Data sources

Spotlight surveys as an index of devil density

The Tasmanian Government has conducted standardised annual spotlighting surveys at up to 172 transects across Tasmania (Fig. 2a; n = 5761) from 1985 to 2019 (Table S1). The surveys record all sightings of non-domestic mammalian wildlife species, including devils (Hocking & Driessen 1992), along 10-km road transects. Transects are driven at a constant speed of 20 km h⁻¹, with one person using a handheld spotlight to observe animals on both sides of the road (for details, see Hocking & Driessen 1992; Hollings et al. 2014). Transects are surveyed once per year during the summer months, ensuring comparability between years, but precluding the use of techniques that require repeat surveys within a year, like occupancy modelling. We treat the count of devils per transect as an index of devil density, and henceforth refer to it as ‘relative density’.

Disease spread

We collated records of DFTD locations including those already published from 1996 to 2015 (Lazenby et al. 2018) and recent cases of DFTD in new areas until September 2020. Lazenby et al. (2018) reported locations of lab-confirmed DFTD samples until 2015. We additionally used DFTD locations reported in Hawkins et al. (2006) and McCallum et al. (2007), some of which included cases with clinical signs of DFTD but were not lab-confirmed, which is important before the disease was formally identified. Because we aimed to model the progression of the disease front into new areas, we retained only the earliest arrival of DFTD in each 10 × 10 km² grid cell across Tasmania, leaving 83 records (Fig. 3).

There is little trapping data from south-west Tasmania because the region is largely inaccessible. To survey this area for DFTD, we used records from recent camera-trap surveys. Although cameras are less sensitive for detecting small tumours, they regularly detect tumours when they become larger. In this case, cameras observed tumours in areas with confirmed cases of DFTD but did not detect DFTD along the south-west coast (2016–2020), where live trapping in 2015 also did not detect DFTD. We have therefore included eight absence locations along the south-west coast (Fig. 3). Additionally, one long-term trapping site in the north-west is currently free of disease (Fig. 3). Based on a continuation of the pattern of spread, we estimated that DFTD would arrive at these disease-free sites in 2022 (Fig. 3B). Future disease spread may differ from this estimate, but any departures will have only a small effect on the population estimates because the influence of these data points relates to a small, low-density area of Tasmania.

Modelling spatial data using integrated nested Laplace approximation

We visualised the spatial spread of DFTD and modelled changes in devil density using integrated nested Laplace approximation (INLA) (Illian et al. 2013), an accurate and computationally fast option for Bayesian inference from spatial data. We used the inlabru R package (Bachl et al. 2019; R Core Team 2019), which builds on the R-INLA package (Rue et al. 2009; Bakka et al. 2018). Spatial dependence between observations is modelled using a Gaussian random field, which is a spatially continuous process where random variables at any point in space are normally distributed, and are spatially correlated with other random points via a continuous correlation process (Bachl et al. 2019). The Gaussian random field is approximated by a stochastic partial differential equation (SPDE) (for details, see Lindgren et al. 2011). In all models, we used a Matérn correlation structure for the SPDE (Table S6).

Modelling the pre-DFTD devil population

We spatially modelled devil relative density at the time of DFTD discovery using the count of devils per spotlight transect from 1985 to 1996 as the response variable. We created temporally static continuous variables for the proportional cover of four major habitat classes comprising 84% of Tasmania: (1) wet eucalypt and rainforest (%wetEuc, 28% of Tasmania), (2) dry eucalypt forest (%dryEuc, 24%), (3) buttongrass moorlands (%butGrass, 9%), and (4) agricultural land (%agric, 23%). We excluded %dryEuc from the models because it was negatively correlated with %wetEuc (Pearson's r = −0.65). We modelled a non-linear effect of ‘survey year’ (1985–1996) using a one-dimensional SPDE. Finally, to model spatial correlations not accounted for by covariates, as well as correlations between repeated surveys at a location, we created (1) a temporally static two-dimensional SPDE and (2) a spatiotemporal SPDE. See Table S6 for details and ecological justification of these variables and Fig. S1 for a vegetation map.

We followed the model selection advice of Illian et al. (2013) when inferring the effect of spatial covariates in models that also include spatial random fields. We began by fitting a model with the three vegetation covariates and ‘survey year’. Using this model, we tested whether devil counts best conformed to a Poisson or negative binomial distribution. Then, we fitted all simpler combinations of the vegetation covariates, aiming to select the statistically important vegetation covariates. Next, we added a temporally static SPDE, and finally a spatiotemporal SPDE (see Table S7 for models). We selected the best model using a leave-one-out cross-validation quantity, the conditional predictive ordinate (CPO), with smaller values of −2 × Σ(logCPO) indicating better fit (Pettit 1990). To screen for violations of assumptions, we spatially examined CPO scores and histograms of the predictive integral transform, and visually examined Pearson residuals against model estimates (Conn et al. 2018). From the best model, we produced a predictive map of devil relative density across Tasmania as a function of the vegetation covariates and random field, with year set to 1996. We did this using the predict function of inlabru, which repeatedly draws samples from the posterior distributions of the model parameters.

Pattern-oriented diffusion simulation of the spatial spread of DFTD

To investigate the effect of host density on the spatial spread of DFTD, we developed a grid-based, stochastic-diffusion simulation. We parameterised this model using a pattern-oriented framework, which provides a systematic, data-oriented way of calibrating complex simulation models (Grimm et al. 2005; Grimm & Railsback 2012). Specifically, we used Approximate Bayesian Computation (ABC) using the abc package (Csilléry et al. 2012) in R. This involved running many versions of the model, each with different parameters drawn from vaguely specified prior distributions. Using summary statistics from the simulations, ABC selects only the models that are close to reproducing ‘target’ statistics calculated from the observed data, from which ABC estimates the posterior parameter distributions (Csilléry et al. 2010; Csilléry et al. 2012).

To initiate the simulation, we seeded one grid cell in north-east Tasmania with DFTD at a location between the first two observed cases of DFTD. We started the simulation in 1990 because genomic evidence suggests that although DFTD probably emerged in the 1980s, it was not until the mid-1990s that the effective reproduction number increased and DFTD began to spread more widely (Patton et al. 2020). In each of 31 timesteps (1990–2020), the probability of DFTD spreading into an unoccupied grid cell was first determined by the distance, s, from an occupied cell. For cells within s distance, the odds, Y, of DFTD spreading into a cell was:

where β₁ is an intercept and β₂ is a coefficient for the effect of devil relative density (previous section). The probability of diffusing into a new cell was stochastically determined by sampling from the binomial distribution with a probability of exp(Y)/(1 + exp(Y)). We assumed that once grid cells were infected by DFTD, they remained so thereafter, which is broadly true at the landscape scale.

We used ABC to estimate the posterior distributions of s, β₁ and β₂. We considered parameters for β₁ and β₂ to be important if credible intervals did not span zero. We evaluated the simulations on their ability to correctly estimate the year of arrival at 83 DFTD locations and the absence of DFTD in 9 DFTD-free locations. See Appendix S2 for model details and see Appendix S3 for R code.

To visually compare the results of the ABC-parameterised simulation with the observed data, we created an interpolated map of DFTD first cases. Using inlabru (Bachl et al. 2019) in R, we modelled the year of DFTD arrival using a Gaussian distribution in response to a spatial random field only (Table S6). From this model, we produced a smooth map of estimated disease-arrival times. Because this model is based solely on a spatial random field, it provides no direct inference about the processes responsible for the pattern of disease spread. Nevertheless, because it directly fits the data, it has higher descriptive fidelity than the diffusion model. We therefore use the diffusion model to interpret the processes driving DFTD spread, while using the random-field-map for the subsequent models investigating population effects.

Integrating multiple data sources into a joint-likelihood model

We integrated the density and spotlight datasets into a Bayesian joint-likelihood model. Joint likelihood models combine multiple data sources into single integrated models that estimate a shared set of parameters (Miller et al. 2019; Isaac et al. 2020). The integrated model has sub-models for each data source, with some or all parameters shared between the sub-models (Bachl et al. 2019; Miller et al. 2019). We fitted the joint-likelihood model using the inlabru R package (tutorials in Bachl et al. 2019; Watson et al. 2019). To model spatiotemporal changes to devil density from the spotlighting and density datasets, we created explanatory variables for ‘survey year’ (1985–2019) and the model-estimated number of years since DFTD arrival to a site (‘yrsDFTD’; 0–23 years), which we estimated from the random-field-map of disease spread (Fig. 3B). Non-linear effects of ‘survey year’ and ‘yrsDFTD’ were modelled using one-dimensional SPDEs (Table S6). As previously described, we modelled the effect of three vegetation types: %wetEuc, %agric and %butGrass. Finally, to model spatial correlations not accounted for by covariates, we included in separate models a temporally static two-dimensional SPDE and a spatiotemporal SPDE that allows the random field to change through time (Table S6).

We followed the same model selection process as for the pre-DFTD model, first by selecting the important environmental covariates, and then adding spatial random fields (Illian et al. 2013). For the spotlighting sub-model, the response variable was the count of devils observed on a transect (Poisson or negative binomial distribution). For the density sub-model, the response variable was the estimated devil density for each trapping session (devils/km²; gamma or Weibull distribution). All models used the default link function. The most complex joint-likelihood model took the form of

where β₁ and β₂ are intercepts for each sub-model, f₃ and f₄ are shared non-linear effects, β₅, β₆, β₇ are shared fixed effects, SPDE is a shared spatial random field and β₈ is a scaling constant that modifies f₃ (see chapter 3 of Krainski et al. 2019). We included the scaling constant because initial exploration of the two datasets suggested that the spotlight data slightly overstated the decline in devil density. See Table S9 for the structure of all fitted models. From the density sub-model of the best joint model, we produced predictive maps of devil density across Tasmania at various points from 1985 to 2035 (predict function of inlabru). To estimate the total devil abundance, we multiplied density estimates weighted by the area of each grid location across Tasmania. See Appendix S4 for example R code.

Density-dependent spatial spread of DFTD

Devil relative density varied substantially across Tasmania at the time of DFTD discovery (Fig. 3A). The best model of pre-DFTD spotlight detections included a spatiotemporal random field and negative effects of wet eucalypt/rainforest and buttongrass (Table S7). As a result, devil relative density was highest in the central and eastern part of Tasmania, where vegetation is dominated by dry eucalypt forests and woodlands (Fig. 3A).

The diffusion simulation of DFTD spread suggests that devil density played a key role in mediating the initial spatial spread of DFTD. Within a timestep, the ABC posteriors estimated that DFTD was able to diffuse into grid cells within ~ 18 km of already-occupied cells, with the probability of doing so strongly influenced by the relative devil density of the receiving grid cell (β_{relativeDensity} = 7.75, 95% CI: 6.89-8.29) (Table S8; Fig. S5). This model goes some way to explain why DFTD spread south rapidly in the decade after ‘break-out’, as it moved through an area with high relative densities (Fig. 3). From the mid-2000s, the spread of DFTD was substantially slower, as the western and southern disease-fronts crossed areas of lower relative densities (Fig. 3). The diffusion model correctly predicted that much of south-west Tasmania, a rugged area with low devil densities (Hawkins et al. 2006), is currently free of DFTD. The diffusion model and random-field-model estimate that DFTD occupies 91% and 96% of Tasmania (Fig. 3) respectively, with high uncertainty in southern Tasmania, where data is sparse (Fig. S4).

Devil population declines

The joint-likelihood model revealed a strong negative effect of ‘yrsDFTD’, with local devil densities declining by an average of 76% 10 years after disease arrival, at which point the population decline tends to level off, with 82% decline after 23 years (Fig. 4C). The joint model revealed a positive effect of ‘survey year’, and negative effects of %butGrass and %wetEuc (Fig. 4; Table 1; Fig. S6). Devil density was steadily rising before the discovery of DFTD, peaking in 1996 at a Tasmania-wide mean of 0.84 devils/km² (95% CI: 0.61–1.08) and a total population of 53 000 (95% CI: 39 600–71 800) (Fig. 5). By 2020, estimated mean density had declined to 0.27/km² (0.20–0.36) and the total population had declined by 68% to 16 900 (12 500–23 100) (Fig. 5).

To project forward to the scenario where DFTD will occupy all of Tasmania, we made the simplifying assumption, based on a continuation of disease spread trends, that DFTD will occupy all of Tasmania by 2022. Based on this assumption, our model forecasts a continuing but slowing decline of total devil abundance (Fig. 5), suggesting it should plateau at 11 900 devils (95% CI: 6300–18 600). Overall, this would represent a 78% decline in total abundance. To date, no local extinctions have been documented, with devil populations persisting at all monitoring sites, albeit at much lower densities (Fig. S2).

Density-dependent spatial spread of DFTD

Our pattern-oriented diffusion simulation suggests that DFTD spread most rapidly through areas of high host density. This raises an interesting point about spatial scale: although transmission within devil populations may be maintained by frequency-dependent processes (McCallum et al. 2009), the spatial spread of DFTD was apparently density-dependent. Using a simple diffusion model, van den Bosch et al. (1992) show that the spread of an invading organism is driven by a combination of the host movement rate and the intrinsic rate of increase. Both movement rate and interactions between devils could increase in response to competition. At high devil densities, carrion and live prey are less available per capita (Cunningham et al. 2018) and aggressive interactions at carcasses are more common (Hamede et al. 2008). Female devils in high density populations have larger home ranges (Comte et al. 2020) and disperse larger distances (Lachish et al. 2011; Storfer et al. 2017). Other studies, for instance of European badgers, show that larger home ranges can lead to increased potential for pathogen transmission (Woodroffe et al. 2006), and simulations show that greater host movement can increase the probability of a pandemic establishing (Cross et al. 2005). Adult devils sometimes engage in long-distance excursions of ~ 15–25 km (M. Jones, unpublished tracking data). These are likely to be more numerous at high densities, and could act as rare long-distance transmission events, which have been shown in other systems to substantially accelerate disease spread (Smith et al. 2002; Russell et al. 2005; Smith et al. 2005; Meentemeyer et al. 2011). Our simulation model was a first step in establishing a probable link between host density and the spatial spread of DFTD. Future studies should unpick the mechanisms that depend on density, and incorporate other drivers or barriers of DFTD spread, both of which would likely require a finer scale of study that matches the scale of transmission and host movement.

Population trends and conservation

Our estimate of pre-DFTD devil population size is less than half the previous estimate of 130 000–150 000 (Hawkins et al. 2008), which would require average densities across Tasmania of 2.15 devils/km². Our estimates suggest that only 1.3% of Tasmania had densities of at least 2.15 devils/km² at the time of DFTD discovery (Fig. 5B). This discrepancy might have two main causes. First, SECR has produced smaller density estimates than older methods. SECR uses the spatial detection histories of animals to estimate the effective sampling area (Borchers & Efford 2008), which can differ substantially between similar-sized trapping arrays (Table S5). In contrast, older methods defined the sampling area based on a buffer around trap sites without considering how animal movement around study sites influences the effective survey area (Hawkins et al. 2008). Second, previous extrapolations seemingly suffered from a common form of site selection bias, whereby study sites are selected in high-density areas (Fournier et al. 2019). Extrapolating such density estimates to areas with lower suitability, such as the Tasmanian south-west (Jones & Rose 1996; Hawkins et al. 2006), is likely to result in an overestimated population size. The integration of multiple datasets in our analysis allowed us to incorporate information from a broader range of environments, including low-suitability habitat, while harnessing the favourable qualities of each dataset (high-quality density estimates and long-term, wide-spread spotlight counts).

Based on the persistence of devils at all long-term diseased sites, our model predicts the overall population is likely to stabilise within the next 10 years. This supports recent simulations suggesting the most likely long-term outcomes are either the coexistence of devils and DFTD, or DFTD fading out (Wells et al. 2019), with genomic evidence suggesting a transition towards endemism (Patton et al. 2020). These stabilising trends reflect a growing body of research suggesting that devils are potentially adapting to DFTD in the face of this extreme selective pressure (Epstein et al. 2016; Ruiz-Aravena et al. 2018; Margres et al. 2018a; Fraik et al. 2020). Several individual devils have demonstrated natural tumour regressions in association with an immune response (Pye et al. 2016a), with tumour regression potentially related to genomic variation in both host (Margres et al. 2018b) and tumour (Margres et al. 2020). Nevertheless, it remains unclear how the genomic changes detected in long-term diseased areas (Epstein et al. 2016) relate to functional traits in devil-DFTD interactions, and whether genomic changes are involved in the persistence and even recovery of some populations.

Despite revealing 25 years of ongoing population decline, our results suggest the species no longer meets the criteria for Endangered status under the IUCN Red List. Because the Red List evaluates population reductions over the longer of 10 years or three generations (IUCN Standards & Petitions Committee 2019), the severe devil population decline before 2010 is essentially excluded from consideration. Our modelling suggests the species now qualifies for Vulnerable status based on a 31% population decline from 2011 to 2020 (criterion A2), and a reproductively mature population size that is likely to be < 10 000 but > 2500 individuals within the next decade (criterion C1). Given the population has declined by 68% over the last 25 years, numbers continue to decline, and the trend is not reversible with current knowledge, we strongly caution that the potential down-listing of the species does not mean the species is secure. This is particularly so in the face of new and uncertain threats, including the discovery in 2014 of a second, independently evolved facial tumour (DFT2) which is spreading through southern Tasmania (Pye et al. 2016b; James et al. 2019).

Although the outlook for the wild devil population is undoubtedly more positive than it was a decade ago (McCallum et al. 2009), devils are currently well below ecologically functional densities across much of Tasmania. Devil declines have had cascading ecological effects, such as carrion accumulation (Cunningham et al. 2018), mesopredator release with effects on small and medium-sized mammals (Hollings et al. 2014; Hollings et al. 2016; Cunningham et al. 2020), and the relaxation of anti-predator behaviours by prey (Hollings et al. 2015; Cunningham et al. 2019a; Cunningham et al. 2019b). In the the online data repository, we provide annual rasters of estimated devil densities from 1985 to 2035, which we expect will be useful for improving our understanding of the ecological effects of devils and identifying thresholds that could provide longer term targets for population recovery.

Given DFTD-induced extinction of the devil now seems unlikely, we suggest several management priorities. First, we emphasise the importance of continued monitoring across the species' geographic range, particularly following the discovery of DFT2 (Pye et al. 2016b). Second, because the now-small devil population is more exposed to other threatening processes (De Castro & Bolker 2005; McCallum 2012), it is an ongoing priority to minimise additional stressors like vehicle collisions and habitat destruction. A third exciting priority is that we can attempt to accelerate the pace of evolution by identifying and then moving advantageous genotypes to areas lacking them (McCallum 2012). Crucially, these genotypes need to come from populations that are under selective pressure by DFTD (Hohenlohe et al. 2019; Hamede et al. 2020). It is, however, important to recognise the potential for DFTD to evolve in response to changes in the host population, and that selecting for resistant devils might inadvertently select for more virulent tumours. Before intervening to boost adaptation, it is therefore important to better understand (1) how genotype influences phenotype in both devils and DFTD, and (2) how these traits influence the persistence of devils in long-diseased populations.

Concluding remarks

Modelling spatial dynamics of pathogens in wildlife populations remains a major challenge (White et al. 2018), but is critical for managing emerging disease threats, both to wildlife themselves and to human or livestock populations to which these pathogens may spill over. Our study of DFTD as it has spread across almost the entire geographic range of its sole host takes advantage of recent advances in pattern-oriented modelling, as well as joint modelling of multiple datasets. Diffusion-based approaches are often considered to be high-level general frameworks not well suited to providing specific predictions (White et al. 2018). By re-imagining a diffusion model as a multi-layer, grid-based simulation, our framework can accommodate complex processes that would otherwise be intractable using an analytical diffusion model. Our highly flexible simulation shows that diffusion-based models can provide explicit quantitative information on the relationship between host density and spatial spread, which should have broad, real-world applications to other wildlife disease systems, and invading organisms more generally. Ours is, however, one of few studies of emerging infectious diseases with plentiful `spatiotemporal data on both host and pathogen populations from the time of disease emergence. This highlights the importance of long-term monitoring programs. Regular, joint analysis of general-purpose survey datasets that monitor a large suite of species would be valuable for the early detection of population declines or disease emergence at a point where management interventions can be effective. Our analysis involved the use of survey data that was established to monitor harvested herbivore species, but has now provided valuable insights into the influence of host density on infectious disease spread and the population effects of an emerging infectious disease that did not exist when the surveys were established.