DOI: 10.5061/dryad.98sf7m0t8
title: Demography of American black bears (Ursus americanus) in a semiarid environment

description: 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.
description: <em>Mark-Recapture study</em> 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. <em>Survival
 rates</em> 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 <em>X</em>, h0(t) is the
 baseline hazard function β1, β2, …, βp are the coefficients for the
 predictor variables <em>X1</em>, <em>X2</em>, …,
 <em>Xp</em>. 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<strong>
 </strong>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. <em>Fecundity
 rates</em> 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. <em>Matrix Transition Model and
 Analysis</em> 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
 <em>sm</em> to indicate the probability of surviving and
 transitioning to a new stage (matrix sub diagonal), and the term
 <em>ss </em>indicated the probability of surviving and staying
 in the same stage (matrix diagonal). We used <em>f</em> 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
 (<em>f</em>), growth (<em>sm</em>, transition from
 one age stage to another), and stasis (<em>ss</em>, 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).
description: # Demography of American black bears (Ursus americanus) in a semiarid
 environment
 [https://doi.org/10.5061/dryad.98sf7m0t8](https://doi.org/10.5061/dryad.98sf7m0t8) ## Description of the data and file structure ### Files and variables #### File: Age-Specific\_Survivorship.csv **Description:**  This CSV file contains data collected from a mark-recapture study during 1991 - 2019. We calculated the age-specific average survival rate for each cohort. The average survival rate of each cohort was later used in the matrix transition model as matrix elements to retrieve important demographic information about this population of North American black bears (*Ursus americanus*) found in a semiarid environment.  ##### Variables * Cohort: Yearling = 1 year to 2 years; Subadult = 2 years to 4 years; Prime-aged Adult = 4 years to 14 years; Old Adult = 15 years and older. * Sex: M = male; F = female; U = unknown * Cubs and Yearlings: NV = not visited; number = number of cubs or yearlings present in den; period (.) = no cubs or yearlings present * Enter and Exit:  Enter = first observation of individual during the year; Exit = last observation of individual during the year; the year starts on February 1st of that year to include cubs * Days from last sighting: the number of days since the individual black bear was previously observed by the researchers. * Status: the status of an individual black bear is either recorded as being alive, dead, or unknown. If the status is unknown, the individual black bear would be marked as dead. * Status Number: 1=alive; 2=dead #### File: Old\_Adult\_Fecundity.csv **Description:**  This CSV file contains data from the mark-recapture study (1991 - 2019) specific to calculating the average fecundity rate of old adults. Old adults as well as prime-aged adults are the only cohorts out of the five total cohorts that we determined are capable of reproduction in this population. Therefore, the data found in this file is specific to the reproductive output of old adults. Cubs are included in this file as they indicate the fecundity of the two cohorts. Cubs themselves are incapable of reproduction. All adults are females, no old adult males were used in the calculations. ##### Variables * Year: year when observation was made * Old Adult F w/cubs: number of old adult females with cubs present * Old Adult F w/o cubs: number of old adult females with cubs absent * Total Old Adult F: combined number of old adult females regardless of cubs * Total cubs: number of cubs * Total M cubs: number of only male cubs * Total F cubs: number of only female cubs * Total Unk cubs: number of cubs with unknown sex * Fecundity (Total cubs/Total Old Adult F): fecundity of total cubs (both males + females) divided by the total old adult females from the same year * Fecundity ([Total cubs/Total Old Adult F]*0.5): fecundity of total cubs (both males + females) divided by the total old adult females from the same year then multiplied by 0.5 for the assumption that on average, half the total cubs is 50% * Fecundity (Total F cubs/Total Old Adult F): total number of female cubs divided by the total number of old adult females from the same year * Sum or Average of rows 4 to 27: The average for each column across the entire duration of the study * period (.) = no individuals were observed during the study year. #### File: Prime-Aged\_Adult\_Fecundity.csv **Description:**  This CSV file contains data from the mark-recapture study (1991 - 2019) specific to calculating the average fecundity rate of prime-aged adults (4 to 14 years). The data found in this file is specific to the reproductive output of prime-aged adults. Cubs are included in this file as they indicate the fecundity of prime-aged adults. However, cubs themselves are incapable of reproduction. All adults are females, no prime-aged adult males were used in the calculations. ##### Variables * Year: year when observation was made * Adult F w/cubs: number of prime-aged adult females with cubs present * Adult F w/o cubs: number of prime-aged adult females with cubs absent * Total Adult F: combined number of prime-aged adult females regardless of cubs * Total cubs: number of cubs * Total M cubs: number of only male cubs * Total F cubs: number of only female cubs * Total Unk cubs: number of cubs with unknown sex * Fecundity (Total cubs/Total Adult F): fecundity of total cubs (both males + females) divided by the total prime-aged adult females from the same year * Fecundity ([Total cubs/Total Adult F]*0.5): fecundity of total cubs (both males + females) divided by the total prime-aged adult females from the same year then multiplied by 0.5 for the assumption of on average, half the total cubs is 50% * Fecundity (Total F cubs/Total Adult F): total number of female cubs divided by the total number of prime-aged adult females from the same year * Sum or Average of rows 2 to 27: The average for each column across the entire duration of the study ## Code/software For the Age-Specific Survivorship CSV file, we used the program R.