Estimating plant abundance using inflated beta distributions: Applied learnings from a lichen-caribou ecosystem.

Quantifying abundance and distribution of plant species can be difficult because data are often inflated with zero values due to rarity or absence from many ecosystems. Terrestrial fruticose lichens (Cladonia and Cetraria spp.) occupy a narrow ecological niche and have been linked to the diets of declining caribou and reindeer populations (Rangifer tarandus) across their global distribution, and conditions related to their abundance and distribution are not well understood. We attempted to measure effects related to the occupancy and abundance of terrestrial fruticose lichens by sampling and simultaneously modeling two discrete conditions: absence and abundance. We sampled the proportion cover of terrestrial lichens at 438 vegetation plots, including 98 plots having zero lichens. A zero-inflated beta regression model was employed to simultaneously estimate both the absence and the proportion cover of terrestrial fruticose lichens using fine resolution satellite imagery and light detection and ranging (LiDAR) derived covariates. The probability of lichen absence significantly increased with shallower groundwater, taller vegetation, and increased Sphagnum moss cover. Vegetation productivity, Sphagnum moss cover, and seasonal changes in photosynthetic capacity were negatively related to the abundances of terrestrial lichens. Inflated beta regression reliably estimated the abundance of terrestrial lichens (R2 = .74) which was interpolated on a map at fine resolution across a caribou range to support ecological conservation and reclamation. Results demonstrate that sampling for and simultaneously estimating both occupancy and abundance offer a powerful approach to improve statistical estimation and expand ecological inference in an applied setting. Learnings are broadly applicable to studying species that are rare, occupy narrow niches, or where the response variable is a proportion value containing zero or one, which is typical of vegetation cover data.