Quantile equivalence for evaluating habitat management or restoration objectives

Background/Question/Methods

Equivalence testing is an approach for using common statistical procedures to provide more enlightened statements about parameter estimates in relation to effects sizes deemed to be of scientific importance rather than just zero effect.  These equivalence regions in my application are intervals of vegetation conditions deemed desirable from an ecological or conservation perspective.  Confidence intervals for regression quantile estimates are introduced as a general method for conducting quantile equivalence analyses for either equivalence or inequivalence hypotheses that involve heterogeneous data distributions where comparisons of means are of limited value.  I demonstrate the utility of the quantile equivalence framework for evaluating vegetation monitoring data obtained at the Arapaho National Wildlife Refuge in northern Colorado with respect to their Comprehensive Conservation Plan objectives for upland sagebrush and riparian/meadow habitats.  

Results/Conclusions

The objectives for upland sagebrush habitat specified that 809 of the 5,781 total ha should have shrub composition >=70% sagebrush, 20-30% canopy cover of sagebrush >=25 cm height, >=20% canopy cover of grasses, and >=10% canopy cover of forbs on average over 4-years.  The quantile equivalence analyses demonstrated that sampling variability (n = 511) interpreted under either the null hypothesis of equivalence (liberal, benefit-of-doubt) or null hypothesis of inequivalence (conservative, fail-safe) indicated this objective was easily satisfied only for the shrub composition and grass cover components (>3,000 ha).  There were 809 to 1,214 ha (conservative to liberal) with >=10% forb cover and 289 to 1,156 ha with 20-30% sagebrush cover, but only 57 to 181 ha of upland that met the combination of all four conditions in close (<30 m) spatial proximity.  Increasing the permissible spatial proximity of the forb and sagebrush cover components to 300 m increased the area satisfying all four conditions to 181 to 780 ha.  In the riparian/meadow habitat (n = 389), there were only 411 to 734 ha of the desired 2,137 to 2,305 ha that met the combination of <=10 cm duff depth, <=5% bare ground, <=75:25 grass:forb ratio, and 1 – 3 dm visual obstruction reading (VOR).