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