Modeling avian abundance from replicated counts using binomial mixture models

Abundance estimation in ecology is usually accomplished by capture–recapture, removal, or distance sampling methods. These may be hard to implement at large spatial scales. In contrast, binomial mixture models enable abundance estimation without individual identification, based simply on temporally and spatially replicated counts. Here, we evaluate mixture models using data from the national breeding bird monitoring program in Switzerland, where some 250 1-km² quadrats are surveyed using the territory mapping method three times during each breeding season. We chose eight species with contrasting distribution (wide–narrow), abundance (high–low), and detectability (easy–difficult). Abundance was modeled as a random effect with a Poisson or negative binomial distribution, with mean affected by forest cover, elevation, and route length. Detectability was a logit-linear function of survey date, survey date-by-elevation, and sampling effort (time per transect unit). Resulting covariate effects and parameter estimates were consistent with expectations. Detectability per territory (for three surveys) ranged from 0.66 to 0.94 (mean 0.84) for easy species, and from 0.16 to 0.83 (mean 0.53) for difficult species, depended on survey effort for two easy and all four difficult species, and changed seasonally for three easy and three difficult species. Abundance was positively related to route length in three high-abundance and one low-abundance (one easy and three difficult) species, and increased with forest cover in five forest species, decreased for two nonforest species, and was unaffected for a generalist species. Abundance estimates under the most parsimonious mixture models were between 1.1 and 8.9 (median 1.8) times greater than estimates based on territory mapping; hence, three surveys were insufficient to detect all territories for each species. We conclude that binomial mixture models are an important new approach for estimating abundance corrected for detectability when only repeated-count data are available. Future developments envisioned include estimation of trend, occupancy, and total regional abundance.