Prediction of annual tree growth and survival for thinned and unthinned even-aged maritime pine stands in Portugal from data with different time measurement intervals
Artigo de Conferência
An annual individual tree survival and growth model was developed for pure even-aged stands of maritime
pine in Portugal, using a large data set containing irregularly time-spaced measurements and considering
thinning effects. The model is distance-independent and is based on a function for diameter
growth, a function for height growth and a survival function. Two approaches are compared for modeling
annual tree growth. The first approach directly estimates a future diameter or height using well-known
growth functions formulated in difference form. The second approach estimates diameter or height using
a function in differential form estimating the increment over a year period. In both approaches, the function
parameters were related to tree and stand variables reflecting the competition status of the tree as
well as of a thinning response factor. Variable growth and survival rates were assumed in the modeling
approaches. An iterative method was used to continuously update tree and stand attributes using a cutoff
to convert the survival probability for a living or a dead tree. The individual tree diameter growth
model and the survival probability model were fitted simultaneously using seemingly unrelated regression
(SUR). Parameters of the height function were obtained separately as the number of observations for
height was much lower than the number of observations for diameter, which may affect the statistical
inference and the estimation of contemporaneous cross-equation error correlation inherent to the system
of equations. PRESS residuals were used to evaluate the predictive performance of the diameter and the
height growth functions. Additional statistics based in the log likelihood function and also in the survival
probability were computed to evaluate the survival function. The second modeling approach, which integrates
components of growth expansion and decline, performed slightly better than the first approach. A
variable accounting for the thinning response that was tested proved to be significant for predicting
diameter growth, even if the model already included competition-related explanatory variables, namely
the basal area of trees larger than the subject tree. However, this thinning response factor was not significant
for predicting height growth.
The Portuguese national forest strategy published in 2006 divided the Portuguese forest territory into three main functions: wood production, multifunctional systems and protected areas. Wood production is mostly related with pure even-aged stands of two species, the maritime pine (Pinus pinaster Ait.) and the blue gum (Eucalyptus globulus Labill.). Sustainable forest management of these productive areas requires adequate prediction of stocks and growth. To face the challenge of fast changing scenarios, growth models need to provide adequate predictions in a wide range of time intervals. Individual-tree growth and yield models are especially useful for management planning, because they are capable of simulating a wide variety of management activities, particularly thinning. They often describe annual changes in growth and survival of individual-tree providing detailed information about stand structure and composition. Available data sets for fitting individual-tree models frequently have measurement intervals greater than 1 year and many times these intervals are irregularly spaced. Also thinning can occur between measurements. This causes difficulty when modelling annual tree growth and survival. An annual individual-tree growth and survival model is developed for pure even-aged stands of maritime pine in Portugal, using data with irregularly spaced measurement time intervals and considering thinning effects. The central components of the model are the equation for diameter growth, the equation for height growth and a survival function. Variable growth and survival rates are assumed in the modelling approach. The model is distance-independent and will be useful for intensively managed areas of pure even-aged stands of maritime pine in Portugal.
