Estimating species richness: the Michaelis-Menten model revisited

The Michaelis-Menten model has been widely used to estimate the richness (S) of species pools, but is largely untested. We tested whether (1) species accumulation curves follow the form predicted by the model, (2) the model gives unbiased estimates ((S) over cap and (B) over cap, respectively) of S and of the sample size, B, needed to detect S/2 species, and (3) performance is robust to community structure. Performance varied with community structure. For model communities with species-abundance distributions based on MacArthur's broken-stick model with 100 or 1000 species, deviations from predicted accumulation curves were slight, and (S) over cap and (B) over cap were unbiased (P greater than or equal to 0.18). For broken-stick communities with 10 species, (S) over cap and (B) over cap overestimated S and B by an average of 17% and 63%, respectively (P < 0.001). For model communities with species-abundance distributions based on Tokeshi's (1990) random-fraction model with 10, 100, or 1000 species, deviations from predicted accumulation curves were large; on average, (S) over cap underestimated S by 7-37% (P < 0.001), and (for S = 100 or 1000) (B) over cap underestimated B by 67-80% (P < 0.001). Vascular plant inventories (S = 42 to 99 species) also showed large deviations from predicted curves; on average, (S) over cap underestimated S by 35% (P < 0.001) and (B) over cap underestimated B by 72% (P < 0.001). Because most natural communities are better described by the random-fraction than the broken-stick model, we suggest the Michaelis-Menten model will typically yield poor estimates of S. Moreover, we argue that accepted criteria for evaluating estimators of S are inadequate.