Jeremy Van Cleve

Matthew Herron

Peter Conlin

Mathieu Forget
email: forget@bio.ens.psl.eu

Sandrine Adiba

Silvia De Monte
email: silvia.de.monte@bio.ens.psl.eu

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Keywords: Dictyostelium discoideum, evolution of social behaviour, cheating, multicellularity, microbial social strategies

The 'social amoeba' Dictyostelium discoideum, where aggregation of genetically heterogeneous cells produces functional collective structures, epitomizes social conflicts associated with multicellular organization. 'Cheater' populations that have a higher chance -quantified by a positive spore bias -of surviving to the next generation when mixed with cooperators bear a selective advantage. Their spread is thus expected to undermine collective functions over evolutionary times. In this review, we discuss the two main approaches adopted to conceptualize social conflicts in Dictyostelium discoideum: describing social interactions as a property of cell populations (strains), or as a result of individual cell choices during the developmental process. These two points of view are often held equivalent and used interchangeably. While the population-level view grants more direct evolutionary inference, however, the cell-level interpretation reveals that such evolutionary predictions may be modified if mechanisms such as dependence on the environment, development and intrinsic unpredictability of cell fate choices are taken into account. We conclude by proposing a set of open questions that in our opinion lie at the core of a multi-scale description of aggregative life cycles, where the formulation of predictive evolutionary models would include cell-level mechanisms responsible for spore bias alongside population-level descriptors of multicellular organization.

Introduction

Many unicellular organisms spend at least part of their lifetime within associations that have a functional role, as they allow their composing cells to resist stress, to be defended against predators, or to engage in collective behaviour. Multicellular organization has been integrated in life cycles, that in some cases alternate periods of growth as single cells, and phasestypically triggered by nutrient depletion -where initially sparse cells gather in more or less complex multicellular aggregates [START_REF] Du | The Evolution of Aggregative Multicellularity and Cell-Cell Communication in the Dictyostelia[END_REF][START_REF] Grosberg | The evolution of multicellularity: a minor major transition? en[END_REF]. The transition from a chiefly unicellular life style to such aggregative life cycles occurred at least six times independently along the tree of life and in all major eukaryotic clades [START_REF] Du | The Evolution of Aggregative Multicellularity and Cell-Cell Communication in the Dictyostelia[END_REF][START_REF] Parfrey | Multicellularity arose several times in the evolution of eukaryotes[END_REF]. Its repeated emergence suggests this form of multicellular organization is not the outcome of serendipity, but may reflect general organization principles [START_REF] Del Angel | Interplay of mesoscale physics and agent-like behaviors in the parallel evolution of aggregative multicellularity[END_REF][START_REF] Gestel | On the origin of biological construction, with a focus on multicellularity[END_REF][START_REF] Grosberg | The evolution of multicellularity: a minor major transition? en[END_REF].

The social amoeba Dictyostelium discoideum has been widely used to identify such principles and to explore the action of selection on cellular collective organization. The evolutionarily stability of its multicellular life cycle, despite conflicts among cells that adopt different social strategies, makes it a model organism for addressing both the maintenance of cooperative behaviour [START_REF] Medina | Cooperation and conflict in the social amoeba Dictyostelium discoideum[END_REF][START_REF] Strassmann | Evolution of cooperation and control of cheating in a social microbe[END_REF] and the evolutionary emergence of new levels of organization [START_REF] Gestel | On the origin of biological construction, with a focus on multicellularity[END_REF].

D. discoideum's life cycle comprises a vegetative phase, where cells grow in isolation, and a collective social phase induced by starvation [START_REF] Kessin | Dictyostelium: evolution, cell biology, and the development of multicellularity[END_REF]. The multicellular phase starts with aggregation, when cells converge towards aggregating centers by chemotaxis guided by the gradient of a signalling molecule, cyclic adenosine monophosphate (cAMP) [START_REF] Devreotes | Chemotaxis in eukaryotic cells: a focus on leukocytes and Dictyostelium[END_REF][START_REF] Fisher | Quantitative analysis of cell motility and chemotaxis in Dictyostelium discoideum by using an image processing system and a novel chemotaxis chamber providing stationary chemical gradients[END_REF]. Eventually, most cells in the population belong to multicellular aggregates, or mounds, each composed of tens of thousands individual cells.

Later, mounds elongate into slugs, chemotactic and phototactic worm-like structures with the ability to sense and move towards bright and dry environments, like the soil surface [START_REF] Bonner | The orientation to light and the extermely sensitive orientation to temperature gradients in the slime mold Dictyostelium discoideum[END_REF][START_REF] Raper | Pseudoplasmodium formation and organization in Dictyostelium discoideum[END_REF]. Here, slugs produce fruiting bodies that can be picked up by insects and dispersed [START_REF] Smith | Fruiting bodies of the social amoeba Dictyostelium discoideum increase spore transport by Drosophila[END_REF]. Starting from the mound stage at latest, cells proceed to differentiate into several tissues [START_REF] Early | Two distinct populations of prestalk cells within the tip of the migratory Dictyostelium slug with differing fates at culmination[END_REF][START_REF] Kessin | Dictyostelium: evolution, cell biology, and the development of multicellularity[END_REF]. Because of their prevalence and their ease of detection, most attention has been given to two cell types: spores, that seed the following generation, and stalk cells, that support the spore mass. Analogous to somatic cells in metazoans, stalk cells die.

Giving up one own's descendants to favour spore dispersal is considered the most extreme degree of altruistic behavior, and raises the question of the evolutionary stability of such arrangement [START_REF] Strassmann | Evolution of cooperation and control of cheating in a social microbe[END_REF]. In 'paradigmatic' multicellular organisms with single-cell bottleneck followed by clonal growth, conflicts between different cell types (e.g.

between normal and cancer cells [START_REF] Aktipis | Cancer across the tree of life: cooperation and cheating in multicellularity[END_REF]) can get resolved by purging entire cell lineages (Godfrey- [START_REF]Darwinian Populations and Natural Selection[END_REF]. Their disruptive effect is instead enhanced when multicellular aggregates are genetically heterogeneous [START_REF] Buss | Somatic cell parasitism and the evolution of somatic tissue compatibility[END_REF]. In Dictyostelium, different genotypes can coexist within a same fruiting body both in the wild and in the lab, indicating that this organism has found solutions to curb fitness effects and evolutionary impacts of such conflicts.

The first fundamental issue when considering the action of selection on multicellular organization is how to measure differential fitness between co-aggregating genotypes. In Dictyostelium, reproductive success can be evaluated at the end of the life cycle, when cells are terminally differentiated into spores or stalk. Spore cells are indeed the only fraction of the population that is able to survive long periods of starvation, and reproductive success hinges upon their production. Moreover, cells that die forming the stalk provide a clear advantage to spores. Due to these features, shared also by other organisms such as Myxobacteria [START_REF] Velicer | Developmental cheating in the social bacterium Myxococcus xanthus[END_REF], genotypes that tend to form an increased fraction of spores when mixed in chimerae are commonly called 'cheaters'. Strains that -being found in lesser proportion in the spores -get exploited by virtue of their disproportional contribution to the stalk, are called instead 'cooperators'. Practically, social strategies are assessed in chimerae obtained by mixing, prior to aggregation, cells belonging to two different strains. Spore bias is then typically quantified as the percentage of one strain in the spore pool, relative to the percentage of cells of that strain in the initial mix [START_REF] Gilbert | High relatedness maintains multicellular cooperation in a social amoeba by controlling cheater mutants[END_REF][START_REF] Kuzdzal-Fick | An invitation to die: initiators of sociality in a social amoeba become selfish spores[END_REF][START_REF] Kuzdzal-Fick | High relatedness is necessary and sufficient to maintain multicellularity in Dictyostelium[END_REF] (this assumes that the spore-to-stalk ratio within fruiting bodies is constant, but see [START_REF] Buttery | Complex genotype interactions influence social fitness during the developmental phase of the social amoeba Dictyostelium discoideum[END_REF][START_REF] Buttery | Quantification of social behavior in D. discoideum reveals complex fixed and facultative strategies[END_REF] for generalizations). All else being equal, then, a cheater strain will see its frequency increased in the population of vegetative cells ensuing from spore germination in the following generations.

In the domain of evolutionary biology, most attention has been devoted to understanding why in Dictyostelium selection of cheater strains does not doom collective function altogether.

The intuition that the advantage reaped by cheaters within one life cycle will result, if aggregation occurs over and again, in the long-term demise of cooperators matches well the formalism of evolutionary game theory [START_REF] Hofbauer | Evolutionary Games and Population Dynamics[END_REF]. Games that oppose cooperators and cheaters, such as the Prisoner's Dilemma or Public Good Games, typically predict that unbridled natural selection is expected to wipe out cooperation.

In this review, we step back and examine the observational bases of different conceptual models for social interactions in Dictyostelium, paying particular attention to the evolutionary expectations associated to the existence of cheaters. We first discuss the conditions for maintaining cooperative behaviour under the assumption that the outcome of interactions between strains are exclusively determined at the genetic level. We successively review the growing literature on non-genetic (chance, environment and social context) dependence of the developmental process, which ultimately produces a given partition of cells in spores or stalk. Although it is largely unknown how much such dependence can alter quantitatively the outcome of strain interactions, the possibly large evolutionary consequences of a variable relation between a genotype and spore bias motivates delving into the underlying cell-level mechanisms, which we discuss in the second part of the paper. Finally, we discuss possible solutions to describing cell behaviour on multiple spatial and temporal scales, and to selecting null and predictive models for the evolution of aggregative multicellular organisms.

Strategies of interacting strains

Spore bias is traditionally measured in chimerae where two different strains are mixed -often in equal proportions -at starvation, after which cells undergo only one more cell division.

When strains are equivalent, thus, the fraction of spores belonging to one strain is expected to be equal to the proportion of that strain in the initial mix. Deviations from this 'neutral' composition of the spore mass quantify the degree of cheating of one with respect to another strain [START_REF] Gilbert | High relatedness maintains multicellular cooperation in a social amoeba by controlling cheater mutants[END_REF][START_REF] Kuzdzal-Fick | An invitation to die: initiators of sociality in a social amoeba become selfish spores[END_REF][START_REF] Kuzdzal-Fick | High relatedness is necessary and sufficient to maintain multicellularity in Dictyostelium[END_REF].

Cheating behaviour is thus defined at the level of interacting populations of cells, connecting directly the genotype of the strain to the outcome of the social interactions. For instance, 'obligate cheaters' are genotypes, found in natural isolates or derived from lab strains, that have a positive spore bias when mixed with other strains, but that cannot develop alone [START_REF] Buss | Somatic cell parasitism and the evolution of somatic tissue compatibility[END_REF][START_REF] Ennis | Dictyostelium amoebae lacking an F-box protein form spores rather than stalk in chimeras with wild type[END_REF][START_REF] Kuzdzal-Fick | High relatedness is necessary and sufficient to maintain multicellularity in Dictyostelium[END_REF]. Such strains always have a reproductive advantage over different genotypes, however they cannot disperse if they meet a strain of their same kind.

The reproductive output in chimerae can thus be formalized as the payoff of a game opposing individual strains. Cheater genotypes exploit cooperator genotypes by enhancing their own representation in the following generation. Such a situation is represented by the Prisoner's Dilemma, a two-player game whose chief feature is that cheating is always the most rational option if the strategy of the partner is unknown, even though the best result is achieved when the two cooperate. Evolutionary game theory predicts that, after many rounds of the game (here, cycles of co-aggregation) in which players (here, strains with a fixed associated social strategy) meet at random, cooperators will be outnumbered by cheaters.

The problem of maintaining or evolving cooperation in two-players games has found several solutions in the general framework of game theory [START_REF] Nowak | Five rules for the evolution of cooperation[END_REF]. In the case of Dictyostelium, the most commonly invoked means of preventing the invasion of cheaters is kin selection, where high genetic relatedness is the key condition for cooperative behavior to be favoured by natural selection (WE [START_REF] Kerr | Evolution of the mechanism of caste determination in the genus melipona[END_REF][START_REF] Strassmann | Evolution of cooperation and control of cheating in a social microbe[END_REF]. According to Hamilton's rule [START_REF] Hamilton | The genetical evolution of social behaviour. I. eng[END_REF], in order for altruistic genes to increase in frequency, the level of genetic relatedness r between the cooperator and the recipient of the cooperative act must exceed c/b, where c is the cost paid by the cooperator and b is the benefit received by the recipient.

Originally, the relatedness r in a population was defined, based on genetic identity by descent, as the probability that two random individuals share the same allele at one given social locus.

Subsequently, other measures of social interaction bias towards individuals that carry the cooperative allele have been proposed as proxies for relatedness, most notably the frequency of cells of a given type in the population [START_REF] Queller | Genetic relatedness in viscous populations[END_REF]. More generally, cooperative behaviour is expected to spread as long as cooperative individuals have a sufficiently higher chance of interacting with other cooperators than with cheaters, thus assort positively, and this independent of identity by descent [START_REF] Fletcher | A simple and general explanation for the evolution of altruism[END_REF]. Relatedness, and generally assortment, are population-level statistics, that describe the average behaviour of cells of a given genotype in the population. As well as strain interaction parameters, they can in principle vary in time, but are usually considered to be constant across multiple aggregation cycles. Under these assumptions, sociobiology maintains that strong relatedness explains the maintenance of cooperative social behaviour against the spread of cheating in aggregative multicellular organisms [START_REF] Medina | Cooperation and conflict in the social amoeba Dictyostelium discoideum[END_REF][START_REF] Strassmann | Altruism and social cheating in the social amoeba Dictyostelium discoideum[END_REF].

Genetic assortment between strains

Evidence of genetic assortment in D. discoideum populations both in natural and artificial environments has been put forward in support of the importance of kin selection. In natural populations, assortment was quantified based on genetic identity. Relatedness between strains was estimated by polymorphism in microsatellite sequences, even though these were not strictly located in genes responsible for social behaviour. These molecular studies found higher levels of relatedness within fruiting bodies compared to soil samples [START_REF] Fortunato | Co-occurrence in nature of different clones of the social amoeba, Dictyostelium discoideum[END_REF][START_REF] Gilbert | High relatedness maintains multicellular cooperation in a social amoeba by controlling cheater mutants[END_REF]. In the laboratory, where chimerae of couples of strains are obtained in standardized conditions, one can quantitatively assess the dependence of cheating intensity on strain proximity. Mixing natural clones in 15 co-aggregations, Strassman and colleagues found a positive correlation between spore bias and genetic distance [START_REF] Strassmann | Altruism and social cheating in the social amoeba Dictyostelium discoideum[END_REF]. Analysis of the composition of fruiting bodies, instead of the proportion of spores in the population, found that genetically distant strains segregate more than closer ones [START_REF] Ostrowski | Kin discrimination increases with genetic distance in a social amoeba[END_REF]. Similar observations realized in lab-created chimerae of D. purpureum and D. giganteum [START_REF] Sathe | Genetic heterogeneity in wild isolates of cellular slime mold social groups[END_REF] confirmed that strains of two species mix to varying degrees, with strains genetically farther apart often segregating in separate multicellular aggregates.

These studies support the idea that even though strains may be unable to completely exclude each other from groups, they can bias group composition so as to reduce genetic dissimilarity. However, the permanence of the social identity -as a cooperator or a cheaterof a given strain now hinges upon how aggregation takes place and on the extent to which genes control the partitioning of cells into groups (what in physics would be called structure at the 'mesoscale').

Cell assortment, as measured by proxies such as genetic relatedness, can be achieved in multiple ways. First, it can be the consequence of 'passive' mechanisms, that do not require any particular adaptation for strain-specific recognition. Passive sources of assortment are thus most relevant for explaining how multicellular organization emerged from unicellular ancestors, before more sophisticated means of cell-cell signalling were set in place. Passive mechanisms include limited dispersal in a spatially extended environment, whereby populations are structured in clusters of genetically identical individuals [START_REF] Hamilton | The genetical evolution of social behaviour. I. eng[END_REF]. Limited dispersal can for instance explain why a regional pool of species is not fully represented in single fruiting bodies that assemble from locally aggregated cells. Non-specific differences in physical properties, such as adhesion or motility can moreover result in non-uniform mixing and sustain cooperative behaviour even when cells are initially uniformly distributed in space [START_REF] Garcia | Differential adhesion between moving particles as a mechanism for the evolution of social groups[END_REF][START_REF] Garcia | The evolution of adhesiveness as a social adaptation[END_REF][START_REF] Gestel | Phenotypic Heterogeneity and the Evolution of Bacterial Life Cycles[END_REF][START_REF] Joshi | Mobility can promote the evolution of cooperation via emergent self-assortment dynamics[END_REF].

Second, high assortment can be achieved through active sorting that makes cells group preferentially with cells of the same genotype, a mechanism also known as 'kin discrimination'. D. discoideum possesses a number of specific genes involved with cell-cell adhesion that are expressed during both aggregation and development, and that are central to multicellular organization [START_REF] Glöckner | The multicellularity genes of dictyostelid social amoebas[END_REF]. In particular, the family of Tiger genes coding for transmembrane proteins provides a lock-and-key mechanism for adhesion between cells that carry a same allele (Benabentos et al., 2009). Analogous to self versus non-self-recognition mediated by major histone compatibility loci, Tiger genes display a 40-fold elevation in genetic diversity compared to the rest of the genome (Benabentos et al., 2009;[START_REF] Flowers | Variation, sex, and social cooperation: molecular population genetics of the social amoeba Dictyostelium discoideum[END_REF][START_REF] Ostrowski | Genomic signatures of cooperation and conflict in the social amoeba[END_REF]. Such a high degree of polymorphism is consistent with the idea that recognition with high genetic resolution is essential to achieve efficient segregation between co-aggregating strains [START_REF] Gruenheit | A polychromatic 'greenbeard' locus determines patterns of cooperation in a social amoeba[END_REF][START_REF] Ostrowski | Enforcing cooperation in the social amoebae[END_REF].

The role of Tiger genes as 'green beards', that is as molecular tags of cooperative behaviour, was also supported by the observation that segregation in aggregate formation positively correlates with the distance in Tiger genes sequences. Together with the polymorphism of Tiger sequences observed in the wild, this points to a mechanism for highly specific recognition among strains that, being genetically related, produce chimeric slugs with more efficient collective motility [START_REF] Gruenheit | A polychromatic 'greenbeard' locus determines patterns of cooperation in a social amoeba[END_REF]. At what life cycle stage -aggregate formation or multicellular development -Tiger genes mainly affect the outcome of interactions between strains is however still unclear. The distinction is not futile, in that molecular mechanisms may be expected to provide a firmer basis to genetically-determined strategies if the bias arises during multicellular, canalized, development, rather than in the aggregation phase, more susceptible to environmental variability.

Evolutionary dynamics of genotypes

In order to ascertain if the degree of assortment provided by a given mechanism is sufficient to explain the stability of cooperation in Dictyostelium, one would ideally like to check that Hamilton's rule applies quantitatively. A major obstacle to this is the difficulty of measuring the relevant parameters, first and foremost relatedness, without assuming a priori that they are constant for any given couple of strains. What can be done, instead, is to check that changes in strain frequencies on long time scales are consistent with observations realized on a single aggregation cycle.

Experimental evolution assays have been conducted by repeating cycles of aggregation and dispersal in conditions that are as close as possible to producing random cell encounters ('low relatedness' conditions) [START_REF] Kuzdzal-Fick | High relatedness is necessary and sufficient to maintain multicellularity in Dictyostelium[END_REF]. Strains that increased in frequency in 30 cycles also produced a larger share of spores than the ancestral strain which was used to seed all the experimental lines. Estimation of the mutation rate from ('high relatedness') lines propagated clonally in a separate experiment moreover indicated that the change in frequency, estimated via a population genetics model, was not quantitatively compatible with random drift [START_REF] Kuzdzal-Fick | High relatedness is necessary and sufficient to maintain multicellularity in Dictyostelium[END_REF]. It was therefore explained as a consequence of the selective advantage conferred by cheating. Exclusion of cooperators by cheater strains was however not observed. Not all experimental evolution assays, on the other hand, support the hypothesis that selection always favours cheating strains. In an experiment involving mixtures of 8 environmentally collected strains, 10 cycles of aggregation-dispersal were repeated, starting from either high or low cell density [START_REF] Saxer | Cheating does not explain selective differences at high and low relatedness in a social amoeba[END_REF]. The weak population bottleneck associated to the first condition resulted in lower relatedness within fruiting bodies and in higher variability in the strains that eventually dominate the population. According to kin selection theory, such dominant clones were expected to cheat both on clones that were excluded, and on those that evolved in the less competitive, high-relatedness assay. This prediction was not verified in the experiment, suggesting that clone frequency dynamics was not primarily driven by social conflicts.

Other than direct evolutionary experiments, methods from population genetics have been deployed in natural populations to reveal selection acting on cheating. The genomic signatures of 'social genes', i.e. genes preferentially expressed during the multicellular phase of the life cycle, display signs of rapid evolution (high rate of non-synonymous mutations) compared to the rest of the genome [START_REF] Sucgang | Comparative genomics of the social amoebae Dictyostelium discoideum and Dictyostelium purpureum[END_REF]. This result, however, has been subsequently interpreted as the effect of diluted selection, occurring when the expression of social genes is temporally restricted to the multicellular phase of the life cycle [START_REF] Oliveira | Conditional expression explains molecular evolution of social genes in a microbe[END_REF]. When this effect is taken into account, previously reported differences in the level of polymorphism between pre-stalk and pre-spore genes [START_REF] Noh | Genetic signatures of microbial altruism and cheating in social amoebas in the wild[END_REF] are no longer detected, making it impossible to conclude on the role of kin selection in shaping the evolution of social interactions in D. discoideum.

Association of a genotype -through its social behaviour -to its expected evolutionary consequences thus appears insufficient to explain the evolutionary dynamics of aggregative multicellular organization. Part of the problem may stem from representing multicellular function as the product of a game that opposes cooperating and cheating players, where these players are the strains co-aggregating in a chimera. This view makes an immediate and enticing link to the Prisoner's Dilemma that reposes on assumptions that are not routinely tested, such as the existence of 'strategies' that are genetically set and invariable.

In more mechanistic terms, one can also consider the population-level outcome of strain interactions as the effective description (at a macroscopic, population-level scale) of celllevel interactions among cooperator and cheater strains [START_REF] Peña | Gains from switching and evolutionary stability in multi-player matrix games[END_REF][START_REF] Peña | Evolutionary dynamics of collective action in spatially structured populations[END_REF][START_REF] Van Cleve | Stags, Hawks, and Doves: Social Evolution Theory and Individual Variation in Cooperation[END_REF]. 'Interaction payoffs' for a given pair of strains now depend on population structure, that is dynamic and not purely established by genes. Therefore, there is no guarantee that they can be permanently associated to a given genotype, whose associated social role (if it is a cheater and how much it cheats) is bound to change during the evolutionary process. Perhaps more disturbingly, effective games may describe situations where cheaters do not beat cooperators over repeated random encounters, so that the existence of Dictyostelium strains that vary in spore allocation would not represent an evolutionary paradox. As we discuss later, for instance, if strains play an effective snowdrift game, the evolutionary stable strategy is a polymorphic state [START_REF] Doebeli | The Evolutionary Origin of Cooperators and Defectors[END_REF].

The question is then how is spore bias generated and to what extent is there genetic control over the outcome of strain-level interactions. In the following, we discuss the experimental evidence that spore bias depends also on the physiological conditions and social environment experienced by cells, so that the genotype controls only partially the result of social interactions, which has important implications as to what should be the null expectations for the evolution of aggregative multicellular life cycles.

Cell-level strategies

A central feature of aggregative multicellularity in Dictyostelium is that genetically identical cells differentiate into spores or stalk (see [START_REF] Brown | Regulation of cell-fate determination in Dictyostelium[END_REF] for a review of the underlying molecular processes). Viewed at the cellular level, cheating of one cell that is part of a binary chimera is then associated to a probability of becoming a spore higher than for cells of the other strain. This alternative point of view has implications in the way strategies are conceptualized. With the exception of few obligate cheater strains, that only form spores and can be thought of playing 'pure strategies', a cell-level strategy now reflects any single player's 'choice' between two alternative fates, one allowing survival, and the other leading to death.

A way to formalize such choice is to consider that every strain is characterized by the probability that any of its cells will cooperate -forming the stalk -or cheat -becoming a spore. Such genetically-encoded strategy would not change in time. However, the outcome of interactions between a focal cell and multiple other cells will generally depend on the social structure of the population, notably the size and composition of multi-player groups [START_REF] Gokhale | Evolutionary Multiplayer Games[END_REF][START_REF] Peña | Evolutionary dynamics of collective action in spatially structured populations[END_REF]. It can turn out that strains composed by cells that have a higher probability of producing spores are unable to outcompete more cooperative strains [START_REF] Hudson | Altruism, cheating, and anticheater adaptations in cellular slime molds[END_REF][START_REF] Matsuda | Evolutionarily stable stalk to spore ratio in cellular slime molds and the law of equalization in net incomes[END_REF][START_REF] Uchinomiya | Evolution of stalk/spore ratio in a social amoeba: Cellto-cell interaction via a signaling chemical shaped by cheating risk[END_REF]. A simple scenario when this happens is the so-called 'Simpson's paradox', reflecting the fact that, when individuals interact in groups, the difference in payoff of two strategies can have opposite sign if one considers single individuals within groups or the (weighted) average across all the population [START_REF] Chuang | Simpson's Paradox in a Synthetic Microbial System[END_REF]. Applied to Dictyostelium, this means that even though strains that produce more spores are advantaged in every group, their overall spore production -averaged over aggregates of different composition -would be diminished by the poor performance of fruiting bodies dominated by cheaters. Thus, cell-level cheating would not translate into strain-level cheating.

Stepping back from the notion that cheating is a strain-level genetically-determined strategy, in this section we consider alternate conceptual models of how cellular fate is determined in chimerae, and their expected consequences on the evolutionary dynamics of strains that display positive spore bias (summarized in Table 1). In particular, we would like to stress that in these frameworks 'cheaters' -defined as usual through binary mixes of equal amounts of genetically different cells -are not expected to be systematically selectively favoured. This observation questions whether the existing classification of social behaviour is relevant for addressing the evolution of aggregative multicellularity. Moreover, it highlights the need for a better understanding of the mechanisms underpinning differences in spore production.

Cellular 'lotteries'

Genes are at the basis of cellular behaviour and dictate how external inputs are translated into specific phenotypic states. However, the probability that single Dictyostelium cells turn Table 1. Conceptual models for the evolution of cell-level behavioural strategies that do not lead to the unconditional evolutionary success of 'cheater' strains (as defined based on spore bias in a given environment).

into a spore or contribute to the stalk can be also affected by factors other than the genotype.

Ample evidence exists that phenotypic heterogeneity, and in particular non-genetic differences among cells that were established before the beginning of the multicellular phase, can bias developmental fate [START_REF] Chattwood | Non-genetic heterogeneity and cell fate choice in Dictyostelium discoideum. en. Development[END_REF].

In the Supplementary Information, we review several experimental studies correlating the probability that isogenic cells develop into a spore with its phenotypic state before and during multicellular development. These investigations, summarized in Table S1 of the SI, reveal that decisions at the cellular level may reflect factors out of direct genetic control, such as the history of the cell during vegetative growth -e.g. the availability and quality of food -or the phase of the cell cycle at the moment of starvation. Notably, the relevant phenotypic traits of the cell may change depending on its social context, as we will discuss later. Although it is not yet clear how, during development, initially heterogeneous cellular phenotypic features are translated into settled social roles (we discuss a few hypotheses in the SI), weakening the causal relationship between a cell's social behaviour and its genes opens the door to establish alternative null models for the evolutionary dynamics.

Let us consider first the extreme case where spore bias is determined independently of the cell's genotype, so that selection acts on purely phenotypic variation [START_REF] Nanjundiah | Many roads lead to Rome: Neutral phenotypes in microorganisms[END_REF]. Such scenario, represented by 'lottery' or 'musical chairs' conceptual models, has been invoked as a mechanism mitigating the success of cheating strains [START_REF] Rainey | Precarious development: The uncertain social life of cellular slime molds[END_REF][START_REF] Strassmann | Evolution of cooperation and control of cheating in a social microbe[END_REF].

Several factors affecting cell fate in monoclonal populations could contribute to loosening the link between the genotype of a cell and its probability of turning into a spore. A potential intrinsic source of unbiased phenotypic heterogeneity is the necessity of any cell to progress through the cell cycle. If, as discussed in the Supplementary Information for monoclonal populations, the cell cycle phase is not synchronized in the population, and it sets the probability of forming a spore, then the fate of any focal cell will be essentially determined by the time when starvation occurs. Like in a "musical chair" game, the moment when aggregation starts is out of one cell's direct control, making cell fate choice a stochastic decision independent of the genes. As long as cell cycle phase is uniformly distributed in the overall population, a cell indeed cannot predict what its phase is relative to cells of its own or another strain.

Population-level observations that cultures can be synchronized by cold shock, release from stationary phase or treatment with drugs that block the cell cycle [START_REF] Araki | Cell-cycle progression during the development of Dictyostelium discoideum and its relation to the subsequent cell-sorting in the multicellular structures. en. Development[END_REF][START_REF] Maeda | A new method for inducing synchronous growth of Dictyostelium discoideum cells using temperature shifts[END_REF][START_REF] Weijer | A revision of the Dyctiostelium discoideum cell cycle[END_REF] indicate that cell cycles are generally desynchronized.

This is also supported by a quantitative mathematical model of phase drift along lineages, indicating that cells loose rapidly synchronization in typical D. discoideum culture conditions [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF], even though they may not in other circumstances [START_REF] Segota | Spontaneous emergence of largescale cell cycle synchronization in amoeba colonies[END_REF].

Unpredictability in cell-fate decision could moreover be the consequence of external rather than internal contingency: independent of the genotype, some cells may happen to be better fed than others after having encountered different amounts of food, or food of different quality. Such contingencies are expected to affect every cell in similar manner before aggregation starts. As a consequence, reproductive success would not be a heritable trait associated to any given genotype. Nanjundiah and co-workers proposed that the 'quality' of a cell when it faces starvation, established from a combination of genotype, environment and historical contingency, underpins the probability of developing into a spore [START_REF] Zahavi | An individual-level selection model for the apparent altruism exhibited by cellular slime moulds[END_REF]. The stalk would be composed chiefly by cells that are anyways condemned by their poor nutritional status, while spores would comprise cells that have a higher chance of survival. In this perspective, not only cheating would not be expected to swipe through the population, but the conflicting nature itself of the interactions within the multicellular stage would be downsized.

Environmental fluctuations and bet-hedging

Although the weight of stochasticity relative to genetic determinism in cell fate determination is unknown, pure lottery models seem unrealistic, as cell fate is certainly affected by genes. Evolutionary outcomes similar to lottery models are nonetheless obtained when the genetically-encoded probability of becoming a spore varies in time: spore bias can be predicted in any given environment based on the genotype, but the genotype's frequency in the long term depends on the sequence of conditions cells experience. Such contrast between short-term and evolutionary success is commonly encountered in microbial species, where multiple phenotypes -including those that appear maladapted to a specific environmental context -coexist within monoclonal populations [START_REF] Ackermann | A functional perspective on phenotypic heterogeneity in microorganisms[END_REF][START_REF] Grimbergen | Microbial bet-hedging: the power of being different[END_REF].

Single-cell stochastic transitions between phenotypes with different adaptive value allow strains to cope with a varying environment by hedging their bets among several alternative behaviours [START_REF] Kussell | Phenotypic diversity, population growth, and information in fluctuating environments[END_REF]. Instead of supposing, as in lottery models, that cell fate is independent of the genotype, bet-hedging models assume that all strains face the same type of reproductive uncertainty. Let us consider the previously discussed case of different cell quality [START_REF] Zahavi | An individual-level selection model for the apparent altruism exhibited by cellular slime moulds[END_REF]. Even if cells of a given strain have a higher quality in one specific environment, such relative advantage may reverse in other environments. Averaging over multiple aggregation-dispersion cycles in variable conditions, different strains may end up having the same overall success.

These concepts have been specifically applied to study the evolution of the so-called 'loner' strategy, adopted by Dictyostelium cells that do not join at all multicellular aggregates. In games traditionally opposing cheating to cooperation, addition of such a strategy is sufficient to avert the tragedy of the commons [START_REF] Hauert | Volunteering as red queen mechanism for cooperation in public goods games[END_REF]. In Dictyostelium, the loner strategy has been proposed as a way to prevent the invasion of cheaters [START_REF] Dubravcic | An evolutionarily significant unicellular strategy in response to starvation in Dictyostelium social amoebae[END_REF][START_REF] Tarnita | Fitness tradeoffs between spores and nonaggregating cells can explain the coexistence of diverse genotypes in cellular slime molds[END_REF]. The potential relevance of non-aggregated cells has been supported by experimental observations both on lab and wild strains. A sizeable fraction of cells is indeed invariably found outside aggregates. These cells are able to start vegetative growth faster than aggregated cells when nutrients are renewed shortly after aggregation, but they cannot survive long period of starvation [START_REF] Dubravcic | An evolutionarily significant unicellular strategy in response to starvation in Dictyostelium social amoebae[END_REF][START_REF] Rossine | Eco-evolutionary significance of "loners[END_REF][START_REF] Tarnita | Fitness tradeoffs between spores and nonaggregating cells can explain the coexistence of diverse genotypes in cellular slime molds[END_REF]. The partition of a population in loner and aggregated components was modelled as the consequence of a cell-level stochastic choice, where the genotype determines the probability of staying alone [START_REF] Dubravcic | An evolutionarily significant unicellular strategy in response to starvation in Dictyostelium social amoebae[END_REF][START_REF] Martínez-García | Lack of ecological and life history context can create the illusion of social interactions in Dictyostelium discoideum[END_REF][START_REF] Tarnita | Fitness tradeoffs between spores and nonaggregating cells can explain the coexistence of diverse genotypes in cellular slime molds[END_REF]. Even if cell fate choice within aggregates is genotype-independent, different strains vary in spore production because of their differential contribution to aggregates. Numerical simulations showed that frequent replenishment of nutrients favours genotypes that have a larger fraction of solitary cells, whereas more aggregative types that commit to social behaviour have an advantage in times of famine. On longer time scales, environmental unpredictability and limited dispersal lead, independent of relatedness, to coexistence of multiple genotypes in spite of differences in their social behaviour.

Cell-level response to social context

Phenotypic variability is not only influenced by extrinsic fluctuations that affect all cells equally.

Even before multicellular groups can be clearly distinguished, the local environment of one cell is indeed dictated by other cells present within the same local neighbourhood. Similarly, in multicellular aggregates, cells interact with each other through chemical signals (as reviewed in [START_REF] Loomis | Cell signaling during development of Dictyostelium[END_REF]) and mechanical forces. Such local 'social' environment is particularly important in determining cell fate, and thus strain dominance, in chimerae. This was recently supported by a RNA-sequencing study reporting that chimeric development (relative to clonal development) induces a plastic response in the expression of genes involved in cytoskeleton organization, cAMP signaling, DNA replication and cell cycle regulation [START_REF] Noh | Wild Dictyostelium discoideum social amoebae show plastic responses to the presence of nonrelatives during multicellular development[END_REF]. When strategies are considered at the level of single cells, a manifestation of social context-dependence is that spore bias depends not only on the genotype, but also on how many cells belong to one or another of the co-aggregating strains.

Numerous studies indicate that frequency-dependent changes in spore bias is the rule rather than the exception in chimerae of both D. discoideum [START_REF] Gilbert | High relatedness maintains multicellular cooperation in a social amoeba by controlling cheater mutants[END_REF][START_REF] Madgwick | Strategic investment explains patterns of cooperation and cheating in a microbe[END_REF] and other dictyostelids [START_REF] Sathe | Complex interactions underpin social behaviour in Dictyostelium giganteum[END_REF]. Strains identified as cheaters by mixing equal amounts of cells of two genotypes thus have variable success against a cooperator counterpart when their relative proportions are changed. In particular, when they make up most of the population, the proportion of spores that a cheater strain produces may be upper bounded if the stalk/spore ratio is maintained. Moreover, in a chimera composed of a mutant that does not produce stalk cells [START_REF] Buss | Somatic cell parasitism and the evolution of somatic tissue compatibility[END_REF] and a strain that develops normally, an increase in the proportion of cheater cells may produce disproportionately large, prone to collapse, spore heads and thus undercut the reproductive success of the cheater itself.

When frequency-dependence is taken into account in game-theoretical models for interacting strains, repeated rounds of co-aggregation can yield different evolutionary predictions, only a subset of which predict cheating as the winning strategy. For instance, if spore bias is positive when cheaters are rare and negative when they are common, as in the snowdrift game, the evolutionary dynamics will lead to regimes of coexistence of opposite social strategies.

Though context-dependent cell behaviour is often neglected when evolutionary projections are based on strain-level dominance of genotypes, a few mechanisms involving density or frequency of cells have been recently considered in their population-level effects on spore bias.

As discussed earlier in this section, a possible source of indirect effects on the proportion of spores produced by one strain in a chimera is the partition between aggregated and nonaggregated cells. When exploring the mechanistic bases of this partitioning, the probability of being a loner was found to depend, other than on the genotype, on cell density and environmental factors such as the hardness of the agar substrate [START_REF] Rossine | Eco-evolutionary significance of "loners[END_REF]. Such dependence on both the biotic and abiotic context was explained by a mathematical model where the cell decision to aggregate is stochastic and conditional on a locally established quorum. In a genetic chimera, the probability that one cell of a given strain aggregates therefore depends on the nature and the proportion of other co-aggregating strains. For instance, strains that tend to aggregate less can still contribute to aggregation of another strain, and they do so more efficiently when they are more dense. The end result of cell self-organization in groups is then frequency dependence, which can sustain coexistence of multiple strains over evolutionary times.

Cells can also modify their behaviour within multicellular aggregates, in response to proportions of co-aggregating strains. Within slugs, for instance, the concentration of diffusive compounds was suggested to be the key mediator of cell-level frequency-dependent fate determination [START_REF] Parkinson | A simple mechanism for complex social behavior[END_REF] (discussed in more detail in the Supplementary Information). Responsiveness to diffusible stalk-inducing factors (e.g. Differentiation Induction Factors (DIF)) in particular, but also their production, was indeed found to reflect the linear social hierarchy of strains previously established based on cheating ability [START_REF] Buttery | Complex genotype interactions influence social fitness during the developmental phase of the social amoeba Dictyostelium discoideum[END_REF]. When considering the mechanistic bases of cellular strategies, complex behavioural patterns -whereby strains would adjust their behaviour depending on the social partner -were therefore suggested to follow from simple principles of context-dependent decision-making, that naturally lead to frequency-dependent interactions [START_REF] Hudson | Altruism, cheating, and anticheater adaptations in cellular slime molds[END_REF][START_REF] Madgwick | Strategic investment explains patterns of cooperation and cheating in a microbe[END_REF][START_REF] Matsuda | Evolutionarily stable stalk to spore ratio in cellular slime molds and the law of equalization in net incomes[END_REF].

In conclusion, spore bias is a population-level manifestation of cell-level mechanisms that span ranges of genetic vs epigenetic determinism and that respond differently to the abiotic and biotic context. In pairwise interactions, the contribution of different factors with distinct and independent effects on strains fitness was quantified by an analysis of variance [START_REF] Buttery | Complex genotype interactions influence social fitness during the developmental phase of the social amoeba Dictyostelium discoideum[END_REF]. Variation in contribution to the spore head in binary chimerae of natural clones was partitioned in three components: indirect genetic effects of the social partner's genotype, direct effect of the strain's own genotype, and epistatic interactions between the genotypes of the two partners. The first component reflects the influence of the competing strain on the focal strain's social behavior. The others connect to cell-level behaviour in a monoclonal population and in a chimera (other than the previously mentioned strain-level effects), respectively. The strain genotype (i.e the second component) was found to explain 57.6% of the variation in spore production, thus dominating the two terms linked to social interactions between strains. The importance of epistasis (23%) moreover suggests that the social context is as important as strain-level effects [START_REF] Buttery | Complex genotype interactions influence social fitness during the developmental phase of the social amoeba Dictyostelium discoideum[END_REF].

Without a mechanistic model able to explain how the partition in these three orthogonal components is realized, and what is the origin of the epistatic effects, such statistical analysis is however of limited application to evolutionary studies involving other strains or conditions of aggregation. It nonetheless suggests that natural selection may select cooperative behaviours despite their apparent failure in pair-wise competition.

Discussion

In this review, we pointed out that the predicted evolutionary fate of strains that, in chimerae, produce more than their fair share of spores depends on how such 'cheating' is achieved and formalized. Central to this picture is the level at which social behaviour is assessed, and the extent to which it is rooted in the genotype -thus invariable on ecological time scales. We wish now to discuss conceptual and experimental approaches that we deem most promising in advancing knowledge of how multicellular organization in Dictyostelium got established and is maintained. Primarily, this requires identifying what are the material bases of conflicts within multicellular aggregates, so as to ascertain what strains, and in which circumstances, are expected to see their evolutionary success curtailed by the peculiar structure of aggregative multicellular life cycles.

Describing social behaviour at multiple scales

Connecting cell-level to collective-level behavior is a classic undertaking not only for evolutionary biology [START_REF] Okasha | Evolution and the levels of selection[END_REF], but also for mechanistic bottom-up approaches to tissue organization [START_REF] Ladoux | Mechanobiology of collective cell behaviours[END_REF]. Bottom-up approaches describing cell mechanics and movement aim at classifying behaviours that emerge from interactions of units with differential physical properties. They yielded important insights, for instance, on how cells sort within tissues [START_REF] Beatrici | Cell sorting based on motility differences[END_REF][START_REF] Steinberg | Differential adhesion in morphogenesis: a modern view[END_REF], and in particular on differentiation in Dictyostelium [START_REF] Maree | How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum[END_REF]. Although they remain simplified representations, these models are easier to interface with cell-level observations and can provide explicit descriptions of the origin of biases in aggregate composition and in spatial distribution of cells, as well as of the evolution of collective functionality [START_REF] Colizzi | Evolution of multicellularity by collective integration of spatial information[END_REF][START_REF] Garcia | The evolution of adhesiveness as a social adaptation[END_REF][START_REF] Gestel | Phenotypic Heterogeneity and the Evolution of Bacterial Life Cycles[END_REF][START_REF] Guttal | Social interactions, information use, and the evolution of collective migration[END_REF][START_REF] Joshi | Mobility can promote the evolution of cooperation via emergent self-assortment dynamics[END_REF][START_REF] Staps | Emergence of diverse life cycles and life histories at the origin of multicellularity[END_REF]. Their integration into general evolutionary frameworks is, however, less straightforward. It often relies on numerical simulation and poses the problem of how to estimate -let alone evolve -the large number of parameters involved in microscopic descriptions. Simple mechanistic approaches, on the other hand, are useful tools for exploring the multiplicity of existing life cycles beyond that of Dictyostelium and to evaluate the role of selection acting at different levels of biological organization (De [START_REF] Monte | Nascent multicellular life and the emergence of individuality[END_REF][START_REF] Gestel | On the origin of biological construction, with a focus on multicellularity[END_REF][START_REF] Rainey | Resolving conflicts during the evolutionary transition to multicellular life[END_REF].

Other approaches connecting cells and multicellular structures rely on representation of fitness at multiple levels to infer the evolutionary dynamics. Multi-level selection proposes that trade-offs between benefits and costs to the lower-level units can be scaled up to determine fitness at the collective level [START_REF] Michod | Evolution of individuality during the transition from unicellular to multicellular life[END_REF]. Similarly to the sociobiological approach, that is based on translating individual-level costs and benefits into inclusive fitness as a property of a whole population [START_REF] Gardner | Inclusive fitness: 50 years on[END_REF][START_REF] Kerr | Generalization of the Price equation for evolutionary change[END_REF], the statistical description of the outcome of interactions does not inform on the processes underlying population-level success. Though these approaches have the great advantage of permitting elegant generalizations and exploitation of tools developed for population genetics, the existence and magnitude of genetically-determined, individual fitness costs and benefits are not easy to assess without elucidating the mechanisms underlying population-level statistics.

Finding meaningful ways to connect cell-and collective-level properties in assemblies that contain a collection of genotypes and phenotypes, and such that cell-level traits result in the functionality of the ensemble, is a central problem also in more general settings, like microbial communities [START_REF] Doulcier | Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity[END_REF][START_REF] Liautaud | Superorganisms or loose collections of species? A unifying theory of community patterns along environmental gradients[END_REF][START_REF] Tarnita | Fast evolution unlocks forbidden communities[END_REF]. There, evolution of system-level properties through mutations in traits affecting species interactions, some of which of mutualistic or cooperative nature, is considered possible despite -and maybe thanks to -the high diversity among interacting cells. Viewing evolution of muticellularity in Dictyostelium, as well as in other microbes that form genetically heterogeneous aggregates, as an instance of community-level evolution may be useful for explaining the first emergence of higher levels of organization.

Stochastic vs deterministic bases of behaviour

The second challenge for formalizing selective differences among Dictyostelium strains is to evaluate the importance of cell-level stochasticity and the extent to which this can be effectively captured by deterministic models. Advances in single-cell observation techniques revealed the ubiquity of cell-to-cell phenotypic variation, invisible to population-level measures [START_REF] Altschuler | Cellular heterogeneity: do differences make a difference? en[END_REF]. Intracellular fluctuations, for instance due to small numbers of transcription factors, combined with nonlinearities in gene regulation networks, are believed to be major determinants of phenotypic heterogeneity in microbes and beyond [START_REF] Balázsi | Cellular decision making and biological noise: From microbes to mammals[END_REF][START_REF] Norman | Stochastic switching of cell fate in microbes[END_REF][START_REF] Perkins | Strategies for cellular decision-making[END_REF] and are increasingly considered as key factors influencing their evolutionary dynamics [START_REF] Boxtel C Van | Taking chances and making mistakes: non-genetic phenotypic heterogeneity and its consequences for surviving in dynamic environments[END_REF][START_REF] Draghi | Links between evolutionary processes and phenotypic robustness in microbes[END_REF]. The presence, within a monoclonal cell population, of phenotypes that are maladapted to a given environment at any given time is explained by their long-term advantages. Indeed, in rapidly fluctuating environmental conditions, bet-hedging among alternative phenotypes confers an overall advantage [START_REF] Grimbergen | Microbial bet-hedging: the power of being different[END_REF][START_REF] Kussell | Phenotypic diversity, population growth, and information in fluctuating environments[END_REF].

Stochastic choices are thought to be involved at different moments of the life cycle of Dictyostelium, with possible implications on the final differentiation in stalk and spores: at the onset of aggregation, in establishing aggregation centers [START_REF] Gregor | The onset of collective behavior in social amoebae[END_REF][START_REF] Sgro | From intracellular signaling to population oscillations: bridging size-and time-scales in collective behavior[END_REF]; during aggregation, in the decisions whether to follow the cAMP gradient [START_REF] Rossine | Eco-evolutionary significance of "loners[END_REF]; and during development, in mixing of pre-spore and pre-stalk cells within a slug [START_REF] Weijer | Morphogenetic cell movement in Dictyostelium[END_REF].

On the other hand, phenotypic heterogeneity can also result from deterministic sources, such as the distribution of cell cycle phase in asynchronously dividing cultures [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF][START_REF] Jang | Initial cell type choice in Dictyostelium[END_REF] or the spatial distribution of cell density [START_REF] Vidal-Henriquez | Spontaneous center formation in Dictyostelium discoideum[END_REF].

The extent to which different sources of variability can be treated as equivalent, when one only considers their population-level collective effects, is an open question. Spiking gene expression, for instance, produces regular population-level oscillations if cells respond to an external forcing, and an average stable signal if integrated over the timescale of aggregation [START_REF] Corrigan | Regulation of transcriptional bursting by a naturally oscillating signal[END_REF]. It has moreover been proposed that heterogeneity in gene expression, with possibly long-term consequences on cell fate, results from modulation of spiking frequency, that happens on very fast time scales compared to the developmental process. Distributed individual cell choices, either driven by stochastic fluctuations or by asynchronicity, might indeed average out and be effectively represented by deterministic equations [START_REF] Antolović | Generation of single-cell transcript variability by repression[END_REF].

In evolutionary game theory, mixed strategies describe cases when players have a fixed probability of adopting alternative fixed behaviours. For sufficiently simple games, the evolutionary predictions of the deterministic 'mean field' equations are identical to the case when a corresponding fraction of the population adopts one of the strategies [START_REF] Hofbauer | Evolutionary Games and Population Dynamics[END_REF]. Even in more complicated situations, when players interact in groups, the evolution of behavioural frequencies can be described by effective macroscopic equations [START_REF] Peña | Evolutionary dynamics of collective action in spatially structured populations[END_REF]. Stochasticity is then encompassed by the same deterministic theoretical framework used for fixed strategies. What can be lost in this transition is however the relation between the microscopic definition of a social behaviour and its macroscopic -thus also evolutionary -characterization. Determining whether a microscopic behaviour, say a higher probability of forming spores, is going to lead to the expected demise of more cooperative variants requires knowledge of many other factors, including population structure, responsiveness and game synergy (Van Cleve, 2017), which are not easily assessed and are not guaranteed to remain constant during evolution.

Interplay of different time scales

Finally, a major obstacle to connecting individual-level stochastic behaviour and strain-level spore bias in Dictyostelium is that social and abiotic environments experienced by cells change on time scales comparable with the developmental process. In other words, the phenotypic state of one cell and that of the surrounding population can feed-back onto one another during one life cycle. Such feedback potentially allows cells to evaluate the composition of the aggregate and consequently adjust their developmental fate (turning into spores or stalk).

Strain-level decisions would then be dictated by 'strategic' cell-level choices within one single generation rather than by long-term evolutionary processes [START_REF] Madgwick | Strategic investment explains patterns of cooperation and cheating in a microbe[END_REF]. Recently, molecular tools have been used to start examining how such decision-making is implemented during the process of aggregation and development [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF][START_REF] Nichols | Cell and molecular transitions during efficient dedifferentiation[END_REF].

The third major conceptual challenge in improving evolutionary models is hence to describe context-dependence in a mechanistic fashion. Predictions of different models may then be compared to experimental data and with each other, so as to pinpoint which biological features are essential and which can be neglected with respect to their evolutionary consequences.

It is generally accepted that when the conditions experienced by a cell do not vary too fast, the optimal strategy for coping with fluctuations is sensing the environment and switching phenotype accordingly [START_REF] Kussell | Phenotypic diversity, population growth, and information in fluctuating environments[END_REF]. Such kind of response can occur on a rapid time scale -especially if it involves metabolic rather than regulation changes -and provides an important source of phenotypic heterogeneity [START_REF] Schreiber | Environmental drivers of metabolic heterogeneity in clonal microbial populations[END_REF].

Particularly important for Dictyostelium are variations in the social environment associated to its peculiar life cycle. The combination of short-term cell-level competition within clonal aggregates and long-term organization has been addressed in relation to the evolution of multicellular life cycles [START_REF] Hochberg | The coevolution of cooperation and dispersal in social groups and its implications for the emergence of multicellularity[END_REF][START_REF] Rainey | Cheats as first propagules: A new hypothesis for the evolution of individuality during the transition from single cells to multicellularity[END_REF][START_REF] Wolinsky | Evolution of regulated phenotypic expression during a transition to multicellularity[END_REF]. Phenotypes that would be classified as cheats in the social phase were pointed out to have other functions, such as allowing reproduction of the higher-level structure and division of labour. More generally, feedbacks between ecology and the resulting evolutionary dynamics essentially influence the fate of cheating [START_REF] Lion | Theoretical approaches in evolutionary ecology: environmental feedback as a unifying perspective[END_REF][START_REF] Tilman | Evolutionary games with environmental feedbacks[END_REF][START_REF] Weitz | An oscillating tragedy of the commons in replicator dynamics with game-environment feedback[END_REF]. Traits that underpin conflicting strategies within the multicellular phase, but that also affect behaviour of isolated cells -for instance cell motility -have been shown to give rise to eco-evolutionary cycles akin to aggregative multicellular life cycles, where social 'cooperators' and 'cheaters' coexist [START_REF] Miele | Aggregative cycles evolve as a solution to conflicts in social investment[END_REF]. This model predicts that selection for escalating social conflicts drives the emergence of a temporal alternation of solitary living and phases when social conflicts manifest within aggregates. Moreover, it proposes that a metapopulation structure may not be essential for maintaining strain diversity: evolution would lead to an effectively neutral regime, where exclusion of mutant strategies becomes progressively slower.

Quantifying the importance of eco-evolutionary feedbacks poses major experimental challenges, as it requires to follow individual cells and their environment throughout the developmental cycle. Methodological advances in high-resolution single-cell microscopy [START_REF] Sgro | From intracellular signaling to population oscillations: bridging size-and time-scales in collective behavior[END_REF] and in the use of molecular markers [START_REF] Muramoto | Live imaging of the Dictyostelium cell cycle reveals widespread S phase during development, a G2 bias in spore differentiation and a premitotic checkpoint[END_REF] allow us nowadays to access the internal state of single cells at the same time as they undergo major rearrangements of their environmental context, paving the way to define models that integrate processes across spatial and temporal scales.

On the theoretical side, new models that explicitly describe, along with developmental choices, the self-organized population structure may illuminate on the ecological mechanisms underpinning evolutionary dynamics. Comparison with data would be possible beyond the resolution of population-level observables, thus achieving further integration of theory and observations.

Physiological state

Already 50 years ago, cultures grown on glucose were reported to have a positive spore bias when mixed with cells from a similar strain (carrying a marker mutation that does not affect development) grown in poorer medium [START_REF] Leach | Cell sorting out during the differentiation of mixtures of metabolically distinct populations of Dictyostelium discoideum[END_REF]. The quality of nutrients provided during vegetative growth has since then been confirmed to affect not only cell fate at the end of development [START_REF] Takeuchi | Prestalk and prespore differentiation during development of Dictyostelium discoideum[END_REF], but also the probability to join aggregates at all [START_REF] Dubravcic | An evolutionarily significant unicellular strategy in response to starvation in Dictyostelium social amoebae[END_REF]. Similarly, cells at varying degrees of starvation show a differential tendency to become spores. Cultures that have been starved for four hours before aggregation have a positive spore bias when mixed with freshly harvested cells of the same strain (Kuzdzal-Fick, Queller, et al., 2010).

Differences in quality and duration of feeding result in heterogeneity of the physiological state of the cell, which can bias later developmental stages. Cells whose intracellular pH was artificially decreased, for instance, were found to be biased towards the stalk pathway [START_REF] Kubohara | Cytoplasmic Ca2+ and H+ concentrations determine cell fate in Dictyostelium discoideum[END_REF]. Similarly, concentration of Ca 2+ , bimodally distributed in freshly starved amoebae, has been correlated with spore bias: lower intracellular calcium concentration is associated to a higher probability to become spores [START_REF] Azhar | A Ca2+-Dependent Early Functional Heterogeneity in Amoebae ofDictyostelium discoideum,Revealed by Flow Cytometry[END_REF]. Finally, it was recently reported that cells with higher concentration of ATP before aggregation maintain such differential throughout development and eventually produce stalk cells [START_REF] Hiraoka | Intracellular ATP levels influence cell fates in Dictyostelium discoideum differentiation[END_REF].

In natural conditions, food location and quality, duration of starvation or intracellular concentrations are largely independent of the cell genotype. For instance, variations in the environmental concentration of folic acid, a chemo-attractant produced by bacteria may result in heterogeneous intracellular calcium concentration [START_REF] Yumura | Intracellular free calcium responses during chemotaxis of Dictyostelium cells[END_REF]. Therefore, it is likely that the effects of physiological heterogeneity on spore bias evidenced in laboratory conditions are relevant for wild populations as well.

Cell cycle phase

In addition to environmental variability, phenotypic heterogeneity may also arise as a consequence of intrinsically variable cellular processes. Previously mentioned physiological conditions affecting cell fate biases, indeed, appear to be linked to one other through their relation with cell cycle phase. Cytosolic Ca 2+ concentration [START_REF] Azhar | Cell cycle phase, cellular Ca2+ and development in Dictyostelium discoideum[END_REF][START_REF] Jang | Initial cell type choice in Dictyostelium[END_REF] and intra-cellular pH [START_REF] Aerts | Cytoplasmic pH and the regulation of the dictyostelium cell cycle[END_REF] have been shown to vary during the cell cycle. This is also the case for two factors that play a central role in cellular organization within the multicellular slug, whose effects we discuss below in greater detail: sensitivity to a family of diffusive compounds responsible for differentiation into stalk cells (DIF) (CR Thompson and Kay, 2000a) and cell motility [START_REF] Walmod | Cell-cycle-dependent regulation of cell motility and determination of the role of Rac1. en[END_REF]. The phase of advancement in the cell cycle could thus result in phenotypic heterogeneity within a monoclonal population, and influence the ultimate developmental choice of any given cell.

Numerous studies support the notion that cell cycle phase at the onset of aggregation influences spore bias. The correlation between cell cycle phase in synchronized cultures and the frequency in the spore pool has been known for forty years (Zada-Hames and [START_REF] Ashworth | The cell cycle and its relationship to development in Dictyostelium discoideum[END_REF]. Experiments using cell cycle inhibitors [START_REF] Gomer | A cell-cycle phase-associated cell-type choice mechanism monitors the cell cycle rather than using an independent timer[END_REF] or release from stationary phase [START_REF] Weijer | Separation of Dictyostelium discoideum cells into density classes throughout their development and their relationship to the later cell types[END_REF] as means to synchronize cell cultures confirmed that cell cycle position at starvation reflects into developmental cell fate. By using single-cell RNA-seq Thompson and co-workers recently provided a molecular characterization of such observations [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF]. They analyzed the transcriptome of a monoclonal vegetative population of D. discoideum strain AX3 and identified more than 1600 genes that can be divided, based on their level of expression, in two clusters. One cluster is specifically expressed in cells that are in phase S/M, whereas the second is composed of genes expressed in late G2 phase cells. Then, using pre-spore and pre-stalk markers, they mapped cell cycle position to cell fate and showed that M/S phase cells mostly differentiate into stalk cells, whereas late G2 cells are enriched in spores. Consistently with a direct link between cell cycle phase and cell fate, the ratio of G2 to M/S phase cells in a population is around 4:1, which closely matches the ratio of spores/stalk cells within a fruiting body [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF].

Cell cycle phase effects on development led Maeda and colleagues to propose the existence of a checkpoint in the late G2 phase, where cells bifurcate between growth and differentiation [START_REF] Maeda | Cell-cycle checkpoint for transition from cell division to differentiation. en. Development[END_REF]. In cultures synchronized by a cold shock [START_REF] Ohmori | The developmental fate of Dictyostelium discoideum cells depends greatly on the cell-cycle position at the onset of starvation[END_REF], indeed, cells starved in mid-G2 phase (before the checkpoint) initiate aggregation more rapidly than cells starved in late G2 phase, and are more likely to become spores.

The correlation between cell cycle advancement and developmental timing was further supported through PCA analysis on single-cell transcriptomic data [START_REF] Antolović | Transition state dynamics during a stochastic fate choice[END_REF].

As early as at the mound stage, cells display heterogeneity in developmental advancement.

The principal components of such variability also capture differences in cell cycle stages.

Cell cycle phase is thus considered to be a determinant factor -though minor in amplitude compared to overall changes in the transcriptome throughout development -in determining eventual developmental choices [START_REF] Antolović | Transition state dynamics during a stochastic fate choice[END_REF].

A consequence of the correlation between cell cycle phase and developmental fate is that cell-level strategy -the probability that a cell becomes a spore -is determined by phase positioning relative to the population, thus potentially decorrelating genotype and behaviour.

Consistent with this view is the capacity of cells to reprogram their development when their local environment is perturbed. For instance, if one part of a slug is experimentally removed, cell fate decision are reassessed [START_REF] Raper | Pseudoplasmodium formation and organization in Dictyostelium discoideum[END_REF]. Similarly, once extracted from their social context by dissolving a slug into fresh medium, cells de-differentiate and resume unicellular growth [START_REF] Soll | Morphogenesis in the slime mold Dictyostelium discoideum[END_REF] in a way that is highly robust to mutations in developmental genes [START_REF] Nichols | Cell and molecular transitions during efficient dedifferentiation[END_REF].

The question is then: How can phenotypic differences established at the beginning of aggregation affect, much later, a cell's social behavior?

Cell phenotype through development

Several mechanisms are believed to be involved in transforming phenotypic differences at the beginning of multicellular development into divergent cell fates. Single-cell tracking [START_REF] Araki | Cell-cycle progression during the development of Dictyostelium discoideum and its relation to the subsequent cell-sorting in the multicellular structures. en. Development[END_REF][START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF][START_REF] Houle | A glycosylation mutation affects cell fate in chimeras of Dictyostelium discoideum[END_REF][START_REF] Jang | Initial cell type choice in Dictyostelium[END_REF] and mathematical models [START_REF] Maree | How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum[END_REF][START_REF] Umeda | Cell sorting by differential cell motility: a model for pattern formation in Dictyostelium[END_REF] indicated two main (non-exclusive) ways whereby cell fate gets established.

First, cells could be primed to respond differently to differentiation signals that are equally available to all cells within an aggregate. Among the signals exchanged by co-developing cells, Differentiation Induction Factors (DIF) affect cell fate by inducing differentiation into stalk [START_REF] Jang | Initial cell type choice in Dictyostelium[END_REF][START_REF] Kay | Purification of stalk-cell-inducing morphogens from Dictyostelium discoideum[END_REF]. While extracellular concentrations in the mound gets readily homogenized by diffusion and cell mixing, cells differ in their responsiveness to DIF [START_REF] Chattwood | Non-genetic heterogeneity and cell fate choice in Dictyostelium discoideum. en. Development[END_REF]. This parameter is correlated with cell physiology at the onset of aggregation. For instance, cells fed on a medium containing glucose, as well as those in a late phase of the cell cycle exhibit a lower DIF responsiveness with respect to cells grown without glucose and those in an early cell cycle phase (CR Thompson and Kay, 2000a). Moreover, DIF responsiveness is also affected by heterogeneity in intracellular Ca 2+ established before the multicellular phase. Of the two subpopulations with low and high Ca 2+ content observed in freshly starved cultures, only the latter increases the uptake of extracellular Ca 2+ upon stimulation with one molecule of the DIF family, DIF-1 [START_REF] Azhar | Stimulation by DIF causes an increase of intracellular Ca2+ in Dictyostelium discoideum[END_REF].

Second, the geometry of the aggregate could impose or reinforce patterns through direct cell-cell contacts or morphogen gradients. Positional information within the mound and the slug is associated to the cell's eventual developmental fate. Phenotypic heterogeneity at the onset of aggregation could hence bias terminal differentiation by influencing where a cell is located within multicellular aggregates. The correlation between cell position and cell fate appears to get established as soon as cells organize into streams by attaching headto-tail during their migration towards the mound [START_REF] Fujimori | Tissue self-organization based on collective cell migration by contact activation of locomotion and chemotaxis. en[END_REF]. Maeda suggested that cell positioning during aggregation plays a central role in connecting cell cycle phase and developmental fate [START_REF] Maeda | Cell-cycle checkpoint for transition from cell division to differentiation. en. Development[END_REF]. When facing starvation, cells that have passed the checkpoint between growth and differentiation would stop dividing and act as autonomously pulsing aggregation centres [START_REF] Wang | Cell cycle phase in Dictyostelium discoideum is correlated with the expression of cyclic AMP production, detection, and degradation[END_REF]. By attracting cells at other stages of the cell cycle, they would gain a head start in establishing their position in the mound [START_REF] Maeda | Cell-cycle checkpoint for transition from cell division to differentiation. en. Development[END_REF], and subsequently gather at the center of the aggregates, a position thought to be linked with pre-spore fate [START_REF] Huang | Cells at the center of Dictyostelium aggregates become spores[END_REF].

As well as in the mound, position along the slug axis is associated to different cell fates in the future fruiting body: cells at the back of the slug tend to turn into spores, whereas most of those at the front form the stalk. In a clonal population, cells may sort during slug migration on the basis of motility [START_REF] Strandkvist | A kinetic mechanism for cell sorting based on local variations in cell motility[END_REF] or adhesion [START_REF] Houle | A glycosylation mutation affects cell fate in chimeras of Dictyostelium discoideum[END_REF]. Even though the exact role of differential motility and adhesion in establishing positional information is not yet completely worked out, their involvement in cell fate determination was confirmed by a recent single-cell transcriptomic study. Genes involved in cell motility and, to a lesser extent, in cell-cell adhesion were indeed found to be up-regulated in pre-stalk relative to pre-spore cells, indicating a likely role of cell sorting in establishing tissue organization [START_REF] Antolović | Transition state dynamics during a stochastic fate choice[END_REF]. Both calcium concentration [START_REF] Azhar | A Ca2+-Dependent Early Functional Heterogeneity in Amoebae ofDictyostelium discoideum,Revealed by Flow Cytometry[END_REF] and pH (Van Duijn and Inouye, 1991) differences, moreover, can result in heterogeneity in cell motility, which is also known to vary with the phase of the cell cycle [START_REF] Walmod | Cell-cycle-dependent regulation of cell motility and determination of the role of Rac1. en[END_REF]. Analysis of a handful of trajectories suggests that, corresponding to bimodality in calcium concentration at the onset of development [START_REF] Azhar | A Ca2+-Dependent Early Functional Heterogeneity in Amoebae ofDictyostelium discoideum,Revealed by Flow Cytometry[END_REF], also cell motility could be bimodally distributed [START_REF] Goury-Sistla | Bimodal distribution of motility and cell fate in Dictyostelium discoideum[END_REF]. Already in 1957 John Tyler Bonner suggested that faster cells would position themselves to the front of the slug, thus becoming stalk with a higher probability [START_REF] Bonner | A Theory of the Control of Differentiation in the Cellular Slime Molds[END_REF]. Motility differences have moreover been recently related to the evolutionary emergence of aggregative multicellular life cycles [START_REF] Miele | Aggregative cycles evolve as a solution to conflicts in social investment[END_REF]. However, for heterogeneity in motility at the onset of development to affect cell fate, it is necessary that motility differences are maintained after starvation, something for which there is mixed and indirect evidence. On one side, permanence could be associated to differentials in concentration of ATP [START_REF] Hiraoka | Intracellular ATP levels influence cell fates in Dictyostelium discoideum differentiation[END_REF]. This compound indeed is involved both in cytoskeleton-mediated cell contraction [START_REF] Clarke | Myosin filaments in cytoskeletons ofDictyostelium amoebae[END_REF] and is consistently higher in pre-stalk cells, that show enhanced speed and cAMP chemotaxis [START_REF] Hiraoka | Intracellular ATP levels influence cell fates in Dictyostelium discoideum differentiation[END_REF]. Observations of vegetative cells, on the other hand, show that motility can change relatively rapidly in time, and reflect the rate of encounters with other cells (d'Alessandro et al., 2018). Moreover, recent observations of cells from disaggregated slugs observed two sub-populations moving at different speed, but these did not correspond to pre-stalk and pre-spore sub-populations [START_REF] Nichols | Cell and molecular transitions during efficient dedifferentiation[END_REF].

PEER COMMUNITY IN EVOLUTIONARY BIOLOGY

Acknowledgements

The authors thank Christophe Anjard for comments and discussions, and the insightful comments of the PCI editor and reviewers. In particular, we thank Jeremy Van Cleve for suggesting the relevance of effective snowdrift games, and Peter Conlin for that of the Simpson's paradox. This study was supported by the French Government under the program Investissements d'Avenir (ANR-10-LABX-54 MEMOLIFE and ANR-11-IDEX-0001-02PSL), and the ANR project ADHeC. Version 2 of this preprint has been peer-reviewed and recommended by Peer Community In Evolutionary Biology (https://doi.org/10.24072/pci.evolbiol.100122).

Supplementary material

Supplementary Informations are available in Appendix

Conflict of interest disclosure

The authors of this preprint declare that they have no financial conflict of interest with the content of this article.

Supplementary Information

Link between phenotypic heterogeneity at the onset of aggregation and developmental fate in Dictyostelium.

Even in monoclonal populations, in which every cells share the exact same genotype, a combination of extrinsic and intrinsic stochastic factors causes cells to display phenotypic heterogeneity. In Dictyostelium, the effect of phenotypic differences can be conveniently assessed by mixing populations that differ in their preparation protocol and/or their physiological state.

Spore bias induced by non-genetic factors can be measured, after marking one of the two sub-populations, exactly as discussed in the introduction. The effects of non-genetic factors on social behaviour can thus be quantified by comparing the number of spores produced by each culture with the expectation from their proportions in the initial mix. In this document, we review evidence for the existence of multiple, and likely non-independent, sources of phenotypic bias (summarized in Table S1). Moreover, we discuss the possible mechanisms connecting phenotypic heterogeneity during vegetative growth to cell fate determination during development.

Cell phenotypes

Positive correlates to spore bias Reference(s)

Glucose concentration

Cells being fed with extra glucose [START_REF] Leach | Cell sorting out during the differentiation of mixtures of metabolically distinct populations of Dictyostelium discoideum[END_REF] Intracellular calcium Low intracellular calcium [START_REF] Azhar | A Ca2+-Dependent Early Functional Heterogeneity in Amoebae ofDictyostelium discoideum,Revealed by Flow Cytometry[END_REF][START_REF] Kubohara | Pharmacological evidence that stalk cell differentiation involves increases in the intracellular Ca2+ and H+ concentrations in Dictyostelium discoideum: H+, Ca2+ and cell differentiation. en. Development[END_REF] Intracellular pH High pH [START_REF] Kubohara | Pharmacological evidence that stalk cell differentiation involves increases in the intracellular Ca2+ and H+ concentrations in Dictyostelium discoideum: H+, Ca2+ and cell differentiation. en. Development[END_REF] Intracellular ATP Low ATP [START_REF] Hiraoka | Intracellular ATP levels influence cell fates in Dictyostelium discoideum differentiation[END_REF] Starvation timing

Earlier starvation before aggregation is started [START_REF] Kuzdzal-Fick | An invitation to die: initiators of sociality in a social amoeba become selfish spores[END_REF] Cell cycle progression Late cell cycle phase [START_REF] Gruenheit | Cell cycle heterogeneity can generate robust cell type proportioning[END_REF][START_REF] Ohmori | The developmental fate of Dictyostelium discoideum cells depends greatly on the cell-cycle position at the onset of starvation[END_REF][START_REF] Ashworth | The cell cycle and its relationship to development in Dictyostelium discoideum[END_REF] Sensitivity to DIF Higher sensitivity to DIF (CR Thompson and Kay, 2000b) Cell motility Slower cells (theoretical prediction) [START_REF] Bonner | A Theory of the Control of Differentiation in the Cellular Slime Molds[END_REF] Table S1. Phenotypic factors affecting cell fate, relation between their value at the onset of aggregation in binary chimerae and spore bias.