Introduction

Microorganisms in nature coexist in highly diverse communities. In these communities, not all species perform the same functions and therefore cooperative interactions, among others, can emerge that can benefit the whole community (Crespi, 2001; Smith and Schuster, 2019). These cooperative functions are usually extracellular, involving excreted products and metabolites that can be considered “public goods” because they can benefit the entire community. However, extracellular functions, such as complex substrate degradation (e.g., cellulose), are particularly susceptible to exploitation: i.e., cheaters benefiting from a public good without contributing to it. This is because both the means (e.g., extracellular enzymes) and the products of substrate degradation (e.g., glucose) take place outside the cell (extracellular public goods) and are therefore vulnerable to cheating. The situation where cheaters emerge to exploit a shared resource was coined the “tragedy of the commons” by Garrett Hardin (Hardin, 1968), drawing from William F. Lloyd’s example of unregulated cattle grazing in a common pasture (Lloyd, 1833). This theory describes how the emergence of cheaters leads to the inevitable demise of the whole group; the cheater either takes up too many resources or the cheating behaviour propagates, leading to the same result. Cheating has been widely studied as a means of negative, competitive interaction between organisms and communities (Strassmann, Zhu and Queller, 2000; Velicer, Kroos and Lenski, 2000; Schusteret al. , 2017; De Leenheer, Schuster and Smith, 2019). Existing studies show that cheaters should be detrimental for the system in which they emerge, because their lower fitness costs allow them to allocate additional resources to growth and reproduction, thus outcompeting the other species. However, this situation shares similar characteristics and caveats with the competitive exclusion principle (Gause, 1934; Hardin, 1960) – regardless of reduced fitness costs, cheaters do not have the same access to the public good as producers (Letten, Ke and Fukami, 2017). Hardin’s tragedy of the commons also overlooks the fact that natural biological systems are inherently reactive and, to an extent, self-regulating (Foster, 2004; Rankin, Bargum and Kokko, 2007; Ostrowski et al. , 2015). Examples of self-regulation include host policing (Oono, Anderson and Denison, 2011), the cost of selfishness (density-dependent metabolic costs create negative frequency-dependent selection (MacLean, 2008; Morris, 2015)), quorum sensing (Dandekar, Chugani and Greenberg, 2012) or kin selection in heterogeneous environments (Kreft, 2004; Mitri and Foster, 2013). Indeed, the idea that any public good will be catastrophically exploited has been heavily criticised (Dahlman, 1991; Ostrom, 1999, 2015).
Several experimental systems have shown dynamics that closely resemble a “tragedy of the commons”. However, the systems continue to persist, with no runaway exploitation taking place. Such dynamics play out in predator-prey (Jones et al. , 2009; Becks et al. , 2010, 2012; Blasius et al. , 2020) and host-parasite models in chemostats (Smith and Thieme, 2012; Frickel, Sieber and Becks, 2016). The “tragedy of the commons” assumes that microbial cheating is a “prisoner’s dilemma” game; coexistence only depends on both players cooperating, as otherwise cheaters overwhelm the population causing the system to collapse. Instead, given the abundance of cooperative relationships between species in communities (West et al. , 2007; Morris et al. , 2013), the interaction between producers and cheaters is more likely to be a “snowdrift” game (Smith and Schuster, 2019). The snowdrift game model is inspired by the metaphor of a snow shoveler (producer or cooperator) who pays the cost of cleaning a path in the snow, with cheaters being able to use the clean path without incurring extra costs to the shoveler (Sugden, 2005). Under these circumstances, producers will continue to invest in public goods despite exploitation by cheaters so long as they continue to obtain sufficient benefits (Gore, Youk and van Oudenaarden, 2009). The Black Queen Hypothesis (BQH) describes a similar scenario (Morris, Lenski and Zinser, 2012). The main difference between a “snowdrift” dynamic and the BQH is that, in a BQH scenario, public good producers maintain some benefits that are not available to the cheater (Mas et al. , 2016) (i.e., immediate access (Estrela, Morris and Kerr, 2016), akin to partial privatization (Pande et al. , 2015; Estrela, Morris and Kerr, 2016)). Contrastingly, in a “snowdrift” situation, the producer cedes any exclusive advantages to resolve the conflict (Smith, 1976). The BQH has been presented to describe the situation where, in planktonic microbial communities, selection promotes loss of extracellular functions involving public goods, allowing cheaters to emerge (Morris, Lenski and Zinser, 2012). This leads to a community where only a critical minimum of species perform a shared function, possibly allowing for dependencies and cooperative interactions to develop from the beneficiary species (Sachs and Hollowell, 2012; Morris, Papoulis and Lenski, 2014; Mas et al. , 2016). This raises the question of whether “snowdrift” situations are still conducive to stable coexistence.
Indeed, many studies have shown that cheaters may not only be non-destructive, but might promote biodiversity and cooperative behaviour in microbial communities (Leinweber, Fredrik Inglis and Kümmerli, 2017; Veit, 2019). In one example, wild-type
Saccharomyces cerevisiae populations produce invertase that degrades sucrose into glucose. Glucose quickly diffuses from the cells, allowing for the emergence of non-producer cheaters (Gore, Youk and van Oudenaarden, 2009). The authors showed that cheaters promoted cooperation in the experimental system by keeping glucose concentrations low, thus preventing the inhibition of invertase production. Leinweber and her collaborators have also shown that cheater mutants ofPseudomonas aeruginosa act to increase intraspecific competition, promoting coexistence with Burkholderia cenocepacia , with iron as a single limiting resource (Leinweber, Fredrik Inglis and Kümmerli, 2017). Motivated by these findings, we ask the following question: given that cheaters are ecologically and evolutionarily inevitable, how are public good producers and public good cheaters able to coexist? Based on recent findings on the ecological relevance of cheaters, we propose a mechanism for how cheaters might act to stabilise systems, rather than destabilising them in the classical sense. We also build on the existing literature, to show that cheaters can be crucial to the promotion and maintenance of cooperative behaviours and networks. To address our question, we develop a theoretical mixed chemostat coculture model to test for evolutionarily stable states (ESSs) of coexistence and abundance dynamics between a producer and a cheater organism provided with a single complex substrate resource. We then proceed to parameterise the model with real data, from the literature.