DOI: 10.5061/dryad.2z34tmpnj
title: Sampling bias exaggerates a textbook example of a trophic cascade

description: Understanding trophic cascades in terrestrial wildlife communities is a
 major challenge because these systems are difficult to sample properly. We
 show how a tradition of nonrandom sampling has confounded this
 understanding in a textbook system (Yellowstone National Park) where
 carnivore [Canis lupus (wolf)] recovery is associated with a trophic
 cascade involving changes in herbivore [Cervus canadensis (elk)] behavior
 and density that promote plant regeneration. Long-term data indicate a
 practice of sampling only the tallest young plants overestimated
 regeneration of overstory aspen (Populus tremuloides) by a factor of 3-8
 compared to random sampling because it favored plants taller than the
 preferred browsing height of elk and overlooked non-regenerating aspen
 stands. Random sampling described a trophic cascade, but it was weaker
 than the one that nonrandom sampling described. Our findings highlight the
 critical importance of basic sampling principles (e.g., randomization) for
 achieving an accurate understanding of trophic cascades in terrestrial
 wildlife systems.
description: We measured browsing and height of young aspen (≥ 1 year-old) in
 113 plots distributed randomly across the study area (Fig. 1). Each plot
 was a 1 × 20 m belt transect located randomly within an aspen stand that
 was itself randomly selected from an inventory of stands with respect to
 high and low wolf-use areas (Ripple et al. 2001). The inventory was a list
 of 992 grid cells (240 × 360 m) that contained at least one stand
 (Appendix S1). A “stand” was a group of tree-size aspen (&gt;10 cm
 diameter at breast height) in which each tree was ≤ 30 m from every other
 tree. One hundred and thirteen grid cells were randomly selected from the
 inventory (~11% of 992 cells), one stand was randomly selected from each
 cell, and one plot was randomly established in each stand. Each plot
 likely represented a genetically-independent sample (Appendix
 S1). We measured aspen at the end of the growing season
 (late July to September), focusing on plants ≤ 600 cm tall, which we
 termed “young aspen.” For each stand, we measured every young aspen within
 a plot (‘random stems’) and each of the five tallest young aspen within
 the stand (‘5T stems’). For all young aspen, we measured browsing status
 (browsed or unbrowsed) and height of the leader (tallest) stem. A leader
 was ‘browsed’ if its growth from the previous growing season had been
 eaten, which we identified by a sharp, pruned edge at the base of the
 current year’s growth. Most plots were measured nearly every year since
 1999 (Ripple et al. 2001) and our analysis focused on data from 10 years
 (2007-2014, 2016-2017) in which sampled stands included measurements of
 random and 5T stems. Elk were likely the primary ungulate species browsing
 young aspen in our plots during the study (Fig. S1).
description: This dataset has 18,792 records, including 18,623 records of
 individual young aspen (plants &gt; 1 year-old & &lt; 600
 cm) and 169 records of plots with no young aspen ("zero plots").
 Records of individual young aspen (N = 18,623) were used in the majority
 of analyses (Fig. 2-5a,b), including generalized linear mixed models
 (GLMMs) that tested how the effect of year on browsing, height, and
 recruitment of stems differed by sampling method. This dataset was also
 used to model the effect of stem height on browsing to estimate the
 preferred browse height (PBH) and browse escape height (BEH). The full
 dataset that includes plots with no young aspen was only used to calculate
 the percentage of plots and stands each year with median heights greater
 than 200 (Fig. 5c) or 300 cm (Fig. 5d).   The dataframe
 has the following 6 columns:    Plot:
 individual identifier for each of 113 plots distributed randomly across
 the study area. Each plot was a 1 × 20 m belt transect located randomly
 within an aspen stand  Year: year in which aspen was
 sampled Tree: individual identifier for each stem
 within a plot Browse: denotes the browsing status
 (browsed = 1,unbrowsed = 0) of the leader (tallest) stem. A leader was
 ‘browsed’ if its growth from the previous growing season had been
 eaten Height: height (cm) of the leader stem of each
 individual aspen Type: sampling method. Every young
 aspen within a plot is a "random" stem, and each of the five
 tallest young aspen within the stand is a "5T" stem.
 Plots that had no young aspen in a given year have a
 value of "NA" for browse and height.
description: # Sampling bias exaggerates a textbook example of a trophic cascade
 [https://doi.org/10.5061/dryad.2z34tmpnj](https://doi.org/10.5061/dryad.2z34tmpnj) This repository contains the data and code necessary to replicate the analysis published in: Brice, E.M., Larsen, E.J. & MacNulty, D.R. (2021) Sampling bias exaggerates a textbook example of a trophic cascade. Ecology Letters. The repository was updated in November 2023 to include the data and code to create Figure 1 of "Nonrandom sampling measures the occurrence but not the strength of a textbook trophic cascade," which is a Technical Note in response to Painter et al.'s 2023 comment on "Sampling bias exaggerates a textbook example of a trophic cascade" (Brice et al., Ecology Letters, 2022). ## Description of the data and file structure The CSV file “Aspen\_Data.csv” contains data used for analysis of aspen browsing and stem height in northern Yellowstone National Park from 2007-2017. The dataset has 18,792 records, including 18,623 records of individual young aspen (plants ≥ 1 year-old & ≤ 600 cm) and 169 records of plots with no young aspen (“zero plots”). The dataframe has the following 6 columns: 1. Plot: individual identifier for each of 113 plots distributed randomly across the study area. Each plot was a 1 × 20 m belt transect located randomly within an aspen stand 2. Year: year in which aspen was sampled 3. Tree: individual identifier for each stem within a plot 4. Browse: denotes the browsing status (browsed = 1,unbrowsed = 0) of the leader (tallest) stem. A leader was ‘browsed’ if its growth from the previous growing season had been eaten 5. Height: height (cm) of the leader stem of each individual aspen 6. Type: sampling method. Every young aspen within a plot is a “random” stem, and each of the five tallest young aspen within the stand is a “5T” stem. Plots that had no young aspen in a given year have a value of "NA" for browse and height. This dataset was used in Brice et al. 2022. For MacNulty et al. 2023 (Technical comment on Brice et al. 2022), we used the "CAG\_data.csv" file, which has 14,095 records of individual young aspen (plants ≥ 1 year-old & ≤ 600 cm) measured from 2007-2017. The dataframe has the following columns: 1. Plot: individual identifier for each of 113 plots distributed randomly across the study area. Each plot was a 1 × 20 m belt transect located randomly within an aspen stand 2. Year: year in which aspen was sampled 3. Height: height (cm) of the leader stem of each individual aspen 4. Browse: denotes the browsing status (browsed = 1,unbrowsed = 0) of the leader (tallest) stem. A leader was ‘browsed’ if its growth from the previous growing season had been eaten 5. CAG: current annual growth of the leader stem (cm) ## Code/Software All of our analysis was conducted in R, and the code for Brice et al. 2022 has been included as an R Markdown file and PDF version. These files contain all of the code and instruction necessary to completely replicate our results and figures. There is an additional R Markdown file, titled "MacNultyEtAl\_EcoLetters\_2023\_RCode.RMD," which has the code to replicate the model and figure included in our Technical Note (MacNulty et al. 2023).