Devil Facial Tumour Disease (DFTD) is a recently emerged disease that is now widespread and represents a serious threat to the Tasmanian devil, Sarcophilus harrisii, the world's largest extant marsupial carnivore (Hawkins et al. 2006). A cancerous disease, DFTD appears to be consistently fatal with no evidence of recovery or natural immunity yet observed (Hawkins et al. 2006). Investigations of the aetiology of this disease are still in their infancy and neither the latency period nor the exact transmission mode is known (Loh et al. 2006). Recent cytogenetic work has shown that tumours in different devils have identical chromosomal rearrangements, suggesting that DFTD is transmitted from animal to animal by direct transmission of a ‘rogue’ cell line, probably during social interactions (Pearse & Swift 2006). Only one other known tumour, the sexually transmitted Canine Transmissible Venereal Sarcoma (CTVS) of dogs, is transmitted in a similar manner (Das & Das 2000).
Currently recorded in over 51% of the island of Tasmania, DFTD has resulted in a decline of 41% in the wild devil population, with local declines of up to 83% having been recorded (Hawkins et al. 2006). The loss of a vertebrate predator can have wide-ranging negative effects on the rest of the ecosystem (Sih et al. 1985; Schmitz, Hamback & Beckerman 2000). Decline in devil numbers may allow the meso-predator release of feral cat populations and the establishment of foxes (Bloomfield, Mooney & Emms 2005; Saunders et al. 2006). It is imperative therefore to establish effective management regimes to mitigate the impacts of this disease for this iconic species.
In the absence of a vaccine or treatment, options for managing the disease in wild populations are limited. One of the few possibilities available is removing infected individuals in an attempt to reduce transmission to susceptible animals (McCallum & Jones 2006). Monitoring disease dynamics in ‘removal’ vs. ‘control’ areas could provide information on how transmission rates vary with population density (Bradshaw, McMahon & Brook 2006). While ideal, evaluating this strategy experimentally in replicated control and treatment populations is logistically and financially demanding. In addition, the benefit to the population of reducing the force of infection needs to be balanced against the reproductive contribution of the individuals removed. Demographic models provide an inexpensive efficient means of assessing the likely outcome of management actions and are therefore necessary to determine the utility of this strategy. These models require field estimates of the vital rates of infected and uninfected animals, together with the force of infection as a function of disease prevalence.
Detecting population impacts of pathogens necessitates either direct monitoring of traits of infected vs. uninfected individuals in diseased populations or, ideally, determining changes in demographic parameters following disease outbreaks in long-term study populations, where data are available from before the start of the epidemic (McCallum 1994). Long-term studies of disease in wild populations are rare (Mutze et al. 2002; Williams et al. 2002b) with most investigations of disease impacts commonly undertaken retrospectively or opportunistically so that the pathogen is either already endemic or declining in the system before investigation begins (Telfer et al. 2002; Hall et al. 2006). Several recent long-term studies, however, where disease was detected part-way through the study, have detected negative impacts of pathogens on survival rates and population abundance (Arthur, Ramsey & Efford 2004; Faustino et al. 2004; Wilmers et al. 2006).
The detection of DFTD in 2001 in a population of Tasmanian devils that had been monitored since 1999 provided a valuable opportunity to examine the impacts of this debilitating disease on demographic parameters. Here we report on the impact of DFTD within an intensively trapped population of individually marked devils on the east coast of Tasmania. Using both traditional mark–recapture models and more recently developed multistate mark–recapture models we investigate the impact of DFTD on age- and sex-specific apparent survival rates and also examine the pattern of variation in infection rates (transition rates from healthy to diseased states) within the population in relation to disease prevalence. Finally, we employ reverse-time mark–recapture models to investigate the effect of DFTD on population growth rate.
Study area, trapping method and data collection
Tasmanian devils were trapped within a 160 km2 site comprising the entire Freycinet Peninsula (42°03′53″S, 148°17′14″E, Fig. 1) on the east coast of Tasmania. The Peninsula is dominated by rugged granite peaks rising to 600 m. The vegetation consists of dry sclerophyll forests and coastal heath, small areas of wet eucalypt forest and tea-tree swamp with Eucalyptus amygdalina, E. globulus, E. ovata, Kunzea ambigua, Melaleuca and Epacris spp., the dominant species. Land tenure is predominantly national park and Crown Land conservation area, but also includes farmland (sheep/cattle) and private rural/bush block residential land.
The site has been trapped as four contiguous trapping regions (Bicheno, 41 km2; Northern, 50 km2; Southern, 40 km2; Peninsula, 26 km2) up to four times a year since 1999. Trapping periods were typically seven nights in each region with trap numbers varying slightly (mean trap-nights per 4-week trip = 657 ± 10·7). Traps were placed at strategic sites an average of 2 km apart that were most likely to catch devils (crossroads, creek/road junctions, alongside creeks). In 2004 the fine wire-mesh cage traps were replaced by a newly designed PVC pipe trap (diameter 315 mm × length 875 mm) to reduce the risk of tooth damage and for ease of cleaning to minimize disease transmission. Traps were baited with a variety of meats, and checked daily. Accidental disease transmission was minimized by following a strict protocol, developed by veterinary practitioners involving the sterilization of all equipment and traps with Virkon™ (Antec International, Du Pont Animal Health Solutions, Sudburg, UK), an antibacterial, antiviral, antifungal, DNA denaturing solution and burning sacks and any remaining bait and faeces.
The data set for the analyses in this paper consists of capture histories from 1999 to 2006, obtained in June/July each year, as this was the only consistently sampled period every year. Data from this 4-week winter trapping period were pooled into a single capture occasion per individual. Sampling at this time of year minimized the likelihood of including dispersing juveniles in the data set (the natal dispersal phase occurs post-weaning from December through to March/April; Guiler 1970) and thus introducing bias into the survival estimates.
Identification, ageing and disease detection in trapped devils
Animals were identified via unique ear tattoos (from 1999 to 2003) or via unique microchip transponders (Allflex®, Palmerston North, New Zealand) (from 2004 on). Most individuals in the data set were of known age having been first captured as juveniles. Devils first captured as adults were aged on the basis of skeletal measurements, molar eruption, tooth wear indices and canine overeruption (distance from the dentine-enamel junction to the gum) (Pemberton 1990; M. Jones unpubl. data). This method is precise for ageing devils to 2 years of age. In this study, survival rates were estimated for two age classes only: 1 year olds (subadults) and 2+ year olds (adults). Juveniles and pouch young were not included in analyses.
As there is no pre-clinical diagnostic test for DFTD, detection of the disease is only possible by the visible presentation of tumours. All manifestations of the disease involve the appearance of facial tumours, which are distinctive, often circular and large, ulcerated lesions that occur on the head, neck or inside the mouth. Devils were thoroughly examined both externally and inside the mouth. Although devils were not initially examined with the intensity now used to check for early tumours (initial examination of the mouth was used only for ageing purposes), the disease produces such large, open lesions that even a cursory glance at a trapped animal would raise suspicion of the disease. The health status of an individual was scored on an index from 1 (no apparent DFTD) through 2 and 3 (wounds, inflammations or other irregularities present) to 4 (characteristic DFTD tumours present). Only individuals with definite cases of DFTD (those that scored 4) were included as diseased in these analyses.
Mark–recapture modelling approach
Capture–mark–recapture (CMR) methods were used to estimate age-specific survival rates and to test specific hypotheses of survival patterns and disease infection rates. The standard Cormack–Jolly–Seber (CJS) framework was employed to estimate average survival probabilities of the population as a whole (determined by the relative proportion of diseased vs. healthy individuals and their respective survival rates). Subsequently, a multistate mark–recapture framework was used to estimate ‘state-dependent’ survival probabilities for diseased vs. healthy individuals as well as to estimate transition probabilities between states. Data were analysed using the program mark (White & Burnham 1999).
CJS modelling framework
The CJS model makes the following assumptions. First, the fates of individual animals and individuals in different cohorts are independent. As devils are solitary animals they are unlikely to have correlated survival rates (Pemberton 1990). Second, marks are not lost or overlooked. Tag loss is negligible with tattoos. Microchip failure/loss has also been negligible in this study as individuals in this study site have all been genotyped with no single genotype has ever been assigned to more than one microchip number (M. Jones unpubl. data). Third, there is no mortality during the trapping period, which is instantaneous relative to the length of the survival interval. In this study, some mortality may have occurred during the trapping period, particularly in diseased animals. As each individual is simply recorded as captured or not captured during the 4-week period, any mortality would contribute to heterogeneity in capture probability. O’Brien, Robert & Tiandry (2005) found that mortality within trapping periods does not significantly bias survival estimates if recapture rates are high (> 0·2). Finally, it is assumed that survival and capture probabilities are equivalent across individuals or individuals within groups, which is normally tested with a goodness of fit, GOF, analysis. The parametric bootstrap procedure available in mark (White & Burnham 1999) was used to test the GOF of the CJS and to calculate the variance inflation factor ç (observed deviance/mean deviance from bootstrap replicates), which indicates the degree of overdispersion in the data.
Individual capture histories were grouped by sex and ‘marking group’ (either ‘marked as a subadult’ or ‘marked as an adult’). We investigated the effect of sex, marking group, time and disease on variation in recapture and apparent survival rates (where apparent survival reflects the probability of surviving and remaining on the trapping grid). We also investigated the effect of trapping effort (total trap-nights) and trap type (wire vs. pipe) on recapture rates. Disease was modelled as the population disease prevalence; the proportion of diseased individuals captured in each sampling period, set to zero for the first two intervals. The population was assumed to be disease free for the first two survival intervals (1999–2000, 2000–01) as no diseased devils were captured during any of the monitoring trips prior to June 2001 (including November 2000, January 2001, April 2001). Survival rates were modelled either as time-dependent, a linear function of disease prevalence or constant over the study period as we had no a priori belief as to how disease would impact on survival rates. To reduce the number of models in the candidate set, modelling of the survival rate of the adults marked-as-adults group was limited to either time- or prevalence-dependent, after a preliminary look at the parameter estimates for this group showed a clear trend over time. Model notation is explained in Table 1.
|Sx||Sex effect||φ, p|
|M||Marking group effect|
|s||Subadults of group 1 (marked as subadults)||φ|
|a1||Adults of group 1 (marked as subadults)||φ|
|a2||Adults of group 2 (marked as adults)||φ|
|S > D||Transitions from healthy subadults to diseased adults||ψ|
|H > D||Transitions from healthy adults to diseased adults||ψ|
|P||Disease effect (parameter varies with disease prevalence)||φ, p, ψ, λ|
|TE||Trapping effort (total trap/nights)||p|
|TT||Trap type (either wire mesh or PVC pipe)||p|
|t||Full time dependence||φ, p, ψ, λ|
|•||Constant rate||φ, p, ψ, λ|
Multistate modelling framework
For the multistate models, capture histories were grouped by sex, and captures for each individual were reassigned to one of three states: 1 = subadults (all healthy), 2 = healthy adults or 3 = diseased adults. Subadults must age, so were allowed only one time interval in stratum 1 and were forced to progress either to healthy adults or diseased adults (transitions from 1 → 1 fixed to zero and recapture rate for stratum 1 fixed to zero). Conversely, adults must remain adults (transitions from 2 → 1 and 3 → 1 fixed to zero). Healthy adults could remain healthy adults and diseased adults could remain diseased adults. Diseased adults could not become healthy adults (recovery from DFTD has never been observed) so transitions from 3 → 2 were fixed to zero and recapture rate for stratum 3 was fixed to one (to improve parameter identity issues). Our global model was a reduced parameter model due to sparseness in the data set (we only recorded 36 transitions to diseased states over five intervals). The goodness-of-fit of this reduced parameter model was tested using the median ç approach (White & Burnham 1999). Patterns of variation in apparent survival rates and transition rates between states were examined in relation to time and disease prevalence while the effect of sex was retained in recapture rate models only (based on the results of the CJS modelling above). In addition to the assumptions of the CJS model, multistate models assume that the probability of an individual making a transition between time i and i + 1 depends only on its state at time i (Williams, Conroy & Nichols 2002a). Our current knowledge of the dynamics of this disease (i.e. no observed recovery from DFTD infection and no apparent signs of immunity or resistance to infection by any individual) suggest that this assumption may be a good approximation of the real-world infection process for this disease.
Model ranking process
Ranking of models in the candidate set was based on small sample size corrected Akaike Information Criteria (AICc, Anderson & Burnham 2002). The relative likelihood of each model in a candidate set was estimated with normalized AICc weights (wi, or the index of relative plausibility) with the ratio of wi between any two models indicating the relative proportional support between them. A three-step model ranking process was employed. First, recapture rates were modelled with survival fully parameterized. Then survival and transition rates were modelled using the single best supported recapture model identified in step 1 (based on AICc weight). Finally, the best supported survival and transition rate models were each re-run with all the best supported recapture rate models identified in step 1. Robust parameter estimates were obtained through model averaging, which accounts for model selection uncertainty (Burnham & Anderson 2002).
To examine disease impacts in light of the temporal pattern of infection in the population, changes in the age of infected individuals over time were analysed using a linear regression. The difference between the age of the infected individual and the average age of all other ‘at-risk’ individuals in the population (all the healthy individuals in the population at the previous time period) was used as the dependent variable to control for concurrent changes in the average age of the whole population.
Estimation of population growth rate (λ) and population size
The impact of disease on population rate of change was assessed using reverse-time CMR methods (Pradel models) to estimate the finite rate of change of the adult population (Pradel 1996; Nichols & Hines 2002). In this approach, λ represents the realized population growth rate (the observed change in population size between two time periods) and does not assume constant, ergodic conditions or a stable age distribution. As Pradel models do not allow for age effects, these models were used with a data set consisting of all the adult captures of the individuals in our study. The goodness of fit of the global model (with time variation in all parameters) was tested using the parametric bootstrap method (Cooch & White 2001). Model selection proceeded by modelling recapture rates, then applying constraints to λ, with apparent survival retained as time-dependent in all models. Variation in λ parameters was examined in relation to time and disease prevalence or a constant rate. Model selection proceeded as outlined above with Akaike Information Criteria adjusted for overdispersion (QAICc). Population size each winter was estimated using the popan open population models in mark (White & Burnham 1999), without distinguishing between sexes. Yearly population estimates were derived from models with a constant recapture rate and time-varying survival rates and were obtained for the population as a whole and for the adult component of the population. Young of the year were not included in population estimates.
We captured 448 devils (206 males, 242 females) during the study, two-thirds of which were first captured on the study site as subadults. DFTD was first detected in June 2001 at the northernmost end of the peninsula, with diseased individuals captured sequentially southward in subsequent years (Fig. 4 in Hawkins et al. 2006). There was no difference in age structures between the four trapping regions before disease (log-linear analysis, Δ Dev = 0·380 P = 0·83). A total of 36 diseased (score of 4) individuals were captured during the study. No animal scoring a 4 ever regressed to a lower score. In this study, 5% of females bred as 1 year olds (15 of 242). It is possible that the survival of these females in this year will be more similar to that of other adults due to the cost of reproduction incurred. Classifying these individuals as adults, however, did not alter the results presented below and these individuals were retained in the subadult group.
The parametric bootstrap procedure suggested an acceptable fit of the global model and indicated no overdispersion in the data (1000 bootstrap replicates, P = 0·657; ç = 1·065). The CJS model, however, does not take into account age-specific variation in survival, which we expected in our data set. We compared the fit of the CJS model with a model that kept recapture rate as sex- and time-dependent (preliminary analyses showed no differences in recapture rates between the marking groups or between age classes) and allowed for full age × marking group × time effects in survival rates. This global model was better supported by the data (AICc weight = 0·92) and became our starting point for fitting subsequent models. A GOF test (1000 bootstrap replicates) showed no indication of lack of fit for this model or overdispersion in the data (P = 0·526; ç = 1·008).
The model selection procedure showed that constant and sex-dependent recapture rate models were equally well supported by the data (Table 2). There was little support for models in which recapture rates varied with trapping effort or the type of type used. A model that allowed recapture rates to vary with disease prevalence was also not supported by the data (Table 2). Overall recapture rate was high and fairly uniform throughout the study (0·79 ± 0·044, CI = 0·692–0·862) with males having a slightly higher recapture rate than females, though the confidence intervals overlapped (males; 0·824 95% CI = 0·66–0·92 females; 0·767 95% CI = 0·65–0·86 and CI for the logit transformed beta estimate of the effect of sex included zero, 95% CI = –0·35 to 2·07).
|1. Initial modelling of recapture rates||Sx * M(st/a1t/a2t)||Sx * t||9·46||0·00||49||68·08|
|Sx + t||2·80||0·09||43||75·49|
|2. Modelling the effect of sex||Sx * M(st/a1t/a2t)||•||20·68||0·00||36||88·73|
|Sx * M * P(sP/a1P/a2P)||16·57||0·00||14||132·58|
|Sx * M(st/a1t/a2t) [no S * M * t or S * t]||3·32||0·14||25||95·81|
|Sx * M(st/a1t/a2t) [no S * M * t, S * t, S * a]||3·36||0·14||23||100·19|
|3. Modelling the effect of marking group||M(st/a1t/a2t)||•||0·00||0·99||21||101·14|
|st/a1t = a2t||8·58||0·01||15||122·49|
|4. Modelling the effect of disease*||sP/a1t/a2P||•||0·00||0·35||11||113·45|
|5. Re-employ alternate recapture model (p•) from stage 1 with the best supported survival models from stage 4||sP/a1t/a2P||•||0·51||0·17||11||113·45|
Apparent survival at the population level
All of the best supported survival models in the candidate set included an effect of marking group and an effect of disease but no sex effect (Table 2). Survival rates of males and females did not differ with time or between age groups. In addition, a model that included an interaction between sex and disease prevalence (i.e. survival rates of males and females impacted by disease in different ways) was not supported by the data (Table 2).
There was strong support for the effect of marking group on apparent survival rates. Immediately following disease arrival the survival rate of adults marked-as-adults began to decline and continued to decline virtually to zero at a rate predicted well by disease prevalence in the population (Table 2, Fig. 2). In contrast, the survival rate of adults marked-as-subadults fluctuated over time, was not related to disease prevalence and appeared to be highly variable (Fig. 2, Table 2). This result suggests that older individuals were the first to be impacted by DFTD, because adults of the marked-as-adults group are, on average, older than the adults of the marked-as-subadults group. Analysis of the age of diseased individuals relative to the average age of healthy individuals shows a significant decrease in the age of diseased devils over time (F = 13·45, d.f. = 1, 67, P = 0·0004). Diseased individuals were initially older than the population average (95% confidence interval, 1·18–2·25 years) but after 5 years, this age difference declined (95% confidence interval, 0·10–0·69 years) (Fig. 3).
Apparent survival of subadults, meanwhile, was relatively constant throughout the study period, declining slightly in the latter time periods (Fig. 2). The three models for the apparent survival of subadults (constant over time or varying either with disease prevalence or with time) received equal support (Table 2). While this limits our ability to make inferences, it suggests that the population-level impact of DFTD on apparent survival of subadults has, to date, been comparatively less than that detected for adults.
Multistate capture–recapture models
There was no indication of lack of fit or overdispersion in the data for the global multistate model (ç = 1·007). The apparent survival of diseased adults was estimated as zero, as no diseased devil was ever recaptured. The apparent survival of both healthy adults and healthy subadults meanwhile was best explained by changes in disease prevalence (Table 3). The survival rate of both groups declined immediately following disease arrival and continued to decline as disease prevalence increased over time (Fig. 4). The relationship between subadult survival rate and disease is evidently stronger in this analysis.
|1. Initial recapture rate modelling||St/Ht/D•||Sx||S > Dt/H > Dt||0·00||0·57||29||173·03|
|2. Modelling effect of disease on survival rates||St/Ht/D•||Sx||S > Dt/H > Dt||10·15||0·00||29||175·84|
|3. Modelling effect of disease on transition rates (with the best supported survival model from stage 2)||SP/HP/D•||Sx||S > Dt/H > Dt||8·71||0·00||17||188·86|
|S > DP/H > Dt||6·10||0·02||12||196·76|
|S > Dt/H > D•||2·64||0·10||12||193·30|
|S > Dt/H > DP||2·43||0·12||12||193·10|
|S > DP/H > D•||0·21||0·36||7||201·21|
|S > DP/H > DP||0·00||0·40||7||200·99|
|SP = HP/D•||Sx||S > DP/H > DP||0·68||0·27||6||202·36|
|4. Re-employ alternate recapture rate model (p•) from stage 1 with the best supported models from stage 3||SP/HP/D•||Sx||S > DP/H > D•||0·21||0·24||7||201·21|
|SP/HP/D•||Sx||S > DP/H > DP||0·00||0·27||7||200·99|
Although the decrease in survival rate was slightly more pronounced for adults than for subadults, the two trajectories were similar and the confidence intervals of the parameter estimates overlapped. In fact, a model with these two rates identical was equally well supported by the data (shown in italics in Table 3
Хейл… - прошептала Сьюзан. - Он и есть Северная Дакота. Снова последовало молчание: Стратмор размышлял о том, что она сказала. - Следопыт? - Он, похоже, был озадачен.