Sociality/cooperation is puzzling for the evolutionary biologist

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Sociality and cooperation are pervasive in microbes

Microorganisms display a great variety of social behaviors (Crespi, 2001; Velicer, 2003; West et al., 2007a; Nanjundiah and Sathe, 2011; Celiker and Gore, 2013). Here are some examples among the most studied species:
Dictyostelium discoideum is a social amoeba mostly living in a unicellular state that feeds on bacteria. When food is lacking in their environment, cells have the ability to emit a molecular signal (cAMP) that is relayed by their neighbors. Cells follow cAMP gradients until they gather in structured multicellular aggregates that end up forming a mobile slug guided by phototaxis. The slug then morphs into a fruiting body whose stalk is composed of cells that sacrifice to let other cells (spores) at the top be dispersed and colonize new environments (Jiang et al., 1998; Ponte et al., 1998; Li and Purugganan, 2011; Strassmann and Queller, 2011). Similar multi-cellular stages, where cells undergo differentiation as in metazoans, are found as well in other dyctiostelids, even though aggregation mechanisms differ among species.
Myxococcus xanthus is a bacterium that displays a comparable fruiting body life cycle. M. xanthus participates in other kinds of cooperative endeavors as well, e.g. collective swarming (aggregates form by adhesion of extracellular pili at the cell surface and move cohesively owing to a complex motility system; Shimkets (1986a); Velicer and Yu (2003)) or collective predation (cells secrete enzymes that makes prey digestion possible outside the membrane, thus exploitable by potential cheats).
Saccharomyces cerevisiae (a.k.a. budding yeast) can break sucrose into glucose and fructose by externally secreting an enzyme called invertase. The local concentration of invertase in the medium thus acts as a public goods that might be used by nonproducers. Wild-type yeast also tends to bind together and form aggregates (flocculate) that provides them with better protection from chemical stresses (Smukalla et al., 2008). Multicellular states can also be the outcome of directed evolutionary experiments (Ratcliff et al., 2012).
Pseudomonas aeruginosa produces iron-scavenging siderophores that enable cells to trans-form the environmentally available iron into a form they can feed on. Once emitted outside the cellular membrane, siderophores benefit to any cell in the neighborhood – even potential cheaters – and are as such tantamount to a “common good” (Griffin et al., 2004). Evolutionary experiments evidenced the conflicting propensity to sociality and vulnerability to cheats in Pseu-domonas fluorescens that socialize by over-secreting adhesive polymers (Rainey and Rainey, 2003).
Other noteworthy examples include biofilms, that provides enhanced protection from pre-dation: the extracellular polymeric matrices that hold the films together are made of substances secreted at the individual level (Nadell et al., 2009); the secretion of virulence factors, antibiotics, exopolysaccharides, signaling molecules used in quorum-sensing, etc.
These examples concur to illustrate that numerous forms of cooperation and sociality are observable in the microbial world. However, they do not all display the same level of elabora-tion and possibly do not all pertain to the same step in the evolutionary path toward collective structuring. One must indeed distinguish between acts of cooperation that help neighbors or in-teraction partners in established population and interaction structures, and the very first behaviors that onset those population and interaction structures (Rainey, 2007; Szathmary,´ 2011). Inter-estingly, while many studies focus on the mechanisms supporting the maintenance of the former sophisticated forms of helping traits, far less address the latter. An evolutionary account of the origin of grouping traits is still needed to understand the whole process of microbial sociality.

The tragedy of the commons in microbes

Microorganisms socialize/cooperate in vivo. These behaviors are typically costly: they involve metabolic costs (e.g. to produce enzymes) or even the death of the cell, e.g. in the case of fruiting bodies (Nedelcu et al., 2011). In vitro experiments show that cooperation, while beneficial for the community (WT cooperating-only populations grow faster than mutant cheating-only popu-lations) is generally costly (in chimeric populations of cooperators + cheaters, cheaters perform better) (Rainey and Rainey, 2003; Gore et al., 2009). Thus cooperation is a trait likely to be exploited by non-cooperators that benefit from the cooperation of others while not paying its cost. Through Darwinian lenses, collective welfare is then expected to collapse, and cooperators to go extinct. This seemingly paradoxical stability of social populations despite what is often referred to as a “tragedy of the commons” (Hardin, 1968; Rankin et al., 2007) is the main puzzle of sociality for the evolutionist.
Box 1.1. A brief lexicon on sociality and cooperation
cooperation: a behavior that benefits to one or several recipient(s), and has evolved for this effect.
altruism: a behavior that benefits to one or several recipient(s) and entails a net cost for the actor.
Altruistic acts are a subset of cooperative acts, and are way more challenging to explain.
directly beneficial behavior (or mutualistic cooperation): a behavior that benefits to one or several recipient(s) but profits to the actor as well.
spite: a behavior that imposes a cost on one or several recipient(s) (often at a cost to the actor itself)
sociality: most often, “social” traits are equated to “cooperative” traits in the literature. This leads to the confusion that explaining some forms of cooperation is equivalent to explaining social behavior as a whole. Here, we rather term “social” any trait that enhances the ability of an individual to interact. Sociality could thus refer to a trait that does not provide any benefit to others, i.e. non-cooperative (see Fig. 1.1) In this thesis however, I will focus on social traits that increase individual attachment to a group and enhance group success (e.g. group cohesion), thus also cooperative (see chaps. 2 and 3). Sociality is sometimes referred to as “grouping” (e.g. in Aviles´ (2002), except that in our work it is costly, hence more challenging to account for).
Cooperation refers to any trait that provides a benefit to one or several recipient(s): it can be either directly beneficial (meaning that the cooperator gets a benefit from its own cooperation too) or altruistic (meaning that the cooperator undergoes a net fitness cost from its cooperation). We call sociality any trait that en-hances its carrier’s ability to interact. In some cases sociality can be cooperative, when enhanced grouping increases group gains and benefits to each group member irrespective of its social type.

The chicken-and-egg of cooperation and sociality

The purely “social” (in terms of “sticking together” / forming physical groups, e.g. biofilms, yeast flocs, etc.) traits are often mashed with cooperative traits (e.g. contributing to a public good once cells are already living in collectives). In this work, I argue that genes entailing adhesion / attachment may themselves be interpreted as cooperative genes with “something more”: an increased ability to have interactions with others (blindly with respect to their social types). See Box 1.1. for a distinction between sociality and cooperation: we mean by “cooperative” any trait that provides a benefit to a recipient, and by “social” any trait that enhances an individual’s tendency to interact. In this thesis, we focus on traits that enhance individual’s grouping and group cohesion as well (think for instance of a costly glue that makes individuals adhere together) which are at the same time social and cooperative.

Solving the paradox of cooperation

Game theory is the mathematical framework to address decision-making in rational agents able to adopt several strategies in situations of conflicting interests. In the last few decades, it has been extended to evolutionary biology to describe competition between genetically encoded be-haviors. Individuals garner benefits and costs from their interactions, and the frequency of each trait in the population changes in time with natural selection acting the same way as rational choice of strategies: if a trait codes for a behavior that benefits its carrier (in terms of relative reproductive fitness), it will increase in frequency in the population. Here, we review the main mechanisms suggested in the framework of evolutionary game theory to account for the persis-tence of paradoxical cooperative traits. Numerours attempts to systematize models and classify mechanisms have been made (e.g. by Lehmann and Keller (2006); Nowak (2006); West et al. (2007b)), that bear the ideological standpoints of their authors.

Reciprocity

Modeled on the idea that we humans tend to be more prone to help someone if she has helped us before, Trivers (1971) suggested direct reciprocation as a driving mechanism for coopera-tion in humans, encapsulated by the cathphrase “If you scratch my back, I’ll scratch yours”. In other words: if A helps B, then B helps A. Tit-for-tat strategy was found by Axelrod (1984) to be more successful than most complex strategies in competitions between humans playing the Iterated Prisoner’s Dilemma, but how it applies to animal communities and a fortiori microbes is much less straightforward. Indeed, reciprocation strategies require that interactions are repeated with the same player, and that the individual is able to recognize her interaction partner, mem-orize what she did at the previous timestep and react to the outcome of its last encounter. As a consequence, it remains a very unlikely way toward collective cooperation in microbial species. Even more cognitively demanding is indirect (reputation-based) reciprocation (Nowak and Sigmund, 1998), that can be summed up as “If I’m seen scratching your back, people will scratch mine”: C sees A helping B, then C helps A. Indirect reciprocity thus requires that interactions are conspicuous and that others are able to monitor and memorize what everyone did in the previous time steps.
A last form coined generalized reciprocity, that relies on lighter constraints, was modeled by Pfeiffer et al. (2005): “If someone scratch my back, I’ll scratch the next one”: B is helped by A, B helps C. Individuals base their behavior on their previous encounter, irrespective of their interaction partner. The requirements are basically the same as before minus the memorizing of who did what; yet, generalized reciprocity, as well as other (more complex) conditional strategies (Szolnoki and Perc, 2012), seem out of reach of the simplest organisms.
An other critical shortcoming of reciprocation mechanisms to explain the advent of grouping features is their dyadic aspect by definition.

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Policing (reward / punishment)

Cooperation may be enforced by individuals able to punish free-riders (resp. reward cooperators) (Clutton-Brock and Parker, 1995). The ability to punish (resp. reward) is itself costly. Once again, policing requires the ability for individuals to monitor others’ behaviors and to direct the punishment/reward toward them. Moreover, even though punishment may in principle deter defection, the survival of the cooperative-punisher type is complicated by “second-order free-riders”, i.e. cooperators that do not punish (Sigmund, 2007).
While both theoretical (Boyd et al., 2003) and experimental or observational (Fehr and Gachter,¨ 2002; Flack et al., 2006) studies suggest that policing mechanisms might have an im-portant role in sustaining collective cooperation in humans and other primates, the evidence of punishing/rewarding behaviors in microbes remains at best elusive.

Interactions directed toward genealogical kin

The rough idea behind interactions directed toward kins is encapsulated in this maxim by J.B.S. Haldane: “Would I lay down my life to save my brother? No, but I would to save two brothers or eight cousins”. If for some reason individuals tend to interact mostly with partners that share genes that are identical by descent to their own (i.e. if the actor and recipient are genealogically related), then cooperative behaviors may be promoted if the benefit conferred to kins weighted by the relatedness coefficient between interactants exceeds the cost. This idea is enclosed in the famous rule of Hamilton: rb > c, which has remained, since Hamilton’s pioneering work half a century ago, the formulaic rule of thumb to assess the sustainability of helping behaviors in biological settings (Hamilton, 1964). Yet, its generality is recurrently questioned (Nowak et al., 2010a) and its application by mis-informed experimenters and theoreticians often inaccurate. Indeed, the rigorous evaluation of each parameter (r, b and c) is nowhere near as straightforward as posited by some and rely on complex regression coefficient calculations. For instance, popu-lation genetics calculations show that the “right” r coefficient does not solely includes genealog-ical relations, but also the way population is structured and individuals interact. Even though general (as derived from another totem of population genetics, the Price’s equation (Gardner et al., 2011)), Hamilton’s rule might be of little use to describe the conditions for the evolution of cooperation in experiments and analytical models, some claim (Nowak et al., 2010a). Nonethe-less, Hamilton’s main point remains a milestone in alleviating the challenge of cooperation for species, as diverse as social insects and many microbial species, characterized by a high level of inbreeding (e.g. generated from a single lineage).
In any case, what Hamilton’s rule does not say is how individuals are led to interact preferen-tially with their kins. The two main mechanisms invoked in the literature are kin discrimination (crudely: individuals are able to recognize their brothers and sisters and interact predominantly within the family) or spatial structure (when limited dispersal or environment viscosity imply that lineages remain clustered).

Assortment between cooperators

When cooperators tend, for some reason, to interact more with other cooperators than defectors do, they get a higher average benefit from their interactions that may ultimately offset their cost (Wilson and Dugatkin, 1997; Fletcher and Doebeli, 2009). Assortment has some overlap with the previous family of mechanisms (insofar as if cooperating individuals tend to interact with their kins, de facto they interact with partners likely to share the cooperative gene), but is more general, the mechanisms liable to make cooperators interact together and not based on shared ancestry being numerous. The tricky part is to find those mechanisms. A key lies in the way populations are structured, in terms of spatial structure and interaction structure, motivating researchers to explore how networks, group shapes etc. influence this degree of assortment (see sections 1.5 and 1.6). A particular case is when cooperators interact together because they can identify each other. We refer to the Box 1.2. for a discussion about this issue.
Box 1.2. Green beards
A “green beard” refers to any gene, or set of linked genes, that encodes at the same time for 1) a given behavior; 2) the ability to recognize other carriers of the green beard; 3) the propensity to direct the behavior preferentially towards these carriers. The term was first used by Dawkins to make a hy-pothetical claim (Dawkins, 1976), and examples of green beards proved difficult to find until recently. For most of them, the “green beard” label remains controversial and one can argue that the three above requirements are not always fulfilled. Green beards can be either cooperative toward carriers, or spiteful against non-carriers. Examples of proclaimed green beards include (this list is widely inspired by Brown and Buckling (2008)):
• the csA gene in Dicty (Ponte et al., 1998; Queller et al., 2003) that encodes a cell adhesion protein that binds to homologous adhesion proteins (cooperative);
• the recognition of kins in Proteus mirabilis (Gibbs et al., 2008) (cooperative);
• the FLO1 gene in S. cerevisiae (Smukalla et al., 2008) between sticky cells, though cooperating sticky cells can also connect to nonsticky cells, although less probably (cooperative);
• the “queen-killer” allele in red fire ants (Keller and Ross, 1998) (spiteful);
• genes encoding bacteriocins (kind of chemical weapons) that at the same time make their carriers immune to their effect (Riley and Wertz, 2002) (spiteful);
Green beards may be subject to cheating as, very often, a set of linked genes rather than a single gene encodes the “beard”: there is thus a risk of invasion by mutants that display the tag without the costly behavior. A retort to this can be found in the possibility of multiple beard colors (Jansen and van Baalen, 2006). For instance, the FLO1 gene is known to be highly variable among species (more or less adhesive). In many cases, it is actually difficult to contend with certainty that a given behavior relates to a green beard. Indeed, the “preferentially directed” condition is not necessarily needed to get behaviors that are differentially directed toward carriers or non-carriers. This subtle difference will be more thoroughly developed later on in chapter 2.

Direct benefits

Although situations in which the evolution of a costly cooperative trait is paradoxical are empha-sized in the literature, the evolution of cooperation needs not necessarily be a social dilemma. In some cases, the cost incurred by cooperators is immediately offset by the marginal benefit they get from their own contribution to the group. In the standard Public Goods Games (sec-tion 1.4.2), such case would translate as b > N c. In invertase-secreting yeast, a small proportion of the hydrolized glucose is retained by the producer, advantaging cooperator cells at low frequencies (Gore et al., 2009). Similarly, the bacterium Lactococcus lactis expresses an extracel-lular protease that helps transform milk proteins into digestible peptides. Bachmann et al. (2011) showed that such cooperative behavior can persist owing to a small fraction of the peptides being immediately captured by the proteolytic cells.

Table of contents :

1 Evolutionary game theory for the evolution of cooperation in microbes 
1.1 The intimidating field of social evolution
1.1.1 Sociality/cooperation is puzzling for the evolutionary biologist
1.1.2 A scientific shift in the current approach
1.2 Sociality and cooperation in microbes
1.2.1 Microorganisms are good systems to test evolutionary hypotheses
1.2.2 Sociality and cooperation are pervasive in microbes
1.2.3 The tragedy of the commons in microbes
1.2.4 The chicken-and-egg of cooperation and sociality
1.3 Solving the paradox of cooperation
1.3.1 Reciprocity
1.3.2 Policing (reward / punishment)
1.3.3 Interactions directed toward genealogical kin
1.3.4 Assortment between cooperators
1.3.5 Direct benefits
1.3.6 Game definition
1.4 Game structure
1.4.1 Dyadic games
1.4.2 N-player games
1.4.3 The difficulty finding the right game
1.5 Population structure
1.5.1 Lattices
1.5.2 Graphs
1.5.3 Continuous space
1.6 Group structure
1.6.1 Groups as equivalence classes
1.6.2 Groups as sets
1.6.3 Non-delimited groups
1.7 Outline
2 Group formation and the evolution of sociality 
2.1 Introduction
2.2 General formulation
2.2.1 Hypotheses
2.2.2 Payoff difference for a general aggregation process
2.2.3 Payoff difference: case of no assortment a priori
2.3 Group formation by differential attachment
2.3.1 Description of the toy model
2.3.2 Group size distributions and payoff difference
2.3.3 Evolutionary dynamics and effect of the parameters
2.3.4 Other rules for group formation
2.4 Decoupling cooperation and attachment
2.4.1 Hypotheses
2.4.2 Evolutionary outcome
2.4.3 Conclusion
2.5 Extension to a continuous trait
2.5.1 Changes in the model
2.5.2 Resident / mutant analysis
2.5.3 Application to an aggregation process
2.5.4 Condition for altruism
2.6 Discussion
2.6.1 Social groups formation and evolution
2.6.2 Aggregative sociality in microorganisms
2.6.3 Nonnepotistic greenbeards?
2.6.4 About altruism and direct benefits
2.6.5 Toward a re-evaluation of the group formation step
3 Differential adhesion between moving particles for the evolution of social groups
3.1 Introduction
3.1.1 Main issue
3.1.2 Outline
3.2 Model
3.2.1 Aggregation model
3.2.2 Social dilemma
3.2.3 Evolutionary algorithm
3.3 Results
3.3.1 Local differences in adhesion rule group formation and spatial assortment in the aggregation phase
3.3.2 Assortment and differential volatility between strategies drive the evolution of sociality
3.3.3 Parameters of motion and interaction condition the evolution of sociality
3.4 Discussion
3.4.1 Evolution of sociality via differential adhesion
3.4.2 Strategy assortment and differential volatility
3.4.3 Role of group formation
3.4.4 Conclusion
3.5 Effect of ecological vs. evolutionary time scale
3.5.1 Hypotheses
3.5.2 Evolutionary trajectories
3.5.3 Effect of the generation time
3.5.4 Conclusion: role of time scales
4 Conclusion 
4.1 Main results
4.2 Perspectives for future work
Appendix A Derivation of the payoff difference, general case
Appendix B Group size distributions for differential attachment
Appendix C Condition for sociality to be altruistic for differential attachment
Appendix D Evolutionary algorithm for chapter 3

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