- Title
- Development of density-dependent and density-independent competition models to understand single tree growth responses in eucalyptus stands
- Creator
- Kepe, Lulama Patrick
- Subject
- Forests and forestry -- Mathematical models
- Subject
- Trees -- Growth -- Mathematical models
- Subject
- Eucalyptus grandis
- Date Issued
- 2024-12
- Date
- 2024-12
- Type
- Doctoral theses
- Type
- text
- Identifier
- http://hdl.handle.net/10948/68906
- Identifier
- vital:77161
- Description
- In commercial forest production, predicted yields based on mensuration recommendations are seldom realized, and minimal silvicultural standards based on results from trial blocks do not account for the relationship between initial planting density and final stocking. Growth models designed to investigate management options must employ competition indices to provide reliable predictions under extreme silviculture. The competition a tree experiences until the day of harvest is a strong driver for quality and volume of timber. Hence, this turns the regulation of competition into an integral part of silviculture. According to Little et al. (2003), it is known that, at some stage after canopy closure, individual trees in a stand will begin to compete for resources. To investigate competition amongst individual trees, a re-purposed Bayesian mixed effects model, similar in characteristics to a Sire model used for estimating breeding values, is proposed. In animal breeding models, the Sire Model allows for the inclusion of a numerator relationship matrix containing inbreeding coefficients. In a similar way, documented competition indices are included in the model in an attempt to estimate posterior probabilities of specifically selected individual trees being the strongest growers during different stages in the tree growth cycle. Estimated tree growth indices were determined and used to make probability statements in order to rank the individually selected trees based on the amount of growth observed. A tree growth index is a measurement of a tree’s average growth performance in relation to the average growth performance of all trees on the same plot. As different competition indices are introduced into the model, changes in the probabilities are observed and compared to what is visually observed on the plot, i.e. if the tree with the highest probability of being the strongest grower, is actually not necessarily the largest tree of the group of selected trees, but rather the tree that presented the largest amount of growth of the selected group of trees during that specific growth season. From a randomly selected plot, a group of neighboring trees were randomly selected. Four specifically selected target trees were then identified from this group of 25 selected trees, and analyzed. For this discussion, for example, from our randomly selected group of 25 neighboring trees, tree 54, tree 56, tree 86, and tree 88 were specifically selected for further analysis. For these specifically selected trees, marginal posterior densities for the variance components and random effects were then estimated using the Gibbs Sampler, where competition between the trees was assumed present, as well as for the case where it was assumed that no competition takes place between the individually selected trees. In the latter case, an identity matrix was utilized in the Gibbs sampling algorithm where it was assumed that there is no competition between the trees. Both a distance independent competition index (Lorimer,1983), and a distance dependent index (Hegyi, 1974), were used to generate the numerator relationship matrix A that was used by the Gibbs sampling algorithm in the case where competition was assumed between individual trees. Also a new distance dependent index was proposed and tested in this study as well. Results from the selected plot, with a 1500 stems per hectare (sph) density, indicated that there were no significant differences in the average growth between these selected trees. However, the marginal posterior densities of the fixed effects indicated that there was a significant difference in the average growth rates between the base level conditions and other levels determined for each of these fixed effect factors for the selected trees, since their 95% equal tails credibility intervals, did not contain zero. This therefore indicated that the specific treatment applied on the plot, had a significant effect on the individual tree growth. Results when competition was assumed present, revealed that the estimated marginal posterior densities for the error variance as well as tree variance, were severely positively skewed.
- Description
- Thesis (PhD) -- Faculty of Science, School of Natural Resource Science & Management, 2024
- Format
- computer
- Format
- online resource
- Format
- application/pdf
- Format
- 1 online resource (286 pages)
- Format
- Publisher
- Nelson Mandela University
- Publisher
- Faculty of Science
- Language
- English
- Rights
- Nelson Mandela University
- Rights
- All Rights Reserved
- Rights
- Open Access
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | KEPE, L.pdf | 2 MB | Adobe Acrobat PDF | View Details Download |