Forest modelling: the gamma shape mixture model and simulation of tree diameter distributions

Podlaski, Rafał

doi:10.1007/s13595-017-0629-y

Cited by 28 publications

(15 citation statements)

References 29 publications

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“…The distribution patterns of the data could be examined or simulated using the Weibull and Gamma distribution functions. In recent years, there can be possible of using the Gamma Shape Mixture (GSM) model that correctly approximates the highly skewed distributions and precisely separates the dendrometric data from older and younger stands [ 85 , 86 ].…”

Section: Discussionmentioning

confidence: 99%

Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

Sharma

Vacek

et al. 2017

PLoS ONE

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Height to crown base (HCB) of a tree is an important variable often included as a predictor in various forest models that serve as the fundamental tools for decision-making in forestry. We developed spatially explicit and spatially inexplicit mixed-effects HCB models using measurements from a total 19,404 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) on the permanent sample plots that are located across the Czech Republic. Variables describing site quality, stand density or competition, and species mixing effects were included into the HCB model with use of dominant height (HDOM), basal area of trees larger in diameters than a subject tree (BAL- spatially inexplicit measure) or Hegyi’s competition index (HCI—spatially explicit measure), and basal area proportion of a species of interest (BAPOR), respectively. The parameters describing sample plot-level random effects were included into the HCB model by applying the mixed-effects modelling approach. Among several functional forms evaluated, the logistic function was found most suited to our data. The HCB model for Norway spruce was tested against the data originated from different inventory designs, but model for European beech was tested using partitioned dataset (a part of the main dataset). The variance heteroscedasticity in the residuals was substantially reduced through inclusion of a power variance function into the HCB model. The results showed that spatially explicit model described significantly a larger part of the HCB variations [R2adj = 0.86 (spruce), 0.85 (beech)] than its spatially inexplicit counterpart [R2adj = 0.84 (spruce), 0.83 (beech)]. The HCB increased with increasing competitive interactions described by tree-centered competition measure: BAL or HCI, and species mixing effects described by BAPOR. A test of the mixed-effects HCB model with the random effects estimated using at least four trees per sample plot in the validation data confirmed that the model was precise enough for the prediction of HCB for a range of site quality, tree size, stand density, and stand structure. We therefore recommend measuring of HCB on four randomly selected trees of a species of interest on each sample plot for localizing the mixed-effects model and predicting HCB of the remaining trees on the plot. Growth simulations can be made from the data that lack the values for either crown ratio or HCB using the HCB models.

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Section: Discussionmentioning

confidence: 99%

Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

Sharma

Vacek

et al. 2017

PLoS ONE

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“…The deviance of each DDT from the stand‐level diameter distribution was calculated as the sum of the absolute differences in the proportional abundance of each size class, across all and for each size class. Although gamma‐shape mixture models have recently been successfully applied to approximate and simulate complex diameter structures and identify distinct diameter types (Podlaski, , ), to facilitate comparisons with the broader literature, we classified all DDTs into the archetypical distributions of Janowiak, Nagel, and Webster (). Best (lowest AIC; Burnham & Anderson, ) mixed (repeated measures) regression models (of log 10 tree density/ha on DBH, DBH 2 and DBH 3 size‐class midpoints) using the distributions of each neighbourhood as replicates (random effects) were used to classify DDTs (fixed effect) into the following archetypes: NE, negative exponential (−DBH); IQ, increasing‐q (−DBH 2 or −DBH 3 ); RS, rotated sigmoid (−DBH + DBH 2 − DBH 3 ); CO, concave (−DBH + DBH 2 or −DBH + DBH 3 ) or UNI, unimodal (+DBH − DBH 2 or +DBH − DBH 3 or +DBH 2 − DBH 3 ).…”

Section: Methodsmentioning

confidence: 99%

“…The deviance of each DDT from the stand-level diameter distribution was calculated as the sum of the absolute differences in the proportional abundance of each size class, across all and for each size class. Although gamma-shape mixture models have recently been successfully applied to approximate and simulate complex diameter structures and identify distinct diameter types (Podlaski, 2016(Podlaski, , 2017, to facilitate comparisons with the broader literature, we classified all DDTs into the archetypical distributions of Janowiak, Nagel, and Webster (2008…”

Section: Neighbourhood Quantificationmentioning

confidence: 99%

One shape fits all, but only in the aggregate: Diversity in sub‐stand scale diameter distributions

Zenner

Peck

Sagheb-Talebi

2018

J Vegetation Science

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Questions To what extent are the sub‐stand size class distributions at the neighbourhood patch scale masked at the stand level via spatial smoothing? What are the implications for naturalness assessment of obscuring, at the stand level, structures that arise from endogenous processes at the neighbourhood scale? Location Elborz Mountains, south of the Caspian Sea, Iran. Methods Natural uneven‐aged old‐growth Oriental beech (Fagus orientalis) forest subject to fine‐scale disturbances was stem‐mapped in a 1.2‐ha plot of live trees >7.5 cm DBH; neighbourhoods were delineated across multiple scales using the tree‐centred floating neighbourhood approach of spatial tessellation to connect trees to their natural neighbours. Cluster analysis was used to identify an optimal number of recurring diameter distribution types (DDT) based on the proportion of trees in each of the five size classes. The richness of DDTs was assessed and the extent of DDTs was modelled as a function of tree size. Results The number of member trees and spatial extent increased with neighbourhood scale. While the stand‐level tree size class distribution exhibited a rotated sigmoid shape, the nine most distinct DDTs were characterized by four different distribution shapes (negative exponential, increasing‐q, rotated sigmoid and unimodal) and varied considerably in the abundance of trees in different size classes. Each individual tree contributed to at least three of the nine DDTs, which were nonetheless spatially distinct and varied in extent with size class composition. As expected, all metrics exhibited spatial smoothing (i.e., increasing homogeneity with increasing scale) as small, heterogeneous tree neighbourhoods were expanded into larger neighbourhoods with more similar average composition, which converged on a rotated sigmoid shape at the broadest scale. Conclusions The stand‐level rotated sigmoid distribution reflected spatial smoothing across more heterogeneous fine‐scale tree neighbourhood patches. Further studies are needed to assess if a better measure of natural forest structure may be the diversity of sub‐stand structures and the contribution of individual trees to that diversity, rather than an aggregated metric that averages across the hallmark heterogeneity of neighbourhood dynamics.

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“…With these assumptions, the α and β values were calculated (for detailed information, see Venturini et al 2008). Generally, the GSM model is very useful for modelling differentiated data sets (Venturini et al 2008;Podlaski 2017).…”

Section: Identification Of Dbh Structural Typesmentioning

confidence: 99%

Can forest structural diversity be a response to anthropogenic stress? A case study in old-growth fir Abies alba Mill. stands

Podlaski

2018

Annals of Forest Science

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& Key message From 1973 to 1991, Polish SO 2 emissions above 3250 Gg/year resulted in a decline of fir Abies alba Mill. After stresses connected with these emissions, five main diameter at breast height (DBH) structural types were described. This type of heterogeneous forest structure is supposed to increase forest resistance and resilience to abiotic, biotic and anthropogenic disturbances. & Context The analyses of forest structure are important under the current scenario of global change, since heterogeneous structures allow for better responses to disturbances. Forests with more complex structures should present greater vitality. & Aims The main hypotheses were as follows: (1) the temporal changes of atmospheric SO 2 emissions caused (a) the abrupt changes in the tree DBH radial increment and (b) the death of fir trees; and (2) atmospheric SO 2 emissions and related fir decline and recovery processes ultimately result in the development of stands characterised by diverse DBH structures. & Methods Radial growth trends of 49 and 215 fir trees in the older and younger generations, respectively, and 85 dead fir trees were evaluated. Using data collected in 32 stands, the DBH structural types were identified, and the shapes of these types were illustrated. & Results The structural diversification of forest patches may influence forest resistance and resilience to disturbances; five main structural types were identified: ML1 and ML2 represent DBH distributions of multi-layered stands, and OS, TS1 and TS2 represent DBH distributions of one-and two-storied stands. & Conclusion Structural diversity of forests was a response to SO 2 emissions; fir trees had the ability to increase their radial growth, although there were still high SO 2 emissions.

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Forest modelling: the gamma shape mixture model and simulation of tree diameter distributions

Cited by 28 publications

References 29 publications

Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

Modelling individual tree height to crown base of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.)

One shape fits all, but only in the aggregate: Diversity in sub‐stand scale diameter distributions

Can forest structural diversity be a response to anthropogenic stress? A case study in old-growth fir Abies alba Mill. stands

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