For rate estimation between temperate and tropical, I'd suggest using
OUwie, as it's made for exactly this question: map tropical/temperate on
the tree, try the "BMS" model to estimate the rate of evolution in
temperate and tropical taxa (note that I'm one of the authors, so take this
bias into account). There are other models, too, to allow you to test
things like whether temperate and tropical taxa have different evolutionary
means, and you can compare these models to Brownian motion models,
depending on your question. Note that in theory, these methods should be
robust to random sampling of taxa.

For your first question, you could estimate the amount of phylogenetic
signal, create a much larger tree under some branching process, transform
the branch lengths to match your phylogenetic signal, simulate traits on
this transformed tree, then subsample back and estimate the phylogenetic
signal on the untransformed but pruned simulated tree. Ideally, the
parameter estimate you get from the simulated data matches the true
parameter, suggesting that sampling does not matter for phylogenetic
signal. Frankly, I'd be surprised if random sampling does matter for
signal, though some biased sampling (even from taxonomic bias, of not
separating two populations into different species until they are "different
enough") could have an effect.

Best,
Brian

_______________________________________
Brian O'Meara
Assistant Professor
Dept. of Ecology & Evolutionary Biology
U. of Tennessee, Knoxville
http://www.brianomeara.info

Postdoc collaborators wanted: Check NIMBioS' website
Calendar: http://www.brianomeara.info/calendars/omeara


On Mon, May 5, 2014 at 11:33 AM, [email protected] <
[email protected]> wrote:

> Hi Imran,
>
> I'm by no means an expert on phylogenetic signal with incomplete
> phylogenies but I would check out the GEIGER package, specifically the
> "mecca" function. I think mecca is set up to do estimates based on
> incomplete tip sampling.
>
> Cheers,
> -Dan Gates
> PhD candidate
> Smith/Pilson Lab University of Colorado/Nebraska
> http://ec2-54-186-114-109.us-west-2.compute.amazonaws.com:8080/DanielJGates
> ________________________________________
> From: [email protected] <[email protected]>
> on behalf of imran khaliq <[email protected]>
> Sent: Monday, May 5, 2014 5:15 AM
> To: [email protected]
> Subject: [R-sig-phylo] Phylogenetic signal,     variation in rates and
> sample size
>
> Dear All,
> I am trying to understand the effects of incomplete phylogenies on the
> phylogenetic signal. I am using different trees and I have at least 100
> species in each tree but still these are only 2 % of total species. So how
> can I be sure that results are generalize enough to apply on the whole
> group? Secondly, if I want to compare varaition in trait's rates in two
> groups e.g. tropical and temperate, what methods are appropriate to
> estiamte the evolutionary rates. I tried Brownian rate parameter estimation
> by tranforming the branch lengths according to the lambda values of trait
> in each group.  It gives me lower varaince for the group that has higher
> lambda value and that is confusing. In fact with the same trait values, if
> I transform the branch lengths of the tree with different lamda values it
> gives me higher varaince for higher lambda value.
> Can anyone help me?
>
> Best regards,
> Imran
>
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>
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