Beware count models: Hazard models give clearer picture of richness change

Traditional tools to analyze changes in species richness in the presence of abundance differences (e.g., rarefaction, asymptotic estimators) confound changes in total abundance, relative abundance, and richness. This means that even when equipped with high-quality insect data, it is difficult to discern changes in diversity when abundance is also changing. Straightforward approaches based on using generalized linear models to model raw counts also give misleading answers. In particular, count models with negative binomial error distributions and the log link, a natural-seeming approach, likewise conflate abundance changes with diversity changes. We hypothesized that “hazard models” using the complementary log-log (cloglog) link could avoid or ameliorate this problem.

We simulated changes in total, but not relative, abundances in communities with different species abundance distributions, with the goal of finding a model suitable for at least the null case. We fit generalized linear models with negative binomial, logit, and cloglog links to the simulated data and compare the estimated richness effects. We show that, when the species-abundance distribution is known, the hazard model (but not others) consistently avoids false-positive errors in diversity estimates. We also explored the feasibility of using information about the species abundance distribution inferred directly from typical insect count data. Our simulations highlight major problems in standard diversity analyses, and identify opportunities to refine efforts to document and understand biodiversity change.