Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Recently developing hierarchical community models (HCMs) accounting for incomplete sampling are promising approaches to understand community organization. However, pros and cons of incorporating incomplete sampling in the analysis and related design issues remain unknown. In this study, we compared HCM and canonical redundancy analysis (RDA) carried out with 10 different dissimilarity coefficients to evaluate how each approach restores true community abundance data sampled with imperfect detection. We conducted simulation experiments with varying numbers of sampling sites, visits, mean detectability and mean abundance. Performance of HCM was measured by estimates of "expected" (mean) abundance ( $$ ) and realized abundance ( $$ : direct estimate of site- and species-specific abundance). We also compared HCM and different types of RDA (normal, partial, and weighted), all performed with the same ten different dissimilarity coefficients, with unequal number of visits to sampling sites. In addition, we applied the models to a virtual survey carried out on the Barro Colorado Island tree plot data for which we know true community abundance. Simulation experiments showed that $$ yielded by HCM best restored the underlying abundance of constituent species among 12 abundance estimates by HCM and RDA regardless if the sampling was equal or unequal. Mean abundance predominantly affected the performance of HCM and RDA while $$ yielded by HCM had comparable performance to percentage difference and Gower dissimilarity coefficients of RDA. Relative performance of RDA types depended on the combination of dissimilarity coefficients and the distribution of sampling effort. Best performance of $$ followed by $$ , percentage difference and Gower dissimilarity were also observed for the analysis of tree plot data, and graphical plots (triplots) based on $$ rather than $$ clearly separated the effects of two environmental covariates on the abundance of constituent species. Under our conditions of model evaluation and the method, we concluded that, in terms of assessing the environmental dependence of abundance, HCMs and RDA can have comparable performance if we can choose appropriate dissimilarity coefficients for RDA. However, since HCMs provide straightforward biological interpretations of parameter estimates and flexibility of the analysis, HCMs would be useful in many situations as well as conventional canonical ordinations.