# Sample rarefaction (Mao's tau)

Sample rarefaction requires a matrix of presence-absence data (abundances treated as presences), with taxa in rows and samples in columns. Sample-based rarefaction (also known as the species accumulation curve) is applicable when a number of samples are available, from which species richness is to be estimated as a function of number of samples. PAST implements the analytical solution known as "Mao’s tau", with standard deviation. In the graphical plot, the standard errors are converted to 95 percent confidence intervals. See Colwell et al. (2004) for details. Mathematical equations are also given in the Past manual.

For modeling and extrapolating the curve using the Michaelis-Menten equation, use the Copy Data button, paste to a new Past spreadsheet, and use the nonlinear fitting module in the Model menu.

#### Reference

Colwell, R.K., C.X. Mao & J. Chang. 2004. Interpolating, extrapolating, and comparing incidence-based species accumulation curves. *Ecology* 85:2717-2727.