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Spatial analysis is of primary importance in forestry. Many factors that affect tree development have spatial components and can be sampled across geographic space. Some examples of spatially structured factors that affect tree growth include soil composition, water availability, and growing space. Our goals for this dissertation were to test the efficacy of spatial analysis tools in a forestry setting and make recommendations for their use. Reliable spatial analysis tools will lead to more effective statistical testing and can lead to useful mapping of spatial patterns. The data for this project is from simulated even aged loblolly pine stands (Pinus taeda L.). These simulated stands are grown at regular spacing and we impose a range of parameters on the stands to simulate many possible scenarios. In chapter 3 of this dissertation we perform a sensitivity analysis to determine if our methods are suitable for further research and applications. In chapter 4 we perform our analysis on more realistic data generated by a spatially-explicit stand simulator, PTAEDA 4.1. In chapter 3 we performed a statistical simulation of plantation stands without effects of competition and mortality. We used redundancy analysis (RDA) to quantify spatial variability, partial redundancy analysis (pRDA) to test for spatial dependence, and spatially constrained cluster analysis to map soil productivity. Our results indicated that RDA and pRDA are reliable methods and future evaluation is appropriate. The results from the spatially constrained cluster analysis were less clear. The success or failure of the clustering algorithm could not be disentangled from the success or failure of the selection criterion used to predict the number of clusters. Further investigations should address this concern. In chapter 4 we used PTAEDA 4.1, a loblolly stand simulator, to simulate a range of site conditions and produce data that we could use for analysis. The results showed that RDA and pRDA were not reliable methods and ready for the field. Spatially constrained cluster analysis performed poorly when more realistic data was used and because of this further use was uncertain. It was clear from the results that levels of variation and spatial pattern complexity of microsites influenced the success rate of the methods. Both RDA and pRDA were less successful with higher levels of variation in the data and with increased spatial pattern complexity. In chapter 5 we related the coefficient of variation from our simulations in (chapters 3 and 4) to two sets of real plot data, including a clonal set and open pollinated set. We then implemented a spatial analysis of the real plot data. Our spatial analysis results of the two comparable data sets were unaffected by genetic variability indicating that the primary source of variability across plots appears to be soil and other factors, not genetic related. Ph. D.

Forest measurements are inherently spatial. Soil productivity varies spatially at fine scales and tree growth responds by changes in growth-age trajectories. Measuring spatial variability is a perquisite to more effective analysis and statistical testing. In this study, current techniques of partial redundancy analysis and constrained cluster analysis are used to explore how spatial variables determine structure in a managed regular spaced plantation. We will test for spatial relationships in the data and then explore how those spatial relationships are manifested into spatially recognizable structures. The objectives of this research are to measure, test, and map spatial variability in simulated forest plots. Partial redundancy analysis was found to be a good method for detecting the presence or absence of spatial relationships (~95% accuracy). We found that the Calinski-Harabasz method consistently performed better at detecting the correct number of clusters when compared to several other methods. While there is still more work that can be done we believe that constrained cluster analysis has promising applications in forestry and that the Calinski-Harabasz criterion will be most useful. Master of Science