Predicting dispersal and recruitment of Miconia calvescens (Melastomataceae) in Australian tropical rainforests

Miconia calvescens (Melastomataceae) is a serious invader in the tropical Pacific, including the Hawaiian and Tahitian Islands, and currently poses a major threat to native biodiversity in the Wet Tropics of Australia. The species is fleshy-fruited, small-seeded and shade tolerant, and thus has the potential to be dispersed widely and recruit in relatively intact rainforest habitats, displacing native species. Understanding and predicting the rate of spread is critical for the design and implementation of effective management actions. We used an individual-based model incorporating a dispersal function derived from dispersal curves for similar berry-fruited native species, and life-history parameters of fecundity and mortality to predict the spatial structure of a Miconia population after a 30 year time period. We compared the modelled population spatial structure to that of an actual infestation in the rainforests of north Queensland. Our goal was to assess how well the model predicts actual dispersion and to identify potential barriers and conduits to seed movement and seedling establishment. The model overpredicts overall population size and the spatial extent of the actual infestation, predicting individuals to occur at a maximum 1,750 m from the source compared with the maximum distance of any detected individual in the actual infestation of 1,191 m. We identify several characteristic features of managed invasive populations that make comparisons between modelled outcomes and actual infestations difficult. Our results suggest that the model’s ability to predict both spatial structure and spread of the population will be improved by incorporating a spatially explicit element, with dispersal and recruitment probabilities that reflect the relative suitability of different parts of the landscape for these processes.

New efforts at biological control of Mikania micrantha H.B.K. (Asteraceae) in Papua New Guinea and Fiji.

New efforts at biological control of Miconia calvescens (Melastomataceae) is a serious invader in the tropical Pacific, including the Hawaiian and Tahitian Islands, and currently poses a major threat to native biodiversity in the Wet Tropics of Australia. The species is fleshy-fruited, small-seeded and shade tolerant, and thus has the potential to be dispersed widely and recruit in relatively intact rainforest habitats, displacing native species. Understanding and predicting the rate of spread is critical for the design and implementation of effective management actions. We used an individual-based model incorporating a dispersal function derived from dispersal curves for similar berry-fruited native species, and life-history parameters of fecundity and mortality to predict the spatial structure of a Miconia population after a 30 year time period. We compared the modelled population spatial structure to that of an actual infestation in the rainforests of north Queensland. Our goal was to assess how well the model predicts actual dispersion and to identify potential barriers and conduits to seed movement and seedling establishment. The model overpredicts overall population size and the spatial extent of the actual infestation, predicting individuals to occur at a maximum 1,750 m from the source compared with the maximum distance of any detected individual in the actual infestation of 1,191 m. We identify several characteristic features of managed invasive populations that make comparisons between modelled outcomes and actual infestations difficult. Our results suggest that the model’s ability to predict both spatial structure and spread of the population will be improved by incorporating a spatially explicit element, with dispersal and recruitment probabilities that reflect the relative suitability of different parts of the landscape for these processes. Mikania micrantha H.B.K. (Asteraceae) in Papua New Guinea and Fiji.

A Hierarchical System of Learning Automata

A learning automaton operating in a random environment updates its action probabilities on the basis of the reactions of the environment, so that asymptotically it chooses the optimal action. When the number of actions is large the automaton becomes slow because there are too many updatings to be made at each instant. A hierarchical system of such automata with assured c-optimality is suggested to overcome that problem.The learning algorithm for the hierarchical system turns out to be a simple modification of the absolutely expedient algorithm known in the literature. The parameters of the algorithm at each level in the hierarchy depend only on the parameters and the action probabilities of the previous level. It follows that to minimize the number of updatings per cycle each automaton in the hierarchy need have only two or three actions.

Dynamic Bayesian network inferencing for non-homogeneous complex systems

Dynamic Bayesian Networks (DBNs) provide a versatile platform for predicting and analysing the behaviour of complex systems. As such, they are well suited to the prediction of complex ecosystem population trajectories under anthropogenic disturbances such as the dredging of marine seagrass ecosystems. However, DBNs assume a homogeneous Markov chain whereas a key characteristics of complex ecosystems is the presence of feedback loops, path dependencies and regime changes whereby the behaviour of the system can vary based on past states. This paper develops a method based on the small world structure of complex systems networks to modularise a non-homogeneous DBN and enable the computation of posterior marginal probabilities given evidence in forwards inference. It also provides an approach for an approximate solution for backwards inference as convergence is not guaranteed for a path dependent system. When applied to the seagrass dredging problem, the incorporation of path dependency can implement conditional absorption and allows release from the zero state in line with environmental and ecological observations. As dredging has a marked global impact on seagrass and other marine ecosystems of high environmental and economic value, using such a complex systems model to develop practical ways to meet the needs of conservation and industry through enhancing resistance and/or recovery is of paramount importance.

Early detection of type 2 diabetes mellitus in Chinese and Indian adult population

Objectives of this study were to determine secular trends of diabetes prevalence in China and develop simple risk assessment algorithms for screening individuals with high-risk for diabetes or with undiagnosed diabetes in Chinese and Indian adults. Two consecutive population based surveys in Chinese and a prospective study in Mauritian Indians were involved in this study. The Chinese surveys were conducted in randomly selected populations aged 20-74 years in 2001-2002 (n=14 592) and 35-74 years in 2006 (n=4416). A two-step screening strategy using fasting capillary plasma glucose (FCG) as first-line screening test followed by standard 2-hour 75g oral glucose tolerance tests (OGTTs) was applied to 12 436 individuals in 2001, while OGTTs were administrated to all participants together with FCG in 2006 and to 2156 subjects in 2002. In Mauritius, two consecutive population based surveys were conducted in Mauritian Indians aged 20-65 years in 1987 and 1992; 3094 Indians (1141 men), who were not diagnosed as diabetes at baseline, were reexamined with OGTTs in 1992 and/or 1998. Diabetes and pre-diabetes was defined following 2006 World Health Organization/ International Diabetes Federation Criteria. Age-standardized, as well as age- and sex-specific, prevalence of diabetes and pre-diabetes in adult Chinese was significantly increased from 12.2% and 15.4% in 2001 to 16.0% and 21.2% in 2006, respectively. A simple Chinese diabetes risk score was developed based on the data of Chinese survey 2001-2002 and validated in the population of survey 2006. The risk scores based on β coefficients derived from the final Logistic regression model ranged from 3 – 32. When the score was applied to the population of survey 2006, the area under operating characteristic curve (AUC) of the score for screening undiagnosed diabetes was 0.67 (95% CI, 0.65-0.70), which was lower than the AUC of FCG (0.76 [0.74-0.79]), but similar to that of HbA1c (0.68 [0.65-0.71]). At a cut-off point of 14, the sensitivity and specificity of the risk score in screening undiagnosed diabetes was 0.84 (0.81-0.88) and 0.40 (0.38-0.41). In Mauritian Indian, body mass index (BMI), waist girth, family history of diabetes (FH), and glucose was confirmed to be independent risk predictors for developing diabetes. Predicted probabilities for developing diabetes derived from a simple Cox regression model fitted with sex, FH, BMI and waist girth ranged from 0.05 to 0.64 in men and 0.03 to 0.49 in women. To predict the onset of diabetes, the AUC of the predicted probabilities was 0.62 (95% CI, 0.56-0.68) in men and 0.64(0.59-0.69) in women. At a cut-off point of 0.12, the sensitivity and specificity was 0.72(0.71-0.74) and 0.47(0.45-0.49) in men; and 0.77(0.75-0.78) and 0.50(0.48-0.52) in women, respectively. In conclusion, there was a rapid increase in prevalence of diabetes in Chinese adults from 2001 to 2006. The simple risk assessment algorithms based on age, obesity and family history of diabetes showed a moderate discrimination of diabetes from non-diabetes, which may be used as first line screening tool for diabetes and pre-diabetes, and for health promotion purpose in Chinese and Indians.

Performance of slotted ALOHA satellite channels with finite buffer

The behaviour of the slotted ALOHA satellite channel with a finite buffer at each of the user terminals is studied. Approximate relationships between the queuing delay, overflow probabilities and buffer size are derived as functions of the system input parameters (i.e. the number of users, the traffic intensity, the transmission and the retransmission probabilities) for two cases found in the literature: the symmetric case (same transmission and retransmission probabilities), and the asymmetric case (transmission probability far greater than the retransmission probability). For comparison, the channel performance with an infinite buffer is also derived. Additionally, the stability condition for the system is defined in the latter case. The analysis carried out in the paper reveals that the queuing delays are quite significant, especially under high traffic conditions.

On the probability of dizygotic twins being concordant for two alleles at multiple polymorphic loci

Accurate determination of same-sex twin zygosity is important for medical, scientific and personal reasons. Determination may be based upon questionnaire data, blood group, enzyme isoforms and fetal membrane examination, but assignment of zygosity must ultimately be confirmed by genotypic data. Here methods are reviewed for calculating average probabilities of correctly concluding a twin pair is monozygotic, given they share the same genotypes across all loci for commonly utilized multiplex short tandem repeat (STR) kits.

Phased-Mission Analysis for Evaluating the Effectiveness of Aerospace Computing-Systems

Effectiveness evaluation of aerospace fault-tolerant computing systems used in a phased-mission environment is rather tricky and difficult because of the interaction of its several degraded performance levels with the multiple objectives of the mission and the use environment. Part I uses an approach based on multiobjective phased-mission analysis to evaluate the effectiveness of a distributed avionics architecture used in a transport aircraft. Part II views the computing system as a multistate s-coherent structure. Lower bounds on the probabilities of accomplishing various levels of performance are evaluated.

Multiaction learning automata possessing ergodicity of the mean

Multiaction learning automata which update their action probabilities on the basis of the responses they get from an environment are considered in this paper. The automata update the probabilities according to whether the environment responds with a reward or a penalty. Learning automata are said to possess ergodicity of the mean if the mean action probability is the state probability (or unconditional probability) of an ergodic Markov chain. In an earlier paper [11] we considered the problem of a two-action learning automaton being ergodic in the mean (EM). The family of such automata was characterized completely by proving the necessary and sufficient conditions for automata to be EM. In this paper, we generalize the results of [11] and obtain necessary and sufficient conditions for the multiaction learning automaton to be EM. These conditions involve two families of probability updating functions. It is shown that for the automaton to be EM the two families must be linearly dependent. The vector defining the linear dependence is the only vector parameter which controls the rate of convergence of the automaton. Further, the technique for reducing the variance of the limiting distribution is discussed. Just as in the two-action case, it is shown that the set of absolutely expedient schemes and the set of schemes which possess ergodicity of the mean are mutually disjoint.

Essays on socially optimal phosphorus policies in crop production

Phosphorus is a nutrient needed in crop production. While boosting crop yields it may also accelerate eutrophication in the surface waters receiving the phosphorus runoff. The privately optimal level of phosphorus use is determined by the input and output prices, and the crop response to phosphorus. Socially optimal use also takes into account the impact of phosphorus runoff on water quality. Increased eutrophication decreases the economic value of surface waters by Deteriorating fish stocks, curtailing the potential for recreational activities and by increasing the probabilities of mass algae blooms. In this dissertation, the optimal use of phosphorus is modelled as a dynamic optimization problem. The potentially plant available phosphorus accumulated in soil is treated as a dynamic state variable, the control variable being the annual phosphorus fertilization. For crop response to phosphorus, the state variable is more important than the annual fertilization. The level of this state variable is also a key determinant of the runoff of dissolved, reactive phosphorus. Also the loss of particulate phosphorus due to erosion is considered in the thesis, as well as its mitigation by constructing vegetative buffers. The dynamic model is applied for crop production on clay soils. At the steady state, the analysis focuses on the effects of prices, damage parameterization, discount rate and soil phosphorus carryover capacity on optimal steady state phosphorus use. The economic instruments needed to sustain the social optimum are also analyzed. According to the results the economic incentives should be conditioned on soil phosphorus values directly, rather than on annual phosphorus applications. The results also emphasize the substantial effects the differences in varying discount rates of the farmer and the social planner have on optimal instruments. The thesis analyzes the optimal soil phosphorus paths from its alternative initial levels. It also examines how erosion susceptibility of a parcel affects these optimal paths. The results underline the significance of the prevailing soil phosphorus status on optimal fertilization levels. With very high initial soil phosphorus levels, both the privately and socially optimal phosphorus application levels are close to zero as the state variable is driven towards its steady state. The soil phosphorus processes are slow. Therefore, depleting high phosphorus soils may take decades. The thesis also presents a methodologically interesting phenomenon in problems of maximizing the flow of discounted payoffs. When both the benefits and damages are related to the same state variable, the steady state solution may have an interesting property, under very general conditions: The tail of the payoffs of the privately optimal path as well as the steady state may provide a higher social welfare than the respective tail of the socially optimal path. The result is formalized and an applied to the created framework of optimal phosphorus use.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Assessing the combined effect of asbestos exposure and smoking on lung cancer: a Bayesian approach

We review the literature on the combined association between lung cancer and two environmental exposures, asbestos exposure and smoking, and explore a Bayesian approach to assess evidence of interaction between the exposures. The meta-analysis combines separate indices of additive and multiplicative relationships and multivariate relative risk estimates. By making inferences on posterior probabilities we can explore both the form and strength of interaction. This analysis may be more informative than providing evidence to support one relation over another on the basis of statistical significance. Overall, we find evidence for a more than additive and less than multiplicative relation.

Impacts of level of utilisation by grazing on an Astrebla (Mitchell grass) grassland in north-western Queensland between 1984 and 2010. 1. Herbage mass and population dynamics of Astrebla spp

Managing large variations in herbage production, resulting from highly variable seasonal rainfall, provides a major challenge for the sustainable management of Astrebla (Mitchell grass) grasslands in Australia. A grazing study with sheep was conducted between 1984 and 2010 on an Astrebla grassland in northern Queensland to describe the effects of a range of levels of utilisation of the herbage at the end of the summer growing season (April–May in northern Australia) on the sustainability of these grasslands. In unreplicated paddocks, sheep numbers were adjusted annually to achieve 0, 10, 20, 30, 50 and 80% utilisation of the herbage mass at the end of the summer over the ensuing 12 months. Higher levels of utilisation reduced both total and Astrebla spp. herbage mass because of the effects of higher utilisation on Astrebla spp. and this effect was accentuated by drought. The tussock density of Astrebla spp. varied widely among years but with few treatment differences until 2005 when density was reduced at the 50% level of utilisation. A major change in density resulted from a large recruitment of Astrebla spp. in 1989 that influenced its density for the remainder of the study. Basal area of the tussocks fluctuated among years, with increases due to rainfall and decreases during droughts. Seasonal rainfall was more influential than level of utilisation in changes to the basal area of perennial grasses. Drought resulted in the death of Astrebla spp. tussocks and this effect was accentuated at higher levels of utilisation. A series of three grazing exclosures were used to examine the recovery of the density and basal area of Astrebla spp. after it had been reduced by 80% utilisation over the preceding 9 years. This recovery study indicated that, although grazing exclusion was useful in the recovery of Astrebla spp., above-average rainfall was the major factor driving increases in the basal area of perennial grasses. Spring values of the Southern Oscillation Index and associated rainfall probabilities were considered to have potential for understanding the dynamics of Astrebla spp. It was concluded that Astrebla grassland remained sustainable after 26 years when grazed at up to 30% utilisation, while, at 50% utilisation, they became unsustainable after 20 years. Results from this study emphasised the need to maintain the population of Astrebla spp. tussocks.

Statistical significance of sequential firing patterns in multi-neuronal spike trains

Sequential firings with fixed time delays are frequently observed in simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts. In this paper we present a method for assessing the significance of such correlations. We specify the null hypothesis in terms of a bound on the conditional probabilities that characterize the influence of one neuron on another. This method of testing significance is more general than the currently available methods since under our null hypothesis we do not assume that the spiking processes of different neurons are independent. The structure of our null hypothesis also allows us to rank order the detected patterns. We demonstrate our method on simulated spike trains.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.