Availability of AFS.

The three scenarios considered within this group of simulations showed different patterns associated with the effects of poisoning on survival (Table 2). When survival of adults decreases because of poisoning and survival of young increases due to their use of AFS (scenarios 1 and 2, Fig. 5), population trajectories decreased over years (scenario 1: λ = 0.961±0.002; scenario 2: λ = 0.932±0.002). However, extinction probabilities were not equal in the first and the second scenarios. When the impact of poisoning was stochastic with no clear trend over time (scenario 1 Table 2), probabilities of extinction were nil, although some trajectories attained the quasi-extinction threshold (scenario 1 Fig. 5). Conversely, ARIMA analysis indicated that the way in which poisoning impacted our bearded vulture population (i.e., the colour of the environmental noise) depended on the age-class considered. For instance, the decrease of survival among birds older than 4y old during 1986–2007 (a = 0.264, b = 0.241) showed a long-term temporal autocorrelation (i.e., red noise), whereas for birds up to 4y old (a = −0.018, b = 0.250) survival exhibited a short-term temporal autocorrelation (i.e., blue noise). This temporal autocorrelation in the impact of poisoning, the most realistic situation (scenario 2 Table 2), increased the extinction probabilities of the whole population to its maximum value (p_e(t = 50) = 1, mean extinction time: 10.2 years±0.28, see scenario 2 Fig. 5). Note that for these two poison-impacted scenarios the mean trajectories were quite similar, except for the largest variability expected in population trajectories when the impact of poisoning was temporally correlated (scenario 2 Fig. 5).

Increments in the survival rate of adult birds up to that expected when poisoning was near nil (at the beginning of the time series, scenario 3 Table 2) combined with a high survival rate of young (maintained through AFS) predicted a marked increment in the number of breeding territories (λ = 1.014±0.001; scenario 3 Fig. 5).

No availability of AFS.

In the two final scenarios we considered population trajectories under different pressures of poisoning but no availability of AFS. Populations suffering from negative effects of poisoning on survival rates but not managed with AFS (scenario 4 Table 2) showed a lower population growth rate and a slightly higher probability of extinction in the time horizon of 50y than its most conservative counterpart (scenario 1: λ = 0.961±0.002, p_e(t = 50) = 0; scenario 4: λ = 0.932±0.002, p_e(t = 50) = 0.05; Fig. 5). However, in a scenario of no poisoning and no AFS (scenario 5 Table 2), population numbers are somewhat lower although still rather stable (scenario 5: λ = 1.000±0.001; scenario 3: λ = 1.016±0.001; Fig. 5).

Population monitoring.

The European range of the bearded vultures covers the Pyrenees, Alps, Corsica and Crete. Contrary to the other regions, the Southern face of the Pyrenees has been intensively monitored within the framework of the Species' Recovery Plan in the Autonomous Communities of the Basque Country, Navarra, Aragón and Catalonia. Here, programs to monitor population trends, breeding parameters, and survival rates (including a specific capture-mark-resighting sub-programme) have been performed. Although birds move several kilometres during the dispersal period, the bulk of the non-breeding fraction is largely attached to the AFS just opened within this range [17]. Regrettably, while the Northern face of the Pyrenees (the French population) has also been well monitored through the years, no capture-mark-resighting programme has been performed. Thus, our study focused on the Spanish population alone (no breeding territories scattered outside the Pyrenees have been recorded in Spain). However, as this is the largest population, and where non-breeding birds aggregate, results may be representative of the entire Pyrenean core.

During 1985 to 2007, from early November to August, all known potential territories were visited (2–3 visits/breeding season) to search for signs of occupancy (territorial and/or courtship activity, nest arrangement/building), and to record reproductive parameters. We considered a territory as occupied when a pair was present breeding and/or showing territorial behaviour. We considered a controlled pair or territory as successfully bred when a fledgling was observed during the last part of the breeding period (see [34] for further details).

Capture and resighting.

During 1987 to 2005, 95 birds of different ages (see below for details) were captured, marked with darvic bands and wing tags and safely released in the study area (for details on capture and marking procedures, see [35]). Each individual was provided with two wing tags with the same alphanumeric code (one per wing) to reduce the probability of being non-identifiable after losing one mark.

From 1988 to 2006, marked individuals were searched for by visiting AFS located within the study area (mainly large AFS) and territories [17]. Only resighting carried out during the first period of each year (from early January to late April) were taken into account to meet the requisite of capture-recapture modelling of having longer non-recapturing seasons than capturing seasons (e.g. [36]–[37]).

Loss of wing tags.

Since one of the key assumptions of CMR models is that marks are never lost, we explored such potential bias in our study. From the 21 tagged birds found dead during the study period, only two (at 5 and 6y old) had lost one of the two wing marks while the rest (19 individuals) retained the two marks. Age distribution of birds found dead was not biased (median = 6y old, range = 1–16). Using birds seen for the last time (i.e. never seen again, n = 26), 5 still retained one mark at older ages (range = 11–20y old) while the others (21) retained the two marks (range = 8–17y old). Finally, it is worth noting that 6 birds whose wing bands were lost were identified at AFS and breeding territories through their engraved rings by using telescopes. We thus concluded that the potential bias of mark lost in our study should be relatively low.

Resighting probabilities.

Birds were grouped by their age at release as fledglings (54%) or by their plumage characteristics, into 7 additional age-classes (from 1y old to older than 6y old [31]). Thus, the age of each group was fitted in all models to avoid extra parameters for estimation. Several modelling approaches were possible with the data set available, since some radio-tracked birds were found dead while others were recorded alive. However, the existence of several age-groups at release, the low number of recoveries and the high resighting probabilities (see Results below) advised us to use simple uni-state, live-resighting models, which are also more appropriate for testing some biological hypotheses such as temporal variation in survival.

Basic assumptions of CMR models were assessed through Goodness-of-Fit Test of the Cormack-Jolly-Seber (CJS) model [φ_t, p_t], using only birds released as fledglings (n = 51 individuals). Although the global test did not show a deviation from the CJS model (, P = 0.862), the TEST2.CT was statistically significant (N(0,1) signed statistic for trap-dependence = −3.1376, p = 0.0017), indicating a trap-happiness phenomenon. Due to the low number of birds released each year, most of the contingency tables had frequencies that were too low and their chi-square tests were not always reliable.

Trap-happiness was likely because some young birds visit the AFS more frequently during their first years of life than others, generating heterogeneity in their resighting probabilities. Moreover, there is a general pattern of reduction in the use of AFS with age, mainly from 6y old and older when the probability of territory acquisition increases [17], [32]. Thus, to test for such age effects on resighting probabilities, we progressively eliminated the resights performed at different ages (from 1y old to 6y old) from the original data set to run GOF tests for each reduced data set. The GOF test for birds of 5y old and older was the only one with a TEST2.CT that was not significant (N(0,1) signed statistic for trap-dependence = −1.8942, P = 0.0582), supporting previous predictions. We thus began with a general model [φ_t, p_5a*t], with no inflation factor. We then progressively reduced the number of age classes in resighting probabilities for testing for a simpler age-structure in this parameter, ending with a model with no age effects (see Results). All models were fitted using E-Surge software, which allows for the testing of individual covariates [38].

Survival probabilities.

Age was introduced to test for variations in survival with this individual covariate, with no specific trend or following a trend, as it has been found in other demographic studies (e.g. juveniles showing lower survival than adults, see [21]). Thus, linear and quadratic trends at the logit scale (noted by A and A2 in models, respectively) for variations in age in survival and resighting probabilities were tested. Many models testing potential effects of age (not necessarily showing a trend as in the previous models) grouped the younger age-classes (i.e. birds up to 4y old, noted as 1_4 in models) while the older age-classes were kept separate (i.e. birds of 5y old onwards, noted as 5 in models). Additional groupings also based on ecological knowledge of the species were further tested, namely: birds up to 5y old (noted as 1–5 in models), birds from 6 to 8y old, and individuals being >8y old. Roughly, these categories correspond to immature (non-adult) birds, non-breeding adults and territorial breeding adults (see [32]), respectively. This allowed us to avoid over-parameterized models with high numbers of age-classes, a problem that did not occur when age was introduced as a trend.

After assessing changes in survival associated with age, we tested whether the survival of bearded vultures showed a temporal decrease (i.e., time as a linear trend in the logit scale, noted as T in models) that reflect increments in poisoning during the last two decades (see above). According to our previous prediction of reduced use of AFS as the bird ages, we tested whether this temporal effect of poisoning was stronger for adult (>5y old birds) than for young individuals. Thus, additive effects of age-class (young vs. adult) and time were tested in both survival and resighting probabilities. To test the actual positive effect of AFS on individual survival, we obtained an individual rate of use of AFS corrected by age, survival and resighting probabilities. Thus, we calculated the proportion of times each individual was recorded at AFS out of the total number of censuses performed annually. These values, standardized by subtracting the mean value expected for each age class and then dividing the difference by the corresponding standard deviation, were averaged across years to calculate an index suitable for inclusion in models as an individual covariate, noted by AFS in models. Notation and selection of models followed common procedures in capture-recapture studies (e.g. [36]–[37]).

Model building and assumptions.

We built a predictive stochastic age-structured population model (only for females) to explore the functional dependence of λ (the population growth rate) on the demographic rates of the study population (see Fig. 6). This kind of perturbation analysis allows us to identify potential management targets because variations in demographic parameters with high sensitivity (or elasticity) produce large changes in λ. We also built a retrospective stochastic population model (also using the observed variability in vital rates, see [24]) to detect whether parameters used in the predictive model were reliable and described with certainty the behaviour of the population. Here, we used the same structure and number of replications as that described for the predictive model (see below), but run over the period for which data were collected (20 years), setting the initial population size to that estimated in 1985 (i.e. 37 breeding females).

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Figure 6. Life cycle of the bearded vulture study population with post-breeding census.

The nodes show the different age-classes considered in the models: J for juveniles and S_i for survival of each age-class i; F: fecundity (reproductive success); sr: sex ratio (0.5); P_i: breeding probability of each age-class i. The model is only for females.

https://doi.org/10.1371/journal.pone.0004084.g006

Parameter estimations.

Details on the effects of density-dependence on fecundity are well known [14] and can be introduced accurately in our model. Additional field data suggest that other parameters might also be affected by density-dependence in recent times, such as the proportion of breeders, which has decreased with time. Conversely, density-dependence was not considered in the recruitment curve, because of the scarce information available on this parameter (see below), or in survival rates because the relationship found was mainly attributed to the increase in poisoning instead of as a result of increments in population size (see Results). Here, we did not set any carrying capacity in the study system because 1) a large proportion of foraging resources are of human origin (AFS) and this can be modified in the future due to recent warnings on its usefulness [14], [39], and 2) it is difficult to assess how many breeding habitats are still available in the Pyrenees and neighbouring mountain ranges [16]. Our main interest from population modelling was thus to identify the most sensitive parameters of λ (particularly whether population projections predict high extinction probabilities), and not to predict how many pairs the study area can hold.

Although age-dependent recruitment proportion was unknown, field data showed that females bred for the first time between 6 and 12y of age [32]. Thus, our population model included 12 age-classes, assuming that full recruitment occurred at this age. Since recruitment in long-lived birds increases progressively with age and we know that up to 40% of sexually mature birds are not breeding [32], we distributed this proportion among our breeding age-classes (from 6 to 11y old) as follows: 20% in the first age-class (less likely breeders) and the remaining 20% equally among the other age-classes up to 11y (more likely breeders). This proportion of sexually mature, non-breeding birds was likely to be density-dependent, since saturation of habitat could increase the proportion of non-breeders (i.e., floater density, e.g. [40] to fit a density-dependent, non-linear function to the proportion of breeders, we assumed that (as recorded with fecundity, see below) it followed a negative exponential curve with a value of 0.4 for maximum density (at the end of the series) and 0 for minimum density (at the beginning of the series).

Estimates of fecundity (mean number of fledglings per pair = 0.52, SD = 0.5 with a binomial distribution because successful breeders raised a single chick) were obtained from 1,028 breeding events recorded in the study area during 1972–2002. Fecundity of bearded vultures was density-dependent, changing negatively not only with density of breeders but with total density [14]. From the field data, we fitted a negative exponential function (which fitted equally well as a logarithmic curve) rather than a linear function because: (a) it was more biologically plausible [41] and (b) the model fit better. Some data suggest that fecundity increases with experience in this species [34], but no information exists on fecundity variation with age. Thus, we did not correct fecundity by age in our age-structured model even though it likely increased with this individual covariate.

We introduced both environmental and demographic stochasticity in our model. The first takes into account temporal variability affecting demographic parameters annually, while the latter was introduced because of the small size (N) of the study population which could affect the binomial distribution, B(N, p_i), of all vital rates i (see above). Since sample variance of survival estimates (i.e. σ², a measure of error variation and covariance in φ_i) was likely high due to the low number of individuals marked and resighted, we estimated only process variance (using MARK software [42]) to introduce it in simulations as a more reliable measure of environmental stochasticity.

Population trajectories.

We ran Monte Carlo simulations using 500 replications of each combination of parameter values (see below, Table 2) to obtain potential population trajectories under different management scenarios (ULM software [43]). Extinction risk was projected on a time horizon of 50 years, which is commonly accepted as a long-term persistence period for bearded vultures following IUCN criteria for threatened species (ca. 3 generation times of the species [44]). Mean value of all trajectories together with its standard error was given for each year of the simulation. Thus, the probability of extinction at time t, p_e(t = 50), was estimated as the ratio of the number of trajectories that have gone extinct after 50 years out of the total number of trajectories. The initial population size was set using the last census of the species in the Spanish Pyrenees (2007, 90 breeding females), and assuming that these females were equally distributed among the 7 breeding age-classes. We then added 60 non-breeding adult females distributed in the above-cited way among the same age-classes. Finally, 100 immature females were also added and distributed among the first 5 age-classes because 40% of the total population was estimated to be immature (authors unpubl. data).

Availability of artificial feeding sites.

We first envisaged that poisoning continues affecting survival rates of vultures. Thus, we used the survival rates of pre-adult and adult birds estimated by our best selected model (scenario 1 in Table 2), which were lower than expected likely due to the effect of poisoning. The variance (once eliminated the variance from sampling error) around the mean value of the survival estimate was introduced in the model to reflect the environmental stochasticity of the poison impact, with no temporal autocorrelation (white environmental noise, e.g. [45]).

Most environmental fluctuations contain strong correlations at a multitude of scales [46]. In this case, the actual temporal dynamics of poisoning (mainly in the long-term) is unknown owing to the lack of field data available. However, strong eruptions of illegal poisoning associated with human-predator-prey conflicts are expected (author unpubl. data). Thus, we performed a second set of simulations (scenario 2, Table 2) considering that the temporal dynamics of poisoning are dominated by fluctuations, both short and long-term, with positive temporal autocorrelation (coloured environmental noise, e.g. [45]). Here, we used the actual temporal variability of survival probabilities φ (see Results) to estimate the coefficients (mean a and variance b) of the function φ_(t+1) = φ_(t)·a +rand·b where t was the time (year), φ was the survival probabilities estimated in the previous CMR analysis and rand was a uniform distribution with range [0, 1]. The coefficient a has distribution ranges of [0<a<1] and [−1<a<0] for red (long-term) and blue (short-term) noise, respectively. Coefficients of this function were estimated by time series analysis using ARIMA (model AR(1)).

Finally, we simulated the behaviour of our population under effective management actions reducing the impact of poisoning (scenario 3 in Table 2), using actual adult survival estimates obtained in our study area but without poison effects (see Results).

No availability of AFS.

This group of simulations allowed us to disentangle the actual usefulness of AFS to mitigate the effects of illegal poison on population persistence. First, we ran retrospective and prospective simulations of the population dynamics of bearded vultures in a scenario of poisoning and no availability of AFS (scenario 4 Table 2) to 1) assess the effectiveness of AFS given their observed trend during the last 20 years, and 2) evaluate the potential effectiveness of AFS on the expected trajectories of the study population. For these purposes, we estimated survival rates of young by fixing the beta parameter in the likelihood function estimated for the covariate “use of AFS” to 0 (see results). Survival estimates for adults was that estimated through our best CMR model (Table 1). Then, we simulated an alternative scenario in which there were no poison effects and AFS were not available. Here, survival estimates of adults were those obtained at the beginning of the study period (see Results) while survival of young was obtained as in the previous scenario of no AFS (scenario 5 Table 2).