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A research report submitted to the Faculty of Sciences, University of the Witwatersrand, Johannesburg in partial fulfilment of the requirements for the degree of Masters of Science in Environmental Sciences, 2017 / Modern tree biomass allometry makes use of “form factor”, which is the ratio of the true volume to the apparent volume. However, there is no database of form factors of South African trees, hence this study was undertaken to assess the possibility of assigning form factors to trees in a quick and easy way, either by visual assessment of an image of the tree or by simple field measurements. Stem diameter, taper and node length data for 112 trees was collected using both in situ and in-lab measurements from photos taken of the same trees in the field. The data were used to model tree volume using the fractal properties of branching architecture. The estimated tree volume was then used along with basal diameter and tree height to calculate the form factor. Results showed that measurements taken off images underestimated stem diameter and node length by 4% and 5% respectively, but the fractal allometry relationships developed using either the manual in-field or image analysis approach were not statistically different. This proves that dry season photography is sufficiently accurate for establishing relationships needed to construct a fractal model of tree volume. The image analysis approach requires a clear unobstructed view of the sample tree. This requirement made the approach less effective as when trees were in close proximity and when branches overlapped. The time taken using the photographic approach was twice the amount taken for the manual in-field. Form factor varied between species, but the variation was not statistically significant (p=0.579). The mean form factor per species ranged from 0.43 to 0.69. Form factors were negatively correlated with wood density (-0.177), basal diameter (-0.547) and height (-0.649). Due to the unavailability of an independent tree biomass dataset, it was impossible to validate the allometric equations based on estimated form factors and wood density. The inclusion of form factor was shown to improve the accuracy of biomass estimation by 11%. Principal component analysis showed that form factors can be assigned using tree height and the form quotient. / XL2018

Many species from economically important genera remain rooting recalcitrant, prohibiting the commercialisation of many species in forestry and horticulture, and hindering genetic improvement by conventional breeding or recombinant DNA technology, where vegetative propagation is often used to preserve the genetic fidelity of elite progeny. Two cherry species (Prunus avium and P. padus) were used as models in this study to investigate the physiological and genetic manipulation of adventitious rooting. Mature trees are typically more difficult to propagate vegetatively than their juvenile counterparts. For some trees, micropropagation can circumvent certain effects of ageing and maturation, restoring shoot vigour and rooting, but the mechanism(s) involved have not been elucidated. During micropropagation, subculture interval was found not to be the predominant factor promoting the 'apparent rejuvenation' of mature P. avium tissue. 'Apparently rejuvenated' ex vitro and hedged (putatively) mature P. avium trees were treated with gibberellins predicted to have a range of structural related activities. GA, improved the rooting of cuttings from hedged (putatively) mature cherry, but not from ex vitro trees. Methodology to regenerate adventitious shoots from P. avium leaf explants was developed, (putative) transgenic P. padus plants were produced by an Agrobacterium tumefaciens mediated strategy. Auxin redistribution in planta is postulated to require a component of active transport; inhibition of the predominantly basipetal transport has profound effects on rooting. The putative function of the Arabidopsis thaliana AtAUX1 gene is that of a cellular auxin influx carrier, possibly, as described by the chemiosmotic hypothesis. This thesis examined the hypothesis that transformation with the AtAUX1 gene would enhance the delivery of the root-inducing signal to improve rooting of P. padus, a species which is rooting recalcitrant and more or less obligate on exogenous auxin for this process. However, all six, constitutively expressed, Cauliflower Mosaic Virus 35S promoter driven, 35S::AtAUX1, transgenic shoot lines had reduced rooting.

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I investigate use of the simulated annealing heuristic to seek phylogenetic trees judged optimal according to the principle of parsimony. I begin by looking into the central data structure in phylogenetic research, the tree. I discuss why it is usually necessary to employ a heuristic, rather than an exact method, when seeking parsimonious trees. I summarise different heuristic approaches. I explain how to use the program LVB, written to use simulated annealing in the search for parsimonious trees. I use LVB, with different combinations of values for parameters controlling the annealing search, to re-analyse two DNA sequence data matrices, one of 50 objects and one of 365 objects. Equations to estimate suitable control parameters, on the basis of desired run time and quality of result, are fitted to data obtained by these analyses. Future directions of research are discussed.

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A network is a system that involves movement or flow of some commodities such as goods and services. In fact any structure that is in the form of a system of components some of which interact can be considered as a network. In network design the problem is often to construct economical and reliable networks which satisfy certain requirements and which are optimal according to some criterion such as cost, output or performance. Graph theory is useful when the requirements of the network can be expressed in terms of graph parameters, usually as bounds. Some of the graph parameters that have been considered include: degree; distance; diameter; and connectivity. Problems with these parameter restrictions are usually from a class of NP-complete problems with instances that require exponential computer time to solve by available algorithms.The major focus of this thesis is to develop fast and efficient heuristics for some of these NP-complete problems. The two main topics analysed are Restricted Spanning Trees and Graph Partitioning. The aim of the Restricted Spanning Trees section is to construct the most efficient spanning tree (connected network) subject to various degree constraints. These degree constraints imposed are usually in the form of an upper bound. The upper bound represents the maximum number of connections allowed on a particular vertex. The Graph Partitioning section considers the problem of clustering vertices of the graph into sets such that the overall cost of the edges in the different sets is minimised.Chapter 1 provides the notation and terminology used throughout the thesis and a review and summary of the thesis.A literature review of related work that has been carried out to date is presented in Chapter 2. Some of the more promising results are discussed. The first part of the chapter surveys work related to the Restricted Spanning Tree problem. ++ / Analysis of both exact and heuristic methods is given. The second part of Chapter 2 provides a survey of the Graph Partitioning problem. We discuss the many different approaches that have been proposed to solve this problem. The quality of computational results achieved is discussed.Chapter 3 considers the Degree Constraint Minimum Weight Spanning Tree problem. This problem arises in networks where a given terminal is only allowed connections to a maximum number of specified terminals. We consider a number of cases including: same degree constraint on each vertex; different degree constraint on some vertices; and when the degree constraint is only on one or two vertices. A number of heuristics are developed and implemented and compared against an exact Branch and Cut algorithm. Our computational results demonstrated the value of our better performing heuristics.Chapter 4 considers the complexity of the (1,k)-tree problem. This problem is defined m given a graph G with maximum degree k find a spanning tree T with all vertices having degree 1 or k. Analysis is done on graphs with maximum degree 3, 4 and 5. Results establishing that the (1,3)-tree and (1, 4)-tree problems are NP-complete are presented. Further consideration is also given to the complexity of spanning trees with degree from the set { 1, 3, 5}. Analysis is also carried out on the number of degree one vertices in the (1, k)-tree. Presentation of heuristic procedures to solve this NP-complete problem concludes the chapter.Chapter 5 is devoted to the Graph Partitioning problem. A number of heuristics are presented and extensive computational work carried out. Computational findings support the usefulness of the heuristic methods both in terms of quality and time.We conclude this thesis by detailing some future work that can be carried out.

Amenity trees provide physical, social and economic benefits to people sharing their environment. To maintain the benefits that many people have come to expect of trees in their urban landscapes, a viable and dynamic tree population is required. To this end it is necessary to plant new trees or replace existing trees when they require removal. The challenge when replacing mature trees is not simply the process of planting a tree when one is removed, but of the continual replacement of the entire tree population in a planned and managed fashion. In urban landscapes this is not a natural process, and human intervention is required.

Thesis (M.S.)--University of Nevada, Reno, 2005. / "December, 2005." Includes bibliographical references. Online version available on the World Wide Web.