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The log series distribution is described by:

 

 

where each term gives the number of species predicted to have 1,2,3,.n individuals in the sample.

 

The parameter a is estimated by iteration, after which x is calculated.

 

The output is displayed in a tabbed window.

 

logseries

 

The O/E tab displays the observed and expected abundances of the species. These are arranged in abundance classes and the upper column gives the upper bound of each class. The Chart tab shows a plot of the observed and expected frequency distributions arranged by class. The Observed are plotted as a histogram and the Expected as a green line. The Param/Chi tab presents the estimated values for a, x and the results of a Chi-Squared test of the observed and expected observations. If the value of p is < 0.05 then the distributions are significantly different at the 5% level. The goodness of fit results are displayed in a rich text window. To move around the displayed text click on the text and then use the arrow keys on the keyboard. These results can be copied and pasted in to other applications by selecting Copy from the Edit menu in the normal Windows manner.

 

It has been suggested that SHE analysis is one of the best ways of deciding if a log series log normal or brocken strick model gives the best fit to the observed data.