Entropy and Biodiversity
Some time ago I stumbled upon a post on n-Category Café (which is, by the way, a blog that is definitely worth reading); here is part 1 and part 2.
The post introduces the concepts of entropy and diversity (and cardinality) in the field of biology. While I'm acquainted with the definition of entropy in information theory (and, slightly less, physics), I found really beautiful that those concepts could be applied in a very elegant way in population biology.
The first part applies the entropy definition to a finite probability space, representing an ecosystem with several species. Each probability shows how a particular species is frequent, namely the probability to encounter an indivual of that species. The entropy represent the diversity of the ecosystem, or, in a very rough language, how in "a good state" is the ecosystem.
The second part extends to a finite probability metric space. In this space, the probability has the same meaning as before. The metric distance among the points in the space grasps the idea of how a species is similar to one another. Thus, a low distance between two species means that these two are quite similar.
From the diversity you could derive the entropy and the cardinality of a probability (metric) space.
Intrigued by the post, I wrote a small ruby gem to calculate the entropy, the diversity and the cardinality for a probability space with or without a metric. The gem is on rubygems.org,entropy_gem, and the source code is on github.
I'm wondering if, passing from information theory to population biology to computer science again, these concepts could be applied in the field of machine learning, perhaps in genetic programming or any algorithm inspired by the mechanisms on evolutionary biology.
Tell me if you have any suggestion, comment or correction.
