This paper presents a standardized metric for quantifying the rate change in community structure of complex mixed microbial cultures such as those maintained in biological wastewater treatment systems. Quantifying the stability of microbial community structures is a first step toward more aggressive monitoring and control of biological systems for greater reliability in contaminant removal. Statistical analysis of compositions that uniquely specify the balance of populations of species in a mixed culture sample can be used to specify a biosolids community state as a unique position in an orthogonal coordinate system. Changes in biosolids state are observable as a trajectory within this coordinate space, and the rate of passage along this trajectory relates to the population dynamics. The geometric interpretation and the statistical analysis methods necessary for the proposed calculation methodology are introduced by way of simulated case studies with a simple model system. With the example of this model system, concepts of changing microbial community shape and size are contrasted. The rate change in community structure is defined geometrically in terms of a rate change in relative proportions of the characteristic community shape at constant biomass. A change in biomass is defined as the rate change in the quantity of biosolids at constant shape. The method robustness with respect to random measurement error was also demonstrated using the model system. The potential applications of the approach are presented with experimental data of microbial fatty acid compositions extracted from samples during the operation of bench-scale bioreactors degrading contaminants found in pulp mill wastewater. Scaling the level of population dynamics with a metric that is independent of chemotypic content presents a standard for direct comparisons of community responses between distinct cultures and experiments.
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