Estimating global arthropod species richness: refining probabilistic models using probability bounds analysis

A key challenge in the estimation of tropical arthropod species richness is the appropriate management of the large uncertainties associated with any model. Such uncertainties had largely been ignored until recently, when we attempted to account for uncertainty associated with model variables, using Monte Carlo analysis. This model is restricted by various assumptions. Here, we use a technique known as probability bounds analysis to assess the influence of assumptions about (1) distributional form and (2) dependencies between variables, and to construct probability bounds around the original model prediction distribution. The original Monte Carlo model yielded a median estimate of 6.1 million species, with a 90 % confidence interval of [3.6, 11.4]. Here we found that the probability bounds (p-bounds) surrounding this cumulative distribution were very broad, owing to uncertainties in distributional form and dependencies between variables. Replacing the implicit assumption of pure statistical independence between variables in the model with no dependency assumptions resulted in lower and upper p-bounds at 0.5 cumulative probability (i.e., at the median estimate) of 2.9-12.7 million. From here, replacing probability distributions with probability boxes, which represent classes of distributions, led to even wider bounds (2.4-20.0 million at 0.5 cumulative probability). Even the 100th percentile of the uppermost bound produced (i.e., the absolutely most conservative scenario) did not encompass the well-known hyper-estimate of 30 million species of tropical arthropods. This supports the lower estimates made by several authors over the last two decades.