Inference for changes in biodiversity

We wish to formally test for changes in the taxonomic diversity of a community, especially in the presence of high latent diversity. Drawing on the meta-analysis literature, we construct a model for diversity that accounts for covariate effects as well as sampling variability. This permits inference for changes in richness with covariates and also a test for homogeneity. We argue that we can use the principles of shrinkage estimation to improve richness estimation in this nonstandard context, which is especially important given the high variance of richness estimators and the increasing abundance of community composition data. We demonstrate the methodology under simulation, in a gut microbiome study (testing for a decrease in richness with antibiotics), and in a soil microbiome study (testing for homogeneity of replicates). We believe that this is the first formal procedure for analyzing changes in species richness.