factor of two. The improved power and accuracy provided by L A suggest that it would be fruitful to reexamine population spatial dispersion data in the literature using the analytical estimator ( L A). As an illustration, the power and accuracy of L R and L A to detect non-random spatial dispersions is compared using generated populations and six stands of mapped trees in Connecticut.

Distance-dependent models for predicting the development of mixed coniferous forests in Finland

Distance-dependent growth models and crown models, based on extensive material, were built for Scots pine and Norway spruce growing in a mixed forest. The crown ratio was also used as a predictor in a diameter growth model to better describe the thinning reaction. The effect of crown ratio on the growth dynamics was studied in simulation examples. Monte Carlo simulation was used to correct the bias caused by nonlinear transformations of predictors and response. After thinnings the crown ratio as a predictor was found to be a clear growth-retarding factor. The growth retarding effect was stronger among pines with thinnings from below, whereas the estimated yield of spruces over rotation was slightly greater when the crown ratio was included than without it. With each type of thinning the effect of crown ratio on pine growth was almost the same, but the growth of spruces was clearly delayed when the stand was thinned from above. Simulation examples also showed that it is profitable to raise the proportion of spruces during rotation, since spruces maintain the growth more vigorous at older ages. The total yield during 90 years rotation was about 20% higher if the stand was transformed into a pure spruce stand instead of pine.

Tree-selection algorithms for optimizing thinning using a distance-dependent growth model

When a distance-dependent yield model is used in growth simulation and optimization, the stand is described by a plot on which the trees are described by species, DBH, height, age, coordinates, and other characteristics. Optimizing a distance-dependent model requires that the trees to be removed in a thinning treatment be specified individually and that a special algorithm be developed for this selection. This algorithm affects the formulation of the optimization problem. In this study, we compared four different problem formulations for optimizing a distance-dependent yield model: (1) Harvest percentages in different diameter classes were utilized together with a tree-selection algorithm proposed earlier; this algorithm removed trees on the basis of competitive status. The algorithm was fixed, i.e., it was not amenable to numerical optimization. (2) Minimum distances between remaining trees were used as decision variables. (3) Minimum distances were used with harvest percentages and the existing tree-selection algorithm. (4) The tree-selection algorithm was made dependent on two parameters, which were optimized together with harvest percentages in different diameter classes. Based on case optimizations in pure and mixed conifer stands, the fourth formulation was considered to be the best one from the standpoint of simplicity of optimization and in terms of the objective function value.

Tree-selection algorithms for optimizing thinning using a distance-dependent growth model

Tree-selection algorithms for optimizing thinning using a distance-dependent growth model