Dear All,
I am trying to fit expected species abundance distributions to observed
data. I found in Hubbell's book (page 292 Hubbell, S. P. 2001,The Unified
Neutral Theory of Biodiversity and Biogeography. Princeton University Press)
the log likelihood function:
F = Sum for all r [Obsr * log(Expr/Obsr) – (Exp – Obsr)]
Where r are the classes of abundance, Obsr the observed abundance in class
r, and Expr the expected abundance in class r. I am not sure if there is a
type error and Exp is the same as Expr, or something else.
I have tried to understand the derivation of this function by comparing it
with the log likelihood function for a multinomial distribution, and with
the G-test. The first term in the sum must be related to fitting frequency
distribution data, but I have been unable to make sense of the second term.
The total number of species is not fixed, and I note that as the expected
number of species goes up, the first term becomes larger and larger. Does
the second term (Exp – Obsr) control for this in some way? And if so, are
Exp and Expr the same?
Thanks in advance for all suggestions
Maria
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