Andrew P. Robinson

Nonlinear mixed-effects models (NLMMs) provide a flexible framework for modeling repeated-measures trajectories. However, how best to forecast future observations, especially at ages well beyond those represented in the data, remains relatively underexamined. In this study, we develop a Chapman–Richards NLMM with a spatial-power autocorrelation structure for irregularly spaced repeated measures and compare three forecasting strategies: (i) population-averaged forecasts based on the fixed-effects component only; (ii) subject-specific forecasts in which empirical best linear unbiased predictors (EBLUPs) of the random effects are obtained via a first-order Taylor series expansion with an iterative Newton–Raphson update, including the case of new progenies not used in model fitting; and (iii) forecasts that combine the population-averaged prediction with prior repeated measures through the fitted autocorrelation matrix. Forecast accuracy was assessed with progeny-level validation under fully held-out and partially observed scenarios, using root mean square prediction error (RMSPE) and mean absolute error (MAE), and was examined as a function of: (i) the number of available prior measures and (ii) the accuracy of the fixed-effects component of the NLMM. The methods were illustrated with repeated-measures data from hybrid spruce (Picea engelmannii Parry ex Engelmann × Picea glauca (Moench) Voss) progeny trials at three planting sites in British Columbia, Canada, with measurement ages from 2 to 42 years. Subject-specific forecasts had the lowest prediction errors when sufficient prior measures were available and were also the least affected by misspecification of the fixed-effects component. With only two prior measurements, autocorrelation-based forecasts had the lowest or tied-lowest observed errors, although differences among the three approaches were small. Using all measurements taken before age 42, subject-specific forecasts of height at age 42 achieved an RMSPE of 0.50 m. With only two prior measurements, the corresponding RMSPEs were approximately 1.31–1.33 m across the forecasting approaches. Although demonstrated with a single hybrid spruce dataset from three planting sites, the comparison is, in principle, applicable to other repeated-measures settings in which long-horizon predictions are required from short observation histories; broader applicability remains to be confirmed.

Rising temperatures and increased drought intensity are driving accelerated tree mortality rates worldwide. We investigated how these changes affect the carrying capacity of mountain ash forests (Eucalyptus regnans), the world's tallest flowering plant and one of the most carbon-dense forests on Earth (450-819 tonnes carbon per hectare).Using data from a large network of silvicultural experiments collected between 1947 and 2000 in southeastern Australia, we quantified temporal trends in mortality rates and carrying capacity, and their relationships to spatiotemporal climate variations. We analyzed how maximum stand density changes with tree size (self-thinning line) across different climatic conditions and over time, disentangling spatial variation among sites from temporal variation within sites.Our results show forests growing in the warmest and driest conditions (highest vapour pressure deficit) had the lowest carrying capacity. This capacity further decreased with rising temperatures. Each one-degree Celsius increase in mean annual temperature was associated with a 9% reduction in carrying capacity. Based on these relationships, a projected three-degree Celsius increase by 2080 (CSIRO RCP8.5 scenario) could reduce tree density and carbon stocks by 24%, equivalent to losing 240,000 hectares of mature mountain ash forests or releasing 108 million tonnes of carbon.Trees that died were 0.62 times the size of living trees (i.e., they were suppressed), with no detectable effect of climate on this ratio. These findings demonstrate that reduced carrying capacity could undermine carbon sequestration and global forest restoration efforts, particularly in seasonally dry regions where warming accelerates water limitations. We discuss implications for incorporating changing carrying capacity into forest management and carbon accounting.

Invasive non‐native species are organisms that can significantly harm societal and natural values, such as agriculture, social amenities, the environment, and native species and ecosystems. To efficiently prepare for the incursion of invasive species and incursion response, it is essential to predict their potential impacts across this range of values. Several critical system‐level factors influence these impacts, including the introduction pathways, the availability of host material, climate suitability, and the extent and vulnerability of affected agricultural or environmental assets. A crucial factor that is incursion‐specific and therefore unpredictable beforehand is the size of an outbreak at the time that it is detected. How large the established invading population is will curtail the range of viable management options: if it is small then eradication may be affordable and provide net benefits, whereas if it is too large then eradication may be impossible. We propose a statistical model for this random variable that enables its use in decision‐support systems. Our study concentrates on surveillance systems that use fixed traps to detect mobile organisms. Using survival analysis, we analyze the relationship between surveillance and the detection event of a pest, where the detection event is held to be analogous to a failure event in survival analysis. This allows us to link the probability density function (PDF) of infestation size at detection to the instantaneous probability of detecting an incursion, assuming it has not been detected earlier, namely the hazard function. This allows us to capture or integrate out the consequent uncertainty of the maturity of the incursion at the time of detection. We then introduce an approximation using the Weibull distribution. We show that the approximation is supportable when dealing with a small fixed number of traps ( n ) or a lower probability of detection per trap ( p ). Furthermore, by assuming a relationship between the population size at detection and the time it remains undetected, we can estimate the PDF for the population's duration of occupancy. Finally, a computer program is developed for the analysis, using the Mediterranean fruit fly (medfly) as a case study, to demonstrate its application. By modeling the population size of an invasive species at the moment it is first detected, we offer insights that can guide effective control and eradication measures and inform broader invasivespecies management practices.

At-border interventions are a critical step along the biosecurity continuum, to measure and control the risks associated with the cross-border movement of people and goods. Air passengers are a high-volume pathway for a range of biosecurity risk materials, against which various interventions may be used (e.g., manual searches, detector dogs, x-rays, etc.). Tasmania is an island state, and its environment and industries have benefited from a low level of invasive pests due to their geographic isolation. Therefore, relatively strict at-border interventions are used to prevent the entry of new pests, including some serious invasive pests already present on mainland Australia (e.g., Queensland (Bactrocera tryoni) and Mediterranean (Ceratitis capitata) fruit fly). Using a large interception database for domestic air passengers entering the southern Australian state of Tasmania from mainland Australia, this study applies common statistical modelling tools to assess the efficacy of interventions (namely, dog detectors, and bag searches), and to identify pathway risk factors (e.g., flight origin/route). This analysis considered the effects of interventions on both voluntary declarations by passengers and also detections of undeclared risk material on passengers. The analysis also focused on biosecurity risk items generally (e.g., fruits and vegetables, meat products, cut flowers), and items that are specifically considered to be fruit-fly hosts. The results highlight that active at-border interventions and the presence of biosecurity inspectors capture a significant volume of biosecurity risk items at the border, and detector dogs have particularly strong positive effects on the rate of interceptions, particularly for items detected on passengers. Conducting bag searches also appears to increase interceptions, both by increasing the rate of items being detected and by encouraging voluntary declarations. Sensitivity analyses then test the robustness of results to modelling implementation methods and distributional assumptions. This study demonstrates how statistical modelling can provide robust insights into biosecurity interventions and risk factors along pathways, and further highlights the value of high-quality interception data resources for informing and improving biosecurity systems.

It is well known that the increasing globalisation of human movement and trade has led to substantial range expansions of many taxa, and as a consequence, is increasingly exposing countries to novel biosecurity threats. This increased exposure to novel threats is expected to be exacerbated by a changing climate as trade patterns and species distributions change. In many countries biosecurity regulators are already struggling to contend with the increased exposure to pests and diseases, and as such, must shift towards a pro-active strategy of anticipating risk. However, to anticipate risk, regulators must make better use of the data they collect (e.g. border interceptions) and develop models capable of forecasting biosecurity propagule pressure and establishment exposure as a function of changing trade, human population, and species distributions. In this project, we develop a highly innovative model framework that simulates annual changes in international trade patterns (imports & exports) as a function of climate change impacts on crop productivity, labour productivity (via heat stress) and the amount of arable land. These simulated changes in global trade are then coupled with border interception data, and annual predicted changes in the geographic distributions of both human populations and threat climate suitability to estimate climate-induced changes in: 1) contamination rates for imports from different trading partners, 2) the total amount of biosecurity risk material arriving at Australia’s borders, and 3) its exposure to an establishment event (Figure 1.1). Conceptual diagram of innovative biosecurity forecasting model. The model is made up of two primary sub-modules: 1) The Economic submodel, which incorporates climate change damages (e.g. crop productivity & heat stress) and simulates these impacts on global import and export trade patterns; 2) The Ecological submodel that estimates threat climate suitability, country-by-commodity contamination rates, and then links these to predicted changes in both global trade flows (i.e. outputs from the Economic submodel) and human population to approximate country-specific propagule pressure and establishment exposure. Here, we provide an in-depth description of both the trade and biosecurity risk sub-models. We then illustrate the model’s implementation and outputs under two different climate scenarios (RCP 4.5 and RCP 8.5) for the purposes of forecasting temporal changes in: 1) global and regional economic trade; and 2) the amount of biosecurity risk material arriving at Australia’s border (i.e. propagule pressure) and what it may mean for establishment exposure. In illustrating the biosecurity risk, we focused on five plant pests deemed by the Department of Agriculture, Fisheries and Forestry (DAFF) as an exemplar of different hitch-hiking functional groups. The exemplar threats examined were: Overwintering – brown marmorated stink bug (BMSB; Halyomorpha halys) Egg laying – Spongy moth (Lymantria dispar) Nesting – Asian honey bee (Apis cerana) Sheltering – Giant African snail (Lissachatina fulica) Internal storage – Khapra beetle (Trogoderma granarium). Global and regional economic trade consequences of climate change The climate-enhanced trade model shows significant changes in trade patterns globally. Climate change impacts various countries differently, causing substantial changes in national incomes, productive capacity, and imports and exports around the world. This occurs even with relatively limited damage functions from global warming. Indeed, with limited damage functions (crop productivity losses, labour productivity losses due to heat stress, and loss of arable land from ocean inundation), the impact on national income in Australia from climate change is relatively small (e.g., damages from more substantive sea level rise and storm surge are not included). However, damages to trading partners and changes in imports to Australia, as well as the rest of the world, are considerable. To allow for easy interrogation of these predicted trade impacts, we have developed an interactive dashboard¹ that allows users to examine changes in trade patterns – by country, commodity and climate change scenario – for user selected imports by country and total values. The following summarise the key findings from the select damage functions employed within this analysis: Western African regions fare the worst in terms of overall GDP impacts, with the region at large experiencing roughly a 20% loss to GDP. The second most affected region is South Asia² with Pakistan bearing the greatest damages. Some countries emerged relatively unscathed, prominently those located in North America, Europe, Russia, and Oceania. In terms of climate change related damages to key Australian trading partners, we find that losses in China and Southeast Asia³ are the most consequential. Here labour productivity shocks due to heat stress lead to losses in manufacturing sector imports such as Motor vehicles and Electronic equipment. As the largest exporter of manufacturing goods and a key region affected by climate change, China sees the largest decline in exports, however most of South and Southeast Asia fares worse in terms of relative losses with India and Indonesia seeing over 10% losses. Conversely, net gains are made across several European regions, particularly Germany and the UK. The greatest heterogeneity within macroeconomic sector was observed among agricultural imports and in particular crop sectors in large part due to the varied mix of exporters for each crop type and differential impacts experienced. The largest absolute increase among food- and agriculture-related sectors is seen within Vegetables, fruit, nuts with large increases in exports from OECD regions and China. The climate change damage functions employed here likely vastly underestimate the true costs of climate change impacts for a number of reasons. These include the following: Recent scholarship suggests that large damages to GDP are already being experienced (Romanello et al., 2023) whereas the earlier work used here (with the exception of crop productivity) includes minimal damages at early timesteps. Further, the anticipated impacts from warming may be far larger (particularly at later timesteps) if climate sensitivities have been misestimated (leading to more extreme associated temperature paths) or tipping points are triggered. The application of damages used within the current study is limited in terms of scope, with damages due to human health impacts and changes in tourism trends missing. In addition to the limited scope, some damages that have been implemented have not been fully allocated to all affected sectors. For example, sea level rise is understood entirely within the purview of loss of arable land while physical capital depreciation and impacts to manufacturing hubs located on coastal areas is not currently simulated. Sociopolitical consequences of climate change such as armed conflict and forced migration are not included. Diminished social resilience due to climate change related impacts (e.g., rising food insecurity) has the potential to feed back into the economy in myriad ways, potentially cascading into additional economic damages and/or altered trade patterns. Although limited climate change damages have been implemented, large changes in socioeconomic trends including economic and demographic growth are anticipated to occur within the long-term time horizon used within the current study. Such changes affect key Australian trade partners and have the potential to alter the composition of imports at a magnitude equal to or surpassing climate change impacts. Full simulation of both socioeconomic pathways as well as climate change impacts is currently a CEBRA priority. Changes in pest propagule pressure & establishment exposure hitting Australia. While this report focuses on long-term trends in annual propagule pressure and establishment exposure hitting Australia’s border, the model is capable of estimating such trends for all 70 global regions and can be readily updated with new interception data. As such, to facilitate interrogation of model outputs, we have developed leaflet interactive maps for each of the five threats. Included in these maps are information⁴ about temporal trends in pest pressure, establishment exposure (if threat is influenced by climate suitability) and proportion of risk attributable to each infected exporters and commodity sector. The following summarise the key findings we found by running the model for the five exemplar threats: Out of the five exemplar threats, brown marmorated stink bug (BMSB; Halyomorpha halys) posed the greatest propagule pressure and established risk to Australia. This was followed by giant African snail (Lissachatina fulica), Khapra beetle (Trogoderma granarium), Asian honey bee (Apis cerana), and then spongy moth (Lymantria dispar). Imports of manufacturing commodities (e.g. electronic equipment, motor vehicles and parts, plastics and metals) from infected countries posed the greatest risk of hitch-hiker contamination, with some exporting regions posing greater risk than others. We detected marginal (albeit uncertain) positive impacts of potential area of suitable climate on the contamination rates coming from infected exporting regions for BMSB and to a lesser extent Spongy moth. This meant that in exporting regions where climate suitability is predicted to increase (e.g. Canada & United Kingdom for BMSB), contamination rates will be higher. By contrast, in regions where climate suitability is expected to decrease (e.g. Italy for BMSB), contamination rates are expected to decline. Area of suitable climate had no discernable impacts on contamination rates associated with Asian honey bee or giant African snail.⁵ Differences in trends in predicted propagule pressure (i.e. number of contaminated lines) hitting Australia’s border between the two climate scenarios were found to be small and highly uncertain for all threats examined in this report. Multiple reasons are attributable to this: There are compensatory effects occurring, whereby reductions (due to either decreased trade or climate-induced declines in contamination likelihoods) in contaminated items from one infected exporter is made up by increases in another. Climate impacts on exports and imports of manufactured goods – the commodity types with highest likelihoods of containing most of the modelled hitch-hikers used in this study – are likely to be severely underestimated. Recent work (Romanello et al., 2023) suggests that the existing set of damages included may severely underestimate the true impacts of climate change, especially on manufacturing sectors. Extending the trade model to include a larger set of damage functions, particularly those that encompass physical capital depreciation due to sea level rise and other disasters magnified by climate change (e.g., bushfires), is expected to result in significantly greater economic impacts within affected manufacturing and related sectors. This in turn will manifest in more significant impacts on global export and import flows, and thus, the total pest pressure expected at Australia’s border. There remains significant uncertainty on how climate suitability in exporting regions impacts contamination rates. While our model detected marginal positive relationships between contamination rates and area of suitable climate for some threats (e.g. BMSB), uncertainty is partly driven by the number of infected exporting countries containing the threat and how variable climate suitability is within and among those trading partners. This uncertainty could be further reduced by including additional interception data from other countries (e.g. New Zealand) as well as incorporating additional information on other factors likely to impact contamination likelihoods such as known extent of established populations, time since establishment, or other factors that can inform population size in exporting country. Trends in Australia’s exposure to potential BMSB or Spongy moth establishment were expected to decline overtime due to a combination of reduced propagule pressure (caused by declines in volume of trade from high risk trading partners and/or climate-induced declines contamination rates), and declines in climatic suitability at Australian locations where goods are likely to be unpacked. These declines were most pronounced under the worst-case climate scenario (RCP 8.5). By contrast, no discernable trends were found for Asian honey bee or giant African snail – mostly due to 1) minor impacts on trade volumes from infected exporters; 2) negligible impacts of climate suitability on contamination rates; and 3) climate suitability in locations import goods are most likely to be unpacked remaining relatively stable (i.e. where urban centres are predicted to remain). Potential model utility We believe that this new model provides the necessary information needed for governments and industry to better anticipate – and therefore manage and adapt to – future climate change impacts on domestic and international economies, global trade, and exposure to biosecurity risk. The current work may serve as a foundation for informing policy decisions as well as a range of downstream models. For example model outputs can be used: to directly inform both short-term and long-term policies associated with border screening effort among different commodities and exporters, threat prioritisation and developing or updating Import Risk Assessments (IRAs). as inputs into other models used by DAFF such as: the post-border pest establishment likelihood model edmaps (Camac et al., 2020, 2021b)⁶ for informing post-border surveillance & establishment potential, the Risk Return Resource Allocation (RRRA) model, and CEBRA’s value model (Dodd et al., 2021) for informing potential damages accrued over time by an exotic threat and the benefits of different mitigation strategies. to identify regions and economic sectors most susceptible to changing climate, and thus, provide governments with the necessary foresight to plan and adapt to potential impacts.

The rise of globalization has led to a sharp increase in international trade with high volumes of containers, goods, and items moving across the world. Unfortunately, these trade pathways also facilitate the movement of unwanted pests, weeds, diseases, and pathogens. Each item could contain biosecurity risk material, but it is impractical to inspect every item. Instead, inspection efforts typically focus on high‐risk items. However, low risk does not imply no risk. It is crucial to monitor the low‐risk pathways to ensure that they are and remain low risk. To do so, many approaches would seek to estimate the risk to some precision, but increasingly lower risks require more samples. On a low‐risk pathway that can be afforded only limited inspection resources, it makes more sense to assign fewer samples to the lower risk activities. We approach the problem by introducing two thresholds. Our method focuses on letting us know whether the risk is below certain thresholds, rather than estimating the risk precisely. This method also allows us to detect a significant change in risk. Our approach typically requires less sampling than previous methods, while still providing evidence to regulators to help them efficiently and effectively allocate inspection effort.

This paper proposes a surveillance model for plant pests that can optimally allocate resources among survey tools with varying properties. While some survey tools are highly specific for the detection of a single pest species, others are more generalized. There is considerable variation in the cost and sensitivity of these tools, but there are no guidelines or frameworks for identifying which tools are most cost‐effective when used in surveillance programs that target the detection of newly invaded populations. To address this gap, we applied our model to design a trapping surveillance program in New Zealand for bark‐ and wood‐boring insects, some of the most serious forest pests worldwide. Our findings show that exclusively utilizing generalized traps (GTs) proves to be highly cost‐effective across a wide range of scenarios, particularly when they are capable of capturing all pest species. Implementing surveillance programs that only employ specialized traps (ST) is cost‐effective only when these traps can detect highly damaging pests. However, even in such cases, they significantly lag in cost‐effectiveness compared to GT‐only programs due to their restricted coverage. When both GTs and STs are used in an integrated surveillance program, the total expected cost (TEC) generally diminishes when compared to programs relying on a single type of trap. However, this relative reduction in TEC is only marginally larger than that achieved with GT‐only programs, as long as highly damaging species can be detected by GTs. The proportion of STs among the optimal required traps fluctuates based on several factors, including the relative pricing of GTs and STs, pest arrival rates, potential damage, and, more prominently, the coverage capacity of GTs. Our analysis suggests that deploying GTs extensively across landscapes appears to be more cost‐effective in areas with either very high or very low levels of relative risk density, potential damage, and arrival rate. Finally, STs are less likely to be required when the pests that are detected by those tools have a higher likelihood of successful eradication because delaying detection becomes less costly for these species.

Mathematical aggregation of probabilistic expert judgments often involves weighted linear combinations of experts’ elicited probability distributions of uncertain quantities. Experts’ weights are commonly derived from calibration experiments based on the experts’ performance scores, where performance is evaluated in terms of the calibration and the informativeness of the elicited distributions. This is referred to as Cooke’s method, or the classical model (CM), for aggregating probabilistic expert judgments. The performance scores are derived from experiments, so they are uncertain and, therefore, can be represented by random variables. As a consequence, the experts’ weights are also random variables. We focus on addressing the underlying uncertainty when calculating experts’ weights to be used in a mathematical aggregation of expert elicited distributions. This paper investigates the potential of applying an empirical Bayes development of the James–Stein shrinkage estimation technique on the CM’s weights to derive shrinkage weights with reduced mean squared errors. We analyze 51 professional CM expert elicitation studies. We investigate the differences between the classical and the (new) shrinkage CM weights and the benefits of using the new weights. In theory, the outcome of a probabilistic model using the shrinkage weights should be better than that obtained when using the classical weights because shrinkage estimation techniques reduce the mean squared errors of estimators in general. In particular, the empirical Bayes shrinkage method used here reduces the assigned weights for those experts with larger variances in the corresponding sampling distributions of weights in the experiment. We measure improvement of the aggregated judgments in a cross-validation setting using two studies that can afford such an approach. Contrary to expectations, the results are inconclusive. However, in practice, we can use the proposed shrinkage weights to increase the reliability of derived weights when only small-sized experiments are available. We demonstrate the latter on 49 post-2006 professional CM expert elicitation studies.