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.

A Middle/High School That Teaches Complex Systems Through Games??!

A new school is opening in New York for grades 6-12 that completely blows my mind. The Quest to Learn school combines games and complex systems in a way that pretty much would have made my life as a teenager. Hell, I wouldn't mind going back to high school now if I got to go here. I'll let them describe it:

Mission critical at Quest is a translation of the underlying form of games into a powerful pedagogical model for its 6-12th graders. Games work as rule-based learning systems, creating worlds in which players actively participate, use strategic thinking to make choices, solve complex problems, seek content knowledge, receive constant feedback, and consider the point of view of others. As is the case with many of the games played by young people today, Quest is designed to enable students to “take on” the identities and behaviors of explorers, mathematicians, historians, writers, and evolutionary biologists as they work through a dynamic, challenge-based curriculum with content-rich questing to learn at its core. It’s important to note that Quest is not a school whose curriculum is made up of the play of commercial videogames, but rather a school that uses the underlying design principles of games to create highly immersive, game-like learning experiences. Games and other forms of digital media serve another useful purpose at Quest: they serve to model the complexity and promise of “systems.” Understanding and accounting for this complexity is a fundamental literacy of the 21st century.

Elsewhere they go into a bit more detail about how games are used to teach different subject areas:

At Quest students learn standards‐based content within classes that we call domains. These domains organize disciplinary knowledge in 21st certain ways—around big ideas that require expertise in two or more traditional subjects, like math and science, or ELA and social studies. One of our domains— The Way Things Work—is an integrated math and science class organized around ideas from design and engineering: taking systems apart and putting them back together again. Another domain—Codeworlds—is an integrated ELA, math, and computer programming class organized around the big idea of symbolic systems, language, syntax, and grammar. A third domain—Being, Space and Place—an integrated ELA and social studies class—is organized around the big idea of the individual and their relationship to community and networks of knowledge, across time and space. Wellness is the last of our integrated domains, a class that combines the study of health, socio‐emotional issues, nutrition, movement, organizational strategies, and communication skills.

OMG!OMG!OMG!OMG!

One of my favorite aspects of this school is that they have a separate staff of game designers working together with their teachers. As a former teacher I can tell you that designing good, creative lessons is a relatively different skill-set from actually implementing these lessons in front of a class and following up with your students, and that doing both well requires more time than is physically possible without traveling at relativistic speeds. So having designers who are there at the school and understand the teachers' needs, and who have the time to make great lessons, is a really really good idea.

At IIASA

This is just a brief note to let everyone know I'm spending the summer at IIASA, a scientific policy research institute located just outside of Vienna. IIASA focus on systems analysis of global problems such as climate change, land use, demographic changes, public health, ecology, and energy. They don't seem to use the phrase "complex systems" much, but they're clearly talking about the same thing.

I happen to be one of 53 lucky graduate students to be selected for this year's Young Scholars Summer Program, meaning I get to paid to live in Vienna and do research. Can't really complain about that. Tomorrow I get to hear mini-presentations on everyone's research proposals, which should be very interesting. My own project will be on the long term, gradual evolution of cooperation in spatially structured populations, using a mathematical framework known as adaptive dynamics.

I'm expecting to learn a lot here, and I'll share as much as I can with you readers. Looking forward to it!