Estimating
Morphological Diversity *

Microbial
ecology analyzes the relations and interactions between
a microbial community and its environment. An important
characteristic of the community used in this analysis
is its morphological diversity. The index of morphological
diversity d of the organisms found in a community
sample is defined by one of several formulas, all
suggested by Boltzmann's work in thermodynamics.
For example,

d = - p_{1} log p_{1} - p_{2}
log p_{2} - p_{3} log p_{3}
- ...,

where p_{j} is the fraction of morphological
type j in the sample (so p_{1}+p_{2}+...=1).

The usual method for measuring these fractions uses
a computer assisted analysis of a sequence of digital
images taken of the community being analyzed. An experimenter
typically acquires 36 photo microscope images taken
randomly across a slide prepared from the microbial
community sample (one roll of film). Each photograph
is scanned and digitally segmented to yield an improved
image that has been reduced to only the objects of
interest (the microbes themselves). A pattern recognition
routine then classifies the microbial morphotypes
on each image and reports the fractions of each morphotype
found.

How quickly does this index of diversity converge
to its maximum observed value? How many microbes (hence
images) must be examined in order to estimate the
diversity index of the community with a given level
of confidence.

The deliverable from this project will be an interactive
Excel macro prepared in Visual Basic that provides
a sequential decision algorithm for how many photos
must be processed and analyzed. The first photo is
scanned, image processed, and diversity computed.
The second photo is processed similarly and its data
are joined with the first to compute a more accurate
estimate of diversity. The third photo is processed
and its data are aggregated with the data from the
first two photos to estimate the diversity. And so
forth.

When can we break off the process? When is it no longer
worthwhile to continue? With what confidence can we
state the diversity of this population at the n-th
step? Since the answers depend on the intrinsic diversity
present in the community being examined, communities
spanning a range of diversity will be provided for
evaluation.

The manager for this project will be Ronen Peretz,
Professor of Mathematics.

* This summary prepared by C. R. MacCluer and R. E.
Svetic with the assistance of F. B. Dazzo, Professor
of Microbiology at Michigan State University.

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