Estimating Ongoing Evolution by Repeated Sampling with "Long" Time Intervals.
Is there a way to construct dendrograms similar to those used in phylogenetics
but
with 2 main differences:
(1) Instead of observing at one time, small samples from a very large
population are taken at regular intervals, so that some observed cells could
easily correspond to an internal node rather than a leaf.
(2) There is no obvious outgroup; root should if possible be estimated by
presuming that observations from later time points are on average farther from
root.
More specifically, consider a large, heterogeneous, unstably evolving in vitro
cell
culture apparently not subject to a Hayflick limit. In our feasibility study, a
sample of 20 cells were tested at t=0 for about 100 different numerical aspects
of
their karyotype (for each cell an ordered vector of 100 numbers is measured from
the genome; the individual numbers all have the same order of magnitude).
About 15 cell generations later the observation is repeated and similarly four
more
times for a total of 120 cells over a time span of about 60 cell generations. I
would like to estimate the behavior of the major subclones – Are some spinning
off
new karyotypes? Which ones, if any, are in the process of taking over? Are some
being outcompeted? And so on.
Various difference matrices and binary dendrograms with the cells as leaves are
easily constructed and are suggestive. For example at timepoint 5 one karyotype
which was prominent, with lots of duplicates, for timepoints 1-4 disappears from
the samples. But the dendrograms themselves don’t really use the fact that
observations were made at six consective times rather than simultaneously; and
they
require me to make a guess about where root is. There must be a better way to
use
the data. I assume people who work, say, on development of drug-resistant
bacterial
lineages have thought this through in some detail and developed R software for
it
but I wasn’t able to locate anything.
Thanks in Advance, Ray Sachs, Dept. Math, UCB
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