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The dynamics of bacteria-plasmid systems. (English) Zbl 0806.92017
The authors introduce a general model for the dynamics of a system containing a single plasmid type and a single bacterial cell type. The general model admits multiple equilibria, two of which are plasmid-free. For the particular case of mortality being a linear function of population size, multiple equilibrium states and threshold values exist. This illustrates that, in some cases, the establishment of a population of plasmids may depend on the introduction of plasmids at sufficiently high levels. In the linear mortality case, a locally asymptotically stable equilibrium with coexistence of plasmids and bacteria is possible. The authors also analyze, for a general monotonically increasing mortality function, the case in which plasmids confer a net cost on their hosts and demonstrate that it is possible for an asymptotically stable equilibrium with plasmids and bacteria coexisting to exist, i.e. for such plasmids to become established in the bacterial population.
Reviewer: A.Hausrath (Boise)

MSC:
92D25 Population dynamics (general)
92D40 Ecology
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[1] Anderson, R. M., May, R. M.: Population biology of infectious diseases: I. Nature 280, 361-367 (1979) · doi:10.1038/280361a0
[2] Baya, A. M., Brayton, P. R., Brown, V. L., Grimes, D. J., Russek-Cohen, E., Colwell, R. R.: Coincident plasmids and antimicrobial resistance in marine-bacteria isolated from polluted and unpolluted Atlantic-ocean samples. Appl. Environ. 51, 1285-1292 (1986)
[3] Dwyer, G., Levin, S. A., Buttel, L.: A simulation model of the population dynamics and evolution of myxomatosis. Ecol. Monogr. 60, 423-447 (1990) · doi:10.2307/1943014
[4] Fenner, F., Ratcliffe, R. N.: Myxomatosis. London: Cambridge University Press 1965
[5] Kelman, A., Anderson, W., Falkow, S., Federoff N. V., Levin, S. A.: Introduction of recombinant DNA-engineered organisms into the environment. Washington, DC: Natl. Acad. Sci. 1987
[6] Levin, B. R., Lenski, R. E.: Bacteria and phage: a model system for the study of the ecology and coevolution of hosts and parasites. In: Rollinson, D., Anderson, R. M. (eds.) Ecology and genetics of host-parasite interactions. London: Academic Press 1985
[7] Levin, B. R., Stewart, F. M.: Probability of establishing chimeric plasmids in natural populations of bacteria. Science 196, 218-220 (1977) · doi:10.1126/science.847470
[8] Levin, B. R., Stewart, F. M.: The population biology of bacterial plasmids: a priori conditions for the existence of mobilizable nonconjugative factors. Genetics 94, 425-443 (1980)
[9] Levin, S. A.: Some approaches to the modeling of coevolutionary interactions. In: Nitecki, M. (ed.) Coevolution, pp. 21-65. Chicago: University of Chicago Press 1983
[10] Levin, S. A., Pimentel, D.: Selection of intermediate rates of increase in parasite-host systems. Am. Nat. 117, 308-315 (1981) · doi:10.1086/283708
[11] Lewontin, R. C.: Selection for colonizing ability. In: Baker, H. G., Stebbins, G. L. (eds.) The genetics of colonizing species, pp. 77-94. New York: Academic Press 1965
[12] Modi, R. I., Adams, J.: Coevolution in bacterial-plasmid populations. Evolution 45, 656-667 (1991) · doi:10.2307/2409918
[13] Palacios, R., Martinez, E., Flores, M., Romero, D., Brom, S., Dávila, G., Piñero, D.: Organization and dynamics of the Rhizobium genome. A basis for introducing novel arrangements of genetic information into the environment. In: Mooney, H. A., Bernardi, G. (eds.) Introduction of genetically modified organisms into the environment. SCOPE 44, pp. 69-78. Chichester: Wiley 1990
[14] Perelson, A. S., Brendel, V.: Kinetics of complementary RNA-RNA interactions involved in plasmid ColE1 copy number control. J. Mol. Biol. 208, 245-255 (1989) · doi:10.1016/0022-2836(89)90386-0
[15] Segel, L. A., Perelson, A. S.: Plasmid copy number control: A case study of the quasi-steady state assumption. J. Theor. Biol. 158, 481-494 (1992) · doi:10.1016/S0022-5193(05)80711-8
[16] Simonsen, L.: The existence conditions for bacterial plasmids: theory and reality. Microbial Ecol. 22, 187-205 (1991) · doi:10.1007/BF02540223
[17] Stewart, F. M., Levin, B. R.: The population biology of bacterial plasmids: A priori conditions for the existence of conjugationally transmitted factors. Genetics 87, 209-228 (1977)
[18] van der Hoeven, N.: A mathematical model for the coexistence of incompatible, conjugative plasmids in individual bacteria of a bacterial population. J. Theor. Biol. 110, 411-423 (1984) · doi:10.1016/S0022-5193(84)80183-6
[19] van der Hoeven, N.: Coexistence of incompatible plasmids in a bacterial population living under a feast and famine regime. J. Math. Biol. 24, 313-325 (1986) · Zbl 0597.92010
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