S09.4: Models for the fine root dispersion of trees considering interaction effects
✍ Scribed by Konrad Wälder
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 75 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0323-3847
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✦ Synopsis
In this talk an approach for modelling the fine root dispersion of forest trees is given. Dispersion models are indispensable for ecological research. These models contribute to the understanding of the consumption of resources in the soil by the trees. The proposed approach is based on so-called cluster point processes and enables interaction effects between trees to be considered. Without interaction each tree contributes in the same manner to the fine root mass at some location, i.e. the total fine root mass is the sum of the root masses of the participating trees. In the case of interaction this simple sum is replaced by a weighted sum called ordered weighted averaging operator (OWA). The weights of this OWA operator are determined by a Fuzzy measure which controls the type of interaction: a super-additive Fuzzy measure leads to (positive) synergy; negative synergy or redundancy is achieved with sub-additive Fuzzy measures. A Fuzzy measure is a set function which has not to fulfil the additivity assumption of a probability measure. An additive Fuzzy measure is a probability measure and in this case interaction is not considered. It is shown that Fuzzy measures from the Yager and Sugeno family are well suited for modelling interaction effects of forest trees. Using a Yager or Sugeno Fuzzy measure the type of interaction is modelled by an additional parameter which has to be fitted from the given data set. A Bayesian approach for model fitting based on stochastic integration is discussed. Finally, some results from real-case studies in Saxony/Germany are presented.
References:
Näther, W. and Wälder, K. (2003). Experimental design and statistical inference for cluster point processes -with applications to the fruit dispersion of anemochorous forest trees.