Karla et al.,

There isn't, necessarily, a good alternative. If phylogenetic signal
is very poor, our ability to estimate rates is extremely hindered.
There's no rate of evolution in a white noise model -- values are
simply assigned independently of phylogeny.

One thought I had is that you might be able to at least constrain a
hard *minimum* estimate of the rates of evolution by looking at pairs
of sister species. But that may not be very useful depending on what
question is motivating you to measure evolutionary rate. It may not
even be meaningful in terms of capturing any sort of realistic
estimate of a real world process.

The problem here is that rate, in and of itself, is part of our
assumptions about the process being gradual and accruing variance over
time. If change was instead entirely limited to short punctuations,
and punctuations were randomly distributed in time, then asking how
much change there was over some interval of time (i.e. the rate) would
be rather nonsensical. You could 'measure' the rate but it wouldn't
have anything to do with the process generating the data. Perhaps the
thing to consider is, why do you think this data has such poor
phylogenetic signal to begin with?

In addition to Ted's reading list, these concepts were particularly
clarified for me by Gene Hunt's 2012 paper in Paleobiology on the
inseparability of measures of rate from our assumptions about mode:

https://www.cambridge.org/core/journals/paleobiology/article/measuring-rates-of-phenotypic-evolution-and-the-inseparability-of-tempo-and-mode/2906747B67D16EF002DC8B12CCF96B15

I hope this helps,
-Dave B

On Wed, Sep 23, 2020 at 8:42 PM Karla Shikev <karlashi...@gmail.com> wrote:
>
> Thanks, Liam! That was really helpful. But what would be an alternative to
> estimate evolutionary rates in those cases? Simply the sigsq estimate under
> a white noise model? (which I assume is simply the variance in the original
> data?)
>
> Karla
>
> On Wed, Sep 23, 2020 at 10:23 PM Liam J. Revell <liam.rev...@umb.edu> wrote:
>
> > Hi Karla.
> >
> >  > I just wanted to make sure that the estimate of sigma^2 in a BM model
> >  > in fitContinuous is a meaningful measure of the rate of evolution of
> >  > the trait even if its phylogenetic signal is low.
> >
> > I would say that the answer to this question (if it were posed as one)
> > is 'no.' Another way to put this is that sigma^2 is probably not a
> > meaningful measure of the rate of evolution for your character if
> > Brownian motion is a (very) poor fit to your data.
> >
> > It's kind of equivalent to saying 'is the slope of a fitted linear
> > regression a good measure of the rate of change in y as a function of x
> > if a linear model is a very poor fit to my data?' (That is, you can
> > still find a value of the slope that maximizes the probability of your
> > data under a linear model, and this slope accurately give the mean
> > effect of x on y over the range of your observations for x - but it may
> > not mean a whole lot about how x & y genuinely co-vary.)
> >
> > All the best, Liam
> >
> > Liam J. Revell
> > University of Massachusetts Boston
> > Universidad Católica de la Ssma Concepción
> > web: http://faculty.umb.edu/liam.revell/, http://www.phytools.org
> >
> > Academic Director UMass Boston Chile Abroad:
> > https://www.umb.edu/academics/caps/international/biology_chile
> >
> > On 9/23/2020 9:36 PM, Karla Shikev wrote:
> > > **[EXTERNAL SENDER]
> > >
> > > Dear All,
> > >
> > > Thanks for your fantastic feedback. Just a bit more background: I'm
> > > interested both in the phylogenetic signal and the evolutionary rate. I
> > > just wanted to make sure that the estimate of sigma^2 in a BM model in
> > > fitContinuous is a meaningful measure of the rate of evolution of the
> > > trait even if its phylogenetic signal is low.
> > >
> > > thanks again!
> > >
> > > Karla
> > >
> > > On Wed, Sep 23, 2020 at 8:45 PM Theodore Garland
> > > <theodore.garl...@ucr.edu <mailto:theodore.garl...@ucr.edu>> wrote:
> > >
> > >     Carla, I can also suggest looking at some of the papers on this,
> > >     such as:
> > >
> > >     Blomberg, S. P., T. Garland, Jr., and A. R. Ives. 2003. Testing for
> > >     phylogenetic signal in comparative data: behavioral traits are more
> > >     labile. Evolution 57:717–745.
> > >
> > >
> > >     Ives, A. R., P. E. Midford, and T. Garland, Jr. 2007. Within-species
> > >     variation and measurement error in phylogenetic comparative methods.
> > >     Systematic Biology 56:252–270.
> > >
> > >
> > >     Revell, L., L. Harmon, and D. Collar. 2008. Phylogenetic signal,
> > >     evolutionary process, and rate. Systematic Biology 57:591–601.
> > >
> > >
> > >     Hardy, O. J., and S. Pavoine. 2012. Assessing phylogenetic signal
> > >     with measurement error: a comparison of Mantel tests, Blomberg et
> > >     al.’s K, and phylogenetic distograms. Evolution 66:2614–2621.
> > >
> > >
> > >     Cheers,
> > >
> > >     Ted Garland
> > >
> > >
> > >
> > >
> > >     On Wed, Sep 23, 2020 at 4:33 PM Liam J. Revell <liam.rev...@umb.edu
> > >     <mailto:liam.rev...@umb.edu>> wrote:
> > >
> > >         Dear Karla.
> > >
> > >         What do you want to use fitContinuous to do?
> > >
> > >         fitContinuous fits multiple models, some of which will result in
> > >         low
> > >         values of lambda in a test of phylogenetic signal. In fact, this
> > is
> > >         really the main point of fitContinuous: to compare alternative
> > >         models
> > >         for trait evolution. If you just want to estimate the
> > >         most-likely rate
> > >         of evolution assuming a Brownian evolutionary process, you could
> > >         just
> > >         compute the mean squared PIC value (this is the REML estimate of
> > >         sigma^2).
> > >
> > >         fitContinuous can also take into account sampling error in the
> > >         estimation of species means, which can be a cause for low
> > measured
> > >         values of phylogenetic signal.
> > >
> > >         Hope this is of some help Karla.
> > >
> > >         All the best, Liam
> > >
> > >         Liam J. Revell
> > >         University of Massachusetts Boston
> > >         Universidad Católica de la Ssma Concepción
> > >         web: http://faculty.umb.edu/liam.revell/,
> > >         http://www.phytools.org
> > >         <
> > https://nam10.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.phytools.org%2F&data=02%7C01%7Cliam.revell%40umb.edu%7C4b3649722f5c4a9bb0f508d86021d687%7Cb97188711ee94425953c1ace1373eb38%7C0%7C1%7C637365045732071994&sdata=L7HXU2Ljrj89dZ5ql%2FRWMB7ddrReMWnZxdufzJQ2Nvs%3D&reserved=0
> > >
> > >
> > >         Academic Director UMass Boston Chile Abroad:
> > >         https://www.umb.edu/academics/caps/international/biology_chile
> > >
> > >         On 9/23/2020 8:21 PM, Karla Shikev wrote:
> > >          > [EXTERNAL SENDER]
> > >          >
> > >          > Dear friends,
> > >          >
> > >          > I guess this is as much a philosophical question as it is
> > >         methodological. I
> > >          > want to estimate the rate of evolution of a trait (e.g. using
> > the
> > >          > fitContinuous function), but the trait has low phylogenetic
> > >         signal (e.g.
> > >          > lambda close to 0). Does it make sense to use fitContinuous
> > >         on a trait
> > >          > evolving like that?
> > >          >
> > >          > Thanks for your input.
> > >          >
> > >          > Karla
> > >          >
> > >          >          [[alternative HTML version deleted]]
> > >          >
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-- 
David W. Bapst, PhD
Assistant Instructional Professor
Geology & Geophysics
Texas A & M University
https://github.com/dwbapst/paleotree

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