In a recent article and monograph, May (1972May ( , 1973 has demonstrated that many of the models of predator-prey interactions used by ecologists have solutions specifying stable equilibrium points or stable limit cycles. These theoretical results are extremely significant. In the models considered by May, the interacting populations exist in homogeneous habitats. Consequently, it is not necessary to invoke spatial or temporal heterogeneities or nonattainment of equilibria to account for the coexistence of predators and their prey.The models studied by May are, however, nonspecific. The species growth and interactions are described simply as functions of their respective densities. The nature of the habitat, the relationships between the primary resources, and the growth of the prey populations are not specified. Neither is the form of the predation. Consequently the factors responsible for stabilizing the equilibria or limit cycles are described primarily in terms of the properties of the equations rather than in terms of the biology. As a result, this theory is of limited utility for predicting when there will be stable states of coexistence in a given predatorprey situation.Campbell (1961) studied the predator-prey association between bacteria and their viruses. His models were developed from a consideration of the biology of the interacting species, but were not very specific about the nature of the habitat and took no account of the relationship between prey growth and the availability of primary resources.In this investigation, we present models of this bacteriophage-bacteria interaction which are based on specific assumptions about the habitat, the use of primary resources, the population growth, and the nature of the interaction between predator and prey. We consider conditions for equilibria and demonstrate that on a priori grounds, stable states of coexistence are to be anticipated. We then compare the behavior of these models with that of experimental populations of Escherichia coli and its virulent virus T2. I. THEORETICAL CONSIDERATIONS The Basic ModelThe model developed here is an extension of that we used in a study of resource-limited population growth and competition on two trophic levels
Continuous culture populations of the bacterium especially coli and its virulent virus T7 have been studied as a model of a predator—prey in a simple habitat. These organisms maintain apparently stable states of coexistence in: (1) a phage—limited situation where all of the bacteria are sensitive to the coexisting virus and the sole, and potentially limiting carbon source, glucose, is present in excess; and (2) a resource—limited situation where the majority of the bacteria are resistant to these phage and in which there is little free glucose. The composition of these interacting populations is examined in detail and evidence indicating that this simple experimental culture system can support relatively complex communities is presented. In the predator—limited situation, two populations at each of two trophic levels can be maintained; the wild—type bacterial and phage strains, denoted B0 and T70, a mutant bacterial clone which is resistant to T70, denote B1 and a host range mutant phage, T71 which is capable of growth on both B0 and B1. In the resource—limited situation, three populations of bacteria and two populations of phage can coexist. The include the above described clones and a third bacterial strain, B2, which is resistant to both T70 and T71. In phage—free competition, the wild—type B0 bacterial clone has a marked advantage relative to both B1 and B2 while no difference is detected between B1 and B2. When competing for a B0 host, the wild—type T70 phage clone has a marked advantage over T71. The fit of these observations to some previously developed theory of resource—limited growth, competition and predation is discussed and a mechanism to account for the persistence of these communities is presented. The latter assumes that their stability can be attributed solely to intrinsic factors, i.e., the population growth and interaction properties of the organisms in this continuous culture habitat.
Mathematical models are used to ascertain the relationship between the incidence of antibiotic treatment and the frequency of resistant bacteria in the commensal flora of human hosts, as well as the rates at which these frequencies would decline following a cessation of antibiotic use. Recent studies of the population biology of plasmid-encoded and chromosomal antibiotic resistance are reviewed for estimates of the parameters of these models and to evaluate other factors contributing to the fate of antibiotic-resistant bacteria in human hosts. The implications of these theoretical and empirical results to the future of antibacterial chemotherapy are discussed.
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