# RE: [MORPHMET] Multivariate PICs?

```Sarah,

As far as I am aware, MorphoJ estimates a set of PICs one dimension at a time.
Thus, for a multivariate dataset of N species and p-trait dimensions, this will
return a matrix of N-1 by p.  Here, each of the N-1 rows (nodes of the
bifurcating tree) contains a vector of PICs, one per trait dimension.  This
approach is simple to replicate in R: just use the pic function and loop across
trait dimensions. ```
```
Note that this differs from McPeek's formulation of multivariate independent
contrasts (see e.g., McPeek et al. 2008: Am. Nat.). For this approach,
differences in each of the p-dimensions of data are combined in the numerator
of his equation, resulting in a a single PIC for each of the N-1 nodes. As you
mentioned, these are equivalent to the Euclidean distance between taxa
standardized by branch lengths.

While the math of McPeek's procedure is simple enough, I am unaware of a
function in R that estimates these directly. I also do not believe these are
found in MorphoJ, but someone who uses that program could better respond to
that query.

Hope this helps.

Dean

Director of Graduate Education, EEB Program
Professor
Department of Ecology, Evolution, and Organismal Biology
Department of Statistics
Iowa State University
phone: 515-294-3834

-----Original Message-----
From: Sarah Friedman <sarahtfr...@gmail.com>
Sent: Monday, March 19, 2018 2:24 PM
To: MORPHMET <morphmet@morphometrics.org>
Subject: [MORPHMET] Multivariate PICs?

Hi all,

Primarily, I'm wondering if there is a way to calculate phylogenetic
independent contrasts on multivariate shape data in R. However if no R method
exists, I know a method to do this is implemented in MorphoJ, and I could
possibly code an analogous method in R but I'm unsure how the contrasts are
calculated. Does anybody know if the independent contrasts are calculated using
the method described in McPeek (1994), the Euclidean distances between
contrasts on each branch, or another method?

Thanks,
Sarah

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