DOI: 10.5061/dryad.9p8cz8wvp
title: Estimating wildlife populations and their dynamics using multiple data sources and a hierarchical integrated model: the case of California's black bears

description: 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.
description: **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](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