Department of Mathematics

Department of Microbiology

Estimating Morphological Diversity *

In an computer assisted image analysis of microbial community diversity, the operator typically acquires 36 exposures through a photo microscope of different random fields from one prepared slide of the uniformly dispersed, microbial community sample. 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 richness of microbial morphotypes on each image and reports the cumulative frequency of each morphotype found.

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 frequency of organism type j in the sample.

How quickly does this index of diversity converge to its maximum observed value? How many microbes (hence images) must be examined before one can with confidence know the value of the diversity index that is truly reflective of the diversity that exists within the community sample?

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.

*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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