Statistical sampling and modelling for cork oak and eucalyptus stands

M.J. Paulo

Research output: Thesisinternal PhD, WU



This thesis focuses on the use of modern statistical methods to solve problems on sampling, optimal cutting time and agricultural modelling in Portuguese cork oak and eucalyptus stands. The results are contained in five chapters that have been submitted for publication as scientific manuscripts.

The thesis first addresses the decision of when to cut a rotation of eucalyptus production forest. The aim is to optimise the long term volume production, corrected for replant costs. On the long term the total financial yield divided by the total rotation time is an important economical asset. Successive rotations and their growth curves are considered as independent realisations of the same generating process. A Bayesian approach was taken, using Shumacher curves. Prior information on the curve parameters was based on a large number of observed growth curves. For known or accurately estimated curves, a 16% gain in optimisation of cutting times could be achieved, as compared to using a common optimal cutting time. It is assumed that a farmer takes two volume measurements to decide upon the cutting time of a rotation, the first measurement at a fixed age, the second at an age that possibly depends upon the first measurement. Finding the optimal second measurement time is entangled with finding the optimal cutting time. In this thesis, simultaneous optimisation is carried out using numerical methods. The gain in using a variable optimised second measurement time, compared with an optimised fixed measurement time, however, was relatively small (up to 0.1%), which is hardly above the numerical noise level.

A second problem addressed in this thesis concerns estimation of stem diameter growth curves in cork oaks. A data-set of 24 trees was used. A D-optimal experimental design has been compared with equidistant designs to measure trees at particular ages to allow for an optimal estimation of individual growth curves. An experimental design that is locally D-optimal for a central parameter is proposed. This fixed compromise design can be used for all trees. For individual growth curves and under certain conditions that are discussed in the thesis such a design provides better estimates than an equidistant design.

The third study concerns spatial modelling of quantitative cork oak characteristics. Spatial statistical methods are used to analyse cork oak stands, so-called montados. Spatial correlations between neighbouring trees of crown shapes, of crown sizes and of stem sizes are analysed using plots from two montados. A significant correlation is found between tree size and competition from neighbouring trees. In particular, larger trees have a regular spatial distribution in a montado.

The final study in this thesis compares three sampling methods for use in cork oak farms. One method is currently in use by Portuguese farmer's associations to estimate cork value prior to stripping and the other two methods are compared to it. The three sampling methods are applied to two cork oak farms and to simulated stands. The latter are generated with spatial simulation methods on the basis of information obtained elsewhere. The current method has a 15-50% larger bias. For a clustered pattern standard errors are lowest for the current method, but these are considerably higher for a regular or a random pattern.

In conclusion, this thesis shows that modern statistical methods are valuable to improve modelling and sampling of cork oak and eucalyptus forests. In particular, spatial relations among neighbouring trees should preferably be included into management of cork oak farms. Adequate sampling methods are basic to retrieve information of the highest quality.

Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Wageningen University
  • Rasch, D.A.M.K., Promotor, External person
  • Stein, A., Promotor
  • Otten, A., Promotor
Award date4 Nov 2002
Place of PublicationS.l.
Print ISBNs9789058087294
Publication statusPublished - 2002


  • sampling
  • bayesian theory
  • mathematical models
  • statistics


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