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

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.

A network extension of species occupancy models in a patchy environment applied to the Yosemite Toad (Anaxyrus canorus).

A central challenge of conservation biology is using limited data to predict rare species occurrence and identify conservation areas that play a disproportionate role in regional persistence. Where species occupy discrete patches in a landscape, such predictions require data about environmental quality of individual patches and the connectivity among high quality patches. We present a novel extension to species occupancy modeling that blends traditional predictions of individual patch environmental quality with network analysis to estimate connectivity characteristics using limited survey data. We demonstrate this approach using environmental and geospatial attributes to predict observed occupancy patterns of the Yosemite toad (Anaxyrus (= Bufo) canorus) across >2,500 meadows in Yosemite National Park (USA). A. canorus, a Federal Proposed Species, breeds in shallow water associated with meadows. Our generalized linear model (GLM) accurately predicted ~84% of true presence-absence data on a subset of data withheld for testing. The predicted environmental quality of each meadow was iteratively 'boosted' by the quality of neighbors within dispersal distance. We used this park-wide meadow connectivity network to estimate the relative influence of an individual Meadow's 'environmental quality' versus its 'network quality' to predict: a) clusters of high quality breeding meadows potentially linked by dispersal, b) breeding meadows with high environmental quality that are isolated from other such meadows, c) breeding meadows with lower environmental quality where long-term persistence may critically depend on the network neighborhood, and d) breeding meadows with the biggest impact on park-wide breeding patterns. Combined with targeted data on dispersal, genetics, disease, and other potential stressors, these results can guide designation of core conservation areas for A. canorus in Yosemite National Park.