Biodiversity and Entropy

On Tuesday, my Erdos number dropped from infinity to four. That's right: after four years of grad school, I am now officially published!

The article, “A New Phylogenetic Diversity Measure Generlizing the Shannon Index and Its Application to Phyllostomid Bats,” by Ben Allen, Mark Kon, Yaneer Bar-Yam, can be found on the American Naturalist website or, more accessibly, on my professional site.

So what is it about? Glad you asked!

Protecting biodiversity has become a central theme of conservation work over the past few decades. There has been something of a shift in focus from saving particular iconic endangered species, to preserving, as much as possible, the wealth and variety of life on the planet.

However, while biodiversity may seem like an intuitive concept, there is some disgreement about what it means in a formal sense and, in particular, how one might measure it. Given two ecological communities, or the same ecological community at two points in time, is there a way we can say which community is more diverse, or whether diversity has increased or decreased?

Certainly, a good starting point is to focus on species. As the writers of the Biblical flood narrative were in some sense aware, species are the basic unit of ecological reproduction. Thus the number of species (what biologists call the "species richness") is a good measure of the variety of life in a community.

But aren't genes the real unit of heredity, and hence diversity? Is the number of species more important than the variety of genes among those species? Should a forest containing many very closely related tree species be deemed more diverse than another whose species, though fewer, have unique genetic characteristics that make them valuable?

And while we're complicating matters, what about the number of organisms per species? Is a community that is dominated by one species (with numerous others in low proportion) less diverse than one containing an even mixture?


There is no obvious way to combine all this information into a single measure for use in monitoring and comparing ecological communities. Some previously proposed measures have undesirable properties; for example, they may increase, counterintuitively, when a rare species is eliminated.

In this paper we propose a new measure based on one of my favorite ideas in all of science: entropy. You may have heard of entropy from physics, where it measures the "disorderliness" of a physical system. But it is really a far more general concept, used also in mathematics, staticstics, and the theory of automated communication (information theory) in particular. At heart, entropy is a measure of unpredictability. The more entropy in a system, the less able you will be to accurately predict its future behavior.

The connection to diversity is not so much of a stretch: in a highly diverse community, you will be less able to predict what kinds of life you will come across next. Diversity creates unpredictability.

To be fair, we weren't the first to propose a connection between diversity and entropy. This connection is already well-known to conservation biologists. But we showed a new and mathematically elegant way of extending the entropy concept to include both species-level and gene-level diversity. It remains to be seen whether biologists will take up use of our measure, but whatever happens I am happy to have contributed to the conversation.