Microbial Diversity Estimation and Hill Number Calculation Using the Hierarchical Pitman-Yor Process

The human microbiome comprises the microorganisms that inhabit the various locales of the human body and plays a vital role in human health. The composition of a microbial population is often quantified through measures of species diversity, which summarize the number of species along with their relative abundances into a single value. In a finite microbiome sample, there will be species missing from the target population, which will affect the diversity estimates.

We employ a model based on the hierarchical Pitman-Yor (HPY) process to model the species abundance distributions over multiple populations. The model parameters are estimated using a Gibbs sampler. We also derive estimates of species diversity, conditional and unconditional on the observed data, as a function of the HPY parameters. Finally, we derive a general formula for the Hill numbers in the HPY context.

We show that the Gibbs sampler for the HPY model performs well in simulations. We also show that the conditional estimates of diversity from the HPY model improve over naïve estimates when species are missing. Similarly, the conditional HPY estimates tend to perform better than the naïve estimates especially when the number of individuals sampled from a population is small. Finally, we illustrate results of applying the HPY model in an infant gut microbiome dataset.