Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Tissue culture of forest trees: Clonal multiplication of Eucalyptus grandis L

Axillary shoot proliferation was obtained using explants of Eucalyptus grandis L. juvenile and mature stages on a defined medium. Murashige and Skoog medium (MS) supplemented with benzyladenine (BA), naphthalene acetic acid (NAA) and additional thiamine. Excised shoots were induced to root on a sequence of three media: (1) White's medium containing indoleacetic acid (IAA), NAA and indole butyric acid; (IBA), (2) half-strength MS medium with charcoal and (3) half-strength MS liquid medium. The two types of explants differed in rooting response, with juvenile-derived shoots giving 60% rooting and adult-derived ones only 35%. Thus, the factors limiting cloning of selected trees in vitro are determined to be those controlling rooting of shoots in E. grandis.

Characterization of tree-to-tree variation in morphological, nutritional and medicinal properties of Canarium indicum nuts

As part of a feasibility study of the commercialization potential of C. indicum nuts as Agroforestry Tree Products in Papua New Guinea, preliminary characterization studies have examined the tree-to-tree variation in morphological traits (nut and kernel mass and kernel:nut ratio), as well as nutritional (carbohydrate, fat, protein, sodium, vitamin E) and medicinal traits (anti-oxidant activity, anti-inflammatory activity and phenolic content) of kernels from 18 to 72 trees in a small number of different villages of Papua New Guinea (East New Britain Province). There was continuous variation in these traits indicating opportunities for multiple trait cultivar development targeted at food and pharmaceutical markets. Certain traits, for example anti-inflammatory activity, in which tree-to-tree variation was highly significant, present greater opportunities than others, such as saturated:unsaturated fatty acid ratio. This intraspecific variation was greater within populations than between populations. The data presented has allowed the development of a strategy to domesticate C. indicum for cultivation in homegardens and cocoa-coconut agroforests, using a participatory approach aimed at the production of agroforestry tree products (AFTPs) to empower small-holders and enhance their livelihoods and income.

Ceratocystis atrox sp. nov. associated with Phoracantha acanthocera infestations on Eucalyptus grandis in Australia

Ceratocystis spp. include important pathogens of trees as well as apparently saprophytic species. Four species have been recorded on Eucalyptus grandis in Australia, of which only one, C. pirilliformis Barnes and M.J. Wingf., is known to be pathogenic. A recent survey of pests and diseases of Eucalyptus trees in northern Queensland revealed a species of Ceratocystis associated with the tunnels made by the aggressive wood-boring insect Phoracantha acanthocera (Macleay) (Cerambicydae: Coleoptera). The aim of the present study was to identify the fungus based on morphological characteristics and comparisons of DNA sequence data for three gene regions. The fungus peripherally resembles C. fimbriata Ell. and Halst. but differs from this species most obviously by having much darker mycelium, longer ascomatal necks, segmented hyphae and an absence of aleuroconidia. Comparisons of combined sequence data confirmed that the Ceratocystis sp. from P. acanthocera represents an undescribed taxon, which is provided with the name Ceratocystis atrox sp. nov. C. atrox appears to have a close relationship with P. acanthocera, although its role in the biology of the insect is unknown and its pathogenicity has not been considered.

Between-tree variation in fruit quality and fruit mineral concentrations of Hass avocados

Inconsistent internal fruit quality in Hass avocados affects consumer confidence. To determine the influence of individual trees on fruit quality, Hass avocado fruit were harvested from adjacent trees of similar external appearance in 3 commercial orchards in 1998 and 1 orchard in 1999. The trees in each orchard were grown with similar commercial practices and in similar soil types. Within each location, there were significant (P<0.05) differences in the mean ripe fruit quality between trees with respect to fruit body rot severity (mainly anthracnose) with and without cold storage, internal disorders severity due to diffuse discolouration and vascular browning (after cold storage), days to ripen, percentage dry matter, and the percentage of the skin area with purple-black colour when ripe. These effects were also noted in the same orchard in 1999. There were significant (P<0.05) differences in fruit flesh calcium, magnesium, potassium, boron and zinc concentrations between trees. Significant (P<0.05) correlations were observed between average fruit mineral concentrations in each tree (particularly calcium, magnesium and potassium) and body rot severity, percentage dry matter and fruit mass. There was little conclusive evidence that characteristics such as the growth of the non-suberised roots or the degree of scion under- or overgrowth was involved in these tree effects; however, differences between trees with respect to other rootstock characteristics may be involved. The inconsistency of the correlations across sites and years suggested that other factors apart from tree influences could also affect the relationship between fruit minerals and fruit quality.

Sustainable native forest management. Case studies in managing private native forest in southeast Queensland.

The introduction describes productive forest in Queensland and summaries the principles of native forest management that achieve optimum productivity. Case study 1 deals with thinning an even-aged regrowth forest. It shows how thinning the stand actively manages the future composition and structure to improve productivity in the best stems and increase the commercial value of the next harvest. Case study 2 describes restoring productivity in a high-graded spotted gum - ironbark forest. It shows that defective and non-saleable trees should be removed so they do not repress the future stand; and that regeneration should be thinned, retaining the best trees in adequate growing space. Case study 3 discusses on-farm value adding for hardwood forests. It shows how long-term viability and maximum productivity and returns depend on the best management practices and knowing how to obtain the best returns from a range of forest products. Case study 4 examines integrated harvesting in a eucalypt forest. It shows how integrating the harvest enables the full range of timber products are harvested and sold for their maximum value while reducing the amount of waste.

Research note: poplar box (Eucalyptus populnea) growth rates in thinned and intact woodlands in central Queensland

A 19-year data set, which highlights the rapid growth rate in basal area of trees in thinned plots compared with unthinned controls, is presented. These results support the contention that, following tree thinning, basal area of retained trees will increase more rapidly than that of trees on unthinned areas. Indications are that pre-thinning levels in tree basal area will again be reached before the cost of treatment can be recouped by increased pasture and livestock production.

The use of heat-sums to predict harvest dates following potassium chlorate (KClO3) application in longan.

The ability to initiate and manipulate flowering with KClO3 allows flowering of longan, to be triggered outside of the normal flowering season (July-September) in Australia. Fruit maturity following normal flowering will occur approximately six-eight months (180-220 days) from flowering, depending on variety. Out of season flowering will result in differing times to maturity due to different temperature regimes during the maturity period. Knowing how long fruit will take to mature from different KClO3 application dates is potentially a valuable tool for growers to use as it would allow them to time their applications with market opportunities, e.g. Chinese New Year, periods of low volumes or periods of high prices. A simple heat-sum calculation was shown to reliably quantify fruit maturity periods, 2902 and 3432 growing degree days for Kohala and Biew Kiew respectively. Growers can use heat-sum as a predictive tool to allow for efficient planning of harvesting, packaging and freight requirements.

Sapindaceae production and research in Australia.

Australia has an abundance of native Sapindaceae, with a few species that are considered to have an edible aril. A number of these have minor 'bush food' status but have limited commercial potential. Longan, lychee and rambutan were introduced into Australia from the mid 1800s. Serious commercialization of these crops began from the 1970s when farmers in sub-tropical and tropical regions of Australia were seeking new commercial horticultural opportunities. Currently the value of these industries is in the vicinity of $35 M with lychee the predominate crop followed by longan and rambutan respectively. Despite Australia being a minor producer on the world scale it has contributed significantly to the scientific and production developments through the combined efforts of researchers and innovative growers. This paper details the development and status of the commercial Sapindaceae in Australia and highlights production and research activities.

The effect of foliar sprays of the synthetic auxin 3-5-6 TPA, on fruit drop, fruit size and seed development in three lychee (Litchi chinensis) cultivars: Tai So, Fay Zee Sui and Kwai Mai Pink.

Fruit drop in lychee can cause major yield losses in Australia, the severity varying with cultivar and season. Research in China, South Africa and Israel has demonstrated the potential for synthetic auxins used as foliar sprays to reduce fruit drop in lychee. Trials were initiated in Australia to test the efficacy of the synthetic auxin, 3-5-6 Trichloro-2-phridyl-oxyacetic acid (3-5-6 TPA) at 50 ppm on the cultivars Tai So, Fay Zee Sui and Kwai Mai Pink. Results indicate that in most cases the TPA reduced natural fruit drop however the size of the fruit at the time of application affects the response and the ideal application time varies with cultivar; approximately 13 mm fruit length in 'Kwai Mai Pink', 20 mm in 'Fay Zee Sui' and 27 mm in 'Tai So'. If applied too early in 'Tai So', it caused an increase in fruit drop. The TPA was most effective when natural fruit drop was high, reducing fruit drop from 74.7 to 34.9% in 'Kwai Mai Pink' and least effective when natural fruit drop was low. An increase in the percentage of fruit with poorly developed (chicken tongue) seed and slightly larger fruit size was also observed in treated trees.

Wood properties and knot occlusion of plantation grown Eucalyptus dunnii and Corymbia citriodora subsp. variegata in a pruning and thinning experiment.

A 2 × 2 factorial combination of thinned or unthinned, and pruned or unpruned 11-year-old Eucalyptus dunnii (DWG) and 12-year-old Corymbia citriodora subsp. variegata (CCV) was destructively sampled to provide 60 trees in total per species. Two 1.4 m long billets were cut from each tree and were rotary veneered in a spindleless lathe down to a 45 mm diameter core to expose knots which were classified as either alive, partially occluded or fully occluded. Non-destructive evaluation of a wider range of thinning treatments available in these trials was undertaken with Pilodyn and Fakopp tools. Disc samples were also taken for basic density and modulus of elasticity. Differences between treatments for all wood property assessments were generally small and not significantly different.Thinning and pruning had little effect on the stem diameter growth required to achieve occlusion, therefore occlusion would be more rapid after thinning due to more rapid stem diameter growth. The difference between the treatments of greatest management interest, thinned and pruned (T&P) and unthinned and unpruned (UT&UP) were small. The production of higher value clear wood produced after all knots had occluded, measured as the average stem diameter growth over occlusion of the three outermost knots, was approximately 2 centimetres diameter. Two of the treatments can be ruled out as viable management alternatives: (i) the effect of thinning without pruning (T&UP) is clear, leading to a large inner core of stem wood containing knots (large knotty core diameter) and (ii) pruning without thinning (UT&P) results in a small knotty core diameter, however the tree and therefore log diameters are also small.

DNA-based identification of Quambalaria pitereka causing severe leaf blight of Corymbia citriodora in China

Quambalaria spp. include serious plant pathogens, causing leaf and shoot blight of Corymbia and Eucalyptus spp. In this study, a disease resembling Quambalaria leaf blight was observed on young Corymbia citriodora trees in a plantation in the Guangdong Province of China. Comparisons of rDNA sequence data showed that the causal agent of the disease is Q. pitereka. This study provides the first report of Quambalaria leaf blight from China, and it is also the first time that this pathogen has been found on trees outside the native range of Eucalypts.

Quambalaria species: increasing threat to eucalypt plantations in Australia

Spotted gum (Corymbia citriodora subsp. variegata and C. maculata) is a valuable source of commercial timber and suitable for a wide range of different soil types in eastern Australia. The main biological constraint to further expansion of spotted gum plantations is Quambalaria shoot blight caused by the fungus Quambalaria pitereka. Surveys conducted to evaluate the impact of Quambalaria shoot blight have shown that the disease is present in all spotted gum plantations and on a range of Corymbia species and hybrids in subtropical and tropical regions surveyed in eastern Australia. More recently, Q. eucalypti has also been identified from a range of Eucalyptus species in these regions. Both pathogens have also been found associated with foliage blight and die-back of amenity trees and Q. pitereka in native stands of Corymbia species, which is the probable initial infection source for plantations. Infection by Q. pitereka commonly results in the repeated destruction of the growing tips and the subsequent formation of a bushy crown or death of trees in severe cases. In comparison, Q. eucalypti causes small, limited lesions and has in some cases been associated with insect feeding. It has not been recorded as causing severe shoot and stem blight. A better understanding of factors influencing disease development and host-pathogen interactions is essential in the development of a disease management strategy for these poorly understood but important pathogens in the rapidly expanding eucalypt (Corymbia and Eucalyptus spp.) plantation industry in subtropical and tropical eastern Australia.

Quantitative and molecular genetics of juvenile wood traits in radiata and slash/Caribbean pines.

The Juvenile Wood Initiative (JWI) project has been running successfully since July 2003 under a Research Agreement with FWPA and Letters of Association with the consortium partners STBA (Southern Tree Breeding Association), ArborGen and FPQ (Forestry Plantations Queensland). Over the last five and half years, JWI scientists in CSIRO, FPQ, and STBA have completed all 12 major milestones and 28 component milestones according to the project schedule. We have made benchmark progress in understanding the genetic control of wood formation and interrelationships among wood traits. The project has made 15 primary scientific findings and several results have been adopted by industry as summarized below. This progress was detailed in 10 technical reports to funding organizations and industry clients. Team scientists produced 16 scientific manuscripts (8 published, 1 in press, 2 submitted, and several others in the process of submission) and 15 conference papers or presentations. Primary Scientific Findings. The 15 major scientific findings related to wood science, inheritance and the genetic basis of juvenile wood traits are: 1. An optimal method to predict stiffness of standing trees in slash/Caribbean pine is to combine gravimetric basic density from 12 mm increment cores with a standing tree prediction of MoE using a time of flight acoustic tool. This was the most accurate and cheapest way to rank trees for breeding selection for slash/Caribbean hybrid pine. This method was also recommended for radiata pine. 2. Wood density breeding values were predicted for the first time in the STBA breeding population using a large sample of 7,078 trees (increment cores) and it was estimated that selection of the best 250 trees for deployment will produce wood density gains of 12.4%. 3. Large genetic variation for a suite of wood quality traits including density, MFA, spiral grain, shrinkage, acoustic and non-acoustic stiffness (MoE) for clear wood and standing trees were observed. Genetic gains of between 8 and 49% were predicted for these wood quality traits with selection intensity between 1 to 10% for radiata pine. 4. Site had a major effect on juvenile-mature wood transition age and the effect of selective breeding for a shorter juvenile wood formation phase was only moderate (about 10% genetic gain with 10% selection intensity, equivalent to about 2 years reduction of juvenile wood). 5. The study found no usable site by genotype interactions for the wood quality traits of density, MFA and MoE for both radiata and slash/Caribbean pines, suggesting that assessment of wood properties on one or two sites will provide reliable estimates of the genetic worth of individuals for use in future breeding. 6. There were significant and sizable genotype by environment interactions between the mainland and Tasmanian regions and within Tasmania for DBH and branch size. 7. Strong genetic correlations between rings for density, MFA and MoE for both radiata and slash/Caribbean pines were observed. This suggests that selection for improved wood properties in the innermost rings would also result in improvement of wood properties in the subsequent rings, as well as improved average performance of the entire core. 8. Strong genetic correlations between pure species and hybrid performance for each of the wood quality traits were observed in the hybrid pines. Parental performance can be used to identify the hybrid families which are most likely to have superior juvenile wood properties of the slash/Caribbean F1 hybrid in southeast Queensland. 9. Large unfavourable genetic correlations between growth and wood quality traits were a prominent feature in radiata pine, indicating that overcoming this unfavourable genetic correlation will be a major technical issue in progressing radiata pine breeding. 10. The project created the first radiata pine 18 k cDNA microarray and generated 5,952 radiata pine xylogenesis expressed sequence tags (ESTs) which assembled into 3,304 unigenes. 11. A total of 348 genes were identified as preferentially expressed genes in earlywood or latewood while a total of 168 genes were identified as preferentially expressed genes in either juvenile or mature wood. 12. Juvenile earlywood has a distinct transcriptome relative to other stages of wood development. 13. Discovered rapid decay of linkage disequilibrium (LD) in radiata pine with LD decaying to approximately 50% within 1,700 base pairs (within a typical gene). A total of 913 SNPS from sequencing 177,380 base pairs were identified for association genetic studies. 14. 149 SNPs from 44 genes and 255 SNPs from a further 51 genes (total 95 genes) were selected for association analysis with 62 wood traits, and 30 SNPs were shortlisted for their significant association with variation of wood quality traits (density, MFA and MoE) with individual significant SNPs accounting for between 1.9 and 9.7% of the total genetic variation in traits. 15. Index selection using breeding objectives was the most profitable selection method for radiata pine, but in the long term it may not be the most effective in dealing with negative genetic correlations between wood volume and quality traits. A combination of economic and biological approaches may be needed to deal with the strong adverse correlation.

Healthy plantations. A field guide to pests and pathogens of Acacia, Eucalyptus and Pinus in Vietnam.

This book is a resource for those involved ‘on-the-ground’ with growing plantation trees in Vietnam, identifying the pests and diseases found on them, and managing the impacts of these organisms. The book, supported by AusAID’s Vietnam CARD (Cooperation for Agricultural and Rural Development) Program, and draws on the collective, long-standing experience of forest health scientists in Vietnam, Australia and South Africa. The book provides illustrations and information on 23 pests and 25 diseases of Acacia, Eucalyptus and Pinus for Vietnam; four of these species are important biosecurity threats not yet present in Vietnam.