Digital Object Identifier (DOI): 10.1007/s00285-004-0300-8 J. Math. Biol. 50, 645–662 (2005) Mathematical Biology Paul Joyce · Zaid Abdo · Jos´ e M. Ponciano · Leen De Gelder Larry J. Forney · Eva M. Top Modeling the impact of periodic bottlenecks, unidirectional mutation, and observational error in experimental evolution Received: 4 September 2004 / Published online: 20 December 2004 – c  Springer-Verlag 2004 Abstract. Antibiotic resistant bacteria are a constant threat in the battle against infectious diseases. One strategy for reducing their effect is to temporarily discontinue the use of cer- tain antibiotics in the hope that in the absence of the antibiotic the resistant strains will be replaced by the sensitive strains. An experiment where this strategy is employed in vitro [5] produces data which showed a slow accumulation of sensitive mutants. Here we propose a mathematical model and statistical analysis to explain this data. The stochastic model elucidates the trend and error structure of the data. It provides a guide for developing future sampling strategies, and provides a framework for long term predictions of the effects of discontinuing specific antibiotics on the dynamics of resistant bacterial populations. 1. Introduction Bacteria expressing antibiotic resistant genes are of increasing concern. In the presence of an antibiotic the bacteria that carry resistant genes have a tremendous competitive advantage and quickly sweep through the population. Genes encoding resistance to antibiotics are often located on plasmids. It is often assumed that the P. Joyce, Z. Abdo, J. M. Ponciano: Department of Mathematics, Division of Statistics, Ini- tiative in Bioinformatics and Evolutionary Studies (IBEST), P.O. Box 441103, University of Idaho, Moscow, ID 83844-1103, USA. e-mail: Paul Joyce joyce@uidaho.edu L. De Gelder, L. J. Forney, E. M. Top: Department of Biological Science, Initiative in Bioinformatics and Evolutionary Studies (IBEST), P.O. Box 443051, University of Idaho, Moscow, ID 83844-3051, USA. This Research is part of the Initiative in Bioinformatics and Evolutionary Studies (IBEST) at the University of Idaho. Funding was provided by NSF EPSCoR EPS-0080935, NSF EPSCoR, EPS-0132626, and NIH NCRR grant NIH NCRR- 20RR016448. Paul Joyce is also funded by NSF DEB-0089756, and NSF DMS-0072198. Key words or phrases: Mutation rate – Poisson distribution – Bottleneck – Process error – Observational error – Recursion equation Send offprint requests to: Paul Joyce Correspondence to: Paul Joyce