Michaelis-Menten

The asymptotic behaviour of the accumulation curve can also be modelled as the hyperbola:

where Smax and B are fitted constants. This is the Michaelis-Menten equation used in enzyme kinetics and thus there is an extensive literature discussing the estimation of its parameters, which unfortunately presents considerable statistical difficulties. One approach favoured by (Raaijmakers 1987) is to calculate Smax and B using their maximum likelihood estimators. While this method of estimating Smax has been criticised by (Lamas et al. 1991) it seems the best option available and is used by Species Diversity and Richness.

The output presents a series of estimates using 1, 2, 3... and so on samples. Thus to get sensible estimates you must ensure that all the data comes from samples obtained from the same community.

If Number of Random Selections (R) is set > 1 then the sequence samples are selected R times at random from the complete set of samples and the mean estimate calculated. As this removes sample order effects it is generally to be recommended.

By looking at the progressive change in the estimates it is possible to assess if sufficient samples have been taken to stabilise the estimate.

A simple plot of the way the estimate changes with the number of samples used is shown by clicking on the Graph tab in the results window.