Dear William.
The sigma^2 parameter in a fitted Brownian model is a rate in the sense
that it is the rate at which variation (variance) would be expected to
accumulate per unit of time among a set of lineages that were evolving
according to a random diffusion (Brownian) process. If you think it
would be helpful, I can send you the corresponding section from a recent
book I co-authored with Luke Harmon in which Brownian motion (and,
specifically, Brownian motion on a phylogenetic tree) is treated:
https://press.princeton.edu/books/phylogenetic-comparative-methods-in-r.
Please let me know & I'll send you a separate message off-list.
On the other hand, it seems possible that a discrete character evolution
model like the extended Mk model might be more appropriate. When you say
"karyotype" do you mean that the thing you're modeling is the number of
chromosomes in the haploid genome? If so, then I think it makes more
sense to think of chromosomes being added (by fission or genome
duplication) and lost (by fusion) as occurring under a different
stochastic process like a continuous time Markov chain. A little while
ago I wrote a blog post describing a simple model for chromosome number
evolution
(http://blog.phytools.org/2022/07/a-model-for-chromosome-number-evolution.html);
however, I believe there is a more sophisticated literature about this
out there (due, perhaps, to the fact that karyotypic changes are often
associated with speciation events -- something that a simple Mk model
ignores).
All the best, Liam
Liam J. Revell
Professor of Biology, University of Massachusetts Boston
Web: http://faculty.umb.edu/liam.revell/
On 12/14/2022 9:18 AM, William Brown wrote:
CAUTION: EXTERNAL SENDER
I am using fitContinuous to model karyotype evolution and trying to understand
the meaning of the sigma-squared parameter in the output by drawing very simple
trees and phenotype vectors. However, the output sigma-squared values do not
obviously correspond to any obvious variance calculation. Is there an obvious
formula to make some intuitive sense of the output? Perhaps fitContinuous is
the wrong function for getting a rate estimate from a phylogeny and a haploid
karyotype vector.
Thanks for any help,
William
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