On individual tree competition indices, airborne laser scanning, and plot edge bias

Rune Østergaard Pedersen presented a lecture on a predefined topic and defended his doctoral thesis on March 21,  2014. The topic for the trial lecture was “Accounting for symmetric and asymmetric competition in traditional and Lidar-derived competition indices”  and the title of his thesis was “On individual tree competition indices, airborne laser scanning, and plot edge bias”. We congratulate!

Thesis abstract

The thesis comprises an investigation of individual tree competition indices and their ability to predict individual tree growth at breast height in boreal forests located in Norway. The thesis consists of four papers referred to as Paper I-IV.

In Paper I a number of individual tree competition indices were derived from airborne laser scanning. A selection of existing individual tree competition indices were used as benchmarks, and tested against the derived competition indices in data from Østmarka Boreal Reserve. We tested the competition indices for their ability to predict diameter growth at breast height using various fixed search radii to identify competitors. The results show that competition indices based on airborne laser scanning perform as good as, and in some cases even better than existing spatially and non-spatially explicit competition indices, and that search radii beyond approximately 7 m do not increase index performance.

In Paper II we analyze the assumptions used in model evaluation of competition indices, more specifically statistical inference based on competition indices calculated from overlapping samples, using the permanent sample plots of the Norwegian National Forest Inventory located in Hedmark County. Our hypothesis was that sample overlap will cause spatial similarity which will lead to spatial autocorrelation. Competitors were isolated around each subject trees tree by means of a relascope or fixed sampling radius. Using statistical measures of dependence, we were able to show that spatial autocorrelation does not seem to increase the statistical type I error rate. Furthermore, the statistical type I error rate did not seem to correlate with measures of stand structure like the Gini-coefficient and Lorey´s mean height. A significant smoothing effect caused by sample overlap was observed by a decrease in the coefficient of variation of the samples for increasing search radii around the subject trees. However, the level of smoothing on the individual plot seems not to decrease the abilities of the competition indices to predict diameter growth at breast height of trees.

In Paper III I investigate how the components inverse distance and size-ratio in Hegyi´s distance weighted size-ratio behave in a spatially correlated field. I tested different kinds of standardization proposed in the literature to correct for increased spacing at different age-classes. A case study was made in Østmarka Boreal Reserve, which was supplemented by a spatial simulation study under different degrees of spatial autocorrelation and stand structure. A non-spatially explicit competition index was also included in the study. Calculations on the plot level in Østmarka Boreal Reserve of Moran´s I revealed that Hegyi´s competition index in most cases reduces the level of spatial autocorrelation, and statistical type I error in e.g. correlation tests, when compared to the level of spatial autocorrelation observed in diameter at breast height. By fractionizing Hegyi´s competition index into the components inverse distance and size-ratio, I concluded that it is the size-ratio that decreases the positive spatial autocorrelation in the empirical data, especially for the highest levels of Moran´s I in diameter at breast height. For the simulation study this trend was not that clear and spatial autocorrelation also increased for the size-ratio for high mean values of the distribution of diameter at breast height. All tested competition indices seemed particular sensitive to the mean value of the distribution of diameter at breast height, and higher distribution mean values induce positive spatial autocorrelation. The simulated standard deviation of the distributions of diameter at breast height, and the spatial autocorrelation of trees seem to be of less importance. In the study I included local indicators of spatial association (LISA). The empirical data showed that LISA from Hegyi´s competition index was smaller for hotspots when compared to LISA of diameter at breast height (less positive spatial autocorrelation), which is a result of the size-ratio term in Hegyi´s competition index. A non-spatially explicit competition index seems to behave spatially more like diameter at breast height, thus preserving the spatial autocorrelation. An important idea derived from the study is that the best possible spatially explicit competition index to predict individual tree growth is a measure of local spatial autocorrelation of tree growth.

When trees outside the spatial range of the data area affect the trees inside this area, a border effect appears that leads to biased estimates of competition. This is known as plot edge bias. In Paper IV I present new methods for correcting plot edge bias using metrics derived from airborne laser scanning as auxiliary information in multivariate ratio estimators and regression models. Comparisons with existing methods based on simulation and linear expansion show, that the existing methods generally perform better than the ones based on airborne laser scanning. For all of the tested methods improvements in growth predictions measured by the adjusted coefficient of determination and AIC were small and only around one to two percent different from the original data. However, statistical tests showed that they were significant. In many cases plot edge bias correction did not improve predictions of individual tree growth, and the tested competition indices showed large variations in the effectiveness as predictors.  It should be noted that some of the competition indices we derived in Paper I also eliminate plot edge bias, because a buffer of airborne laser data can be taken around the plot, and the physical positions of the competing trees need not to be known.


Professor Erik Næsset, Dept. of Ecology and Natural Resource Management, NMBU (main supervisor)
Professor Terje Gobakken, Dept. of Ecology and Natural Resource Management, NMBU (co-supervisor)
Researcher Ole Martin Bollandsås, Dept. of Ecology and Natural Resource Managenemt, NMBU (co-supervisor)

Evaluation committee

Professor Margarida Tomé, Instituto Superior de Agronomia, Portugal
Associate Professor Phil Radtke, Virginia Tech, USA
Associate Professor Line Nybakken, NMBU


[bibtex file=SkogRoverAll.bib key=Pedersen2014]

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