Appendix C. Sensitivity analysis.
Relative cub detection probability
For the default parameter set (see main document), we assumed that the age distribution of bears detected with scat surveys (for genetic mark-recapture) was identical to the true age distribution of the population. However, it is conceivable that some age classes are less likely to be detected than others. Specifically, feces of cubs may have a lower detection probability than the scat of older bears. If that were the case, using the cub-augmented age distribution (Appendix A in this supplement) would result in an underestimation of the proportion of breeding-age females and consequently the annual number of reproductions. To explore the effects of violating the assumption of equal detection probability of cubs, we ran the model with several different versions of the original age source sample, simulating relative detection probabilities of cubs of 0, 0.25, 0.5, 0.75, and 1 (default). We found that the model was relatively robust to changes in the detection probability of cubs (relative to other age classes); even in the unlikely event that cubs were completely missed during genetic capture occasions (resulting in an older age structure of detected bears), the estimated number of reproductions increases by less than 30% (Fig. C1).
Home range size
For the simulation of home range configuration and home range extension beyond Norway’s boundaries, we used 35 kernel home ranges from 16 bears with cubs monitored in Sweden (Fig. 6 in the main document). This approach was based on the assumption that the sample of 35 home ranges is representative of home ranges for females with cubs in Norway. However, if actual home ranges in Norway are smaller than those in the sample, their extension beyond Norway’s borders is overestimated and hence the number of reproductions attributable to Norway is underestimated. Conversely, if actual home ranges are larger, they may extend even further outside of Norway and consequently using the sample home range set in the model would overestimate the annual number of reproductions. We explored the effect of violations of this assumption by re-running the model with smaller and larger versions of the 35 sample home ranges. We found that as home range sizes increased, the predicted number of reproductions did decline as predicted (Fig. C1). For example, if home ranges of females with cubs in Norway are assumed to be 1.5 times larger than those in the original simulation set, the estimated number of annual reproductions attributable to Norway would decrease by about 15%.
Probability of reproducing
The age- and location-specific probability of producing cubs is implemented during simulations through the logistic regression model, which has been fit to data from female bears monitored in Sweden (see main document). This is based on the probability of observing a given female with cubs at least once during the year. Because observations on nearly all bears begin in the spring, this is equivalent to the probability of observing a female with cubs shortly after den emergence. Nonetheless, it is possible that some reproductions are missed, for example if a female loses her litter sometime between den emergence and the first observation by the Scandinavian Brown Bear Research Project (SBBRP) in that year. We tested the effect that changing the probability of being observed with cubs had on the model-estimated number of reproductions. This was accomplished by running sets of simulations where the probability of reproducing (based on the original fitted GLM, see main document) is multiplied by a factor of 0.75 (i.e. a probability of reproducing that is 75% of the one predicted from the SBBRP’s data), 1 (default), 1.25 and 1.5 (i.e. the probability of reproducing is 1.5 times higher than predicted by the SBBRP). As expected, increasing the probability of reproducing leads to higher estimates of annual reproductions. For example, a 25% increase in the probability of producing cubs will increase the estimated number of reproductions by a similar proportion (Fig. C1). However, even a 25% increase seems unrealistically high, as it would require that current monitoring methods by the SBBRP in Sweden miss that a female has emerged from the den with cubs 25% of the time, even though she is observed. This could occur either by failing to observe a litter of cubs that is present or because the female lost her litter before the first observation in a given year was made. We note that the SBBRP’s monitoring methods are likely to detect almost all instances of den emergence with cubs by monitored females bears, even if the litter is lost before the first observation of the female; females that could have been reproducing, but are not observed with cubs in the spring, are captured and checked for physical signs that they have been nursing young.
FIG. C1. Sensitivity of the model-predicted number of annual brown bear reproductions attributable to Norway in 2009 (a) to changes in the probability of detecting brown bear cubs-of-the-year (cubs) relative to other ages with DNA monitoring, (b) to changes in the size of the set of 35 home ranges used during simulations (an example home range is shown above each value set to help visualize differences in relative size), and (c) to changes in the probability of reproducing (applying a multiplier to age- and region-specific probabilities of reproducing from the GLM described in the main document). The default value for each parameter is indicated with a black triangle. Twenty simulations with 100 cycles each were run for each parameter value. Black horizontal bars indicate the mean of the predicted number of reproductions and gray vertical bars represent the 95% CI around the mean prediction.