Peter Caley

Quantifying uncertainty in predictions of invasiveness

Using the Australian weed risk assessment (WRA) model as an example, we applied a combination of bootstrapping and Bayesian techniques as a means for explicitly estimating the posterior probability of weediness as a function of an import risk assessment model screening score. Our approach provides estimates of uncertainty around model predictions, after correcting for verification bias arising from the original training dataset having a higher proportion of weed species than would be the norm, and incorporates uncertainty in current knowledge of the prior (base-rate) probability of weediness. The results confirm the high sensitivity of the posterior probability of weediness to the base-rate probability of weediness of plants proposed for importation, and demonstrate how uncertainty in this base-rate probability manifests itself in uncertainty surrounding predicted probabilities of weediness. This quantitative estimate of the weediness probability posed by taxa classified using the WRA model, including estimates of uncertainty around this probability for a given WRA score, would enable bio-economic modelling to contribute to the decision process, should this avenue be pursued. Regardless of whether or not this avenue is explored, the explicit estimates of uncertainty around weed classifications will enable managers to make better informed decisions regarding risk. When viewed in terms of likelihood of weed introduction, the current WRA model outcomes of ‘accept’, ‘further evaluate’, or ‘reject’, whilst not always accurate in terms of weed classification, appear consistent with a high expected cost of mistakenly introducing a weed. The methods presented have wider application to the quantitative prediction of invasive species for situations where the base-rate probability of invasiveness is subject to uncertainty, and the accuracy of the screening test imperfect

Assessing growth rates of European rabbit populations using spotlight transect counts

Reliable estimates of population growth rates and densities are fundamental for effective wildlife management programs. We assessed the precision of spotlight-counting as a technique to monitor changes in rabbit abundance by fitting simple population growth models to observed trends in spotlight-count data during an 18-month period of increase in European rabbit (Oryctolagus cuniculus) abundance at sites in North Canterbury, New Zealand. A model-selection approach identified a simple exponential population growth model, allowing the observed rate of increase to differ between spring-summer (Aug-Feb) and autumn-winter (Mar-Jul) to be an adequate description of the observed data. The exponential rate of increase (r) over the study period differed markedly between spring-summer and autumn-winter periods, and averaged 2.3 yr -1 and 2.5 yr -1 for the 2 sites monitored. We used the fitted exponential model to estimate the observation error per spotlight transect. The estimated coefficient of variation for 1 night of counting of 10-km transects was 16%. With such data and model assumptions, only a modest number of surveys would be required to detect, with a high degree of certainty, moderate changes in spotlight-count indices of rabbit abundance either by analysis of variance or log-linear regression.

Quantifying uncertainty in predictions of invasiveness, with emphasis on weed risk assessment

Due to a technical error, the following article has been accepted and published twice. ‘‘Quantifying uncertainty in predictions of invasiveness in predictions of invasiveness, with emphasis on weed risk assesment’’ by P. Caley, W. M. Lonsdale & P.C. Pheloung, published in Volume 8, Issue 2 (pages 277–286) of the Biological Invasions Journal was accidentally published again in Volume 8, Issue 8 (pages 1595–1604).

Long-term ecological trends of flow-dependent ecosystems in a major regulated river basin

The case for restoring water to the environment in the Murray–Darling Basin, Australia, is based mainly on condition assessments, although time series provide valuable information on trends. We assessed trends of 301 ecological time series (mean 23 years, range 1905–2013) in two categories: (1) ‘population’ (abundance, biomass, extent) and (2) ‘non-population’ (condition, occurrence, composition). We analysed trends using log-linear regression, accounting for observation error only, and a state–space model that accounts for observation error and environmental ‘noise’. Of the log-linear series (n=239), 50 (22%) showed statistically significant decline, but 180 (78%) showed no trend. For state–space series (n=197) one increased, but others were stable. Distribution of median exponential rates of increase (r) indicated a small but statistically significant declining trend, though 35–39% of the series were positive. Our analysis only partly supports, though does not refute, prevailing assumptions of recent ecological decline in the Murray–Darling Basin. The pattern is of fluctuating stability, with declines during droughts and recovery after flood. The overall trend from our meta-analysis is consistent with a pattern of historical decline to a hybrid ecosystem followed by slow, recent decline for some components and stability for others, with considerable variation in trends of specific ecological components: in short, there are ecological ‘winners’ and ‘losers’.

Quantifying Extinction Probabilities from Sighting Records: Inference and Uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.

Entry of exotic insects into Australia: Does border interception count match incursion risk?

Interception data collected at the Australian quarantine border on the orders Coleoptera, Hemiptera, Lepidoptera and Diptera during 1986–2005 were cross-referenced to incursion data. For insects from these four orders, detection at the quarantine border was a poor predictor of successful incursions over the corresponding period. Most species that successfully mounted an incursion during the 1986–2005 period were not recorded as being intercepted at the quarantine border over the same period. This may be due to either organisms arriving via pathways that are not subject to border inspection, or that the inspection sensitivity is low, or that species discovered are not reliably identified, recorded and reported. The end result is that the border inspection, at least during the period 1986–2005, would have been largely ineffective as an early warning system for a large proportion of incursions occurring over that period. This finding is contrary to the expectation that interception data is a useful tool for predicting future incursions and opens the question as to whether different approaches to collecting interception data might improve predictive power. That said, within those species that were intercepted, those with a higher interception rate had an increased probability of a recorded incursion, particularly for incursions before 1986, and so supports the argument that propagule pressure is a key factor in invasion establishment.

Inferring the Distribution and Demography of an Invasive Species from Sighting Data: The Red Fox Incursion into Tasmania

A recent study has inferred that the red fox (Vulpes vulpes) is now widespread in Tasmania as of 2010, based on the extraction of fox DNA from predator scats. Heuristically, this inference appears at first glance to be at odds with the lack of recent confirmed discoveries of either road-killed foxes—the last of which occurred in 2006, or hunter killed foxes—the most recent in 2001. This paper demonstrates a method to codify this heuristic analysis and produce inferences consistent with assumptions and data. It does this by formalising the analysis in a transparent and repeatable manner to make inference on the past, present and future distribution of an invasive species. It utilizes Approximate Bayesian Computation to make inferences. Importantly, the method is able to inform management of invasive species within realistic time frames, and can be applied widely. We illustrate the technique using the Tasmanian fox data. Based on the pattern of carcass discoveries of foxes in Tasmania, we infer that the population of foxes in Tasmania is most likely extinct, or restricted in distribution and demographically weak as of 2013. It is possible, though unlikely, that that population is widespread and/or demographically robust. This inference is largely at odds with the inference from the predator scat survey data. Our results suggest the chances of successfully eradicating the introduced red fox population in Tasmania may be significantly higher than previously thought.

Statistical modeling of a larval mosquito population distribution and abundance in residential Brisbane

Container-inhabiting mosquitoes such as Aedes notoscriptus, Aedes aegypti, and Aedes albopictus are potential vectors of a number of arboviruses of significance to human health and domestic animals. To assess the risk of mosquito-borne viruses, residential properties were surveyed for mosquito larvae within the Brisbane area during 2010–2012. A two-stage modeling approach was used to model both the presence/absence of Ae. notoscriptus larvae and abundance of larvae when present. Results indicate the total number of wet containers found on a property is the main driving factor of both presence/absence and abundance of Ae. notoscriptus larvae. The generalized additive modeling approach used indicates more standard logistic regression and odds ratios may overestimate the importance of common covariates. The two-stage modeling also potentially allows for predictions of Ae. notoscriptus abundance and common risk indices that are not possible using traditional logistic regression. Factors influencing the number of wet containers are explored with a view toward risk mitigation.

Quantifying the Establishment Likelihood of Invasive Alien Species Introductions Through Ports with Application to Honeybees in Australia.

The cost of an uncontrolled incursion of invasive alien species (IAS) arising from undetected entry through ports can be substantial, and knowledge of port-specific risks is needed to help allocate limited surveillance resources. Quantifying the establishment likelihood of such an incursion requires quantifying the ability of a species to enter, establish, and spread. Estimation of the approach rate of IAS into ports provides a measure of likelihood of entry. Data on the approach rate of IAS are typically sparse, and the combinations of risk factors relating to country of origin and port of arrival diverse. This presents challenges to making formal statistical inference on establishment likelihood. Here we demonstrate how these challenges can be overcome with judicious use of mixed-effects models when estimating the incursion likelihood into Australia of the European (Apis mellifera) and Asian (A. cerana) honeybees, along with the invasive parasites of biosecurity concern they host (e.g., Varroa destructor). Our results demonstrate how skewed the establishment likelihood is, with one-tenth of the ports accounting for 80% or more of the likelihood for both species. These results have been utilized by biosecurity agencies in the allocation of resources to the surveillance of maritime ports.

Making inference from wildlife collision data: inferring predator absence from prey strikes

Wildlife collision data are ubiquitous, though challenging for making ecological inference due to typically irreducible uncertainty relating to the sampling process. We illustrate a new approach that is useful for generating inference from predator data arising from wildlife collisions. By simply conditioning on a second prey species sampled via the same collision process, and by using a biologically realistic numerical response functions, we can produce a coherent numerical response relationship between predator and prey. This relationship can then be used to make inference on the population size of the predator species, including the probability of extinction. The statistical conditioning enables us to account for unmeasured variation in factors influencing the runway strike incidence for individual airports and to enable valid comparisons. A practical application of the approach for testing hypotheses about the distribution and abundance of a predator species is illustrated using the hypothesized red fox incursion into Tasmania, Australia. We estimate that conditional on the numerical response between fox and lagomorph runway strikes on mainland Australia, the predictive probability of observing no runway strikes of foxes in Tasmania after observing 15 lagomorph strikes is 0.001. We conclude there is enough evidence to safely reject the null hypothesis that there is a widespread red fox population in Tasmania at a population density consistent with prey availability. The method is novel and has potential wider application.