Comparing OU and BM rates of evolution

[Jeremy M. Beaulieu]

Hi all~

Had two quick questions regarding the new brownie. First, is it
appropriate to compare rates between two sub-clades where one was
fitted with an OU model and the other a BM model (I set the model and
used the "opt" for each subclade)? I imagine it is, given that the
only difference between the two models is the inclusion of the alpha
parameter in the OU model.

This leads me to my second question: the output "optimal rate" for a
subclade (using the same commands as above) fitted with an OU model
corresponds to what exactly (i.e. alpha, sigma-squared, etc)? I have
tried to use various packages in R (i.e. geiger and OUCH) to get a
sense of what this optimal rate corresponds to, but have had no luck
thus far. Is it just the same variance per unit of time in a Brownian
model, but corrected for the presence of an optimum?

All the best,

Jeremy

[Brian O'Meara]

Hi, Jeremy. Responses below.

On Mar 9, 2009, at 6:28 PM, Jeremy M. Beaulieu wrote:

>
> Hi all~
>
> Had two quick questions regarding the new brownie. First, is it
> appropriate to compare rates between two sub-clades where one was
> fitted with an OU model and the other a BM model (I set the model and
> used the "opt" for each subclade)? I imagine it is, given that the
> only difference between the two models is the inclusion of the alpha
> parameter in the OU model.

I believe so. And you can think about BM as OU with alpha set to zero.

>
> This leads me to my second question: the output "optimal rate" for a
> subclade (using the same commands as above) fitted with an OU model
> corresponds to what exactly (i.e. alpha, sigma-squared, etc)? I have
> tried to use various packages in R (i.e. geiger and OUCH) to get a
> sense of what this optimal rate corresponds to, but have had no luck
> thus far. Is it just the same variance per unit of time in a Brownian
> model, but corrected for the presence of an optimum?

Sorry -- optimal rate is sigma-squared. Note that OUCH (at least
version 1.2-4) reports sigma, not sigma squared. Brownie's OUSM
results have been tested to match OUCH's. Note that OU1 hasn't been
tested well (and is a hidden option, even in the beta, for that
reason, but you (Jeremy, not other users) may have seen it in a pre-
beta) -- I wouldn't believe OU1 results. I can test OU1 more later,
though.

Does this answer your questions?

Brian


>
> All the best,
>
> Jeremy
> >


________________________________
Brian O'Meara
NESCent
Durham, NC
http://www.brianomeara.info
________________________________

[Jeremy M. Beaulieu]

Brian~

Thanks for the quick response! This does answer my question.

Though, ouch (now at version 2.5-3) was the source of my confusion.
As a side note, the "hansen" function input requires an initial guess
for the sigma parameter but the output lists it as sigma-squared.

In any case, comparing output from brownie and ouch, while the OU rate
estimates are different, (whether or not the ouch output is sigma or
sigma-squared) the likelihoods are the same. So, if anyone has used
this, it seems they could correctly infer an OU model, but find that
the rate parameter to be wrong.

All the best,

Jeremy

[Brian O'Meara]

Hmm, I'll have to dig into the difference a bit more. I know the
OUCH folks were thinking about changing their model to deal with the
root state differently, so perhaps that's the issue. Basically, under
a single mean OU model, the root state will be the mean, though under
a multiple mean model, it needn't be. OUCH 1.2 and Brownie always
estimate the root state as a separate parameter by default (this
could be turned off in OUCH, I think) but maybe this has been
changed. However, let me know if you find anything that points to an
error (especially if the error is in Brownie).

Thanks,
Brian