Knowing how diverse an ecological community is should be a simple matter. At the most basic level, we can go into the field take a sample and count the number of species. I know that when I look into my refrigerator that I have a beer diversity of 2. I have a few Guinness* and a few Duck-Rabbit Porter left over from last weekend.
Is this high diversity or low? Simply knowing the number of kinds of beer in my own refrigerator is not enough. I need comparison! The market down the street is chock-a-block of beer. For the sake of argument will say the market contains 50 kinds of beer and thus my house has low beer diversity in relation. Of course, on the other hand my house has greater beer diversity than the local preschool. At least I hope so!
The metric we just discussed is richness, i.e. what is the beer richness of my house, the supermarket, and the preschool. One of the most common metrics to quantify any ecological community is species richness, the number of species within a locality. The other important concept here is that there is more to diversity than just knowing that a locality has x number of species. It is important than some habitats possess more or less species as this yields information about the underlying ecological and evolutionary processes.
However, richness is just one part of the puzzle. What I didn’t tell is that I have 5 Guinness and 1 Duck-Rabbit Porters. Now just a few days ago, I had exactly 6 Guinness and 6 Duck-Rabbit Porters. So beer richness is unchanged, but diversity lowered. How? The second piece of the puzzle is evenness. Evenness is a measure of the equality or distribution of individuals, in our examples bottles, among species, here kinds of beer. In our example, I had 6 of each and thus high evenness before the weekend. After the weekend, beer diversity became uneven (5 and 1).
You can envision this in an ecological context as well. Two localities both have 5 species and 100 total individuals. But differ in how those species are distributed among species. At locality 1: 96, 1, 1, 1, 1 and locality 2: 20, 20, 20, 20.
Which of these two communities is more even? If you guessed 2 then you are correct! As aside here, evenness can be extremely informative. For example, polluted localities are typically extremely uneven.
Ideally, we would want a way to quantify diversity that would account not only for how many species were at a location but how individuals were distributed through species. As you might guess, we have metrics that do this. At their core, all these metrics basically do something mathematically fancy with the fraction of individuals in each species and then sum all those.
The most prominent and widely used of these is the Shannon-Wiener Index (H’), or Shannon-Weaver Index**. pi here is simply the fraction of individuals in the ith species. So here, we have pi times the log of pi for each species then summed.
Of course we can also separate out evenness and measure this independently with a metric like Peilou’s J’*** (below labeled as E for evenness I presume). Where the H’ from Shannon-Wiener is divided by the maximum value H’ can take (totally equal numbers of individuals among species, S).
Of course this discussion focuses just on species, but we could just as easily quantify the diversity at other taxonomic levels, genus, family, order, class. We could also more ecologically meaningful groups such trophic types, guilds, and body size classes.
This will be an ongoing series with other topics including: morphological diversity; spatial scale and diversity; alpha-,beta-, and gamma-diversity, similarity in composition, genetic diversity, diversity in the deep sea, phlyogenetic diversity, taxonomic relatedness, etc. Feel free to suggest some topic below as well.
*is the plural of Guinness, Guinni?
**Quite an interesting story here. The index was originally developed by Claude Shannon in 1948. Norbert Weiner, who did not help develop this precise index, did lay out definitions and discussion of the relationship of information and entropy in the 1948 book “Cybernetics: or communication and control in the animal and the machine.” In a later book version of Shannon’s 1948 paper, Warren Weaver wrote the introduction spelling out these ideas for a lay audience. Thus, the two versions, Shannon-Weiner and Shannon-Weaver, probably resulted out of Weaver’s introduction and similarity of names. This confusion has largely gone away and almost any new student will learn of the Shannon-Weiner Index.
***Let’s here it for the women representing! Evelyn Christine Pielou (born February 20, 1924) is a statistical ecologist and an emeritus professor of mathematical ecology at University of Lethbridge, Alberta, Canada.