Segregated, structured, distributed models and their role in microbial ecology: A case study based on work done on the filter-feeding ciliateTetrahymena pyriformis

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Abstract
Microbial populations are composed of individual organisms each of which, if environmental circumstances are favorable, is undergoing change of its internal state through the operation of the set of processes that we call the cell cycle. The rate of progression through the cycle is subject to internal controls as well as external influences, and exhibits random as well as deterministic features. Microorganisms of the same species in different stages of the cell cycle have different internal states, and thus, the operation of the cell cycle is by itself sufficient to produce a distribution of states among the individual organisms of a population. In turn, the distribution of states produces distributions of the rates at which the cells of a population carry on their activities. Mathematical models of microbial growth that take the operation of the cell cycle and its consequences into account are more complicated than the kinds of models that are often used in microbial ecology. This paper gives some account of the nature, formulation, and uses of complex growth models. The account is illustrated by work done by the author and his collaborators H. M. Tsuchiya and more recently F. Srienc, as well as by others, on the filter-feeding ciliateTetrahymena pyriformis.