Development of density-dependent and density-independent competition models to understand single tree growth responses in eucalyptus stands
- Authors: Kepe, Lulama Patrick
- Date: 2024-12
- Subjects: Forests and forestry -- Mathematical models , Trees -- Growth -- Mathematical models , Eucalyptus grandis
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10948/68906 , 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. , Thesis (PhD) -- Faculty of Science, School of Natural Resource Science & Management, 2024
- Full Text:
- Date Issued: 2024-12
- Authors: Kepe, Lulama Patrick
- Date: 2024-12
- Subjects: Forests and forestry -- Mathematical models , Trees -- Growth -- Mathematical models , Eucalyptus grandis
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10948/68906 , 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. , Thesis (PhD) -- Faculty of Science, School of Natural Resource Science & Management, 2024
- Full Text:
- Date Issued: 2024-12
The effect of a soil-amending hydrogel on Eucalyptus grandis establishment practices in the Zululand forestry region
- Authors: Viero, Paul Walter Mario
- Date: 2002
- Subjects: Eucalyptus grandis
- Language: English
- Type: Thesis , Masters , MTech (Forestry)
- Identifier: vital:10973 , http://hdl.handle.net/10948/90 , Eucalyptus grandis
- Description: To ensure acceptable survival and initial growth of Eucalyptus grandis clonal and clonal hybrid material planted in the cool temperate and sub-tropical climates of Zululand (KwaZulu-Natal, South Africa) the planting seasons are currently restricted to the winter or summer months respectively. The Zululand coast (sub-tropical climate) experiences traditionally hot and humid summers and as a result Eucalyptus planting is largely restricted to the cool and dry winter months when survival is acceptable (90- 95%). In comparison, the Zululand interior (cool temperate climate) experiences moderately cooler summers followed by drier winters. As a result, the Eucalyptus planting season is reversed to that of the Zululand coast, with most of the planting taking place during the summer months with little or no planting occurring during winter. To ensure adequate transplant survival during and beyond these periods, transplants are planted with large volumes of water at a high cost. To determine whether it was possible to significantly reduce current water volumes at planting and therefore reduce costs, and to potentially extend the current planting seasons, two field trials were initiated during traditionally unsuitable planting periods (winter months for the Zululand interior and summer months for the Zululand coast). These trials were established near Kwambonambi on the Zululand coast and at Ntonjaneni in the Zululand interior. Five levels of water were combined with five levels of hydrogel and applied to the pit at planting in a 5 x 5 factorial treatment design for both trials. The tree variates of mortality, height, groundline diameter, crown diameter, corrected leaf surface index (LSIC) and corrected biomass index (BIC) were assessed at regular intervals until the final measurement dates (118 and 128 days after planting for the Ntonjaneni and Kwambonambi trials respectively). For the Kwambonambi trial, the response of transplant survival to the application water was highly significant (p<0,01) 128 days after planting, but not to the application of the hydrogel. Transplant survival nevertheless conformed to the silviculturally accepted norms of 90-95% using the hydrogel, thus water volumes could be significantly reduced without negatively affecting current survival standards. The lack of the expected response of significantly reduced transplant survival to increasing levels of hydrogel could possibly be attributed to the significant rainfall event (146 mm) that fell two days after trial initiation. Increasing levels of both water and hydrogel resulted in significantly enhanced growth (LSIC and BIC: p<0.01) for the final measurement date. For the Ntonjaneni trial, there was a significant (p<0,01) interaction between hydrogel and water, 118 days after planting. There were significant (p<0,01) differences between water only and all hydrogel treatments, with the hydrogel treatments performing significantly better. Optimum transplant survival for water only treatments was 50% using 4000 ml water while that for hydrogel treatments was 100% using 6 g hydrogel with 1000 ml of water and 12 g hydrogel with 2000 ml of water. The variates, corrected leaf surface index and corrected biomass index indicated that tree growth was significantly enhanced by the addition of a hydrogel over all levels of water. A pot trial was subsequently implemented to ascertain whether the significant increases obtained for initial transplant growth for the sandy clay loam soils of Ntonjaneni were due to an initial but unsustainable positive response of the roots to the presence of the hydrogel, or whether root growth was sustainably advantaged by the presence of the hydrogel. There was a highly significant (p<0,01) response of root biomass and above ground biomass over all levels of hydrogel, including a significant positive linear (p<0,01) relationship between increased root biomass and above ground biomass. This clearly indicated that initial root growth was not negatively affected by the addition of the soil-amending hydrogel Stockosorb 400K.
- Full Text:
- Date Issued: 2002
- Authors: Viero, Paul Walter Mario
- Date: 2002
- Subjects: Eucalyptus grandis
- Language: English
- Type: Thesis , Masters , MTech (Forestry)
- Identifier: vital:10973 , http://hdl.handle.net/10948/90 , Eucalyptus grandis
- Description: To ensure acceptable survival and initial growth of Eucalyptus grandis clonal and clonal hybrid material planted in the cool temperate and sub-tropical climates of Zululand (KwaZulu-Natal, South Africa) the planting seasons are currently restricted to the winter or summer months respectively. The Zululand coast (sub-tropical climate) experiences traditionally hot and humid summers and as a result Eucalyptus planting is largely restricted to the cool and dry winter months when survival is acceptable (90- 95%). In comparison, the Zululand interior (cool temperate climate) experiences moderately cooler summers followed by drier winters. As a result, the Eucalyptus planting season is reversed to that of the Zululand coast, with most of the planting taking place during the summer months with little or no planting occurring during winter. To ensure adequate transplant survival during and beyond these periods, transplants are planted with large volumes of water at a high cost. To determine whether it was possible to significantly reduce current water volumes at planting and therefore reduce costs, and to potentially extend the current planting seasons, two field trials were initiated during traditionally unsuitable planting periods (winter months for the Zululand interior and summer months for the Zululand coast). These trials were established near Kwambonambi on the Zululand coast and at Ntonjaneni in the Zululand interior. Five levels of water were combined with five levels of hydrogel and applied to the pit at planting in a 5 x 5 factorial treatment design for both trials. The tree variates of mortality, height, groundline diameter, crown diameter, corrected leaf surface index (LSIC) and corrected biomass index (BIC) were assessed at regular intervals until the final measurement dates (118 and 128 days after planting for the Ntonjaneni and Kwambonambi trials respectively). For the Kwambonambi trial, the response of transplant survival to the application water was highly significant (p<0,01) 128 days after planting, but not to the application of the hydrogel. Transplant survival nevertheless conformed to the silviculturally accepted norms of 90-95% using the hydrogel, thus water volumes could be significantly reduced without negatively affecting current survival standards. The lack of the expected response of significantly reduced transplant survival to increasing levels of hydrogel could possibly be attributed to the significant rainfall event (146 mm) that fell two days after trial initiation. Increasing levels of both water and hydrogel resulted in significantly enhanced growth (LSIC and BIC: p<0.01) for the final measurement date. For the Ntonjaneni trial, there was a significant (p<0,01) interaction between hydrogel and water, 118 days after planting. There were significant (p<0,01) differences between water only and all hydrogel treatments, with the hydrogel treatments performing significantly better. Optimum transplant survival for water only treatments was 50% using 4000 ml water while that for hydrogel treatments was 100% using 6 g hydrogel with 1000 ml of water and 12 g hydrogel with 2000 ml of water. The variates, corrected leaf surface index and corrected biomass index indicated that tree growth was significantly enhanced by the addition of a hydrogel over all levels of water. A pot trial was subsequently implemented to ascertain whether the significant increases obtained for initial transplant growth for the sandy clay loam soils of Ntonjaneni were due to an initial but unsustainable positive response of the roots to the presence of the hydrogel, or whether root growth was sustainably advantaged by the presence of the hydrogel. There was a highly significant (p<0,01) response of root biomass and above ground biomass over all levels of hydrogel, including a significant positive linear (p<0,01) relationship between increased root biomass and above ground biomass. This clearly indicated that initial root growth was not negatively affected by the addition of the soil-amending hydrogel Stockosorb 400K.
- Full Text:
- Date Issued: 2002
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