Detecting the influence of rare stressors on rare species in Yosemite National Park using a novel stratified permutation test.

J R Matchett,Heather C Mckenny,Matthew L Brooks,Steven M Ostoja,Roland A Knapp,Eric L Berlow,Philip B Stark,Lucas N Joppa,William T Langford

doi:10.1038/srep10702

Abstract

Statistical models often use observational data to predict phenomena; however, interpreting model terms to understand their influence can be problematic. This issue poses a challenge in species conservation where setting priorities requires estimating influences of potential stressors using observational data. We present a novel approach for inferring influence of a rare stressor on a rare species by blending predictive models with nonparametric permutation tests. We illustrate the approach with two case studies involving rare amphibians in Yosemite National Park, USA. The endangered frog, Rana sierrae, is known to be negatively impacted by non-native fish, while the threatened toad, Anaxyrus canorus, is potentially affected by packstock. Both stressors and amphibians are rare, occurring in ~10% of potential habitat patches. We first predict amphibian occupancy with a statistical model that includes all predictors but the stressor to stratify potential habitat by predicted suitability. A stratified permutation test then evaluates the association between stressor and amphibian, all else equal. Our approach confirms the known negative relationship between fish and R. sierrae, but finds no evidence of a negative relationship between current packstock use and A. canorus breeding. Our statistical approach has potential broad application for deriving understanding (not just prediction) from observational data.

Highlights

Control it; and e) Double rarity greatly increases the sample size needed to detect a relationship, when one exists
We present a novel approach using observational data to infer whether a rare stressor affects a rare response variable by blending predictive models with nonparametric permutation tests
We used a previously-published predictive model[2] of A. canorus breeding occupancy to first stratify meadows by predicted suitability for occupancy, and a nonparametric permutation test to evaluate the question: All else equal, does packstock use negatively affect A. canorus breeding occupancy in meadows across the entire Park? We find that the chance of observing these patterns of recent packstock use and A. canorus breeding occupancy across thousands of Yosemite National Park (YNP) meadows would be extremely small if the relationship between packstock and A. canorus occupancy were negative

Summary

Introduction

Control it; and e) Double rarity greatly increases the sample size needed to detect a relationship, when one exists. It is easier to use observational data for prediction than for understanding the relationship between a potential stressor and a response variable. When using observational data for understanding rather than prediction, a standard approach to control for potential confounding factors is to fit a parametric model of the response based on all the predictor variables (including the stressor of interest), to assess whether the coefficient of that stimulus in the fitted model is statistically significant. We present a novel approach using observational data to infer whether a rare stressor affects a rare response variable by blending predictive models with nonparametric permutation tests. The strong negative influence of non-native trout on R. sierrae in lakes has been well documented, including in YNP, using both observational data[3,9,11,12] and experiments[13,14]. The court found in favour of the plaintiffs in part because the USFS had “failed to take a hard look” at potential negative impacts of packstock use on A. canorus before authorising special use permits for the commercial packstock operations[24]

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Results

Conclusion