Theor Ecol (2008) 1:13–19 DOI 10.1007/s12080-007-0001-1 ORIGINAL PAPER Alternative stable states in host–phage dynamics Joshua S. Weitz · Jonathan Dushoff Received: 15 February 2007 / Accepted: 19 April 2007 / Published online: 12 June 2007 © Springer Science + Business Media B.V. 2007 Abstract Bacteriophage are ubiquitous in nature, yet many central aspects of host–phage biology have not been integrated into mathematical models. We pro- pose a novel model of host–phage population dynamics that accounts for the decreased ability of phages to lyse hosts as hosts approach their carrying capacity. In contrast to existing predator–prey-like models, we find a parameter regime in which phages cannot invade a host-only system but, nonetheless, can stably coexist with hosts at lower densities. The finding of alternative stable states suggests clear linkages with observed life history strategies of phages. In addition, we solve a limiting case of the proposed model and show that con- servative predator-prey like systems do not inevitably exhibit population cycles. Finally, we discuss possi- ble extensions of the present model and scenarios for experimental testing. Keywords Bacteriophage · Virus · Evolutionary ecology · Microbial ecology · Bifurcation · Nonlinear dynamics · Population dynamics Introduction Bacteriophages are the most abundant organisms on the planet. They modify population dynamics of hosts J. S. Weitz (B ) School of Biology, Georgia Institute of Technology, Atlanta, GA 30309, USA e-mail: jsweitz@gatech.edu J. Dushoff Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA (Chao et al. 1977; Levin et al. 1977; Lenski 1988), alter nutrient recycling and biogeochemical cycles (Suttle 1994; Fuhrman 1999), and influence the spread of infectious disease (Faruque et al. 2005a,b). The interaction between phage and host is shaped by evo- lutionary mechanisms and ecological context. For ex- ample, recent experiments have shown that phages exploit their hosts (and each other) in a game-theoretic fashion (Turner and Chao 1999; Bull et al. 2006), con- trol ecosystem level process in simple ecological webs (Bohannan and Lenski 1997), and alter selection pres- sure in ways that depend on the spatial scale (Lythgoe and Chao 2003; Forde et al. 2004). Such findings are not confined to the laboratory. Empirical studies rely- ing on combinations of microbiology and metagenomic techniques have revealed unexpected viral diversity (Edwards and Rohwer 2005; Culley et al. 2006), a central role of phages in shuttling genes (Sano et al. 2004; Silander et al. 2005), and evidence that phages alter and enhance host metabolism (Lindell et al. 2004; Sullivan et al. 2005). This revolution in the study of the ecological and evolutionary impacts of phages provides an opportunity to revisit the mathematical description of host–phage dynamics. Do current models adequately describe the dynamics of microbial–viral interactions and do they make testable predictions? Bacteriophage are typically classified as either vir- ulent or temperate. Virulent phages kill their hosts without undergoing an extended intracellular phase, whereas temperate phages can also incorporate their genome into that of the host (Weinbauer 2004). In this paper, we restrict ourselves to the case of vir- ulent phages and associated hosts. The dynamics of virulent phages and hosts have been described, for the most part, using extensions of Lotka–Volterra models