DOI: 10.5061/dryad.rfj6q57f1
title: Data and R computer code from: Summer elk calf survival in a partially migratory population

description: 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. 
description: 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 &gt; |0.5|. We further screened out clearly unimportant
 variables (i.e., P &gt; 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.