ABSTRACT The use of height-diameter models have important applications in the management of eucalyptus plantations. The aim of this paper is to provide adequate height models based on the diameter and stand variables that could be easily used and applied to plantation’s management. The data was based on tests located in Espírito Santo and Bahia. A total of 312 plots, including 35 different treatments (different initial planting densities, number and severity of thinning operations, fertilization regimes, among others), and four different clones. This resulted in 2,407 conditions for 85,608 tree measurements. The constructed equations were based on mixed-effect models, in order to accommodate possible autocorrelations, to address variations between sites and to obtain locally calibrated estimates. Among the different model structures and combination of variables tested and presented, the best model showed a coefficient of determination of 0.953 and 0.988, for the fixed and fixed+random parts, respectively. The model included a random factor for measurements-within-tree and tree-within-plot. The bias of the fixed part was 0.208 cm (0.0659%). We believe the models in this study can have broad applications in management and inventory methods applied to plantations.

Resumo: O objetivo deste trabalho foi analisar a distribuição espacial e o comportamento da riqueza e da diversidade de espécies em um fragmento de campo cerrado, em 2003 e 2014, por meio de krigagem ordinária, no Estado de Minas Gerais. Nos dois anos de monitoramento, as avaliações foram realizadas em um fragmento de 236,85 hectares, em que indivíduos arbóreos foram medidos e identificados em 40 parcelas (1.000 m2). A riqueza foi determinada pelo número de espécies em cada parcela, e a diversidade, pelo índice de diversidade de Shannon. Para o estudo variográfico, foram realizados ajuste e seleção de modelos espaciais. Posteriormente, foi aplicada krigagem ordinária e descrita a distribuição espacial das variáveis avaliadas. Observou-se forte dependência espacial entre riqueza e diversidade de espécies pelo índice de diversidade de Shannon (<25% de grau de dependência espacial). Áreas de baixa e alta diversidade e riqueza de espécies foram identificadas no fragmento de campo cerrado. O comportamento da distribuição espacial mostra relativa estabilidade quanto ao número de espécies e ao índice de diversidade de Shannon nos anos avaliados.

Abstract: The objective of this work was to analyze the spatial distribution and the behavior of species richness and diversity in a shrub savanna fragment, in 2003 and 2014, using ordinary kriging, in the state of Minas Gerais, Brazil. In both evaluation years, the measurements were performed in a fragment with 236.85 hectares, in which individual trees were measured and identified across 40 plots (1,000 m2). Species richness was determined by the total number of species in each plot, and diversity by the Shannon diversity index. For the variogram study, spatial models were fitted and selected. Then, ordinary kriging was applied and the spatial distribution of the assessed variables was described. A strong spatial dependence was observed between species richness and diversity by the Shannon diversity index (<25% spatial dependence degree). Areas of low and high species diversity and richness were found in the shrub savanna fragment. Spatial distribution behavior shows relative stability regarding the number of species and the Shannon diversity index in the evaluated years.

A técnica de amostragem comumente usada em inventários florestais é a amostragem sistemática. Objetivou-se avaliar o estimador da variância da média proposto por Cochran, no procedimento de amostragem sistemática, em florestas com alto e baixo percentual da área amostrado. As áreas contemplaram a vegetação nativa de Minas Gerais. Para verificar o comportamento dos estimadores numa situação com alto percentual de área amostrado, utilizou-se o fragmento onde foi efetuado o censo. Os demais se adequaram às situações de baixo percentual amostrado, observando-se o comportamento da precisão do inventário, a partir do uso do estimador de Cochran. Como resultado para o fragmento onde se fez o censo, a estrutura do coeficiente de correlação proposto por Cochran se manteve, aproximadamente, constante para a área e, reduzindo a intensidade de amostragem, o impacto do estimador de Cochran diminuiu. Para os fragmentos com baixo percentual amostrado, a intensidade amostral é a chave para a correlação proposta por Cochran: impactar na precisão do inventário florestal, sendo indicado o uso desse estimador para fragmentos onde há uma intensidade amostral superior a 10% da área inventariada.

The sampling technique commonly used in forest inventories is the systematic sampling. This study aimed to evaluate the estimator of the variance of the mean proposed by Cochran for a systematic sampling technique in forests with high and low percentages of the sampled area. The study areas comprised native vegetation in Minas Gerais. To assess the efficiency of the estimators in situations involving high sampling rates (determined as the percentage of the area sampled), a fragment where a census was conducted was used. The remaining fragments comprised situations involving low sampling rates, and for these fragments, inventory accuracy was determined using the Cochran estimator. As a result it was observed, in the fragment where the census was conducted, that the structure of the correlation coefficient proposed by Cochran remained approximately constant for the area, and to the extent that sampling rate reduced, the impact of the Cochran estimator on the inventory accuracy decreased. For the fragments with a low sampling rate, it could be inferred that the sampling rate was a key factor for the correlation proposed by Cochran to have an impact on the forest inventory accuracy. The use of this estimator is indicated for fragments with a sampling rate greater than 10% of the area.