Hierarchical Bayesian Models for Estimating the Extent of Plant Pest Invasions A thesis submitted for the degree of Doctor of Philosophy in the Faculty of Science and Technology, Queensland University of Technology By Mark Andrew Stanaway Bachelor of Applied Science (Life Science)(Hons) Principal Supervisor: Kerrie Mengersen Associate Supervisors: Robert Reeves, Grant Hamilton, Peter Whittle Queensland University of Technology Faculty of Science and Technology Mathematical Sciences January 2011 Keywords Bayesian inference, hierarchical Bayesian models, plant biosecurity, surveillance, spiraling whitefly, Aleurodicus dispersus, red banded mango caterpillar, Deanolis sublimbalis, quarantine, non-indigenous species, biological invasions, entomology, agriculture, early detection, market access, area freedom, pest free areas, eradica- tion, Markov chain Monte Carlo, detectability, insect disperal, dispersal modelling. iii Abstract lant biosecurity requires statistical tools to interpret field surveillance data Pin order to manage pest incursions that threaten crop production and trade. Ultimately, management decisions need to be based on the probability that an area is infested or free of a pest. Current informal approaches to delimiting pest extent rely upon expert ecological interpretation of presence / absence data over space and time. Hierarchical Bayesian models provide a cohesive statistical framework that can formally integrate the available information on both pest ecology and data. The overarching method involves constructing an observation model for the surveil- lance data, conditional on the hidden extent of the pest and uncertain detection sensitivity. The extent of the pest is then modelled as a dynamic invasion pro- cess that includes uncertainty in ecological parameters. Modelling approaches to assimilate this information are explored through case studies on spiralling white- fly, Aleurodicus dispersus and red banded mango caterpillar, Deanolis sublimbalis. Markov chain Monte Carlo simulation is used to estimate the probable extent of pests, given the observation and process model conditioned by surveillance data. Statistical methods, based on time-to-event models, are developed to apply hi- erarchical Bayesian models to early detection programs and to demonstrate area freedom from pests. The value of early detection surveillance programs is demonstrated through an ap- plication to interpret surveillance data for exotic plant pests with uncertain spread iv rates. The model suggests that typical early detection programs provide a moderate reduction in the probability of an area being infested but a dramatic reduction in the expected area of incursions at a given time. Estimates of spiralling whitefly ex- tent are examined at local, district and state-wide scales. The local model estimates the rate of natural spread and the influence of host architecture, host suitability and inspector efficiency. These parameter estimates can support the development of robust surveillance programs. Hierarchical Bayesian models for the human-mediated spread of spiralling whitefly are developed for the colonisation of discrete cells connected by a modified gravity model. By estimating dispersal parameters, the model can be used to predict the extent of the pest over time. An extended model predicts the climate restricted distribution of the pest in Queensland. These novel human-mediated movement models are well suited to demonstrating area freedom at coarse spatio-temporal scales. At finer scales, and in the presence of ecological complexity, exploratory models are developed to investigate the capacity for surveillance information to estimate the extent of red banded mango caterpillar. It is apparent that exces- sive uncertainty about observation and ecological parameters can impose limits on inference at the scales required for effective management of response programs. The thesis contributes novel statistical approaches to estimating the extent of pests and develops applications to assist decision-making across a range of plant biose- curity surveillance activities. Hierarchical Bayesian modelling is demonstrated as both a useful analytical tool for estimating pest extent and a natural investigative paradigm for developing and focussing biosecurity programs. v vi Contents Keywords iii Abstract iv List of Tables xiv List of Figures xxi Statement of Original Authorship xxiii Acknowledgements xxv 1 Introduction 1 1.1 Primary Research Aim . 1 1.2 Motivation . 2 1.3 Research Plan . 3 1.4 Scope of Thesis . 5 1.5 Outline of Thesis . 6 vii 2 Literature Review 9 2.1 Inference in Biosecurity . 9 2.2 Hierarchical Bayesian Models . 13 2.2.1 Bayesian approaches . 15 2.2.2 Pest observation models . 18 2.2.3 Invasion process models . 22 2.2.4 Computation . 28 2.3 Bayesian Plant Biosecurity Applications . 31 2.4 Summary . 33 3 Early Detection Surveillance 35 3.1 Introduction . 35 3.2 Model . 38 3.2.1 Overview and notation . 38 3.2.2 Incursion process model . 40 3.2.3 Observation model . 42 3.2.4 Parameters . 44 3.2.5 Inference and interpretation . 46 3.2.6 Computation . 48 3.3 Simulations . 49 3.3.1 Data and methods . 49 viii 3.3.2 Results . 50 3.4 Early Detection Program . 54 3.4.1 Surveillance data and methods . 54 3.4.2 Results . 56 3.5 Discussion . 61 3.6 Summary . 64 4 Whitefly Detection and Natural Spread 67 4.1 Introduction . 67 4.2 Pest Information and Surveillance Program . 69 4.3 Models . 72 4.3.1 Observation model . 72 4.3.2 Growth rates . 74 4.3.3 Spread . 76 4.3.4 Analysis . 77 4.4 Results . 78 4.5 Discussion . 83 4.6 Summary . 87 5 Human-Mediated Dispersal Reliability Analysis 89 5.1 Introduction . 90 5.2 General Incursion Model . 92 ix 5.2.1 Overview . 92 5.2.2 Reliability framework for colonisation . 93 5.2.3 Gravity model . 95 5.3 Data and Observation Model . 99 5.3.1 Spiralling whitefly data . 99 5.3.2 Observation model . 100 5.4 Simulations and Computation . 103 5.5 Results . 105 5.5.1 Likelihoods . 105 5.5.2 Comparison of algorithms . 106 5.5.3 Scalability of models . 106 5.6 Discussion . 108 5.7 Summary . 113 6 Predicting Spiralling Whitefly Distribution 115 6.1 Introduction . 116 6.2 Distribution and Data . 118 6.2.1 Distribution of spiralling whitefly . 118 6.2.2 Surveillance for spiralling whitefly in Queensland . 121 6.2.3 Data . 122 6.3 Mechanistic Models . 124 x 6.3.1 Temperature stress on growth . 124 6.3.2 Movement within zones . 127 6.3.3 Movement between zones . 130 6.4 Hierarchical Model . 132 6.4.1 Observation model . 135 6.4.2 Incorporating the movement model . 138 6.4.3 Computation . 139 6.5 Results . 140 6.6 Discussion . 146 6.7 Summary . 151 7 Mango Caterpillar Invasion Ecology 153 7.1 Introduction . 154 7.2 Overview . 156 7.3 Data and Observation Model . 159 7.4 Local Ecological Process Modelling . 164 7.4.1 Mango fruit development . 164 7.4.2 RBMC life history model . 168 7.4.3 Local population model simulations . 177 7.4.4 Host availability and Allee effects . 180 7.5 Dispersal . 185 xi 7.5.1 Human-mediated dispersal . 186 7.5.2 Long distance wind assisted flight . 188 7.5.3 Directed short distance flight . 189 7.5.4 Dispersal model . 191 7.6 Discussion . 193 7.7 Summary . 196 8 Discussion 199 8.1 Conclusions and Further Work . 199 8.2 Recommendations to Biosecurity . 205 Appendices 211 A Early Detection Model Code 211 B Spiralling Whitefly Natural Spread Code 214 C Gravity Model MCMC Algorithms 217 C.1 Simulated Block Algorithm . 218 C.2 Individual Proposal Algorithm . 219 C.3 MCMC for Chapter 5 and 6 Applications . 222 Bibliography 222 xii List of Tables 3.1 Description of informative priors to describe uncertainty in the ob- servation and ecological characteristics of target pests. 47 3.2 Prior and posterior means and standard deviations for selected pa- rameters and scenarios. Scenarios B and C are used to demonstrate spatial effects only and are omitted. Scenario A) N = 20, D) N = 40, E) N = 10, F) N = 20 and xN = 1. 50 3.3 Summary of prior and posterior estimates of latent variables and parameters for early detection surveillance of bananas in the Cairns district. 56 3.4 Sensitivity of probability of colonisation and estimated area of infes- tation if colonised. Scenario 1 is the original model. Prior values for other scenarios are shown only where they differ from scenario 1. 60 4.1 Temperature dependent survival and fecundity rates for spiralling whitefly from Wen et al. (1994). 75 4.2 Posterior estimates of global parameters for the incursion. 78 xiii 6.1 Details of the zones, arranged roughly north to south. Date of first detection is the date of first collection from the zone, followed by whether it was a public report or a structured survey. Missing val- ues indicate the pest is.