Notes 11-14-08

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Josh, Sam, Dennis, Katie: entropy-based alpha diversity statistics

• Set-up
  • start with one site
  • data=abundances of all observed species
  • tree=subtree with these species, derived from a universal tree (16S, Wu & Eisen, etc)

• Goal
  • Derive a measure of species evenness based on Shannon entropy, but using the tree

• Ideas
  • Josh: start with first principles and derive a new entropy-like measure
    • possibly a solution for 3 species subtrees could be extended to larger trees by tree factorization
  • Sam: weight leaves and compute entropy on weighted species abundances
    • weights based on distance to root node, with edge weights split between descendants
    • similar to Sourav's weights for pairs of species in masking procedure
  • Dennis: need to think about sample space, support for probability distribution
    • could look at n-tuples of species abundances, ordered by position in tree
    • need to consider data configurations (fixed spp abundances with different trees or fixed tree with different abundances) and how one would like them ordered in terms of diversity
  • Katie: cut tree at different times t from the present, and calculate entropy at each t
    • plot of t vs. entropy (or some summary thereof) might be a good measure