Browsing by Author "Gregoire, Timothy G."

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    An analysis of correlated curve trend experiments in Eucalyptus grandis
    Bredenkamp, Brian Victor (Virginia Polytechnic Institute and State University, 1988)
    Correlated curve trend (C.C.T.) experiments in Eucalyptus grandis on the Zululand coast of South Africa were analyzed. Growth parameters were described as functions of age using Schnute’s generalized growth function and parameter estimates were described as functions of stand density. Growth attributes were used as moments of a probability density function to describe a diameter distribution model for the species. Time trends in the relationships between growth parameters and stand density were scrutinized with multiple comparisons of paired means. It was shown that diameter growth in lower size classes ceases under conditions of extreme suppression while growth continues unabated in the larger size classes, resulting in greater dispersion in diameter. Competition mortality was to a large extent confined to the lower size classes and severe mortality results in an apparent increase in mean diameter which precludes use of growth functions which impose an asymptote. Allometric growth was investigated on two different sites and growth trends were shown to be anamorphic between sites. This permits a ratio approach to the estimation of growth and yield on one site based on experimental evidence from another. Thinning effects in terms of diameter and height changes were estimated from simulated thinnings using data from unthinned stands while the results of long-term thinning studies were compared in terms of cumulative volume yields. The age at which mean annual increment culminates was determined and a model for the estimation of m.a.i. as a function of age and stand density was constructed. A critical examination of spacing indices revealed that the slopes thereof were much steeper than those for many other species. The better-known indices of Reineke and Yoda were found to be dependent on age.
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    The analysis of longitudinal ordinal data
    Schabenberger, Oliver (Virginia Tech, 1995)
    Longitudinal data, in which a series of observations is collected on a typically large number of experimental units is one of the most frequent and important sources of quantitative information in forestry. The dependencies among repeated observations for an experimental unit must be accounted for in order to validate statistical estimation and inference in modeling efforts. The recent advances in statistical theory for correlated data created a body of theory which will become of increasing importance as analysts realize the limitations of traditional methods that ignore these dependencies. Longitudinal data fosters research questions that focus on the individual experimental unit rather than the population as in classical cross-sectional data analysis. Mixed model techniques have emerged as powerful tools to address research problems of this kind and are treated extensively in this dissertation. Over the last years interest in modeling quantal responses that take on only a countable, discrete number of possible values has also increased throughout the discipline. The theory of generalized linear models provides the groundwork to embody quantal response models into the toolbox of applied analysts. The focus of this dissertation is to combine modern analytical tools for longitudinal data with regression methods for quantal responses. Special emphasis is placed on ordinal and binary data because of their prevalence in ecological, biological, and environmental statistics. The first chapters review the literature and introduce necessary theory. The second part of this dissertation consists of a case study in which binary and ordinal fusiform rust response on loblolly and slash pine is modeled in a longitudinal data base provided by the East Texas Pine Plantation Research Project.
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    Analysis of timber harvest scheduling under alternative levels of land aggregation: an application to a hypothetical Mexican forest ownership
    Hernandez-Vazquez, Edgardo (Virginia Polytechnic Institute and State University, 1989)
    The problem of optimal land organization was approached via a general methodology to aggregate finely distinguished planning unit areas of an even-aged ponderosa pine forest in Northwestern Mexico. Factor analysis was applied to eighteen timber inventory variables to produce four independent and meaningful constructs that explained 87% of the total variable set’s variation. Next, each planning unit area was characterized by its factor scores and an Euclidean-metric based analysis was applied. The resultant Dendrograrn’s structure helped to define four levels of land aggregation that were evaluated with the same forest management policy. This policy simulated current Mexican forestry guidelines such as replacement stand’s regimes based on maximum mean annual increment, and area volume constraints for timber harvest scheduling. Then, the present value-maximizing timber harvest schedules for each level of land organization was found by using LP Model 1 formulations. Results showed that timber harvesting net benefits varied between 1.3% and 7.0% across levels of land aggregation. This fact was a consequence of the biophysical homogeneity of the forest and the Mexican assumptions of prices and flat costs for overhead and planning. Theoretical considerations indicated that if overhead and planning costs are properly considered for every level of land aggregation, the study’s methodology could show a greater present value difference between alternative levels of land organization.
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    Basal Area Growth and Crown Dynamics in a Loblolly Pine Spacing Trial
    Radtke, Philip J. (Virginia Tech, 1996-08-02)
    Relationships between the culmination of basal area growth and degree of crown closure in loblolly pine (Pinus taeda L.) were investigated. A spacing trial established on the low Appalachian Piedmont and Atlantic Coastal Plain provided the data for the investigation. Test plots were planted at densities ranging from 303 to 2723 stems per acre, and at various rectangular and square spacings. Annual stem and crown measurements were used to derive the sought-after relationships. The age of basal area culmination was found to be inversely related to both planting density and site index. Crown closure was advanced on sites of relatively high quality, exhibiting an approximately linear increase with time from planting until the age of basal area culmination. The slope of this trend increased with planting density. The degree of crown closure at the age of basal area culmination was significantly higher on narrowly-spaced plots than it was on widely-spaced plots; however, it did not vary significantly with site index. Although crown closure is generally accelerated on high quality sites, the relatively early culmination of basal area growth on such sites offsets the increase - the net result being that crown closure at culmination age does not vary significantly with site differences. Crown closure indices can be used to determine whether or not a stand has reached the culmination of basal area growth; however, more readily available information on spacing and site index can be used to make the same prediction. The results of this study might be most useful to modelers of early stand dynamics in loblolly pine and other commercially important pines.
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    A comparison of spatial interpolation techniques in temperature estimation
    Collins, Fred C. (Virginia Tech, 1995-11-05)
    Spatially distributed estimates of meteorological data are becoming increasingly important as inputs to spatially explicit landscape, regional, and global models. Accurate estimates of meteorological values such as temperature, precipitation, and evapotranspiration are required for a number of landscape scale models, including those of regeneration, growth, and mortality in forest ecosystems. Given a set of meteorological data, researchers are confronted with a variety of stochastic and deterministic interpolation methods to estimate meteorological variables at unsampled locations. Depending on the spatial attributes of the data, accuracies may vary widely among different spatial interpolation methods. The choice of spatial interpolator is especially important in mountainous regions where data are sparse and variables may change over short spatial scales. While there have been comparisons of interpolation methods, few research efforts have been directed towards comparing the effectiveness of different spatial interpolators in predicting temperature. Due to the additional effort kriging and cokriging entails, it was decided to compare the effectiveness of kriging and cokriging in estimating mean, maximum, and minimum temperature at unsampled locations with less computationally intensive interpolation techniques such as inverse distance weighted averaging, cubic splining, the fitting of a trend surface, polynomial regression, and the lapse rate method. Eight interpolation techniques (inverse distance squared, optimal inverse distance, cubic splining, trend surface analysis, regression, kriging, cokriging, and the lapse rate method) were compared in their ability to predict temperature at unsampled locations. Temperature data for two regions, two scales (minimum and maximum temperatures) and three temporal scales (10 year mean, seasonal, and daily) were prepared and the eight methods were compared on the basis of bias, MAE, and MSE. In addition, summary statistics of interpolated mean, minimum, and maximum temperatures were recorded to determine how well the interpolated data represented the original temperature values. This dissertation provides evidence that certain apriori data characteristics such as temperature range, temperature variance, and temperature correlation with elevation may influence interpolator choice. The dissertation results also indicate that spatial scale and the relative spatial density and distribution of sampling stations may influence interpolator choice. These results should be of interest to scientists studying global warming. The MAEs associated with interpolation techniques which did not use ancillary information were far greater than the 0.5°F to 1.0°F estimate of global warming over the past 100 years. The use of regression techniques which utilize the relationship between temperature and elevation as ancillary information offers significant improvement over the current inverse distance weighting methods. The dissertation also shows that when station elevations are not representative of regional elevations, bias occurs. In Region 2, stations were underrepresented for higher elevations. Interpolation techniques which did not use elevation as ancillary information were biased 1.0°F to 3.0°F above techniques which used elevation. While it is unclear what the extent of this effect is on a global scale, one would suspect the use of distance weighting techniques would bias global estimates upwards. These dissertation results should also be of interest to scientists who use kriging and cokriging to interpolate irregularly spaced data onto a rectangular grid. The results indicate that when data are isotropic, less subjective methods, such as optimal inverse distance, have lower MAE values. The semivariogram fitting methodology outlined in this dissertation demonstrates how to fit semivariograms iteratively using an indicative goodness of fit (IGF) metric. Semivariogram fitting using an IGF is less subjective and more accurate than traditional fit-by-sight methods. Despite its mathematical elegance, kriging and cokriging did not perform better than many other less computationally intensive methods. In addition, when there is a more intensely sample covariate which is highly correlated, polynomial regression gave far better results than kriging or cokriging. The results of this dissertation should also be of interest to users of geographic information systems (GISs). Because climatic data such as temperature is sampled from an irregular network, a number of interpolation techniques can be used to convert the data to a regular grid for use in visualization, models and GISs. This dissertation shows that the choice of spatial interpolator can influence the resulting data accuracy. In addition, data attributes influence the choice of interpolator. What is dissertation shows, is that through preliminary data analyses, an interpolator may be chosen which yields the most accurate grid for input into a GIS. It should be noted that this dissertation has wider ranging applications beyond the three examples mentioned above. The results should be of interest in any field where point data is interpolated onto a regular grid. Additional application areas include, but are not limited to, medical imaging, scientific visualization, weather forecasting, ecological modeling, forestry, petroleum exploration, and hydrological modeling.
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    Development of a taper equation for Pinus oocarpa Schiede in natural stands of central Honduras
    Regalado, Darlin Noe Perez (Virginia Tech, 1988-06-05)
    Nine taper equations were tested to predict diameters inside bark along the stem for Pinus oocarpa Schiede trees growing in natural stands of central Honduras. A five parameter submodel predicted as well as an eight parameter model proposed by Kozak, 1988. Taper variation was explored between two geographic regions from which trees with different taper were suspected. Results showed that different site classes, not fully accounted for in the model, might have an effect on the prediction of taper in each region. Also, the effect of crown class and live crown ratio on prediction was evaluated. The model selected exhibited different prediction patterns for dominant and suppressed trees. On the other hand, live crown ratio did not appear to affect prediction. A computer program was written to use the taper equation developed to compute total and merchantable volume to different top diameter limits.
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    Dominance/Suppression Competitive Relationships in Loblolly Pine (Pinus taeda L.) Plantations
    Dyer, Michael E. (Virginia Tech, 1997-11-13)
    Data from three long-term field studies with loblolly pine (Pinus taeda L.) plantations were used to examine inequality (Gini coefficient) trends in diameter and the relationship between diameter relative growth rate (r) and initial size. Analysis with two spacing studies shows inequality increases with increasing density. For a given initial density, inequality initially decreases and then begins to increase as trees compete for resources. The slope of the linear relationship between r and relative size also increases with increasing density. The slope is initially negative and switches to positive as competition intensifies. The switch in the slope of the r/size relationship occurs when the crown projection area exceeds 1.05 or when the crown ratio falls below 0.75. These results are consistent with the resource pre-emptive or dominance/suppression theory of intra-specific competition. The r/size trends are not evident when calculations are based on class means as opposed to individual trees. The slope of the r/size relationship is a function of stand height, density, and to a lesser extent, site quality. Density reduction through mid-rotation thinning tends to decrease the slope coefficient. The r/size trends are used to develop a disaggregation model to distribute stand-level basal area growth over an initial tree list. This approach compares well with two other disaggregation models but tends to over predict growth on the largest trees.
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    Effect of manual digitizing error on the accuracy and precision of polygon area and line length
    Keefer, Brenton Jan (Virginia Tech, 1988-11-05)
    Manual digitizing has been recognized by investigators as a significant source of map error in GIS, but the error characteristics have not been well defined. This thesis presents a methodology for simulating manual digitizing error. Stream mode digitizing error was modeled using autoregressive moving average (ARMA) procedures, and point mode digitizing was stochastically simulated using an uniform random model. These models were developed based on quantification of digitizing error collected from several operators. The resulting models were used to evaluate the effect digitizing error had upon polygon size and total line length at varying map accuracy standards. Digitizing error produced no bias in polygon area. The standard deviation of polygon area doubled as the accuracy standard bandwidth doubled, but the standard deviation was always less than 1.6 percent of total area for stream mode digitizing. Smaller polygons (less than 10 square map inches) had more bias and more variance relative to their size than larger polygons. A doubling of the accuracy standard bandwidth caused a quadrupling of line length bias and a doubling to tripling of the line length standard deviation. For stream mode digitizing, reasonable digitizing standards produced line length biases of less than 2 percent of total length and standard deviations of less than 1 percent of total length. Bias and standard deviation both increased with increasing line length (or number of points), but the bias and standard deviation as a percent of total line length remained constant as feature size changed.
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    Effect of upper stem diameter and errors of measurement on the accuracy of volume equations
    Ngong, Fonweban John (Virginia Tech, 1989-06-29)
    Measurements of DBH, upper diameters, merchantable height and total heights were made on 80 standing white oaks (Quercus alba) which were then felled for detailed measurements of the same parameters. The data obtained were used to evaluate the accuracy of standing tree measurements, to develop and compare volume equations that used upper diameter as one of the predictor variables and to examine the contributions of individual predictor variables to total volume prediction bias and precision. Relative bias ranged from 0.85% for DBH measurement errors to 2.88% for total height measurement errors. Relative standard deviation ranged from 1.52% to 10.13% for DBH and total height errors respectively. When both bias and precision ( standard deviation ) were considered jointly, the relative root mean squared error ranged from 1.75% to 10.48% for DBH and total height errors respectively. Upper diameter and merchantable height showed negative bias. A comparison of eight fitted models against the combined variable model revealed a gain in precision and a reduction in bias for models that used upper diameter as a third predictor variable. The improvement as based on the relative root mean squared error ranged from 28.8% to 71.3% for taped measurements. However, models that used upper diameter as a substitute for either DBH or merchantable height performed worse than the combined variable model. An analytic examination of the impact of measurement error on volume prediction bias showed that merchantable height errors accounted for most of the bias and that DBH and upper diameter errors contributed almost equal amounts(in absolute terms) to the volume bias.
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    Egg mass sampling plans for gypsy moth management programs
    Carter, Jane Louise (Virginia Tech, 1992-09-05)
    The goal of this research was to develop gypsy moth egg mass sampling plans that reflect the influence of habitat, changes in egg mass distribution, and provide populations densities or density categories for making control decisions. Sequential egg mass sampling plans for gypsy moth management programs in urban and suburban habitats were developed from 0.01 ha fixed-radius plot samples collected in Loudoun, Fairfax, and Arlington Counties, Virginia. The sampling plans were develop from Wald's sequential probability ratio test and is based on a negative binomial distribution. Operating characteristic and average sample number curves were used to determine the acceptability of the sampling plans. Three sampling plans were developed for the action thresholds of 618, 1,236, and 2,471 egg masses/ha. The use of binomial sampling for low density (<618 egg masses/ha) gypsy moth populations in continuously forested habitats was examined. Fixed- and variable-radius plot egg mass samples were collected in 28 study areas in Virginia, Maryland, and Massachusetts. The relationship between egg mass density and the proportion of trees with zero egg masses was developed. Binomial sampling resulted in a higher relative variability and lower relative efficiency than the fixed- and variable-radius plot sampling method. Binomial sampling was determined not to be an effective sampling method for gypsy moth populations below 618 egg masses/ha. Fixed- and variable-radius plot egg mass samples were taken when leaves were present (summer) and absent (winter) in 136 sample sites in Virginia. A significant difference between summer and winter counts was determined. The relationship between summer and winter counts was quantified using nonparametric Statistics. Winter egg mass counts were found to be 14 to 34 percent higher than summer egg mass counts . The probability of a summer egg mass count exceeding an action threshold was constructed by fitting a logistic curve to empirical data for the action thresholds of 618 and 1,236 egg masses/ha. Egg mass counts need to compensate for differences between summer and winter counts. Alternatively, the probability of a summer egg mass count exceeding an action threshold should be utilized.
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    Evaluating methods for characterizing slope conditions within polygons
    Weih, Robert C. (Virginia Tech, 1991)
    While the applications of Geographic Information Systems (GIS) have progressed from a descriptive tool to a decision making and modeling tool, the understanding of errors and variability of the components of a GIS has lagged behind. Slope is one of these components. This dissertation evaluates different methods for determining and characterizing slope values in polygons and how these methods affect natural resource models. Eight different previously used methods for determining cell slope values were compared using elevation data from the USGS Big Stone Gap, Virginia, Digital Elevation Model. The 28 pairwise comparisons were statistically different, but for practical applications six of the comparisons were similar with an average slope difference of less than one percent. In a decision model the effect of changing just the slope method used to determine cell slope values can influence the results of a model enough to cause almost a 10 fold difference. Since usually the smallest administered unit in natural resource management is the stand (polygon), nine ways of describing the slope of a polygon for 240 polygons using an aggregation of cell slope values were investigated. These polygon descriptors were mean, trim mean, median, mode, first quartile, third quartile, standard deviation, minimum and maximum cell slope value. Also, a new method of determining polygon slope was examined using trend surface techniques, which is not based on aggregation of single cell slope values. The distributions of cell slope values in a polygon cannot be assumed normal since few polygons had a normal distribution. The sensitivity of these polygon slope descriptors to polygon area and surface complexity, based on fractal dimension, was examined and found not to affect these polygon characteristics. The application and logical decisions required to choose an appropriate slope method and polygon slope descriptor(s) based on model objectives are shown in two examples, a harvesting and USLE model. Automating the process of choosing the appropriate polygon slope descriptor(s) and how to integrate these methods in an operational GIS using an Expert System is discussed.
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    Landscape pattern analysis related to forest wildlife resources
    Trani, Margaret Katherine (Virginia Tech, 1996)
    Wildlife management and natural resource policy decisions are increasingly being made at the landscape level. Understanding the relationship between modification and the pattern of land classes may minimize potential impacts and enhance the complement of wildlife species. Twenty-four expressions were selected for landscape analysis that describe the spatial heterogeneity, fragmentation, edge characteristics, and connectivity of pattern. Metric relationships were characterized across a variety of landscapes. Cluster analysis organized the metrics into classes quite different from the classification categories used in the literature. Cluster membership reflected the number of land classes, the amount and distribution of forest cover, number of forest patches, patch position, patch shape, patch radius, and edge length. Cartographic modeling was used to determine how modification influenced landscape pattern. The models depicted spatial relationships resulting from proposed landscape changes. Timber harvest schemes with a few large units and those in clustered arrangements led to less fragmentation than those schemes with several small units or those dispersed across the landscape. The placement of roads had either an invasive or partitioning effect on landscape pattern. Discriminant analysis rated the effectiveness of pattern expressions for environmental assessment. Metric effectiveness differed among the timber harvest, road expansion, and deforestation modification schemes. The utility and limitations of each expression was discussed. Sensitivity analyses examined the effects of changing spatial scale on pattern description. Scale influence was dependent upon landscape complexity, distribution of land classes, and the size and shape of those classes. The loss of ability to detect localized variability, to differentiate among spatial patterns, and to represent boundary detail accompanied the use of large pixels (420m²). There was evidence that spatial scale influences habitat evaluation. Semivariogram analysis assessed the constancy of expression behavior during changes in scale and presented the limits of tolerance for using large pixels in pattern analyses. The variability observed suggested that pattern misrepresentation occurred at coarse resolution levels. The successful application of landscape analysis depends on the ability to quantify pattern. By analyzing and understanding selected aspects of landscape pattern, I have examined how wildlife management can be enhanced through a knowledge of the landscape.
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    Management decision-making tools for mountain pine beetle (Dendroctonus ponderosae) (Coleoptera: Scolytidae) populations in lodgepole pine (Pinus contorta) stands
    Bentz, Barbara Joan (Virginia Tech, 1991-09-18)
    To prevent the buildup of epidemic level mountain pine beetle populations, conditions of the stand environment they inhabit must be altered. Silvicultural treatment is the most effective means for doing this. Preventative treatments work best when applied while mountain pine beetle populations are still at the endemic population level. Therefore, information necessary for making decisions concerning mountain pine beetle populations in lodgepole pine stands needs to be included in the initial silvicultural prescription planning process, at a time before beetle populations reach outbreak numbers. In this dissertation, several quantitative descriptions of the mountain pine beetle/lodgepole pine relationship were investigated. Models were developed to 1) describe the temperature-dependent development of six mountain pine beetle life stages and 2) describe the amount of loss a stand could sustain if an epidemic level population were to occur in the stand. Concepts of mountain pine beetle risk rating were also discussed. These models and additional information pertaining to the mountain pine beetle/lodgepole pine relationship were incorporated into a knowledge-based system, the MPB Advisory System. This system was designed to help U.S. Forest Service silviculturists include decisions concerning mountain pine beetle populations in the stand management process.
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    Methods for Quantitatively Describing Tree Crown Profiles of Loblolly pine (Pinus taeda L.)
    Doruska, Paul F. (Virginia Tech, 1998-06-26)
    Physiological process models, productivity studies, and wildlife abundance studies all require accurate representations of tree crowns. In the past, geometric shapes or flexible mathematical equations approximating geometric shapes were used to represent crown profiles. Crown profile of loblolly pine (Pinus taeda L.) was described using single-regressor, nonparametric regression analysis in an effort to improve crown representations. The resulting profiles were compared to more traditional representations. Nonparametric regression may be applicable when an underlying parametric model cannot be identified. The modeler does not specify a functional form. Rather, a data-driven technique is used to determine the shape a curve. The modeler determines the amount of local curvature to be depicted in the curve. A class of local-polynomial estimators which contains the popular kernel estimator as a special case was investigated. Kernel regression appears to fit closely to the interior data points but often possesses bias problems at the boundaries of the data, a feature less exhibited by local linear or local quadratic regression. When using nonparametric regression, decisions must be made regarding polynomial order and bandwidth. Such decisions depend on the presence of local curvature, desired degree of smoothing, and, for bandwidth in particular, the minimization of some global error criterion. In the present study, a penalized PRESS criterion (PRESS*) was selected as the global error criterion. When individual- tree, crown profile data are available, the technique of nonparametric regression appears capable of capturing more of the tree to tree variation in crown shape than multiple linear regression and other published functional forms. Thus, modelers should consider the use of nonparametric regression when describing crown profiles as well as in any regression situation where traditional techniques perform unsatisfactorily or fail.
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    Minimum tree height sample sizes necessary for accurately estimating merchantable plot volume in Loblolly pine plantations
    Houghton, Damon (Virginia Tech, 1991-05-05)
    The minimum number of tree heights that are necessary, with a probability of 0.95, to obtain a merchantable plot volume estimate of loblolly pine within ± 3, 5, and 10% of the volume observed if all plot trees had been measured for height were determined for all combinations of volume estimation techniques and sample designs examined in this study. The volume estimation techniques examined in this study were: 1) a volume equation using measured tree diameters and either measured heights or height estimates obtained from a plot height-diameter relationship, 2) a volume equation using strata average diameter and average height, and\ 3) a strata volume/basal area ratio estimator. The examined sampling designs were: 1) a simple random sample, 2) a stratified random sample, 3) a stratified systematic sample, and 4) a purposive sample. Both combined and separate stratified estimators were used for volume estimation techniques 2 and 3 when a stratified sample design was used. Of all the possible combinations of volume estimation techniques and sample designs, two combinations, volume estimation technique 1 and a stratified random sample, and volume estimation technique 1 and a purposive sample, are the only combinations that have sample sizes of no more than 30 trees for all three accuracy levels and require the smallest or nearly the smallest number of sample tree heights at these accuracy levels.
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    Modeling the impact of gypsy moth defoliation in individual tree mortality and basal area growth of northern hardwoods of central Pennsylvania
    Amrhein, John Francis (Virginia Tech, 1988-03-15)
    Data for this study were collected by the US Forest Service and the Pennsylvania Bureau of Forestry on nearly 600 plots in central Pennsylvania. Tree and stand characteristics recorded between 1978 and 1985 include estimates of percent defoliation on individual trees. Logistic regression using maximum likelihood estimation was employed to model individual-tree mortality of 15 species in central Pennsylvania that had been defoliated by the gypsy moth. Defoliation was estimated to the nearest ten percent for individual trees. Other variables used for prediction included stand basal area and an individual-tree relative basal area index. Success ranged from no fit for three of the species to an R value (a derivation of Akaike's information criterion) of .613 for white oak. The inclusion of defoliation in the models had a varied effect. For four of the species percent defoliation was not significant. For hickory and white oak respectively, percent defoliation raised the R value by .305 and .290 percentage points. As many as five models for each species were developed: one or two models with no defoliation measure in the model and one each for one, two or three consecutive years of defoliation measures. A beta and gamma function were used to model individual· tree basal area growth for the same 15 species. The models were fit using nonlinear least squares. Variables used include the relative basal area index, stand basal area, site index and a defoliation index that incorporated three years of individual-tree, percent defoliation. The beta and gamma functions fit equally well with values of (1 - relative mean square error) ranging from .1967 to .6290. Results for both models are presented for each species. The defoliation index was a significant variable for five of the fifteen species: white, chestnut, red, and black oak and sassafras.
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    Modeling thinning effects on ring width distribution and wood specific gravity of loblolly pine (Pinus taeda L.)
    Tasissa, Gudaye (Virginia Tech, 1996)
    An appropriate accounting for thinning effects on growth rate and wood quality requires a clear understanding and quantification of these effects. In this regard, four basic interrelated issues were addressed in this study: 1) thinning effects on ring specific gravity 2) thinning effects on ring width distribution 3) thinning effects on stem form, and 4) prediction models for these quantities. The study showed that thinning does not significantly affect ring specific gravity, whereas its effects on ring width distribution and stem form were significant. Thinning increases ring width significantly over most of the tree bole and increases the earlywood and latewood components proportionally maintaining an approximately constant latewood proportion. As a consequence, thinning effects on latewood proportion is not significant; confirming the results obtained in the specific gravity study and further dispelling the concern that thinning may substantially reduce wood specific gravity. Thinning affects stem form by increasing the form exponent especially near the tree base accentuating the neiloid form expected in that area. High up in the stem, the form exponent changes little within a tree and among thinning treatments, with a general tendency towards a paraboloid shape. Differences due to thinning intensities, in general, were not significant indicating the applicability of results within a wide range of densities. Prediction models for ring specific gravity, ring width, latewood proportion and stem profile based on ring, tree, stand and site factors were developed Influences of stand level factors, density measures in particular, in prediction models are minor probably because tree level factors such as, stem diameter at breast height, crown ratio, etc. themselves manifest stand conditions. The mixed-effects analysis technique was used in data analysis to account for correlation among observations from the same subject. Direct covariance modeling yielded better fits than accounting for correlation indirectly using random effects covariates in many cases; however, both could not be accommodated simultaneously. Structures which assume decreasing correlation with increasing distance between observations, such as the first-order autoregressive structure, performed better than alternative specifications. Results consistently showed that accounting for correlation among observations substantially improves the fits over ignoring correlation; effectively addressing the issue of bias in the standard errors of estimates.
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    Modelling inter- and intra-specific competition effects in loblolly pine (Pinus taeda L.) plantations
    Liu, Jiping (Virginia Tech, 1992-04-05)
    Accounting for competition effects is an essential step in building any stand growth simulator. However, accurate modelling of competition effects depends upon a clear understanding of quantitative relationships of various aspects of stand dynamics, including distributional parameters and spatial statistics. This study addressed four aspects of competition effects: 1) competition effects on distributional parameter dynamics of tree size variables; 2) inter-specific (loblolly pine vs. hardwood) and intra-specific competition effects on basal area growth, 3) dynamics of spatial statistical characteristics of DBH and total height, and their relevance to intertree competition, 4) and spatial properties of competition measures by available stand simulators for loblolly pine (Pinus taeda L.) plantations. Competition was found to affect the distribution parameters such as coefficient of variation, skewness, and the general shapes of distributions for diameter measurements, total height, crown width and crown height. Competition expedites size differentiation and thereby increases distribution variability for all variables except crown height. Intertree competition also drives skewness of these variables negative, although the distributions of crown heights tends to be more symmetric. Normality assumption generally holds for diameter measurement, but distributions of total height and crown width deviate from, and those of crown height approach, normality with intensified competition. A set of competition driven equations was developed for the distribution parameters and was validated. The differences of distribution parameters among the variables studied could be attributed to their biological meanings.
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    Ozone effects on red oak root dynamics
    Kelting, Daniel L. (Virginia Tech, 1995-05-05)
    Many research projects concerning the possible deleterious effects of ozone on forest health have been conducted on individual tree species. The common goal of these projects has been to identify mechanisms of damage by ozone, and then extrapolate research results to forests. Results from seedling studies are used to parameterize process-based tree growth models which are used to project mature tree responses to different levels of ozone. This approach has been criticized because nothing is known about differences in seedling and mature-tree responses to ozone. Another problem is that few projects have examined the effects of ozone on below ground processes; therefore, very little data exists for parameterizing the models. In order to address the problem of scaling seedling results to mature trees, and increase our level of understanding of ozone effects on below ground processes, an ozone fumigation experiment on northern red oak seedlings and mature trees was conducted. It was hypothesized that carbon reallocation to replace foliage damaged by ozone would decrease fine-root production and turnover. The red oak trees and seedlings were fumigated for three years with three levels of ozone (subambient, ambient, and 2X ambient) in open-top chambers. After two seasons of exposure, 2X ozone (0.082 ppm 7hr-mean conc.) reduced mature- tree cumulative net fine-root production and turnover by 31 and 41 %, respectively, relative to ambient ozone (0.042 ppm 7hr-mean conc.). For the same time period, ozone had no effect on seedling cumulative fine-root turnover; fine-root production was 25% higher under ambient ozone relative to subambient and 2X ambient ozone. During the summer, 1994, mature tree BUE was reduced by 2X ozone. Decreased fine-root production, turnover, and BUE under 2X ozone for the mature trees indicates that ozone can alter the dynamics of belowground carbon allocation in mature red oak. Since the seedlings were not sensitive to ozone, use of seedling results for modelling purposes may underestimate mature tree responses to ozone.
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    Qualitative response models theory and its application to forestry
    Arabatzis, Alexandros A. (Virginia Tech, 1990-01-04)
    The focus of this dissertation is the theory of qualitative response models and its application to forestry related problems. Qualitative response models constitute a class of regression models used for predicting the result in one of a discrete number of mutually exclusive outcomes. These models, also known as discrete regression models, differ from the usual continuous regression models in that the response variable takes only discrete values. In forestry applications the use of such models has been largely confirmed to mortality studies where only the simplest kind of qualitative response models - a dichotomous (binary) dependent variable model - is applied. However, it is common in forestry to deal with many variables which are either discrete or recorded discretely and need to be formulated by more complex models involving polychotomous dependent variables. The estimation of such complex qualitative response models only recently has been made possible by the development of advanced computer technology. The first objective of this study was to specify dichotomous and polychotomous response models that appear to be suitable for forestry applications and present methods of statistical analysis for these models. The models considered in this study were: the linear probability model, binary logit and probit, ordered and unordered multinomiallogit and probit and McFadden's conditionallogit. Special attention was paid to the following problems: i) how to motivate a qualitative response model which is theoretically correct and statistically manageable, ii) how to estimate and draw inferences about the model parameters, iii) what criteria to use when choosing among competing models and iv) how to detect outlying, high leverage and highly influential observations. The second objective was to exemplify the utility of the above models by considering two, forestry related, case studies. Assessing the merchantability of loblolly pine trees growing on plantations in southern United States and modelling the incidence and spread of fusifonn rust on loblolly and slash pine plantations in east Texas. The results demonstrated the potential of qualitative response models for meaningful implementation in a variety of forestry applications and also, suggested topics for future research work.