The relationship between volume production and stand density, often termed the 'growth-density relationship', has been studied since the beginnings of forestry and yet no conclusive evidence about a general pattern has been established. Throughout the literature claims and counterclaims concerning the growth-density relationship can be found. Different conclusions have been attributed to the diverse range of definitions of volume and stand density among problems with study design and other pitfalls. Using data from two thinning studies representing non-intensively and intensively managed plantations, one spacing trial, and one thinning experiment a comprehensive analysis was performed to examine the growth-density relationship in loblolly pine. Volume production was defined as either gross or net periodic annual increment of total, pulpwood, or sawtimber volume. These definitions of volume production were then related to seven measures of stand density including the number of stems per hectare, basal area per hectare, two measures relative spacing and three measures of stand density index. A generalized exponential and power type function was used to test the hypothesis that volume production follows either an increasing or unimodal pattern with stand density. These patterns were tested using all combinations of the six definitions of volume production and the seven measures of stand density. Significance of the parameters indicated that different patterns existed depending on the type of management (intensive vs. non-intensive), if thinning is performed, and depending on the definitions of growth and density. The growth-density pattern was generally the same between gross and net production although different patterns emerged when comparing total, pulpwood, and sawtimber volumes. The definitions of stand density which used diameter as a measure of average tree size were more highly correlated with volume production and produced similar patterns while the number of stems per hectare was the least correlated. Further analysis was performed to evaluate Langsaeter's hypothesis which states that volume production is constant and optimal across a wide range of stocking. A mixed-model approach was used to test the equality in mean volume production across a range of planting densities and thinning intensities. To account for the effects of age, the equality in mean volume production was tested separately across a range of ages from 8 to 25 years within the spacing trial data and across a range of one to six years since thinning within the thinning experiment. A multiple comparison test indicate that pattern of volume production and stocking is highly related to the two stages of self-thinning. In young stands, within the distance-independent mortality stage, volume production increases with increasing planting density and therefor increasing stocking. During the distance-dependent mortality stage the assumption of constant and optimal volume production across a wide range of stocking is generally correct. However when mortality began to reduce canopy closure to the point that the residual stand could not recover gaps in the canopy a decline in volume production occurred resulting in a decreasing relationship with increasing stocking. Finally, a system of equations were constructed to describe volume production at the individual tree and stand levels. From this model it was determined that stand level volume production follow an increasing pattern with stand density. / Ph. D.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aimed to evaluate the morphology and describe the growth of competing and free individual trees of Cordia trichotoma (Vell.) Arráb. ex Steud. The study of free from competition trees was held in the Central region of the state of Rio Grande do Sul, in the cities of Santa Maria and Silveira Martins, and trees under competition were measured in the Campo de Instrução do Ministério do Exército of Santa Maria - CISM and also in Silveira Martins. Competing and free trees larger than 5 centimeters of dbh were numbered and its dendrometric, morphometric and qualitative were measured. The increment data of the last 4 years was obtained from two increment cores collected using Pressler borer. Competition between trees in the forest was calculated based on the number of trees per hectare obtained from the methodologies of Spurr, Bitterlich and Prodan. The louro-pardo trees growing free of competition, has diameter at breast height, crown diameter and the salience index similar to the developed under competition. Under competition, this species invests more in total height, commercial height and height of the crown, however, has less crown length, lower crown percentage and index scope. The louros growing free of competition have periodic annual diameter increment (IPAd) and basal area (IPAg) significantly higher than those under competition. The IPAg this species of free of tree competition can be predicted by dbh, crown factor (fac) and crown density (dec) by two different models, but the model that best fits the data was: IPAg = 0.6665. and 0.0725. (fac.dec). dbh, which considers the fac and dec as discrete variables to determine the slope. The IPAg of louro-pardo under competition can be predicted by the estimated increment from free of competition trees and subtracting the estimated difference between the increments of louros under and free of competition: IPAg = [(0,6665 e 0,0725. (fac.dec) . dap)] [562,28. (N(GBit))-0,585]. The model ln IPAg = 0,5456 . ln dap + 0,1412 . (fac . dec) - 0,00008905 . N(GBit) which has no relationship to the previous model can be used as well, to estimate the increment for louro-pardo under competition, with some advantages over the previous one. / Este trabalho teve como objetivo avaliar a morfometria e descrever o incremento de árvores individuais livres e em competição de Cordia Trichotoma (Vell.) Arráb. ex Steud. O estudo das árvores livres de competição foi realizado na região Central do estado do Rio Grande do Sul, nas cidades de Santa Maria e Silveira Martins e as árvores sob concorrência foram mensuradas no Campo de Instrução do Ministério do Exército de Santa Maria CISM e também em Silveira Martins. Para cada árvore livre e sob competição, foram numeradas as que possuíam dap igual ou superior a 5 cm, e medidas suas variáveis dendrométricas, morfométricas e qualitativas. Os dados de incremento dos últimos 4 anos foram obtidos pela análise de duas baguetas, coletados com a utilização do trado de Pressler. Para a determinação da concorrência entre as árvores na floresta, foi calculado o número de árvores por hectare baseados nas metodologias de Spurr, Bitterlich e Prodan. O louro-pardo quando cresceu livre de competição, apresentou diâmetro a altura do peito (dap), diâmetro de copa e índice de saliência semelhante ao que se desenvolveu em competição. Quando sob competição, esta espécie investiu mais em altura total, altura comercial, altura de início da copa, porém, apresentou menor comprimento de copa, percentagem de copa e índice de abrangência. Os louros quando cresceram livres de competição apresentaram incremento periódico anual em diâmetro (IPAd) e em área basal (IPAg) significativamente superiores quando comparados aos sob competição. O IPAg desta espécie livre de competição pode ser predito pelo dap, pelo fator de copa (fac) e densidade de copa (dec) a partir de dois modelos distintos sendo que o modelo que apresentou melhores ajustes foi: IPAg = 0,6665 . e 0,0725.(fac.dec) . dap pelo qual considera o fac e dec como variáveis discretas para determinar o coeficiente angular. O IPAg do louro-pardo sob competição pode ser predito pela estimativa de incremento que ele atinge quando cresce livre de competição subtraído pela estimativa da diferença de incrementos entre os louros livres e sob competição: IPAg = [(0,6665 e 0,0725. (fac.dec) . dap)] [562,28. (N(GBit))-0,585]. O modelo ln IPAg = 0,5456 . ln dap + 0,1412 . (fac . dec) - 0,00008905 . N(GBit) pelo qual não tem relação com o incremento das árvores livres também pode ser utilizado para a estimativa do incremento dos louros sob competição, com algumas vantagens em relação ao anterior.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The canopy of trees is most directly responsible for the growth, being influenced by the type of management adopted in afforestation and competition between individuals. Thus, the aim of this study was to describe the morphology and growth of relations Ocotea porosa using mathematical modeling and considering the effect of competition. Data collection was conducted in EMBRAPA / EPAGRI Forest Reserve in Caçador (SC) and the native forest in Laminados AB Company located in Calmon (SC). The Diameter at Breast Height (DBH) dimensions have been found in the sample from 10 cm to 80 cm, whereas random sampling and circular plots of variable area, and the radius of each plot the distance between the tree and the competitor farthest point sampling (central tree). Calculated variables describing the size and competition were the Diameter at Breast Height in shell Diameter at Breast Height shelled, basal area, crown diameter, canopy area, the potential number of trees per hectare, comprehensiveness index, index overhang, formal canopy, the h / d, percentage of canopy index BAL (Basal Area Larger), Hegyi index, indexes Glover and Hool, indexes Tomé and Burkhart, Lorimer index and index of Clark and Evans. The variables whose explained better of the regular annual percentage increase in basal area were diameter at breast height and vitality Cup, being also considered significant in the model the salience index and the BAL competition index. The best model for hypsometric relation was that of Chapman Richards (h = 20,6053.(1 e-0,0615.dbh), taking as an alternative to model of Stofells (ln(h) = 1,68412 + 0,32665.ln(dbh)) and to estimate the canopy diameter was the logarithmic (ln(dc) = -1,76773 + 11,05485.ln(dbh), for symmetric tops, and ln(dc) = -1,19837 + 0,88682.ln(dbh), to represent the asymmetric tops). The estimate of crown diameter to the Diameter at Breast Height will be used separately for locations where there is greater competition from places where there is less competition due to different symmetry as a consequence of this variable. / A copa das árvores é a maior responsável direta pelo crescimento, sendo influenciada pelo tipo de manejo adotado no povoamento florestal e pela concorrência entre os indivíduos. Assim, o objetivo do trabalho foi descrever a morfometria e as relações de crescimento de Ocotea porosa utilizando a modelagem matemática e considerando o efeito da concorrência. A coleta de dados foi realizada na Reserva Florestal EMBRAPA/EPAGRI de Caçador (SC) e em floresta nativa da Empresa Laminados AB localizada no município de Calmon (SC). As dimensões de dap encontradas na amostragem foram de 10 cm até 80 cm, considerando uma amostragem aleatória e parcelas circulares de área variável, sendo o raio de cada parcela a distância entre a árvore concorrente mais distante e o ponto amostral (árvore central). Em cada árvore da unidade amostral foram tomadas: circunferência à altura do peito, espessura de casca, altura total, altura comercial, comprimento de copa, raio de copa, incremento periódico anual percentual em área basal, vitalidade da copa, distribuição dos galhos, qualidade do fuste, posição sociológica e exposição do terreno. As variáveis calculadas que descrevem a dimensão e competição foram o diâmetro à altura do peito com casca, diâmetro à altura do peito sem casca, área basal, diâmetro de copa, área de copa, número potencial de árvores por hectare, índice de abrangência, índice de saliência, formal de copa, relação h/d, percentagem de copa, índice de BAL (Basal Area Larger), índice de Hegyi, índices de Glover e Hool, índices de Tomé e Burkhart, índice de Lorimer e índice de Clark e Evans. As variáveis de maior poder explicativo para o incremento periódico anual percentual em área basal foram o diâmetro à altura do peito e a vitalidade da copa, sendo também consideradas significativas no modelo o índice de saliência e o índice de concorrência de BAL. O melhor modelo para relação hipsométrica foi o de Chapman Richards (h = 20,6053.(1 e-0,0615.dap), tendo como modelo alternativo o de Stofells (ln(h) = 1,68412 + 0,32665.ln(dap)) e para estimar o diâmetro de copa foi o logarítmico (ln(dc) = -1,76773 + 11,05485.ln(dap), para copas simétricas e, ln(dc) = -1,19837 + 0,88682.ln(dap), para representar as copas assimétricas). A estimativa do diâmetro de copa em função do diâmetro á altura do peito deve ser utilizada separadamente para locais onde há maior competição dos locais onde há menor competição devido a simetria diferenciada como consequência dessa variável.