Demographic rates of wild bison
Data files
Oct 15, 2025 version files 43.70 KB
-
birth_rate.csv
12.50 KB
-
female_age_specific_surv.csv
17.48 KB
-
population_trend.csv
2.29 KB
-
R_code.Rmd
9.34 KB
-
README.md
2.09 KB
Abstract
Demographic data were collected on wild bison in Yellowstone National Park to estimate population growth rate, annual survival probability, and fertility. Separate data files exist for each rate or probability. The data for estimating population growth rate include annual counts and management removals. The data for estimating survival and fertility are from adult female bison fit with radio collars. These data are applicable for estimating vital rates of plains bison in North America. Data were collected by the National Park Service.
Dataset DOI: 10.5061/dryad.mkkwh71d5
Description of the data and file structure
Data files included to complete analyses using Program R.
Files and variables
File: birth_rate.csv
Description:
Variables
- id: animal ID
- year: year
- age: age
- calf: A "1" indicates a calf was observed in close association with the dam including nursing. A "0" indicates a calf was never observed with the dam during the calving period. Animals were located at least weekly during the calving period. Estimates likely include some level of neonate loss.
File: female_age_specific_surv.csv
Description: Data file of annual survival observations of adult female bison. Each row of data includes the animal ID, year, age, and survival observation. The year followed the same structure as used for modeling population growth rate, beginning on June 1 of the previous year and ending on May 31 of the indicated year.
Variables
- id: animal ID
- year: year
- age: animal age
- surv: observation of survival. A "1" indicates that the animals was alive at the end of the survival interval. A "0" indicates that an animal was dead. An animal that was removed through management actions during an interval was indicated as a "1".
File: population_trend.csv
Description: Data file of annual counts and removals of bison in Yellowstone National Park. These data were used to estimate the population growth rate. The population undergoes a single birth pulse during May-June. The population was modeled after this birth pulse each year. Winter removals occurred after the birth pulse but prior to the next model update the following year.
Variables
- summer: summer of the biological year during which counting occurred
- winter: winter of the biological year during which removals occurred
- count: number of bison counted
- removal: number of bison removed
File: R_code.Rmd
Description: R markdown file used to run models and estimate parameters.
Counts and Managment Removals
Annual counts were completed during 1901-2024. Counts completed by winter surveys in the initial decades and aerial counts starting in the 1960s. Aerial counts generally occurred in summer. Management removals occurred in winter between counts. Removals were accounted for in estimating population growth rate.
We fit the data to a discrete time model of population growth: y~[t+1]~ = r (y~[t]-r[t]) + e, where y[t]~ is the count during year* t*, r~[t]~ is the removals occurring after count, and* e* is model uncertainty. Bayesian inference and Monte Carlo integration were used to estimate model parameters.
Age-specific survival
Age-specific annual survival probability was estimate from 166 female bison fit with radio collars during 1996-2015. Female bison were a minimum of two years of age at the time of collaring.
We fit the data to binomial model with survival probability given by a linear combination of age using Bayesian inference and Monte Carlo integration.
Age-specific fertility
Age-specific annual fertility rate was estimate from 151 female bison fit with radio collars during 1996-2015. Female bison were a minimum of three years of age at the time of calving. It is rare for a bison to calve at less than three years of age in the Yellowstone population.
We fit the data to binomial model with survival probability given by a linear combination of age, including a quadratic term, using Bayesian inference and Monte Carlo integration.