Alternating lysis and lysogeny is a winning strategy in bacteriophages due to Parrondo's paradox

Temperate bacteriophages lyse or lysogenize host cells depending on various parameters of infection, a key one being the ratio of the number of free viruses to the number of host cells. However, the effect of different propensities of phages for lysis and lysogeny on phage fitness remains an open problem. We explore a nonlinear dynamic evolution model of competition between two phages, one of which is disadvantaged in both the lytic and lysogenic phases. We show that the disadvantaged phage can win the competition by alternating between the lytic and lysogenic phases, each of which individually is a “loser.” This counterintuitive result is analogous to Parrondo’s paradox in game theory, whereby individually losing strategies combine to produce a winning outcome. The results suggest that evolution of phages optimizes the ratio between the lysis and lysogeny propensities rather than the phage burst size in any individual phase. These findings are likely to broadly apply to the evolution of host–parasite interactions.

Bacteriophages outnumber all other reproducing biological entities in the biosphere combined, reaching an estimated instantaneous total of about 10³¹ virus across all biomes (1, 2). Bacteriophages attain this hyperastronomical abundance using two basic strategies of infection that are traditionally classified as lytic and temperate. Lytic phages enter host cells and immediately take over the cellular machinery to produce progeny virions, followed by a programmed burst of the cell (lysis), which releases progeny virions into the environment where they can initiate subsequent rounds of infection (3). In contrast, temperate phages “decide” to follow the lytic or lysogenic strategy at the onset of infection. Under the lysogenic strategy, the phage genome stably integrates into the host genome, becoming a prophage that is inherited by the daughter cells during cell division and thus, propagates vertically with the host, without lysis of host cells. Phage lambda, one of the best-studied models of genetics and molecular biology, is a classic example of lysogeny. Upon sensing an appropriate signal, such as DNA damage, a prophage decides to end lysogeny and reproduce through the lytic pathway (4, 5). Given that an estimated 10²³ infections of bacteria by bacteriophages occur on Earth every second (6), with profound effects on the global ecology as well as human health (1, 7, 8), the evolutionary processes that shape phage replication strategies are of fundamental biological interest and importance.The ability of temperate phages to decide between lysis or lysogeny has drawn considerable attention of theorists, resulting in the development of models aiming to quantify the conditions in which one strategy prevails over the other, or in other words, deciphering the rules of phage lysis vs. lysogeny decisions. Temperate viruses that choose lysogeny are constrained by cellular binary fission, whereas lytic replication can produce large bursts of progeny virions from a single cell. A foundational theoretical study asked the question simply. Why be temperate (9)? The potential benefits of a nonlytic strategy are realized when the host cell density is too low to support lytic growth that would otherwise cause collapse of one or both populations. Furthermore, under these conditions, the frequency of encounters of the phage particles that are released upon host lysis with uninfected host cells is low, such that vertical propagation with the host becomes advantageous for the virus. In essence and put as simply as possible, lysogeny is advantageous in hard times (9). Several recent formal model analyses agree that lysogeny is favored at low host cell density (10–12). However, somewhat paradoxically, lysogeny appears to be the dominant behavior at very high host cell density as well (13, 14). The mechanisms driving viruses toward lysogeny at both low and high host cell densities are not well understood, but differential cellular growth rates, viral adsorption rates, and the structure of the host–phage interaction network all appear to contribute (14, 15). Collectively, these studies underscore the importance of density-dependent dynamics for infection outcomes.The paradigm for the decisions temperate phages make on the lytic vs. lysogenic pathway upon infection is phage lambda. Seminal work on lambda has demonstrated that lysogeny is favored at high virus/host ratios, when multiple lambda virions coinfect the same cell (16). The standard interpretation of these findings is that the coinfection rate is a proxy for host cell density, which drives lambda toward lysogeny at high coinfection rates: that is, low density (17). The genetic circuitry underlying lambda’s lysogenic response has been meticulously dissected over decades of research (5, 18, 19), and additional mechanistic determinants have been identified in later studies (20–24). Directed evolution of lambda yields mutants with different thresholds for switching from lysogeny to lysis (induction), and such heterogeneity has been observed in numerous lambda-like phages (25–27). Moreover, the vast genomic diversity of phages implies a commensurately diverse repertoire of lysis–lysogeny circuits, and indeed, experiments with phages unrelated to lambda have revealed a variety of ways evolution constructed these genetic switches (28–30). In general, how the different propensities for lysis or lysogeny impact phage fitness at different host cell densities (virus/host ratios) and in particular, when in competition with other phages remains an open problem.Inspired by the previous theoretical and experimental studies, we developed a population evolution model to investigate the competition between two phages that differ in their rates of establishing lysogeny based on the ratio of the number of free virions to the number of host cells. In this model, the first phage (P1) has a higher mortality rate, a lower burst size, and a lower infection rate during both lysis and lysogeny compared with the second competing phage (P2). From a game-theoretic perspective, P1 is burdened by two losing strategies. Unexpectedly, analysis of our model shows that, by alternating between these two losing strategies, P1 outcompetes P2 within a large domain of the parameter space. This counterintuitive result is analogous to a phenomenon known as Parrondo’s paradox in game theory (31). Parrondo’s paradox was first conceptualized as an abstraction of flashing Brownian ratchets (32, 33), wherein diffusive particles exhibit unexpected drift when exposed to alternating periodic potentials. The sustained interest in the paradox has since fostered a synergistic interdisciplinary effort. Indeed, manifestations of Parrondo’s paradox have been studied in various biological systems, such as nomadic and colonial lifestyles (34), activity and dormancy in predator–prey systems (35), and unicellular and multicellular phases in organismal life history (36). The fact that the paradox can occur when the game sequence is completely or partially random appears compatible with the inherent stochasticity in biological systems as manifested, for example, in environmental or demographic noise (37).Here, we examine the evolution of different strategies of bacteriophage–host interaction within the framework of Parrondo’s paradox. The analysis of the model developed in this work suggests that alternating between lysis and lysogeny is intrinsically beneficial for a phage within a broad range of model parameters. This conclusion has implications for understanding the evolution of parasite–host interactions in diverse biological contexts.