DOI: 10.5061/dryad.mkkwh71d5
title: Demographic rates of wild bison

description: 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.
description: 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]<sub>-r</sub>[t]<sub>) + <em>e,</em>
 where y</sub>[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.
description: # Demographic rates of wild bison Dataset DOI:
 [10.5061/dryad.mkkwh71d5](https://doi.org/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.