This is usually done by fitting some kind of functional form to the curve, either by eye or by using non-linear regression techniques.
The advantage of the negative exponential function is that it tends to an asymptote which equals the number of species that would be discovered if infinite effort is expended.
However, some theoretical approaches imply that the logarithmic curve may be more appropriate,[citation needed] implying that though species discovery will slow down with increasing effort, it will never entirely cease, so there is no asymptote, and if infinite effort was expended, an infinite number of species would be discovered.
The first theoretical investigation of the species-discovery process was in a classic paper by Fisher, Corbet and Williams (1943), which was based on a large collection of butterflies made in Malaya.
For example, in ethology, it can be applied to the number of distinct fixed action patterns that will be discovered as a function of cumulative effort studying the behaviour of a species of animal; in molecular genetics it is now being applied to the number of distinct genes that are discovered; and in literary studies, it can be used to estimate the total vocabulary of a writer from the given sample of his or her recorded works (see Efron & Thisted, 1976).