The impact of spatial scales and spatial smoothing on the outcome of Bayesian spatial model

Discretization of a geographical region is quite common in spatial analysis. There have been few studies into the impact of different geographical scales on the outcome of spatial models for different spatial patterns. This study aims to investigate the impact of spatial scales and spatial smoothing on the outcomes of modelling spatial point-based data. Given a spatial point-based dataset (such as occurrence of a disease), we study the geographical variation of residual disease risk using regular grid cells. The individual disease risk is modelled using a logistic model with the inclusion of spatially unstructured and/or spatially structured random effects. Three spatial smoothness priors for the spatially structured component are employed in modelling, namely an intrinsic Gaussian Markov random field, a second-order random walk on a lattice, and a Gaussian field with Matern correlation function. We investigate how changes in grid cell size affect model outcomes under different spatial structures and different smoothness priors for the spatial component. A realistic example (the Humberside data) is analyzed and a simulation study is described. Bayesian computation is carried out using an integrated nested Laplace approximation. The results suggest that the performance and predictive capacity of the spatial models improve as the grid cell size decreases for certain spatial structures. It also appears that different spatial smoothness priors should be applied for different patterns of point data.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Spatial prediction on a river network

This article develops methods for spatially predicting daily change of dissolved oxygen (Dochange) at both sampled locations (134 freshwater sites in 2002 and 2003) and other locations of interest throughout a river network in South East Queensland, Australia. In order to deal with the relative sparseness of the monitoring locations in comparison to the number of locations where one might want to make predictions, we make a classification of the river and stream locations. We then implement optimal spatial prediction (ordinary and constrained kriging) from geostatistics. Because of their directed-tree structure, rivers and streams offer special challenges. A complete approach to spatial prediction on a river network is given, with special attention paid to environmental exceedances. The methodology is used to produce a map of Dochange predictions for 2003. Dochange is one of the variables measured as part of the Ecosystem Health Monitoring Program conducted within the Moreton Bay Waterways and Catchments Partnership.

Path information effects in visual and proprioceptive spatial learning

Objects in an environment are often encountered sequentially during spatial learning, forming a path along which object locations are experienced. The present study investigated the effect of spatial information conveyed through the path in visual and proprioceptive learning of a room-sized spatial layout, exploring whether different modalities differentially depend on the integrity of the path. Learning object locations along a coherent path was compared with learning them in a spatially random manner. Path integrity had little effect on visual learning, whereas learning with the coherent path produced better memory performance than random order learning for proprioceptive learning. These results suggest that path information has differential effects in visual and proprioceptive spatial learning, perhaps due to a difference in the way one establishes a reference frame for representing relative locations of objects.

Bayesian hierarchical models for analysing spatial point-based data at a grid level: A comparison of approaches

Spatial data are now prevalent in a wide range of fields including environmental and health science. This has led to the development of a range of approaches for analysing patterns in these data. In this paper, we compare several Bayesian hierarchical models for analysing point-based data based on the discretization of the study region, resulting in grid-based spatial data. The approaches considered include two parametric models and a semiparametric model. We highlight the methodology and computation for each approach. Two simulation studies are undertaken to compare the performance of these models for various structures of simulated point-based data which resemble environmental data. A case study of a real dataset is also conducted to demonstrate a practical application of the modelling approaches. Goodness-of-fit statistics are computed to compare estimates of the intensity functions. The deviance information criterion is also considered as an alternative model evaluation criterion. The results suggest that the adaptive Gaussian Markov random field model performs well for highly sparse point-based data where there are large variations or clustering across the space; whereas the discretized log Gaussian Cox process produces good fit in dense and clustered point-based data. One should generally consider the nature and structure of the point-based data in order to choose the appropriate method in modelling a discretized spatial point-based data.

Principles of goal-directed spatial robot navigation in biomimetic models

Mobile robots and animals alike must effectively navigate their environments in order to achieve their goals. For animals goal-directed navigation facilitates finding food, seeking shelter or migration; similarly robots perform goal-directed navigation to find a charging station, get out of the rain or guide a person to a destination. This similarity in tasks extends to the environment as well; increasingly, mobile robots are operating in the same underwater, ground and aerial environments that animals do. Yet despite these similarities, goal-directed navigation research in robotics and biology has proceeded largely in parallel, linked only by a small amount of interdisciplinary research spanning both areas. Most state-of-the-art robotic navigation systems employ a range of sensors, world representations and navigation algorithms that seem far removed from what we know of how animals navigate; their navigation systems are shaped by key principles of navigation in ‘real-world’ environments including dealing with uncertainty in sensing, landmark observation and world modelling. By contrast, biomimetic animal navigation models produce plausible animal navigation behaviour in a range of laboratory experimental navigation paradigms, typically without addressing many of these robotic navigation principles. In this paper, we attempt to link robotics and biology by reviewing the current state of the art in conventional and biomimetic goal-directed navigation models, focusing on the key principles of goal-oriented robotic navigation and the extent to which these principles have been adapted by biomimetic navigation models and why.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Open access spatial data and collaboration

On 19 June 2015, representatives from over 40 Australian research institutions gathered in Canberra to launch their Open Data Collections. The one day event, hosted by the Australian National Data Service (ANDS), showcased to government and a range of national stakeholders the rich variety of data collections that have been generated through the Major Open Data Collections (MODC) project. Colin Eustace attended the showcase for QUT Library and presented a poster that reflected the work that he and Jodie Vaughan generated through the project. QUT’s Blueprint 4, the University’s five-year institutional strategic plan, outlines the key priorities of developing a commitment to working in partnership with industry, as well as combining disciplinary strengths with interdisciplinary application. The Division of Technology, Information and Learning Support (TILS) has undertaken a number of Australian National Data Service (ANDS) funded projects since 2009 with the aim of developing improved research data management services within the University to support these strategic aims. By leveraging existing tools and systems developed during these projects, the Major Open Data Collection (MODC) project delivered support to multi-disciplinary collaborative research activities through partnership building between QUT researchers and Queensland government agencies, in order to add to and promote the discovery and reuse of a collection of spatially referenced datasets. The MODC project built upon existing Research Data Finder infrastructure (which uses VIVO open source software, developed by Cornell University) to develop a separate collection, Spatial Data Finder (https://researchdatafinder.qut.edu.au/spatial) as the interface to display the spatial data collection. During the course of the project, 62 dataset descriptions were added to Spatial Data Finder, 7 added to Research Data Finder and two added to Software Finder, another separate collection. The project team met with 116 individual researchers and attended 13 school and faculty meetings to promote the MODC project and raise awareness of the Library’s services and resources for research data management.

Seasonal and spatial variations in rare earth elements to identify inter-aquifer linkages and recharge processes in an Australian catchment

With the aim of elucidating the seasonal behaviour of rare earth elements (REEs), surface and groundwaters were collected under dry and wet conditions in different hydrological units of the Teviot Brook catchment (Southeast Queensland, Australia). Sampled waters showed a large degree of variability in both REE abundance and normalised patterns. Overall REE abundance ranged over nearly three orders of magnitude, and was consistently lower in the sedimentary bedrock aquifer (18ppt<∑REE<477ppt) than in the other hydrological systems studied. Abundance was greater in springs draining rhyolitic rocks (∑REE=300 and 2054ppt) than in springs draining basalt ranges (∑REE=25 and 83ppt), yet was highly variable in the shallow alluvial groundwater (16ppt<∑REE<5294ppt) and, to a lesser extent, in streamwater (85ppt<∑REE<2198ppt). Generally, waters that interacted with different rock types had different REE patterns. In order to obtain an unbiased characterisation of REE patterns, the ratios between light and middle REEs (R(M/L)) and the ratios between middle and heavy REEs (R(H/M)) were calculated for each sample. The sedimentary bedrock aquifer waters had highly evolved patterns depleted in light REEs and enriched in middle and heavy REEs (0.17spatial variations. Samples collected from the alluvium exhibited an increasing influence of the sedimentary bedrock from upgradient to downgradient; typically they showed flat patterns in the upstream section of the alluvium (median R(M/L)=0.21 and median R(H/M)=-0.06) gradually evolving towards patterns depleted in light REEs and enriched in middle and heavy REEs downgradient (median R(M/L)=0.48 and median R(H/M)=0.38). To document the seasonal variations in REE patterns, the difference in ratios between dry and wet sampling campaigns was determined for each repeated sampling location. Contributions from the sedimentary bedrock water to the alluvium during the wet season were identified at two locations (increase from R(H/M)=0.03 and 0.35 to R(H/M)=0.62 and 0.89). The effect of recharge through fractured igneous rocks was also observed in two boreholes intercepting the sedimentary bedrock, where the freshly recharged waters likely contributed to the deeper groundwater flow during the wet season (decrease from R(M/L)=0.81 and 0.56 to R(M/L)=0.46 and 0.17). Results from this study suggest that REEs may be usefully applied as indicators of recharge processes and inter-aquifer mixing. They also underline the importance of conducting seasonal sampling campaigns to capture possible short-term variations in REE patterns and abundance, which is essential to enable a better understanding of hydrological and hydrochemical processes in complex geological settings

Missing in space: An evaluation of imputation methods for missing data in spatial analysis of risk factors for type II diabetes

Background Spatial analysis is increasingly important for identifying modifiable geographic risk factors for disease. However, spatial health data from surveys are often incomplete, ranging from missing data for only a few variables, to missing data for many variables. For spatial analyses of health outcomes, selection of an appropriate imputation method is critical in order to produce the most accurate inferences. Methods We present a cross-validation approach to select between three imputation methods for health survey data with correlated lifestyle covariates, using as a case study, type II diabetes mellitus (DM II) risk across 71 Queensland Local Government Areas (LGAs). We compare the accuracy of mean imputation to imputation using multivariate normal and conditional autoregressive prior distributions. Results Choice of imputation method depends upon the application and is not necessarily the most complex method. Mean imputation was selected as the most accurate method in this application. Conclusions Selecting an appropriate imputation method for health survey data, after accounting for spatial correlation and correlation between covariates, allows more complete analysis of geographic risk factors for disease with more confidence in the results to inform public policy decision-making.

On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Spatial and diurnal pattern of protein foraging by Bactrocera tryoni (Froggatt) on a host plant

Background: Queensland fruit fly, Bactrocera tryoni, is the major pest fruit fly in Australia. Protein bait sprays, where insecticides are mixed with spot applications of a protein based food lure, are one of the sustainable pre-harvest fruit fly management strategies used in Australia. Although protein bait sprays do manage fruit fly infestation in the field, there is little science underpinning this technique and so improving its efficacy is difficult. Lacking information includes where and when to apply protein bait in order to best target foraging B. tryoni. As part of new work in this area, we investigated the effect of height of protein on tree and host plant fruiting status on the spatial and temporal protein foraging patterns of B. tryoni. MEthod: The work was conducted in the field using nectarine and guava plants and wild B. tryoni at Redland Bay, Queensland, Australia. Spot sprays of protein bait were applied to the foliage of randomly selected fruiting and non-fruiting trees. Each tree received protein bait spot sprays on the lower and higher foliage at 0530hrs. The number, sex and species of flies that fed on each protein spot were recorded hourly from 0600hrs through to 1800hrs.Results: For nectarines, there was a significant difference in the number of B. tryoni feeding on protein bait placed at different locations within the tree (ANOVA, F = 8.898, p = 0.001). More flies fed on protein placed on higher foliage relative to lower, irrespective of the fruiting status of the nectarine trees. A significant difference was also observed in the diurnal protein feeding pattern of B. tryoni (ANOVA, F = 2.164, p = 0.024), with more flies feeding at 1600hrs. Results for guava are still being collected and will be presented at the meeting.Conclusions: We conclude that B. tryoni effectively forages for protein at heights higher than 1.3m from ground, indicating greater efficacy of protein bait when applied at foliage higher in the canopy. Bactrocera tryoni actively forages for protein throughout the day, with a highest feeding peak at 1600hrs. The lack of significant difference in the spatial protein foraging pattern between fruiting and non-fruiting nectarine trees may be a real result, or may have resulted from the fruiting tree being very close (within 1 – 2 metres) of the non-fruiting tree. This hypothesis is being tested in the guava trial.

Geospatial environmental data modelling applications using remote sensing, GIS and spatial statistics

This thesis presents novel modelling applications for environmental geospatial data using remote sensing, GIS and statistical modelling techniques. The studied themes can be classified into four main themes: (i) to develop advanced geospatial databases. Paper (I) demonstrates the creation of a geospatial database for the Glanville fritillary butterfly (Melitaea cinxia) in the Åland Islands, south-western Finland; (ii) to analyse species diversity and distribution using GIS techniques. Paper (II) presents a diversity and geographical distribution analysis for Scopulini moths at a world-wide scale; (iii) to study spatiotemporal forest cover change. Paper (III) presents a study of exotic and indigenous tree cover change detection in Taita Hills Kenya using airborne imagery and GIS analysis techniques; (iv) to explore predictive modelling techniques using geospatial data. In Paper (IV) human population occurrence and abundance in the Taita Hills highlands was predicted using the generalized additive modelling (GAM) technique. Paper (V) presents techniques to enhance fire prediction and burned area estimation at a regional scale in East Caprivi Namibia. Paper (VI) compares eight state-of-the-art predictive modelling methods to improve fire prediction, burned area estimation and fire risk mapping in East Caprivi Namibia. The results in Paper (I) showed that geospatial data can be managed effectively using advanced relational database management systems. Metapopulation data for Melitaea cinxia butterfly was successfully combined with GPS-delimited habitat patch information and climatic data. Using the geospatial database, spatial analyses were successfully conducted at habitat patch level or at more coarse analysis scales. Moreover, this study showed it appears evident that at a large-scale spatially correlated weather conditions are one of the primary causes of spatially correlated changes in Melitaea cinxia population sizes. In Paper (II) spatiotemporal characteristics of Socupulini moths description, diversity and distribution were analysed at a world-wide scale and for the first time GIS techniques were used for Scopulini moth geographical distribution analysis. This study revealed that Scopulini moths have a cosmopolitan distribution. The majority of the species have been described from the low latitudes, sub-Saharan Africa being the hot spot of species diversity. However, the taxonomical effort has been uneven among biogeographical regions. Paper III showed that forest cover change can be analysed in great detail using modern airborne imagery techniques and historical aerial photographs. However, when spatiotemporal forest cover change is studied care has to be taken in co-registration and image interpretation when historical black and white aerial photography is used. In Paper (IV) human population distribution and abundance could be modelled with fairly good results using geospatial predictors and non-Gaussian predictive modelling techniques. Moreover, land cover layer is not necessary needed as a predictor because first and second-order image texture measurements derived from satellite imagery had more power to explain the variation in dwelling unit occurrence and abundance. Paper V showed that generalized linear model (GLM) is a suitable technique for fire occurrence prediction and for burned area estimation. GLM based burned area estimations were found to be more superior than the existing MODIS burned area product (MCD45A1). However, spatial autocorrelation of fires has to be taken into account when using the GLM technique for fire occurrence prediction. Paper VI showed that novel statistical predictive modelling techniques can be used to improve fire prediction, burned area estimation and fire risk mapping at a regional scale. However, some noticeable variation between different predictive modelling techniques for fire occurrence prediction and burned area estimation existed.

Where and how to conserve: Extending the scope of spatial reserve network design

Ongoing habitat loss and fragmentation threaten much of the biodiversity that we know today. As such, conservation efforts are required if we want to protect biodiversity. Conservation budgets are typically tight, making the cost-effective selection of protected areas difficult. Therefore, reserve design methods have been developed to identify sets of sites, that together represent the species of conservation interest in a cost-effective manner. To be able to select reserve networks, data on species distributions is needed. Such data is often incomplete, but species habitat distribution models (SHDMs) can be used to link the occurrence of the species at the surveyed sites to the environmental conditions at these locations (e.g. climatic, vegetation and soil conditions). The probability of the species occurring at unvisited location is next predicted by the model, based on the environmental conditions of those sites. The spatial configuration of reserve networks is important, because habitat loss around reserves can influence the persistence of species inside the network. Since species differ in their requirements for network configuration, the spatial cohesion of networks needs to be species-specific. A way to account for species-specific requirements is to use spatial variables in SHDMs. Spatial SHDMs allow the evaluation of the effect of reserve network configuration on the probability of occurrence of the species inside the network. Even though reserves are important for conservation, they are not the only option available to conservation planners. To enhance or maintain habitat quality, restoration or maintenance measures are sometimes required. As a result, the number of conservation options per site increases. Currently available reserve selection tools do however not offer the ability to handle multiple, alternative options per site. This thesis extends the existing methodology for reserve design, by offering methods to identify cost-effective conservation planning solutions when multiple, alternative conservation options are available per site. Although restoration and maintenance measures are beneficial to certain species, they can be harmful to other species with different requirements. This introduces trade-offs between species when identifying which conservation action is best applied to which site. The thesis describes how the strength of such trade-offs can be identified, which is useful for assessing consequences of conservation decisions regarding species priorities and budget. Furthermore, the results of the thesis indicate that spatial SHDMs can be successfully used to account for species-specific requirements for spatial cohesion - in the reserve selection (single-option) context as well as in the multi-option context. Accounting for the spatial requirements of multiple species and allowing for several conservation options is however complicated, due to trade-offs in species requirements. It is also shown that spatial SHDMs can be successfully used for gaining information on factors that drive a species spatial distribution. Such information is valuable to conservation planning, as better knowledge on species requirements facilitates the design of networks for species persistence. This methods and results described in this thesis aim to improve species probabilities of persistence, by taking better account of species habitat and spatial requirements. Many real-world conservation planning problems are characterised by a variety of conservation options related to protection, restoration and maintenance of habitat. Planning tools therefore need to be able to incorporate multiple conservation options per site, in order to continue the search for cost-effective conservation planning solutions. Simultaneously, the spatial requirements of species need to be considered. The methods described in this thesis offer a starting point for combining these two relevant aspects of conservation planning.