Department of Mathematics

Department of Microbiology

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 = - p1 log p1 - p2 log p2 - p3 log p3 - ...,

where pj is the fraction of morphological type j in the sample (so p1+p2+...=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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