The American black bear (Ursus americanus) has one of the broadest geographic distributions of any mammalian carnivore in North America. Populations occur from high to low elevations and from mesic to arid environments, and their demographic traits have been documented in a wide variety of environments. However, the demography of American black bears in semiarid environments, which comprise a significant portion of the geographic range, is poorly documented. To fill this gap in understanding, we used data from a long-term mark-recapture study of black bears in the semiarid environment of eastern Utah, USA. Cub and yearling survival were low and adult survival was high relative to other populations. Adult life stages had the highest reproductive value, comprised the largest proportion of the population, and exhibited the highest elasticity contribution to the population growth rate (i.e., λ). Vital rates of black bears in this semiarid environment are skewed toward higher survival of adults, and lower survival of cubs compared to other populations.

Mark-Recapture study

We estimated survival rates from long-term mark-recapture data gathered as part of a 27-year study on American black bears of the East Tavaputs Plateau. During the first 12 years of the study (June to August 1991-2003) female bears were captured and radio-collared, and all bears were tagged in the ear, except for cubs and yearlings. For the entire study (1992 – 2019), collared females were visited in their dens annually during their winter hibernation to count newborn cubs and surviving yearlings. Age of individual bears was determined by 2 methods: (1) direct observation of cubs or yearlings (i.e., year of birth was known) or (2) cementum annuli analysis of a cross-section of the root of an extracted premolar (Palochak, 2004; Willey, 1974).

The data we used to derive survival and fecundity rates consisted of the ID_number, cohort (cub, yearling, subadult, prime-aged adult, and old adult), age in years, sex (female, male, unknown), number of cubs, number of yearlings, first observation of individual, last observation of individual, days from last observation, and survival status. We did not include subadult and adult male bears in the analysis.

Survival rates

To determine the average survival rates for each life stage, we used a Cox proportional hazards model in program R (Team, 2022). This model accommodates staggered entries, where individuals enter the study at different times, and censoring, where the event of interest (e.g., mortality) is not observed for all individuals due to the inability to follow-up or the study ending before the event occurs. These features allow for a more accurate representation of survival over time, even with incomplete data (Cox, 1972). The Cox model is a semi-parametric approach that examines how covariates, such as age and environmental factors, influence the risk of death at any given point in time. Unlike fully parametric models, which require defining the baseline hazard function (the risk of death when all covariates are at baseline levels), the Cox model does not require this step, making it highly flexible and suitable for diverse data and applications (Zhang, 2016). The hazard function in this context refers to the rate or likelihood of an event (e.g., death) occurring at a specific moment, given that the individual has survived up to that time.

The Cox model is expressed as follows:

h(t|X) = h0(t) exp(β1X1 + β2X2 +...+ βpXp)

where h(t|X) is the hazard function at time t given covariates X, h0(t) is the baseline hazard function β1, β2, …, βp are the coefficients for the predictor variables X1, X2, …, Xp. The model assumes proportional hazards, meaning the relative risk of death (the hazard ratio) between two groups remains constant over time (Zhang, 2016). The advantage of the Cox model is its ability to handle censored data, common in survival analysis. Censoring occurs when some individuals have not experienced mortality by the end of the study, so we only know that they survived up to that point. Moreover, the Cox model can incorporate time-dependent covariates, enabling a dynamic analysis of how risk factors influence survival over time (Therneau & Grambsch, 2000).

For our analysis, we formulated four Cox proportional hazards models as follows: 1) constant survival, 2) a model with the effect of maternal age, 3) a model with the effect of cohort, and 4) a model with the combined effect of age and cohort. We compared these models using Akaike’s Information Criterion (AIC) to identify the best fit and then evaluate the effect sizes of covariates based on the β coefficients from the top-performing model (Burnham et al., 2011; Symonds & Moussalli, 2011). When there was uncertainty in model selection, we used model averaging to estimate effect sizes and β coefficients. Each model was also checked for uninformative parameters (Arnold, 2010). We reviewed the model summaries to assess the estimated effects of covariates (constant survival, maternal age, cohort, and the combination of age and cohort) on survival outcomes.

Fecundity rates

To determine fecundity rates, we used females monitored through the use of radio-collars. All females that were ≥ four years old were counted in the breeding pool. We removed any female ≥ 25 years of age from the breeding pool (Noyce, 2010). We classified old adults as ≥ 15 years old and prime-aged adults as 4-14 years of age. We visited dens of females to observe whether they were alone or accompanied by cubs or yearlings as well as the sexes of their offspring.

At the height of the study, we had 15 prime-aged adult females, along with a few old-adult females. There was variation in the number of adult females and old-adult females throughout the study period and we had at least two old-adult females in each year for 12 years during the study.

Matrix Transition Model and Analysis

We developed a transition matrix model based on adult females and their offspring to estimate population growth and additional demographic parameters. In the model, we assumed every cub was born on January 1st and survived through the full year if they were alive through the 15th of October. We assumed density of males does not affect breeding success (Lewis et al., 2014).

We divided the population into five age-based stages: cub (0–1 year-old); yearling (1–2 years old), subadult (2–4 years old), prime-aged adult (4–14 years old), and old adult (15+). We used the term sm to indicate the probability of surviving and transitioning to a new stage (matrix sub diagonal), and the term ss indicated the probability of surviving and staying in the same stage (matrix diagonal). We used f to indicate fecundity or reproduction (matrix upper right corner; Fig. 1A, 1B).

We used the software Unified Life Models (ULM; (Legendre & Clobert, 1995) to evaluate the matrix model and to calculate population growth rate, stable age distribution, reproductive value, and sensitivity and elasticity matrices. We summed elasticity values across all stages for the three demographic processes: fecundity (f), growth (sm, transition from one age stage to another), and stasis (ss, survival without transitioning).

Our matrix transition model differed from the matrix transition model generated by Beston (2011), which used nine life stages. To ensure an accurate comparison between the two models, we combined the nine life stages from the matrix transition model in the meta-analysis (Beston, 2011) into five broader stages: cub, yearling, subadult, adult, and old adult. We selected five life stages due to the assumption that age might influence reproductive output, a pattern supported by research on other mammals (Hilderbrand et al., 2019; Nussey et al., 2008; Promislow & Harvey, 1990).