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Data and R computer code from: Summer elk calf survival in a partially migratory population

Citation

Eacker, Daniel; Berg, Jodi; Hebblewhite, Mark; Merrill, Evelyn (2022), Data and R computer code from: Summer elk calf survival in a partially migratory population, Dryad, Dataset, https://doi.org/10.5061/dryad.rfj6q57f1

Abstract

These data and computer code (written in R, https://www.r-project.org) were created to statistically evaluate a suite of intrinsic and extrinsic risk factors related to calf elk and their mothers' body condition and age. Specifically, known-fate data were collected from 94 elk calves monitored from 2013-2016 in a partially migratory elk (Cervus canadensis) population in Alberta, Canada. Along with adult female data on pregnancy status, age, and body condition, we created a time-to-event dataset that allowed us to analyze calf mortality risk in a time-to-event approach. We also estimated pooled survivorship and cause-specific mortality, as well as stratifying these metrics by migration tactic (resident vs. eastern migrant). Cox proportional hazards models were used to evaluate calf mortality risk in terms of forage biomass (kg/ha), bear predation risk (from an RSF), and other factors that varied between migration tactics. We tested for differences in a number of maternal reproductive parameters (e.g., pregnancy status) and for calf explanatory variables between migrant and resident elk segments. We also use cumulative incidence functions to estimate cause-specific mortality in this multiple carnivore system. Ultimately, we hope that this work helps wildlife managers anticipate how elk calf survival and partial migration dynamics are affected by grizzly bear predation, and our study builds on a long-term partial migration study at the Ya Ha Tinda Ranch in Alberta, Canada. 

Methods

We used a continuous time-to-event approach on a daily mortality timescale to assess factors influencing mortality risk for elk calves over a 90-day period with birth as the origin. We right-censored calves with failed tags (n = 1) and calves that survived past the 90-day period in their year of birth. We used a generalized Kaplan-Meier (KM) estimator to provide estimates of overall calf survival during the 90-day post-calving period. We stratified estimates by sex, year, and migration tactic, then used log-rank tests to test for significant differences in survival among these groups. We report 95% confidence intervals (CI) for KM survival estimates on the complementary log-log scale, which provides better estimates of uncertainty near the boundaries of 0 or 1. We used cumulative incidence functions to estimate cause-specific pooled mortality rates as well as stratified by migration tactic. We assessed factors influencing mortality risk using the Andersen-Gill formulation of the Cox proportional hazards (PH) model because it accommodated time-dependent risk covariates. We evaluated a suite of nested candidate models that included both intrinsic and extrinsic variables. Further, because of the importance of understanding differences in migratory tactics, we conducted Welch’s two-sample t-tests to evaluate differences in terms of adult female elk age and body condition, and calf sex and birth mass; we used a nonparametric Kolmogorov-Smirnov test to investigate phenological differences in calf birth dates. We also tested for differences between migratory tactics across extrinsic variables using a Welch’s two-sample t-test for human disturbance metrics and linear mixed-effects (LME) models with random intercepts to account for correlated observations within calves for forage biomass and predation risk. In summary, grizzly bear predation risk was considered a time-dependent covariate in our mortality risk analysis similar to forage biomass that changed with variation in plant phenology, while other covariates were static through time.

We standardized (by subtracting the mean and dividing by 2 SDs) all continuous predictor variables before analysis to allow relative coefficient comparisons among categorical and continuous predictor variables. We also screened variables for collinearity and avoided including variables in the same model that had a correlation coefficient of > |0.5|. We further screened out clearly unimportant variables (i.e., P > 0.05) before conducting model selection. As a conservative measure, we used Bayesian Information Criterion (BIC) for model selection. We also used model averaging, given the complexity of the full model relative to our sample size, and reported unconditional standard errors and naturally averaged model coefficients (i.e., non-shrinkage estimates). We present only models in 95% of the cumulative weight. We used Monte Carlo sampling to predict survivorship and the 95% uncertainty interval from model-averaged coefficient estimates and the Breslow estimate of the cumulative baseline hazard function.  

For brevity, we provide the time-to-event dataset and analysis code rather than include all of the code, GIS, etc. used to estimate calf-rearing areas and extract risk covariates for each individual. Rather, we provide the data and all code to reproduce all results presented in the manuscript, but we do include some data processing in the analysis code. The code is organized as a series of 4 pdf documents that were created in Rstudio using Rmarkdown. The analysis code is broken into the following sections that mirror the results in the manuscript: I) summary of adult female reproductive parameters and other summary statistics and tests, II) survivorship estimates from Kaplan-Meier along with log-rank tests, III) calf cause-specific morality estimation, and IV) Cox proportional hazards for calf mortality risk analysis.

Funding

National Science Foundation, Award: 1556248

National Science Foundation, Award: 2038704