Repository:
https://github.com/egage/EVMP

Introduction

This document contains code for running ancillary analyses of Elk Vegetation Management Plan (EVMP) data collected through the 2018 sampling season. Analyses are limited to macroplot data from plots established in riparian areas in areas of the elk winter range and Kawuneeche Valley (i.e., “willow” plots, see Zeigenfuss et al. 2011) and is provided as a supplement to the NPS NRR Report “Monitoring of Vegetation Response to Elk Population and Habitat Management in Rocky Mountain National Park - Analysis of Elk Vegetation Management Plan monitoring Data: 2008–2018”. For information on sampling and the broader analysis and interpretation of the results, refer to this report, past analyses [@zeigenfuss2015], and the original EVMP monitoring plan [@zeigenfuss2011].

Methods

Weather and ungulate population data were obtained and explored for use as covariates in analyses of EVMP data. Weather data were obtained from were obtained from the National Climate Data Center for Estes Park (Estes Park 3 SSE, CO US, #52761). Snow depth data were acquired from the Bear Lake Snotel Site (Site #322) located southwest of the core elk winter range. Climate data were analyzed for reference to EVMP data and used to examine the relationship of weather and elk population to EVMP data. Elk population estimates produced by RMNP and outside collaborators (T. Hobbs and H. Abouelezz, unpublished data), produced using a combination of aerial and ground surveys, were used to create annual estimates of the winter population size of elk. A linear model estimated using OLS was used to predict median winter elk as a function of annual precipitation data.

Results

Climate

Estes Park

Annual Precipitation

Daily Maximum Temperature

Bear Lake Snotel

Annual SWE and Accumulated Precipitation

Elk population

T. Hobbs unpublished data

Ordinary least squares regressions of median winter elk numbers (Hobbs unpublished) and accumulated annual precipitation

Modeled elk population estimates (T. Hobbs unpublished data) are negatively correlated with annual precipitation at both the Estes Park and Bear Lake climate stations. The model had moderate explanatory power (R2’ median = 0.24, 909% CI [1.07e-05, 0.45], adj. R2 = 0.07). The model’s intercept, corresponding to elk = 0 and precipitation = 0, is at 1291.28 (90% CI [788.17, 1818.43], 0.04% in ROPE). Precipitation in the model had a probability of 97.56% of being negative and was medium in size (median = -0.79, 100% in ROPE, std. median = -0.51). The algorithm successfully converged (R^ = 1.001) and estimates were stable (ESS = 1846). A similar trend but weaker correlation occurred with Bear Lake precipitation data.

A linear model (estimated using OLS) predicting median elk with annual precipitation explains a significant and substantial proportion of variance (R2 = 0.39, F(1, 13) = 8.16, p = 0.013, adj. R2 = 0.34). The model’s intercept is at 1145 (95% CI [741.20, 1548.84], t(13) = 6.13, p < .001). Within the model, the effect of precipitation is significantly negative (beta = -1.19, 95% CI [-2.09, -0.29], t(13) = -2.86, p < .05; Std. beta = -0.62, 95% CI [-1.09, -0.15]).

Estes Park OLS

lm: elk ~ Estes Park annual prcp
term estimate std_error statistic p_value lower_ci upper_ci
intercept 1145.019 186.920 6.126 0.000 741.203 1548.836
ppt_mm_ann -1.192 0.417 -2.856 0.013 -2.093 -0.290

Bear Lake OLS

A linear model (estimated using OLS) predicting median elk with annual precipitation explains a significant and substantial proportion of variance (R2 = 0.39, F(1, 13) = 8.16, p = 0.013, adj. R2 = 0.34). The model’s intercept is at 1145 (95% CI [741.20, 1548.84], t(13) = 6.13, p < .001). Within the model, the effect of precipitation is significantly negative (beta = -1.19, 95% CI [-2.09, -0.29], t(13) = -2.86, p < .05; Std. beta = -0.62, 95% CI [-1.09, -0.15]). A linear model (estimated using OLS) predicting median elk with annual precipitation explains a significant and substantial proportion of variance (R2 = 0.27, F(1, 13) = 4.73, p = 0.049, adj. R2 = 0.21). The model’s intercept is at 1296 (95% CI [624.48, 1969.37], t(13) = 4.17, p < .01). Within the model, the effect of precipitation is significantly negative (beta = -0.79, 95% CI [-1.58, -5.07e-03], t(13) = -2.17, p < .05; Std. beta = -0.52, 95% CI [-1.03, -3.30e-03]).

lm: elk ~ Bear Lk annual prcp
term estimate std.error statistic p.value
(Intercept) 1296.9234881 311.265186 4.166619 0.001106343
ppt_accum_mm_max -0.7931842 0.364804 -2.174275 0.048743772

Plots of median elk vs precipitation

Bayesian generalized linear model of median winter elk numbers (Hobbs unpublished) and accumulated annual precipitation at the Estes Park climate station.

A Bayesian linear model estimated using MCMC sampling predict median elk with accumulated annual precipitation had moderate explanatory power (R2 = 0.24, 89% CI [1.07e-05, 0.45], adj. R2 = 0.07). The model’s intercept, corresponding to precipitation = 0, is at 1291 (95% CI [619.77, 1912.85]). Within this model the effect of precipitation (Median = -0.79, 0.95% CI [-1.54, -0.01]) had a 97.56% probability of being negative (< 0), but a low probability of being significant or large. The estimation successfully converged (Rhat = 1.001) and the indices are reliable (ESS = 1846).

Session info

R version 4.0.3 (2020-10-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19041)
Run date: 2021 March 18

Package Information
Package Version Reference
dataMaid 1.4.0 Petersen AH, Ekstrøm CT (2019). "dataMaid: Your Assistant forDocumenting Supervised Data Quality Screening in R." _Journal ofStatistical Software_, *90*(6), 1-38. doi: 10.18637/jss.v090.i06 (URL:https://doi.org/10.18637/jss.v090.i06).
dplyr 1.0.4 Hadley Wickham, Romain François, Lionel Henry and Kirill Müller (2021). dplyr: A Grammar of Data Manipulation. R package version 1.0.4. https://CRAN.R-project.org/package=dplyr
DT 0.17 Yihui Xie, Joe Cheng and Xianying Tan (2021). DT: A Wrapper of the JavaScript Library 'DataTables'. R package version 0.17. https://CRAN.R-project.org/package=DT
forcats 0.5.1 Hadley Wickham (2021). forcats: Tools for Working with Categorical Variables (Factors). R package version 0.5.1. https://CRAN.R-project.org/package=forcats
fs 1.5.0 Jim Hester and Hadley Wickham (2020). fs: Cross-Platform File System Operations Based on 'libuv'. R package version 1.5.0. https://CRAN.R-project.org/package=fs
GGally 2.1.1 Barret Schloerke, Di Cook, Joseph Larmarange, Francois Briatte, Moritz Marbach, Edwin Thoen, Amos Elberg and Jason Crowley (2021). GGally: Extension to 'ggplot2'. R package version 2.1.1. https://CRAN.R-project.org/package=GGally
ggcorrplot 0.1.3 Alboukadel Kassambara (2019). ggcorrplot: Visualization of a Correlation Matrix using 'ggplot2'. R package version 0.1.3. https://CRAN.R-project.org/package=ggcorrplot
ggplot2 3.3.3 H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.
ggstance 0.3.5 Lionel Henry, Hadley Wickham and Winston Chang (2020). ggstance: Horizontal 'ggplot2' Components. R package version 0.3.5. https://CRAN.R-project.org/package=ggstance
gt 0.2.2 Richard Iannone, Joe Cheng and Barret Schloerke (2020). gt: Easily Create Presentation-Ready Display Tables. R package version 0.2.2. https://CRAN.R-project.org/package=gt
janitor 2.1.0 Sam Firke (2021). janitor: Simple Tools for Examining and Cleaning Dirty Data. R package version 2.1.0. https://CRAN.R-project.org/package=janitor
knitr 1.31 Yihui Xie (2021). knitr: A General-Purpose Package for Dynamic Report Generation in R. R package version 1.31.
lubridate 1.7.9.2 Garrett Grolemund, Hadley Wickham (2011). Dates and Times Made Easy with lubridate. Journal of Statistical Software, 40(3), 1-25. URL https://www.jstatsoft.org/v40/i03/.
mapview 2.9.0 Tim Appelhans, Florian Detsch, Christoph Reudenbach and Stefan Woellauer (2020). mapview: Interactive Viewing of Spatial Data in R. R package version 2.9.0. https://github.com/r-spatial/mapview
moderndive 0.5.1 Albert Y. Kim and Chester Ismay (2021). moderndive: Tidyverse-Friendly Introductory Linear Regression. R package version 0.5.1. https://CRAN.R-project.org/package=moderndive
purrr 0.3.4 Lionel Henry and Hadley Wickham (2020). purrr: Functional Programming Tools. R package version 0.3.4. https://CRAN.R-project.org/package=purrr
R 4.0.3 R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
Rcpp 1.0.6 Dirk Eddelbuettel and Romain Francois (2011). Rcpp: Seamless R and C++ Integration. Journal of Statistical Software, 40(8), 1-18. URL https://www.jstatsoft.org/v40/i08/.
readr 1.4.0 Hadley Wickham and Jim Hester (2020). readr: Read Rectangular Text Data. R package version 1.4.0. https://CRAN.R-project.org/package=readr
readxl 1.3.1 Hadley Wickham and Jennifer Bryan (2019). readxl: Read Excel Files. R package version 1.3.1. https://CRAN.R-project.org/package=readxl
rstanarm 2.21.1 Goodrich B, Gabry J, Ali I & Brilleman S. (2020). rstanarm: Bayesian applied regression modeling via Stan. R package version 2.21.1 https://mc-stan.org/rstanarm.
sf 0.9.7 Pebesma, E., 2018. Simple Features for R: Standardized Support for Spatial Vector Data. The R Journal 10 (1), 439-446, https://doi.org/10.32614/RJ-2018-009
skimr 2.1.2 Elin Waring, Michael Quinn, Amelia McNamara, Eduardo Arino de la Rubia, Hao Zhu and Shannon Ellis (2020). skimr: Compact and Flexible Summaries of Data. R package version 2.1.2. https://CRAN.R-project.org/package=skimr
stringr 1.4.0 Hadley Wickham (2019). stringr: Simple, Consistent Wrappers for Common String Operations. R package version 1.4.0. https://CRAN.R-project.org/package=stringr
tibble 3.0.6 Kirill Müller and Hadley Wickham (2021). tibble: Simple Data Frames. R package version 3.0.6. https://CRAN.R-project.org/package=tibble
tidyr 1.1.2 Hadley Wickham (2020). tidyr: Tidy Messy Data. R package version 1.1.2. https://CRAN.R-project.org/package=tidyr
tidyverse 1.3.0 Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686
viridis 0.5.1 Simon Garnier (2018). viridis: Default Color Maps from 'matplotlib'. R package version 0.5.1. https://CRAN.R-project.org/package=viridis
viridisLite 0.3.0 Simon Garnier (2018). viridisLite: Default Color Maps from 'matplotlib' (Lite Version). R package version 0.3.0. https://CRAN.R-project.org/package=viridisLite
visdat 0.5.3 Tierney N (2017). "visdat: Visualising Whole Data Frames." _JOSS_,*2*(16), 355. doi: 10.21105/joss.00355 (URL:https://doi.org/10.21105/joss.00355), <URL:http://dx.doi.org/10.21105/joss.00355>.