1. Frequency of singletons – species represented by single individuals – is anomalously high in most large tropical arthropod surveys (average, 32%). 2. We sampled 5965 adult spiders of 352 species (29% singletons) from 1 ha of lowland tropical moist forest in Guyana. 3. Four common hypotheses (small body size, male-biased sex ratio, cryptic habits, clumped distributions) failed to explain singleton frequency. Singletons are larger than other species, not gender-biased, share no particular lifestyle, and are not clumped at 0·25–1 ha scales. 4. Monte Carlo simulation of the best-fit lognormal community shows that the observed data fit a random sample from a community of ∼700 species and 1–2 million individuals, implying approximately 4% true singleton frequency. 5. Undersampling causes systematic negative bias of species richness, and should be the default null hypothesis for singleton frequencies. 6. Drastically greater sampling intensity in tropical arthropod inventory studies is required to yield realistic species richness estimates. 7. The lognormal distribution deserves greater consideration as a richness estimator when under-sampling bias is severe.