Hierarchical models for 2D presence/absence data having ambiguous zeroes: With a biogeographical case study on dingo behaviour

This dissertation is primarily an applied statistical modelling investigation, motivated by a case study comprising real data and real questions. Theoretical questions on modelling and computation of normalization constants arose from pursuit of these data analytic questions. The essence of the thesis can be described as follows. Consider binary data observed on a two-dimensional lattice. A common problem with such data is the ambiguity of zeroes recorded. These may represent zero response given some threshold (presence) or that the threshold has not been triggered (absence). Suppose that the researcher wishes to estimate the effects of covariates on the binary responses, whilst taking into account underlying spatial variation, which is itself of some interest. This situation arises in many contexts and the dingo, cypress and toad case studies described in the motivation chapter are examples of this. Two main approaches to modelling and inference are investigated in this thesis. The first is frequentist and based on generalized linear models, with spatial variation modelled by using a block structure or by smoothing the residuals spatially. The EM algorithm can be used to obtain point estimates, coupled with bootstrapping or asymptotic MLE estimates for standard errors. The second approach is Bayesian and based on a three- or four-tier hierarchical model, comprising a logistic regression with covariates for the data layer, a binary Markov Random field (MRF) for the underlying spatial process, and suitable priors for parameters in these main models. The three-parameter autologistic model is a particular MRF of interest. Markov chain Monte Carlo (MCMC) methods comprising hybrid Metropolis/Gibbs samplers is suitable for computation in this situation. Model performance can be gauged by MCMC diagnostics. Model choice can be assessed by incorporating another tier in the modelling hierarchy. This requires evaluation of a normalization constant, a notoriously difficult problem. Difficulty with estimating the normalization constant for the MRF can be overcome by using a path integral approach, although this is a highly computationally intensive method. Different methods of estimating ratios of normalization constants (N Cs) are investigated, including importance sampling Monte Carlo (ISMC), dependent Monte Carlo based on MCMC simulations (MCMC), and reverse logistic regression (RLR). I develop an idea present though not fully developed in the literature, and propose the Integrated mean canonical statistic (IMCS) method for estimating log NC ratios for binary MRFs. The IMCS method falls within the framework of the newly identified path sampling methods of Gelman & Meng (1998) and outperforms ISMC, MCMC and RLR. It also does not rely on simplifying assumptions, such as ignoring spatio-temporal dependence in the process. A thorough investigation is made of the application of IMCS to the three-parameter Autologistic model. This work introduces background computations required for the full implementation of the four-tier model in Chapter 7. Two different extensions of the three-tier model to a four-tier version are investigated. The first extension incorporates temporal dependence in the underlying spatio-temporal process. The second extensions allows the successes and failures in the data layer to depend on time. The MCMC computational method is extended to incorporate the extra layer. A major contribution of the thesis is the development of a fully Bayesian approach to inference for these hierarchical models for the first time. Note: The author of this thesis has agreed to make it open access but invites people downloading the thesis to send her an email via the 'Contact Author' function.

The influence of habitat heterogeneity on patterns of connectivity among rabbit populations in southern Queensland

Patterns of connectivity among local populations influence the dynamics of regional systems, but most ecological models have concentrated on explaining the effect of connectivity on local population structure using dynamic processes covering short spatial and temporal scales. In this study, a model was developed in an extended spatial system to examine the hypothesis that long term connectivity levels among local populations are influenced by the spatial distribution of resources and other habitat factors. The habitat heterogeneity model was applied to local wild rabbit populations in the semi-arid Mitchell region of southern central Queensland (the Eastern system). Species' specific population parameters which were appropriate for the rabbit in this region were used. The model predicted a wide range of long term connectivity levels among sites, ranging from the extreme isolation of some sites to relatively high interaction probabilities for others. The validity of model assumptions was assessed by regressing model output against independent population genetic data, and explained over 80% of the variation in the highly structured genetic data set. Furthermore, the model was robust, explaining a significant proportion of the variation in the genetic data over a wide range of parameters. The performance of the habitat heterogeneity model was further assessed by simulating the widely reported recent range expansion of the wild rabbit into the Mitchell region from the adjacent, panmictic Western rabbit population system. The model explained well the independently determined genetic characteristics of the Eastern system at different hierarchic levels, from site specific differences (for example, fixation of a single allele in the population at one site), to differences between population systems (absence of an allele in the Eastern system which is present in all Western system sites). The model therefore explained the past and long term processes which have led to the formation and maintenance of the highly structured Eastern rabbit population system. Most animals exhibit sex biased dispersal which may influence long term connectivity levels among local populations, and thus the dynamics of regional systems. When appropriate sex specific dispersal characteristics were used, the habitat heterogeneity model predicted substantially different interaction patterns between female-only and combined male and female dispersal scenarios. In the latter case, model output was validated using data from a bi-parentally inherited genetic marker. Again, the model explained over 80% of the variation in the genetic data. The fact that such a large proportion of variability is explained in two genetic data sets provides very good evidence that habitat heterogeneity influences long term connectivity levels among local rabbit populations in the Mitchell region for both males and females. The habitat heterogeneity model thus provides a powerful approach for understanding the large scale processes that shape regional population systems in general. Therefore the model has the potential to be useful as a tool to aid in the management of those systems, whether it be for pest management or conservation purposes.

The expression of ADAM-9 and -10 in prostate cancer and their regulation by dihydrotestosterone, insulin-like growth Factor-1 and epidermal growth factor

Prostrate Cancer(PCa)is the most common cause of cancer death amongst Western males. PCa occurs in two distinct stages. In its early stage, growth and development is dependent primarily on male sex hormones (androgens) such as testosterone, although other growth factors have roles maintaining PCa cell survival in this stage. In the later stage of PCa development, growth and.maintenance is independent of androgen stimulation and growth factors including Insulin-like Growth Factor -1 (IGf.:·l) and Epidermal Growth Factor (EGF) are thought to have more crucial roles in cell survival and PCa progression. PCa, in its late stages, is highly aggressive and metastatic, that is, tumorigenic cells migrate from the primary site of the body (prostate) and travel via the systemic and lymphatic circulation, residing and colonising in the bone, lymph node, lung, and in more rare cases, the brain. Metastasis involves both cell migration and tissue degradation activities. The degradation of the extracellular matrix (ECM), the tissue surrounding the organ, is mediated in part by members of a family of 26 proteins called the Matrix Metalloproteases (MMPs), whilst ceil adhesion molecules, of which proteins known as Integrins are included, mediate ce11 migration. A family of proteins known as the ADAMs (A Disintegrin . And Metalloprotease domain) were a recently characterised family at the commencement of this study and now comprise 34 members. Because of their dual nature, possessing an active metaiioprotease domain, homologous to that of the MMPs, and an integrin-binding domain capable of regulating cell-cell and cell-ECM contacts, it was thought likely that members of the ADAMs family may have implications for the progression of aggressive cancers such as those ofthe prostate. This study focussed on two particular ADAMs -9 and -10. ADAM-9 has an active metalloprotease domain, which has been shown to degrade constituents of the ECM, including fibronectin, in vitro. It also has an integrin-binding capacity through association with key integrins involved in PCa progression, such as a6~1. ADAM-10 has no such integrin binding activities, but its bovine orthologue, MADM, is able to degrade coHagen type IV, a major component of basement membranes. It is likely human ADAM-10 has the same activity. It is also known to cleave Ll -a protein involved in cell anchorage activities - and collagen type XVII - which is a principal component of the hemidesmosomes of cellular tight junctions. The cleavage of these proteins enables the cell to be released from the surrounding environment and commence migratory activities, as required in metastasis. Previous studies in this laboratory showed the mRNA expression of the five ADAMs -9,- 10, -11, -15 and -17 in PCa cell lines, characteristic of androgen-dependent and androgen independent disease. These studies were furthered by the characterisation of AD AM-9, -10 and -17 mRNA regulation by Dihydrotestosterone (DHT) in the androgen-responsive cell line (LNCaP). ADAM-9 and -10 mRNA levels were elevated in response to DHT stimulation. Further to these observations, the expression of ADAM-9 and -10 was shown in primary prostate biopsies from patients with PCa. ADAM-1 0 was expressed in the cytoplasm and on the ceH membrane in epithelial and basal cells ofbenign prostate glands, but in high-grade PCa glands, ADAM-I 0 expression was localised to the nucleus and its expression levels appeared to be elevated when compared to low-grade PCa glands. These studies provided a strong background for the hypothesis that ADAM-9 and -10 have key roles in the development ofPCa and provided a basis for further studies.The aims of this study were to: 1) characterise the expression, localisation and levels, of ADAM-9 and -10 mRNA and protein in cell models representing characteristics of normal through androgen-dependent to androgen-independent PCa, as well as to expand the primary PCa biopsy data for ADAM-9 and ADAM-10 to encompass PCa bone metastases 2) establish an in vitro cell system, which could express elevated levels of ADAM-1 0 so that functional cell-based assays such as cell migration, invasion and attachment could be carried out, and 3) to extend the previous hormonal regulation data, to fully characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in the hormonal/growth factor responsive cell line LNCaP. For aim 1 (expression of ADAM-9 and -10 mRNA and protein), ADAM-9 and -10 mRNA were characterised by R T -PCR, while their protein products were analysed by Western blot. Both ADAM-9 and -10 mRNA and protein were expressed at readily detectable levels across progressively metastatic PCa cell lines model that represent characteristics of low-grade,. androgen-dependent (LNCaP and C4) to high-grade, androgen-independent (C4-2 and C4-2B) PCa. When the non-tumorigenic prostate cell line RWPE-1 was compared with the metastatic PCa cell line PC-3, differential expression patterns were seen by Western blot analysis. For ADAM-9, the active form was expressed at higher levels in RWPE-1, whilst subcellular fractionation showed that the active form of ADAM-9 was predominantly located in the cell nucleus. For ADAM-I 0, in both of the cell Jines, a nuclear specific isoform of the mature, catalytically active ADAM-I 0 was found. This isoforrn differed by -2 kDa in Mr (smaller) than the cytoplasmic specific isoform. Unprocessed ADAM-I 0 was readily detected in R WPE-1 cell lines but only occasionally detected in PC-3 cell lines. Immunocytochemistry using ADAM-9 and -10 specific antibodies confirmed nuclear, cytoplasmic and membrane expression of both ADAMs in these two cell lines. To examine the possibility of ADAM-9 and -10 being shed into the extracellular environment, membrane vesicles that are constitutively shed from the cell surface and contain membrane-associated proteins were collected from the media of the prostate cell lines RWPE-1, LNCaP and PC-3. ADAM-9 was readily detectable in RWPE- 1 and LNCaP cell membrane vesicles by Western blot analysis, but not in PC-3 cells, whilst the expression of ADAM-I 0 was detected in shed vesicles from each of these prostate cell lines. By Laser Capture Microdissection (LCM), secretory epithelial cells of primary prostate gland biopsies were isolated from benign and malignant glands. These secretory cells, by Western blot analysis, expressed similar Mr bands for ADAM-9 and -10 that were found in PCa cell lines in vitro, indicating that the nuclear specific isoforrn of ADAM-I 0 was present in PCa primary tumours and may represent the predominantly nuclear form of ADAM-I 0 expression, previously shown in high-grade PCa by immunohistochemistry (IHC). ADAM-9 and -10 were also examined by IHC in bone metastases taken from PCa patients at biopsy. Both ADAMs could be detected at levels similar to those shown for Prostate Specific Antigen (PSA) in these biopsies. Furthermore, both ADAM-9 and -10 were predominantly membrane- bound with occasional nuclear expression. For aim 2, to establish a cell system that over-expressed levels of ADAM-10, two fulllength ADAM-I 0 mammalian expression vectors were constructed; ADAM-I 0 was cloned into pcDNA3.1, which contains a CMV promoter, and into pMEP4, containing an inducible metallothionine promoter, whose activity is stimulated by the addition of CdC}z. The efficiency of these two constructs was tested by way of transient transfection in the PCa cell line PC-3, whilst the pcDNA3.1 construct was also tested in the RWPE-1 prostate cell line. Resultant Western blot analysis for all transient transfection assays showed that levels of ADAM-I 0 were not significantly elevated in any case, when compared to levels of the housekeeping gene ~-Tubulin, despite testing various levels of vector DNA, and, for pMEP4, the induction of the transfected cell system with different degrees of stimulation with CdCh to activate the metallothionine promoter post-transfection. Another study in this laboratory found similar results when the same full length ADAM-10 sequence was cloned into a Green Fluorescent Protein (GFP) expressing vector, as no fluorescence was observed by means of transient tran sfection in the same, and other, PCa cell lines. It was hypothesised that the Kozak sequence included in the full-length construct (human ADAMI 0 naturally occurring sequence) is not strong enough to initiate translation in an artificial system, in cells, which, as described in Aim 1, are already expressing readily detectable levels of endogenous ADAM-10. As a result, time constraints prevented any further progress with Aim 2 and functional studies including cell attachment, invasion and migration were unable to be explored. For Aim 3, to characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in LNCaP cells, the levels of ADAM-9 and -10 mRNA were not stimulated by DHT or IGF-I alone, despite our previous observations that initially characterised ADAM-9 and -10 mRNA as being responsive to DHT. However, IGF-1 in synergy with DHT did significantly elevate mRNA levels ofboth ADAMs. In the case of ADAM-9 and -10 protein, the same trends of stimulation as found at the rnRNA level were shown by Western blot analysis when ADAM-9 and -10 signal intensity was normalised with the housekeeping protein ~-Tubulin. For EGF treatment, both ADAM-9 and -10 mRNA and protein levels were significantly elevated, and further investigation vm found this to be the case for each of these ADAMs proteins in the nuclear fractions of LNCaP cells. These studies are the first to describe extensively, the expression and hormonal/growth factor regulation of two members of the ADAMs family ( -9 and -1 0) in PCa. These observations imply that the expression of ADAM-9 and -10 have varied roles in PCa whilst it develops from androgen-sensitive (early stage disease), through to an androgeninsensitive (late-stage), metastatic disease. Further studies are now required to investigate the several key areas of focus that this research has revealed, including: • Investigation of the cellular mechanisms that are involved in actively transporting the ADAMs to the cell's nuclear compartment and the ADAMs functional roles in the cell nucleus. • The construction of a full-length human ADAM-10 mammalian expression construct with the introduction of a new Kozak sequence, that elevates ADAM-I 0 expression in an in vitro cell system are required, so that functional assays such as cell invasion, migration and attachment may be carried out to fmd the functional consequences of ADAM expression on cellular behaviour. • The regulation studies also need to be extended by confirming the preliminary observations that the nuclear levels of ADAMs may also be elevated by hormones and growth factors such as DHT, IGF-1 and EGF, as well as the regulation of levels of plasma membrany vesicle associated ADAM expression. Given the data presented in this study, it is likely the ADAMs have differential roles throughout the development of PCa due to their differential cellular localisation and synergistic growth-factor regulation. These observations, along with those further studies outlined above, are necessary in identifying these specific components ofPCa metastasis to which the ADAMs may contribute.