On estimating the probability of aperiodic outbursts of microbial populations from their fluctuating counts

The irregular sequence of counts of a microbial population, in the absence of observable corresponding environmental changes (e.g., temperature), can be regarded as reflecting the interplay of several unknown or random factor s that favor or inhibit growth. Since these factors tend to balance one ano ther, the fluctuations usually remain within bounds, and only by a coincide nce-when all or most act in unison-does an 'outburst' occur. This situation can be represented mathematically as a sequence of independent random vari ables governed by a probability distribution. The concept was applied to re ported microbial counts of ground meat and wastewater. It is found that the lognormal distribution could serve as a model, and that simulations from t his model are indistinguishable from actual records. The parameters of the lognormal (or other) distribution can then be used to estimate the probabil ity of a population outburst, i.e., an increase above a given threshold. Di oct estimation of the outburst probability based on frequency of occurrenc e is also possible, but in some situations requires an impractically large number of observations. We compare the efficiency of these two methods of e stimation. Such methods enable translation of irregular records of microbia l counts into actual probabilities of an outburst of a given magnitude. Thu s, if the environment remains 'stable' or in dynamic equilibrium, the fluct uations should not be regarded merely as noise, but as a source of informat ion and an indicator of potential population outbursts even where obvious s igns do not exist. (C) 2000 Society for Mathematical Biology.