Study of biological communities subject to imperfect detection: Bias and precision of community N-mixture abundance models in small-sample situations

Community N-mixture abundance models for replicated counts provide a powerful and novel framework for drawing inferences related to species abundance within communities subject to imperfect detection. To assess the performance of these models, and to compare them to related community occupancy models in situations with marginal information, we used simulation to examine the effects of mean abundance (λ¯">(λ¯: 0.1, 0.5, 1, 5), detection probability (p¯">(p¯: 0.1, 0.2, 0.5), and number of sampling sites (n _site : 10, 20, 40) and visits (n _visit : 2, 3, 4) on the bias and precision of species-level parameters (mean abundance and covariate effect) and a community-level parameter (species richness). Bias and imprecision of estimates decreased when any of the four variables (λ¯">(λ¯, p¯">p¯, n _site , n _visit ) increased. Detection probability p¯">p¯ was most important for the estimates of mean abundance, while λ¯">λ¯ was most influential for covariate effect and species richness estimates. For all parameters, increasing n site was more beneficial than increasing n _visit . Minimal conditions for obtaining adequate performance of community abundance models were n site  ≥ 20, p¯">p¯ ≥ 0.2, and λ¯">λ¯ ≥ 0.5. At lower abundance, the performance of community abundance and community occupancy models as species richness estimators were comparable. We then used additive partitioning analysis to reveal that raw species counts can overestimate β diversity both of species richness and the Shannon index, while community abundance models yielded better estimates. Community N-mixture abundance models thus have great potential for use with community ecology or conservation applications provided that replicated counts are available.