Hypsometric equations for toona ciliata with inclusion of covariates/Equacoes hipsometricas para toona ciliata com inclusao de covariantes

The height-diameter relationship is influenced by many variables, making difficult its modeling. The inclusion of covariates by the decomposition of model parameters can improve the model precision and help develop generic height-diameter models. This study aimed to evaluate hypsometric equations and examine the inclusion of covariates for Toona ciliata, species still poorly studied. Four nonlinear equations were evaluated to represent the height as a function of age. The effect of the progeny was included in one of the equations, decomposing the parameters. Five equations, which four are nonlinear ones, were tested to represent the variation of height as a function of the diameter. The parameters of the logistic equation were decomposed and associated to the variable progenies, age, dominant and codominant height. The Asymptotic equation was the most precise to represent the height growth. The inclusion of the variable progeny in the Logistic equation improved its precision. From the set of equations tested for the height diameter relationship, the Exponential equation was the least precise. The inclusion of covariates in the logistic equation improved its precision and among all tested covariates, the dominant and codominant height variable presented the highest gain in precision (23%). Keywords: Toona ciliata; height-age relationship; height-diameter relationship; covariates. A relacao hipsometrica e influenciada por muitas variaveis e isso dificulta a sua modelagem. A adicao de covariantes em uma equacao, por meio da decomposicao de seus parametros, pode melhorar a precisao da mesma e auxiliar na construcao de modelos hipsometricos genericos. Neste estudo objetivou-se avaliar equacoes hipsometricas e testar a inclusao de covariantes para Toona ciliata, especie ainda pouco estudada. Foram avaliados quatro modelos nao lineares para representar a altura em funcao da idade. O efeito da progenie foi incluido em uma das equacoes por meio da decomposicao dos parametros. Para representar a variacao da altura em funcao do diametro foram testadas cinco equacoes, sendo que quatro delas nao lineares. Os parametros de uma das equacoes foram decompostos e associados as variaveis: progenie, idade e altura dominante e codominante. A equacao Assintotica foi mais precisa para representar o crescimento em altura. A inclusao da variavel progenie na equacao Logistica aumentou sua precisao. Dentre as equacoes avaliadas para a relacao altura-diametro, a Exponencial foi a de