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I know how to calculate effective number of types. I can't figure out how to explain it to an audience that has no ecology training or background. Suppose one has 12 (for example) groups, each with a different population. Okay, so we calculate the effective number of types for that region and it's 5.7. How do I get across the concept that "out of twelve total types, with these population counts, that's the same as 5.7 types in that region"? The concept does sort of make the mind boggle a bit.

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    $\begingroup$ I appreciate this is a complex concept, but it would be useful if you gave a reference or two to this. I am not an ecologist and had never heard of this, but have some experience at explaining things. I checked out the top hit on a Google search, but that was clearly too complex for me. However if you suppled links to the accounts that you think are best, someone other than those in the field might be able to help. $\endgroup$
    – David
    Mar 9, 2022 at 23:27

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For a lay audience, I don't think you need to explain too much of the math, just the general concept, and an example will work best.

Let's think about trees. You have 5 types of trees in a forest. If there's 200 of each, that's about as diverse as 5 types can get: we can say there are 5 species of tree in that forest. No controversy.

If, however, there's a different forest with 900 maples, 97 birch, one oak, one locust, and one willow, well, that doesn't seem nearly as diverse, does it? Sure, there are 5 tree types, but it's almost all maples with a few birch, so if you stood in that forest it might feel like there's only effectively one or two types of trees. You want to give that forest a "diversity number" that's smaller than the forest with 200 of each tree, but that somehow accounts for there still being more than just one tree type there: some number between 1 and 5.

There are of course different ways you could weight those rare versus predominant tree types (this would be q in the equation), and there's no single answer that's right for every case, but if you pick a number for how to do that (say, choose q=1), then you can get just one number that lets you say "this place has more diversity than that one" not by just counting the number of species, but also considering their proportions. It will equal the number of species if you have an even distribution, but be less than that if some are rare.

I'd give a couple concrete examples on a slide if you were presenting this to an audience (or possibly a table in a written work) with different proportions to demonstrate how it works out in practice.

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    $\begingroup$ (+1) I think your example with the tree species would be quite effective, and more persuasive to a general audience than considering formally-defined statistical estimates. $\endgroup$
    – Galen
    Mar 10, 2022 at 2:23

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