The Erwin equation of biodiversity: From little steps to quantum leaps in the discovery of tropical insect diversity

Almost 40 years ago, Terry L. Erwin published a seemingly audacious proposition: There may be as many as 30 million species of insects in the world. Here, we translate Erwin's verbal argument into a diversity-ratio model-the Erwin Equation of Biodiversity-and discuss how it has inspired other biodiversity estimates. We categorize, describe the assumptions for, and summarize the most commonly used methods for calculating estimates of global biodiversity. Subsequent diversity-ratio extrapolations have incorporated parameters representing empirical insect specialization ratios, and how insect specialization changes at different spatial scales. Other approaches include macroecological diversity models and diversity curves. For many insect groups with poorly known taxonomies, diversity estimates are based on the opinions of taxonomic experts. We illustrate our current understanding of insect diversity by focusing on the six most speciose insect orders worldwide. For each order, we compiled estimates of the (a) maximum estimated number of species, (b) minimum estimated number of species, and (c) number of currently described species. By integrating these approaches and considering new information, we believe an estimate of 5.5 million species of insects in the world is much too low. New molecular methodologies (e.g., metabarcoding and NGS studies) are revealing daunting numbers of cryptic and previously undescribed species, at the same time increasing our precision but also uncertainty about present estimates. Not until technologies advance and sampling become more comprehensive, especially of tropical biotas, will we be able to make robust estimates of the total number of insect species on Earth.