Estimating wildlife populations and their dynamics using multiple data sources and a hierarchical integrated model: the case of California's black bears
Data files
Jul 01, 2025 version files 22.68 KB
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bear_IPM_data.RDS
3.96 KB
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bear_model_JAGS.R
10.64 KB
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README.md
8.08 KB
Abstract
Accurate monitoring of wildlife populations is critical to their effective conservation and management. For populations that are actively harvested, age-at-harvest (AAH) data provide a valuable source of information about their age and sex structure. Bayesian state space models have been developed to harness this AAH data along with prior knowledge of species’ ecology to estimate population sizes, trends, and underlying demographic rates.
We extended these state-space models further to integrate abundance models using camera trapping data to both inform initial population size and extrapolate to areas without AAH data. Additionally, we formulated a hierarchical integrated model that models the data and populations separately by region while still sharing information across regions to account for socio-ecological differences and informing adaptive local management.
We applied our state-space model to estimate the population size and dynamics of black bears within the hunted areas of California over the last decade and used the integrated camera trapping-based model to extrapolate to the non-hunted areas of California to estimate a total statewide average population size over the last five years of 59,851 individuals (90% credible interval: 49,412 – 70,611).
Data included here include the regional AAH data by year, prior distributions used to fit the model, regional camera trapping and local spatial capture-recapture population estimates and associated standard errors, and R jags code to run the model.
Estimating wildlife populations and their dynamics using multiple data sources and a hierarchical integrated model: the case of California's black bears
Dataset DOI: 10.5061/dryad.9p8cz8wvp
Description of the data and file structure
Data included in this repository include processed black bear harvest data, camera trap (Royle-Nichols) model results, and local spatial capture-recapture model results. The data are formatted for use in a hierarchical integrated model to estimate black bear population size and dynamics across California from 2013-2024.
Files and variables
File: bear_IPM_data.RDS
Description: This RDS file contains the data needed to run the JAGS model in R.
The RDS file contains:
Y: a constant defining the number of years included in the data and model,
A: a constant defining the number of age classes in the data and model,
hr.idx: a matrix with sex = 2 rows and age classes = 10 columns indexing the log hazard ratios for modeling survival of the different sex and age classes. Female groups are specified in the first row and male groups are specified in the second row. Age classes above 3 are grouped together for each sex (hence all females above age class 3 falling in group 4, and all males above age class 3 falling in group 8),
covid: a binary variable capturing 2020 Covid-lockdown effects on hunting taking the value of 0 except for 2020, which takes the value 1,
pr.cll.HS: mean values for the prior normal distribution on the complementary log-log scale for hunting season survival (female, male),
pr.cll.NS: mean value for the prior normal distribution on the complementary log-log scale for non-hunting season survival,
mu.cll.cubSA: mean value for the prior normal distribution on the complementary log-log scale for cub survival from 0-6 months,
mu.cll.cubSB: mean value for the prior normal distribution on the complementary log-log scale for cub survival from 6-18 months,
area_weights: unused in current model, but contains relative areas of each local SCR study area (summing to 1) which could weight their influence,
pr.cll.Report: mean value for the prior normal distribution on the complementary log-log scale for harvest reporting rate
tau.cll.Report: precision (1/variance) value for the prior normal distribution on the complementary log-log scale for harvest reporting rate
tau.LHR: precision (1/variance) of the normal distribution of log hazard ratios for modeling survival of the different sex and age classes,
tau.mu.cll.HS: precision (1/variance) of the prior normal distribution describing the long-term average hunting season survival
tau.mu.cll.NS: precision (1/variance) of the prior normal distribution describing non-hunting season survival
tau.cll.cubSA: precision (1/variance) value for the prior normal distribution on the complementary log-log scale for cub survival from 0-6 months,
tau.cll.cubSB: precision (1/variance) value for the prior normal distribution on the complementary log-log scale for cub survival from 6-18 months,
hs.gama: shape parameter of prior gamma distribution describing annual variation (precision) of hunting season survival,
hs.gamb: rate parameter of prior gamma distribution describing annual variation (precision) of hunting season survival,
ns.gama: shape parameter of prior gamma distribution describing annual variation (precision) of non-hunting season survival,
ns.gamb: rate parameter of prior gamma distribution describing annual variation (precision) of non-hunting season survival,
init.pop.base: relic parameter from non-hierarchical model of black bear populations (unused),
init.pop.scale: relic parameter from non-hierarchical model of black bear populations (unused),
priorCovid: mean of the prior normal distribution describing the effect of Covid lockdowns on hunting season survival,
tauCovid: precision (1/variance) of the prior normal distribution describing the effect of Covid lockdowns on hunting season survival,
priorLS (8 objects): these values represent the gamma shape and rate parameters for prior distributions describing the litter sizes of females in the four different age class groups separated in the model,
priorPR (8 objects): these values represent the two beta shape parameters for prior distributions describing the annual probability of pregnancy of females in the four different age class groups separated in the model,
priorSPa: first shape parameter for the prior beta distribution describing the starting sex ratio in the population,
priorSPb: second shape parameter for the prior beta distribution describing the starting sex ratio in the population,
mu.B.cor: relic parameter from previously published model (unused),
sd.B.cor: relic parameter from previously published model (unused),
Parameters containing ‘low’ or ‘high’: these truncate the above described prior distributions and parameters between these specified low and high values,
sim_initial_pop_structure_f_prop: these numbers represent proportions for each female age class to be filled with the starting population size,
sim_initial_pop_structure_m_prop: these values represent proportions for each male age class to be filled with the starting population size,
lSCR_means: these values represent the mean estimated density (bears/km2) of each local spatial capture-recapture study used to inform the starting population size in the model,
lSCR_prec: these values represent the precision (1/variance) in predicted density (converted from standard error, in bears/km2) of each local spatial capture-recapture study used to inform the starting population size in the model,
RN_means: these values represent the mean predicted abundance (bears/site) from the fitted Royle-Nichols model within each local spatial capture-recapture study area used to inform the starting population size in the model and extrapolate population estimates to non-hunted areas,
RN_prec: these values represent the precision (1/variance) in predicted abundance (bears/site) from the fitted Royle-Nichols model within each local spatial capture-recapture study area used to inform the starting population size in the model and extrapolate population estimates to non-hunted areas,
RN_mean_preds_BCRs: these values represent the mean predicted abundance across entire hunted BCRs from the fitted Royle-Nichols model,
RN_prec_preds_BCR: these values represent the precision (1/variance) associated with the hunted BCR-wide abundance predictions from the fitted Royle-Nichols model,
Mean and precision of abundance predictions in the non-hunted BCRs (8 values): these 8 parameters (starting with either ‘mean’ or ‘prec’) represent the mean and precision for predicted abundances across the 4 non-hunted BCRs,
O_BMR_arr: 3-dimensional array containing the number of total bears harvested and reported across Y years (rows), A age classes (columns), and 5 hunted BCRs (slices),
A1_BMR_arr: 3-dimensional array containing the female age-at-harvest data across Y years (rows), A age classes (columns), and 5 hunted BCRs (slices),
A2_BMR_arr: 3-dimensional array containing the male age-at-harvest data across Y years (rows), A age classes (columns), and 5 hunted BCRs (slices),
O_BMR_aged: 3-dimensional array containing the number of total bears harvested, reported, and aged across Y years (rows), A age classes (columns), and 5 hunted BCRs (slices).
In addition to these data and prior distribution definitions, there is a list of parameters for tracking in the MCMCs for inference
File: bear_model_JAGS.R
Description: This R file contains the code needed to run the JAGS model in R.
Code/software
The software R 4.4.0 or newer and JAGS 4.3.1 are needed to view the data and run the model. The most recent updated versions of the R packages 'rjags' and 'jagsUI' are recommended to load in R to work with the data and run the model.
Access information
Other publicly accessible locations of the data:
- N/A
Data was derived from the following sources:
- N/A