Self-thinning quantifies the reduction in tree numbers due to density-dependent mortality. Maximum size-density relationships (MSDRs) are a component of self-thinning that describe the maximum tree density per unit area obtainable for a given average tree size, often quadratic mean diameter (D). An MSDR species boundary line has been defined as a static upper limit of maximum tree density -- D relationships that applies to all stands of a certain species within a particular geographical area. MSDR dynamic thinning lines have been defined as the maximum tree density obtainable within an individual stand for a particular D which have been shown to vary relative to planting density. Results from this study show that differences in boundary levels of individual stands cause the MSDR species boundary line slope estimate to be sensitive to the range of planting densities within the model fitting dataset. Thus, a second MSDR species boundary line was defined whose slope is the average slope of all MSDR dynamic thinning lines. Mixed-models are presented as a statistical method to obtain an estimate of the population average MSDR dynamic thinning line slope. A common problem when modeling self-thinning is to determine what observations are within generally accepted stages of stand development. Segmented regression is presented as a statistical and less subjective method to determine what observations are within various stages of stand development. Estimates of D and trees per acre (N) where MSDR dynamic thinning lines begin and end on the logarithmic scale were used as response variables and predicted as a function of planting density. Predictions of MSDR dynamic thinning line beginning and ending D and N are used in an alternative MSDR dynamic thinning line slope estimation method. These models show that the maximum value of Reineke's Stand Density Index (SDI) varies relative to planting density. By relating planting density specific Zone of Imminent Competition Mortality boundaries to a MSDR species boundary line, self-thinning was found not to begin at a constant relative SDI. Thus, planting density specific Density Management Diagrams (DMD) showed that self-thinning began at 40 to 72% for planting densities of 605 and 2722 seedlings per acre, respectively. / Ph. D.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The objective of the work was to study the relationship between the density of trees per hectare and the average diameter to a Deciduous Forest, as well as adjust the model to describe this behavior Reineke. The study area is located in the town of Silveira Martins, in the central region of Rio Grande do Sul and is in early stages of succession after agriculture. The information about the number of the trees per hectare and the average diameter were obtained by the method of density-off proposed by Spurr. These plots were sampled in the early stages of a secondary forest, picking up areas where the predominant Camboatá-vermelho (Cupania vernalis). As natural forests have irregular spacing, density is highly variable, therefore, to select only high-density plots were chosen in areas that there was the occurrence of dead individuals. Were tested different methods to estimate the upper limit of the self thinning line: regression analysis (for all data and relative density greater than 60%), correcting the intercept so that the wastes were negative, the manual adjustment, the relative density (DR> 90%) and stochastic frontier analysis. The method that estimated the maximum density was regression analysis with data from at least 60% of maximum density, obtaining a slope of -1.563 for the model of Reineke. There was no significant difference between the powers provided by the different methods. The maximum Stand Density Index was 1779 trees per hectare, to a dg of 25 cm. The density management diagram was constructed on the basis of basal area, number of trees per hectare and diameter of the tree of average basal area. Were used the densities of 15% and 60%, to close the canopy, and the induction of mortality, respectively. The densities were determined proportionally to the maximum density by stand density index (PDI) for a reference diameter of 25 cm in different classes of index 200, since the IDP 1700, to a minimum of 300. Populations whose density is greater than 60% of the maximum were considered overstocked, between 60 and 15% fully stocked, and below 15% under stocked. They recommended a combination of Dendrogram generated in this study with the method of Spurr to guide interventions in the Deciduous Forest. / O objetivo deste trabalho foi estudar a relação entre a densidade de árvores por hectare e o diâmetro médio para uma Floresta Estacional Decidual, bem como, ajustar o modelo Reineke para descrever este comportamento. A área de estudo localiza-se no município de Silveira Martins, na região central do Rio Grande do Sul e encontra-se em estágio inicial de sucessão, após uso agrícola. As informações referentes ao número de árvores por hectare e o diâmetro médio foram obtidas por meio do método de densidade pontual proposto por Spurr. Estas parcelas foram amostradas nos estágios iniciais de uma floresta secundária, escolhendo-se áreas onde predominava o camboatá-vermelho (Cupania vernalis). Como as florestas naturais apresentam espaçamento irregular, a densidade é bastante variável, assim sendo, para selecionar apenas parcelas em alta densidade, foram escolhidas áreas em que se verificava a ocorrência de indivíduos mortos. Foram testados diferentes métodos para estimar o limite superior da linha de autodesbaste: a análise de regressão (para todos os dados e densidade relativa maior que 60%), corrigindo o intercepto para que os resíduos fossem negativos; o ajuste manual; o de densidade relativa (DR>90%) e a análise de fronteira estocástica. O método que melhor estimou a máxima densidade foi a análise de regressão com dados de no mínimo 60% da densidade máxima, obtendo um coeficiente angular de -1,563 para o modelo de Reineke. Não houve diferença significativa entre as potências fornecidas pelos diferentes métodos. O Índice de Densidade de Povoamento máximo foi de 1779 árvores por hectare, para o dg de 25 cm. O diagrama de manejo da densidade foi construído em função da área basal, do número de árvores por hectare e do diâmetro da árvore de área basal média. Foram utilizadas as densidades de 15% e 60%, para o fechamento das copas, e a indução da mortalidade, respectivamente. Os níveis de densidade foram determinados, proporcionalmente, à máxima densidade por índice de densidade do povoamento (IDP), para um diâmetro de referência de 25 cm, em classes de índice de 200, desde o IDP de 1700, até o mínimo de 300. Populações cuja densidade for maior que 60% da máxima foram consideradas superestocadas, entre 60 e 15% estocadas, e abaixo de 15% subestocadas. Recomendou-se a combinação do Dendrograma gerado neste estudo com o método de Spurr para guiar as intervenções na Floresta Estacional Decidual.

The specific objectives of this project were: 1) Determine financial viability of enrolling forest landowners in Chicago Climate Exchange (CCX) forestry carbon offset protocols; 2) Determine financial trade-offs associated with managing loblolly pine (Pinus taeda L.) and Cherrybark oak (Quercus pagoda Raf.) stands for increased carbon sequestration and timber; 3) Examine financial feasibility of increasing carbon accumulation in wood products carbon by extending rotation length of loblolly pine stands; and 4) Explore potential impacts of carbon policies and programs on future carbon accumulation in Mississippi’s forest sector.