The endemic island fox inhabits the six largest of the Channel Islands (Fig. 2) and is the smallest canid in North America (average = 1.9 kg [Roemer et al. 2001c]). C Process variance of the ecological drivers models for annual survival rates. D Estimated density of non-young foxes. F Modifier function to adjust annual estimates of apparent survival rates to account for emigration. G Process variance of the global survival model.
We used analysis of deviance techniques to determine the explanatory power of ecological driver models ( Skalski et al. 1993 , Altwegg et al. 2003 ). We used random effects models in Program MARK to estimate age (i) and network (j) process-specific variance, using the global model (White 2000, White et al. 2001, Burnham and White 2002); we summed the overall global process variance for each age class, Gi, as the mean of these separate network estimates weighted by the inverse of the sample estimate variance for each network (Zhang 2006). For the purposes of the PVA model, we expressed each unspecified process variance, Uij, as a proportion of the maximum possible variance, which for a survival rate is determined by the mean, ¯S (i.e., ¯S[1 ¯S] ) (Morris and Doak 2004; see Simulation Methods: Addition of Indeterminate Process Variation).
Uncertainty, or sampling bias, was estimated for all parameters in each of the best-fitting models for reproduction and survival. Variance of the overall View estimate for each age class was estimated as the inverse of the sum of the inverses of these grid-specific variances (Zhang 2006). The two best supported models for survival probabilities using ecological drivers accounted for more than 90% of the QAICcweight (Appendix; Table 3) and provided good fits with the island- and year-specific predictions of the best categorical effects model ( Fig. 4).
52% of the variance is accounted for by year effects in the best categorical effects model and 39% of the total variation (Table 4). The estimated process variance of the best ecological variable models, C, was 0.010 for adults and 0.010 for pups. Thus, the driver models accounted for a weighted average of 52% of the process variance for adults and 34% for pups.
Notes: Coefficients are shown for the two best ecological driver models, which account for 91% of the cumulative quasi-AICc(QAICc) weight for all driver models considered. The final step in our analysis was a direct search to define the probability surface for the single parameter value of the best modifier model for each of the two apparent survival models. Survival probabilities for young and adults for each year of each simulation were initially determined using one of the two best ecological driver models for survival, given a constant number of eagle equivalents, simulated random rainfall and adult density.
Much of the weather simulation literature begins with daily or even hourly precipitation records. We also added minimal demographic stochasticity to the total annual birth, using the Poisson deviation based on the product of the number of mating females and the annual expected litter size as the annual realized rate. For the survival models, we used the MLE and approximate covariance matrix for the logistic function parameters and assumed a multivariate normal distribution for the coefficients.
For ease of illustration, the sensitivity and elasticity for the survival modifier are shown for the negative value of b2 shown in Eq.
IBPPII
However, a large component likely reflects a combination of the importance of parameters to extinction risk (as in traditional sensitivity analyses) interacting with the uncertainty in our knowledge of these parameters. However, with increasing numbers of eagles, the influence of unexplained variability on dynamics is reduced, with most populations rapidly becoming extinct regardless of the inclusion of this effect (results not shown). Despite the predicted instability in fox numbers, our simulations also suggest that these populations are relatively safe from extinction risk once a moderate population size is reached and golden eagle predation is minimized.
Both previous analyzes were applications of the program Vortex (Lacy et al. 1995), which limited the treatment of density dependence, ecological drivers and unexplained stochasticity in fox demography, and prevented any systematic treatment of parameter and model uncertainty. For example, in their models for foxes on Santa Catalina Island, Kohlmann et al. predicted that an initial population size of 80 ensured a 30-year extinction risk of 1% for the western tip of the island, while our results for the similarly sized San Miguel Island yielded a quasi-extinction risk of 6% on 30 years predict populations of 80. Taken together, integration of both ecological drivers and uncertainty in this island fox PVA not only increased the realism of the models, but also their practical utility for management.
Quantifying and incorporating the impact and uncertainty of the current primary fox threat, the golden eagle, has facilitated comparison of relative extinction risks under different eagle management scenarios (Bakker and Doak, in press). Effects of incorporating different types of uncertainty into simulations of island fox population dynamics. Indeed, in the case of the Southern California region, climate shows considerable evidence of long- and short-term correlations in precipitation patterns (Ropelewski and Halpert 1986, Latif and Barnett 1996, Dettinger et al. 1998).
Results reflect a combination of the influence of each low-level parameter as well as its degree of uncertainty. Fist unattributed process variance as a proportion of the maximum possible variance. Taxonomic and biogeographic relationships of the island fox (Urocyon littoralis) and gray fox (Urocyon cinereoargenteus) of western North America. The components of predation as revealed by a study of small mammal predation of the European pine sawfly.
Annual adult survival of the smallest auklets (Aves, Alcidae) varies depending on large-scale climatic conditions in the North Pacific. Declining survival rates in a reintroduced population of the Mauritius Kestrel: evidence for nonlinear density dependence and environmental stochasticity. The decline of the Steller sea lion in the northeast Pacific: demography, harvest or environment.
Wild boars facilitate hyperpredation by golden eagles and indirectly cause the decline of the island fox. Prepared by the Conservation Biology Institute and The Nature Conservancy for Recovery Coordination Group for the Island Fox Integrated Recovery Team.
