David,
on the top of my head, if no species measurement strictly corresponds to
zero, you may log-transform the data. You may then simulate Brownian
motion in log-transformed values, which will correspond to a boundary of
zero in a linear scale (i.e., the more negative the log number, the
closer the trait value is to zero - but never zero - in a linear scale).
This also explains why you can simulate the evolution of body mass
employing Brownian motion in log-transformed units and no species will
ever be assigned a body mass of zero. On more speculative grounds, this
may simply reflect the fact that many biological processes and their
regulation occur in a multiplicative, not additive, scale.
The problem with regards to this approach is that you cannot really have
any species with a trait = 0 given that the log-transformation is
impossible in this case, so you might add some constant in case this
occurs (caution because the constant would be arbitrary and might have
an impact on the outcome of analyses). Did not think about this for too
long, though.
Hope this helps,
Enrico
El 4/3/11 9:14 p.m., David Bapst escribió:
All-
As far as I understand it, the vast majority of continuous character
analyses assume that the trait is distributed normally and without
bounds. Is there an appropriate transformation to for measurements of
a trait that does have one or more bounds and where some taxa actually
are at that bound? I have several traits where the bound is zero, and
some taxa are actually at zero for this trait. (A practical example is
'spine length', where some taxa have virtually no spine.) And if there
is no transformation applicable, is it analytically appropriate to
remove taxa that have 'zero units' for that trait? Must we convert
these traits to discrete categories to deal with them at all?
As always, I appreciate your advice.
-Dave Bapst, UChicago
--
************************************************************************
Enrico L. Rezende
Departament de Genètica i de Microbiologia
Facultat de Biociències, Edifici Cn
Universitat Autònoma de Barcelona
08193 Bellaterra (Barcelona)
SPAIN
Telephone: +34 93 581 4705
Fax: +34 93 581 2387
E-mail: enrico.reze...@uab.cat
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