Breeding/adult population estimates
In this study, breeders and adults were defined as bears that produced ≥1 offspring between 1998 and 2020, and bears that had the potential ability to breed, respectively. For females, adults included both breeders and bears ≥4 years old (the youngest age of the first mating in this population, reported by Shimozuru, et al. (2017). For males, the youngest age of the first mating in this population was 6 years of age (Shimozuru, et al. , 2020), whereas males potentially reach sexual maturation at 3.5 years of age in the Scandinavian population (Zedrosser, et al. , 2007). In the current analysis, bears ≥4 years old and sexually experienced males (indicated by a parentage analysis) were included in the adult population, which allowed us to compare the breeding/adult population size between sexes. In this study, we estimated the breeding/adult population size as of 2019, the first year of the intensive genetic sampling period. This was because 2019 was expected to be the year when the highest number of breeders/adults would be identified as alive. For example, females identified with cubs for the first time in 2020 could be counted as breeders in 2019. Likewise, all females and males identified in 2019 and/or 2020 were confirmed as breeders if their offspring were sampled during 1998–2020. In addition to breeding experience, some bears were confirmed to be ≥4 years old based on their appearance when identified in an ongoing bear monitoring survey that has been continuously conducted in recent decades in the area between Rusha and Utoro (Shimozuru, et al. , 2020; Shimozuru, et al. , 2017). Some bears were confirmed to be ≥4 years based on the year of first genetic identification, or on the year when their parent was dead (e.g., if the father was dead in 2014, his offspring could potentially be born in 2015, suggesting they were ≥4 years old as of 2019).
First, we calculated the minimum number of breeders, including the existing bears and hypothetical parents. The former included bears identified in 2019 and/or 2020 that were confirmed as sexually experienced based on a parentage analysis. The later included hypothetical parents generated by the COLONY software, which were estimated to produce cubs during 2018–2020. For example, if a 1-year-old bear, killed in 2019, was not assigned a mother from the list of candidate mothers, it was reasonable to assume that his/her mother, although not genetically identified, gave birth in 2018 and was alive until the timing of mother–offspring separation in 2019. Similarly, if a cub-of-the-year, sampled in 2020, was not assigned a father from the list of candidate fathers, it could be assumed that his/her father was alive and mated with the mother in 2019.
Second, we estimated the maximum breeding population size by a pedigree reconstruction approach, based on the simple assumption that the number of breeders would not exceed the total number of parents that produced bears identified in 2019–2020. We estimated the number of breeders that produced bears identified during 2019–2020, but whose mother and/or father (genetically identified during 1998–2018) were not sampled during 2019–2020, or whose mother and/or father were missing from the list of existing candidates sampled during 1998–2020. One of the problems of this approach is that the assumption that each missing parent constitutes a new individual would most likely cause an overestimation (Spitzer, et al. , 2016). In this study, COLONY allowed hypothetical parents to produce multiple offspring, which reduced the likelihood of overestimation due to this issue. Another problem is that it is difficult to know how many of the parents that were identified as alive until 2018, but not sampled during 2019–2020, were still alive as of 2019. To account for mortality among those individuals, we calculated the period between the year of the last identification and 2019, and multiplied it by the survival rate to estimate his/her survival probability. Because the adult survival rate was not investigated in this population, we applied the median value of the survival rates (0.94 for females and 0.89 for males) among the other brown bear populations (0.89–0.96 for females, 0.62–0.94 for males; reviewed in Schwartz 2003). For example, a mother identified as alive in 2017 was counted as 0.88 of an individual (i.e., 0.94 × 0.94). In addition, we assumed that adult bears who had not been sampled for the last 5 years (2016–2020) in the area where successive surveys were conducted were no longer alive. Continuous genetic samples from hair-traps, biopsy darts, and fecal collection have been conducted in the area between Rusha and Utoro (Figure 2; Shimozuru, et al. , 2020; Shimozuru, et al. , 2017), enabling us to assume that those individuals were less likely to be alive.
A similar but more serious concern, reported by Creel and Rosenblatt (2013), was that there is no way to ascertain how many of the hypothetical parents are actually alive. To avoid overestimation, we made several assumptions. First, females ≥30 years old and males ≥28 years old were not counted as breeding individuals. This assumption was based on previous studies regarding reproductive senescence in brown bears (Schwartz, et al. , 2003; Van Daele, et al. , 2001; Zedrosser, et al. , 2007). Upon pedigree reconstruction, the age of each hypothetical parent was estimated based on the age of the oldest offspring and generation intervals. The generation interval between mother and offspring was set at 7.3 years based on our bear monitoring survey in the Rusha area. We calculated the first age when females gave birth to cubs that survived the first year (for eight females = 5–9 years, average of 7.25; Shimozuru, et al. , 2017), and used it as the minimum interval between generations. This value was more realistic than their primiparity age (for 15 females = 5–6 years, average of 5.3; Shimozuru, et al. , 2017), which was more likely to induce overestimation in the current analysis. The generation intervals between father and offspring, i.e., the first age when males sired cubs that survived the first year, was not well investigated in this population. Males become sexually mature at 3.5 years old (Zedrosser, et al. , 2007), but it is rare to gain a reproductive opportunity until physical maturation at around 9–11 years of age (Moriwaki, et al. , 2018; Shimozuru, et al. , 2020; Shirane, et al. , 2020). Therefore, we set the same value (7.3 years) as for females, based on the assumption that the generation intervals between father and offspring were not less than those between mother and offspring. The second assumption was that more than four matrilineal generations do not exist at the same time, which was also based on our bear monitoring survey conducted in the Rusha area. In this area, four generations (offspring, mother, grandmother, and great-grandmother) exist at the same time, but a great-great-grandmother has never been identified (Shimozuru, et al. , 2017). Similarly, our previous pedigree reconstruction conducted in the same population revealed that more than three paternal generations (offspring-father-grandfather) do not exist at the same time (Shimozuru, et al. , 2019). Hypothetical mothers and fathers that correspond to great-great-grandmother and great-grandfather, respectively, were assumed to be dead, and were not counted as breeding individuals in the current analysis. Finally, we calculated the minimum and maximum number of adults, by adding the number of bears confirmed to be ≥4 years old in 2019 (based on the criteria described above) to the minimum and maximum number of breeders.