On estimating the probability of aperiodic outbursts of microbial populations from their fluctuating counts |
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Authors: | Micha Peleg Joseph Horowitz |
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Institution: | (1) Chenoweth Laboratory, University of Massachusetts, Amherst, MA 01003, USA;(2) Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA |
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Abstract: | 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 factors that favor or inhibit
growth. Since these factors tend to balance one another, the fluctuations usually remain within bounds, and only by a coincidence—when
all or most act in unison—does an ‘outburst’ occur. This situation can be represented mathematically as a sequence of independent
random variables governed by a probability distribution. The concept was applied to reported microbial counts of ground meat
and wastewater. It is found that the lognormal distribution could serve as a model, and that simulations from this model are
indistinguishable from actual records. The parameters of the lognormal (or other) distribution can then be used to estimate
the probability of a population outburst, i.e., an increase above a given threshold. Direct estimation of the outburst probability
based on frequency of occurrence is also possible, but in some situations requires an impractically large number of observations.
We compare the efficiency of these two methods of estimation. Such methods enable translation of irregular records of microbial
counts into actual probabilities of an outburst of a given magnitude. Thus, if the environment remains ’stable’ or in dynamic
equilibrium, the fluctuations should not be regarded merely as noise, but as a source of information and an indicator of potential
population outbursts even where obvious signs do not exist. |
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