ecologists, if I have diversity data (Shannon's index) for years and sites how can I produce data just for the sites (explained better below)

Question

I have 3 sites each split into the same 3 zones. With abundance data taken on 4 different years. I have produced diversity index readings for each zone at each site, for each year. If I'm not trying to look at the change over time, how would I go about calculating the values for each zone/site (using each year as a replication). I contemplated using the diversity readings I have already produced to calculate the mean biodiversity at each, i.e. the average diversity over the years at a particular zone/site. or do I rectify the code to sum all the year data for a specific zone/site, and calculate its biodiversity then? I am unsure about this as I cant tell whether doing such would produce an accurate reading as I don't know if doing so would treat the years as replications for the data collection.

Answer 1

The plug-in estimator of Shannon entropy suffers from an inherent bias that is worse with smaller samples. See this answer and its links for details. That's particularly the case if some species were present at a zone/site in some years and not in other years, as an absent species doesn't enter the entropy calculation.

So averaging individual Shannon entropy values for the 4 years might not be a good idea. If, based on your knowledge of the subject matter, you can treat the 4 years effectively as replicates, then a more reliable estimate of Shannon entropy for a zone/site would come from combining all the data from the 4 years first.

Usually, the closer you are to modeling the original data observations the better off you will be. In your case, that would be the counts of members of species as functions of zone/site and other predictors, possibly handled as a Poisson regression or other count-based model. That combines information from all your data to get smoother overall estimates. Then you could use the model estimates of species counts (with their error estimates) to estimate the Shannon entropies (and their associated error estimates), instead of the individual Shannon entropy estimates with their built-in bias.