SHANNON WIENER DIVERSITY INDEX EXAMPLES

Measure of diversity have been of historical significance and their importance still remains today given the obvious declines in habitat quality in almost every ecological system. The Shannon-Wiener diversity index. Historically, the index has been used to measure the effects of habitat quality such as effects of pollution effluents. Recently, newer indices have incorporated habitat parameters and are termed, appropriately enough, Habitat Suitability Indices (HSI). Though the results of the Shannon_Wiener index needs to be used with caution, it provides a good learning tool for comparing two distinct habitats such as an estuarine and near-shore coastal environment.

The S-W index is a measure of the likelihood that the next individual will be the same species as the previous sample.

It combines two quantifiable measures; 1. the species richness S(the number of species in the community) 2. Abundance N (is the total number of individuals in the sample). The index is termed H’ = neg Sum of Pi Ln Pi with higher values indicating increased diversity.

3. Pi = S/N

Species equitability (how even are the numbers of individuals of each species). For instance, say we have a sample of 100 fish containing only 2 species. We would say that the species are equitable if there were 50 of each species. Conversely, if there were 99 of 1 species and only 1 of the other, there would be no equitability. Given this second scenario, we would be pretty confident in our prediction that if we were to sample 1 more individual that it would be the same as the 99 in that sample. Conversely, in the previous scenario, we would have a 50/50 chance at predicting the next species sampled. Get it? Well, an example follows that will hopefully help out.

Evenness J is equal to the H’ divided by maximum possible diversity (ln of S). The values for evenness range from 0 to 1 where a sample of equal numbers of individuals of the same species has a value of 1.

Sample Calculations for Shannon-Weiner Diversity Index

Lets say we have a sample of 256 individuals comprised of 5 species and record the frequency of each of the species. We can then calculate the proportion of each species in the sample (Pi).

Fish Species	Frequency	Pi	ln(Pi)	Pi*ln(Pi)
Species #1	84	0.3281	-1.1144	-0.3656
Species #2	4	0.0156	-4.1589	-0.0650
Species #3	91	0.3555	-1.0343	-0.3677
Species #4	34	0.1328	-2.0188	-0.2681
Species #5	43	0.1680	-1.7840	-0.2997
Sum=	256	1		-1.3661

ln(Pi) is the natural log of that proportion value for each species and the final column is the multiplication of the natural log value and the proportion.

Given a very large sample size with many species (many more than 5) the S-W Index values (H) can range from 0 to ~4.6 using the natural log (versus log10). A value near 0 would indicate that every species in the sample is the same. Conversely, a value near 4.6 would indicate that the number of individuals are evenly distributed between the 5 species. Single values in the middle are a toss up - which is an obvious flaw in the index and is the reason that care should be taken when using such a measure. You should be able to calculate a Shannon-Wiener Diversity Index for a sample given and be able to explain or discuss your results.

FISH SPECIES CHECKLIST
		COUNT
Common Name	Generic Name	Ocean	Estuary Newport	Estuary Core Creek
Atlantic croaker	Micropogon undulatus	100		1
Atlantic menhaden	Brevoortia tyrannus	8
Atlantic stingray	Dasyatis sabina			1
Bay anchovy	Anchoa mitchili			51
Blackcheek tonguefish	Symphurus plagiusa	2
Gulf flounder	Paralichthys albigutta		1
Harvestfish	Peprilus burti	1		1
Northern searobin	Pironotus carolinus		2	4
Pigfish	Orthopristis chrysoptera	3
Pinfish	Lagodon rhomboides		45	10
Whiting	Menticirrhus americanus			1
Silver perch	Bairdiella chrysura	14		18
Silver seatrout	Cynoscion nothus	9
Southern hake			11	134
Spot	Leiostomus xanthurus	100	54	59
Using the data above, calculate a Shannon-Weiner Diversity Index for both the Estuary and Ocean samples.	Please consult the example Calcululations.