# Abundance models

This module can be used for plotting taxon abundances in descending rank order on a linear or logarithmic (Whittaker plot) scale, or number of species in abundance octave classes (as shown when fitting to log-normal distribution). Taxa go in rows. It can also fit the data to one of four different standard abundance models:

- Geometric, where the 2nd most abundant species should have a taxon count of
*k*<1 times the most abundant, the 3rd most abundant a taxon count of*k*times the 2nd most abundant etc. for a constant*k*. With*n*the count of the_{i}*i*th most abundant taxon, we have*n*_{i}= n_{1}k^{i-1}. This will give a straight descending line in the Whittaker plot. Fitting is by simple linear regression of the log abundances. - Log-series, with two parameters
*alpha*and*x*. The fitting algorithm is from Krebs (1989). The number of species with*n*individuals (this equation does not translate directly to the Whittaker plot representation):*S*=_{n}*αx*^{n}/ n - Broken stick (MacArthur 1957). There are no free parameters to be fitted in this model. See the Past manual for mathematical details.
- Log-normal. The fitting algorithm is from Krebs (1989). The logarithm (base 10) of the fitted mean and variance are given. The octaves refer to power-of-2 abundance classes:
Octave Abundance 1 1 2 2-3 3 4-7 4 8-15 5 16-31 6 32-63 7 64-127 ... ... A significance value based on chi-squared is given for each of these models, but the power of the test is not the same for the four models and the significance values should therefore not be compared. It is important, as always, to remember that a high

*p*value can not be taken to imply a good fit. A low value does however imply a bad fit. Also note that the chi-squared tests in Past do not seem to correspond with some other software, possibly because Past use counts rather than the log-transformed values in the Whittaker plots.#### References

Krebs, C.J. 1989.*Ecological Methodology*. Harper & Row, New York.MacArthur, R.H. 1957. On the relative abundance of bird species.

*Proceedings of the National Academy of Sciences, USA*43:293-295.