Calibrating a Jump-Diffusion Model of an endemic invasive: Metamodels, statistics and Qfly

Abstract

Information on population growth and spread of a significant endemic pest such as the Queensland fruit fly (Qfly; Bactrocera tryoni) is highly valuable to biosecurity regulators wanting to evaluate the benefits of surveillance under horticultural Area Wide Management (AWM) schemes. Unfortunately, directly observing a growth model or surveillance performance is not possible due to data constraints. This paper presents a set of novel methods to infer key population and surveillance parameters from available data for a jump-diffusion model. This will form the basis of an economic analysis of AWM for the Sunraysia Pest Free Area (PFA) across south east NSW and north west Victoria. A number of jump-diffusion models of invasive species have now been implemented to represent the different modes of dispersal available to an invasive species. However, as models become more sophisticated we encounter the perennial problem of model calibration. We implement a hierarchical model composed first of landscape 'jumps' by Qfly into the PFA, and represented by a time and spatially varying probability of declarable outbreaks derived from ~150000 monitoring events since 1998. The jumps are climate driven, with a set of time-varying Climex indices of climate, and dependent on land use, road density and other geographic factors. Here, calibration of the 'jumps' is by estimating a generalized additive model. Assigned to each outbreak incident is an outbreak 'duration'. This duration attribute is of key interest as it will largely determine variable costs in a proposed Benefit Cost Analysis (BCA) of the surveillance methodology and new technologies. Early detection is often associated with smaller populations, lower control costs and more rapid control, and hence a decreased duration. The duration attribute is thus modeled directly as a function of the number of Qfly initially captured. Initial captures can in turn be modeled through an integro-difference model of local population growth and diffusion. However, (i) the initial location of outbreaks are unknown; (ii) the probability of detection by the monitoring network needs to be estimated; (iii) the local landscape is assumed homogeneous in the absence of further information; and, (iv) local population growth and dispersal are known to be time-varying. Ad hoc calibration methods such as least squares optimization or regression modelling were used to derive both a time invariant, half Cauchy dispersal kernel and the probability of detecting a local Qfly population, by drawing on results from the published literature. Both of these ad hoc calibrations suffer from significant bias which in future only spatially referenced and time stamped capture data can resolve. Population growth parameters for the integro-difference model were generated from an existing stage-structured and spatially non-explicit model of Qfly population dynamics. A metamodel enabled these growth parameters to be linked to the weekly Climex indices. A time-varying distribution of initial population numbers at time of arrival (i.e. before detection), and a consequent distribution for the time to population detection, could then be simulated. The full procedure allows elements of a monitoring regime, such as the detection efficiency of individual traps or trap density, to be economically valued in future work. While some of the calibrations in this paper are data constrained, data needs for implementation of integro-difference models in the economic valuation of monitoring networks are clear: georeferencing and time stamping of captures, experimental controls for determining growth and mortality, and ease of accessibility to such data to facilitate ready modeling.