[Mesquitelist] Likelihood reconstruction of changes: how to generate a table?

[Wayne Maddison]

With likelihood it's not clear to me exactly how you'd do this. 
Likelihood doesn't measure the probability of a state's occurrence at 
a node, but rather the probability of observing the data given the 
state's occurrence at the node.  We've never tried to calculate the 
likelihood of a change -- i.e. the probability of the data given a 
state change on a branch.  An interesting idea, but I'm not aware 
that anyone has used the calculation.  (It could be done relatively 
easily for categorical characters as a sum of node state 
likelihoods.)  Would you be interested in the sum over all characters 
of the likelihoods of change on a branch?

Another option would be to use stochastic character mapping to 
estimate distributions of total numbers of changes on a branch.  This 
would involve a new module to sum over realizations.

What exactly would you want?

Wayne


At 4:56 PM -0400 8.8.2008, David Fitch wrote:
>Dear Mesquite Users/Designers,
>
>For a matrix of discrete binary characters, how does one output a 
>table that details the likelihood reconstruction of character-state 
>CHANGES ("losses" and "gains") in each character and each branch?
>
>I see that Mesquite can output a table of the probabilities of 
>HAVING a particular state at each branch for each character 
>(Analysis > TraceAllCharacters).  And I see that Mesquite can output 
>a table of changes occurring across a (or many) tree(s) for ONE 
>particular character at a time (Taxa&Trees > 
>SummarizeStateChangesOverTrees).  However, I cannot figure out how 
>to output a table of CHANGES for EACH branch for EACH character.
>
>For example, each character could be represented by a row in the table.
>Each branch is represented by a pair of columns:
>   the 1st column with the number of gains,
>   the 2nd column with the number of losses.
>
>Presumably, the "number of gains" or "number of losses" would not 
>necessarily be integers, because the probability of a particular 
>change may not be 1.0 or 0.0 for a particular branch (unless the 
>decision threshold is applied; e.g. >50% probability for a gain 
>would be scored as a definite gain for that branch).
>
>Any ideas would be very welcome!
>thanks,
>David Fitch
>
>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  ~    ~       -   -
>~ David H. A. Fitch            ~   \  /       /   /
>~ Associate Professor          ~    \/       /   /
>~ Department of Biology        ~     \      /   /
>~ New York University          ~      []   /   /
>~ Main Building, Room 1009     ~       \  /   /
>~ 100 Washington Square East   ~        \/   /
>~ New York, NY  10003          ~         \  /
>~ U S A                        ~          \/
>~ Tel.:  (212) 998-8254        ~           \
>~ Fax:   (212) 995-4015        ~            \
>~ e-mail:  <mailto:david.fitch at nyu.edu>david.fitch at nyu.edu ~             \
>~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
>     <http://www.nyu.edu/projects/fitch/>http://www.nyu.edu/projects/fitch/
>
>
>
>
>
>_______________________________________________
>Mesquitelist mailing list
>Mesquitelist at mesquiteproject.org
>http://mesquiteproject.org/mailman/listinfo/mesquitelist


-- 
--------------------------------------------------------
Wayne Maddison
  Professor and Canada Research Chair
          Depts. of Zoology and Botany and
          Biodiversity Research Centre
  & Director
          Beaty Biodiversity Museum
  6270 University Boulevard
  University of British Columbia
  Vancouver, BC  V6T 1Z4   Canada

email: wmaddisn at interchange.ubc.ca   FAX: +1 604 822-2416

Mesquite: http://mesquiteproject.org
MacClade: http://macclade.org
Salticidae:  http://salticidae.org
Tree of Life: http://tolweb.org
Beaty Biodiversity Museum: http://beatymuseum.ubc.ca
Home page: http://salticidae.org/wpm/home.html